Document text
WAR DEPARTMENT
COAST ARTILLERY
FIELD MANUAL
&
ANTIAIRCRAFT ARTILLERY
GUNNERY, FIRE CONTROL,
AND POSITION FINDING,
ANTIAIRCRAFT GUNS
I|iw 11
FM 4-110
C 2
tiu. 2! «D
PORTLAND;
COAST ARTILLERY FIELD MANUAL
ANTIAIRCRAFT ARTILLERY
GUNNERY, FIRE CONTROL, AND POSITION
FINDING, ANTIAIRCRAFT GUNS
Changes j WAR DEPARTMENT,
No. 2 J Washington, May 2, 1942.
FM 4-110, August 10, 1940, is changed as follows:
fl 160. Operation of Director, M4, When Firing.
*******
f. Procedure in case of interlock .
*******
(2) If the first case of locked condition occurs , restore the
director to normal as follows :
(а) Turn power “OFF.”
(б) With power “OFF,” turn the range handwheel to in-
crease future horizontal range several thousand yards (if
possible, 5,000 yards should be obtained).
(c) Set wind, target velocity, and -rate dials to zero.
( d ) With the azimuth handwheel, increase present azimuth
1,800 mils.
(e) Turn power “ON” and director will clear itself of the
locked condition; after all prediction has settled out, the direc-
tor is ready for operation.
(3) If the second case of locked position occurs, restore the
director to normal as follows:
(а) Turn power “OFF.”
(б) Remove right cover plate. (This should be done in a
place free from floating particles of dust. Care must be taken
to prevent dirt from entering the mechanism.)
(c) Set wind, target velocity, and rate dials to zero.
(d) Disconnect lead R2 on terminal block M.
(e) Connect a wire jumper between terminals 14 and R1 on
the quadrant switch.
(f ) With the azimuth handwheel, increase present azimuth
1,800 mils.
455788 * — 42
COAST ARTILLERY FIELD MANUAL
(g) Watching the future range dial, connect a Jumper be-
tween terminals 15 and 5 on terminal blocks H and L and
when future range is approximately 5,000 yards, remove this
jumper. This closes the circuit to the constant speed and
difference motors.
(h) Remove wire jumper from terminals 14 and El. Re-
place terminal R2.
(£) With the range handwheel, decrease present range about
1,500 yards. Set the range rate dial to zero.
(/) Turn power “ON” and director will clear itself. After
prediction has settled out, replace right cover plate and
director is ready for operation.
[A. G. 062.11 (1-30-42).] (C 2, May 2, 1942.)
By order of the Secretary of War :
G. C. MARSHALL,
Chief of Staff .
Official :
J. A. ULIO,
Major General ,
The Adjutant General .
ft
V. %■ GOVERNMENT PRINTING OPP1CI ( f*41
FM 4-110
COAST ARTILLERY
FIELD MANUAL
ANTIAIRCRAFT ARTILLERY
GUNNERY, FIRE CONTROL,
AND POSITION FINDING,
ANTIAIRCRAFT GUNS
Prepared under direction of the
Chief of Coast Artillery
UNITED STATES
GOVERNMENT PRINTING OFFICE
WASHINGTON : 1940
WAR DEPARTMENT,
Washington, August 10, 1940 .
PM 4-110, Coast Artillery Meld Manual, Antiaircraft Artil-
lery, Gunnery, Fire Control, and Position Finding, Antiair-
craft Guns, is published for the information and guidance of
all concerned.
[A. G. 062.11 (6-10-40).]
By order of the Secretary of War:
G. C. MARSHALL,
Chief of Staff.
Official:
E. S. ADAMS,
Major General,
The Adjutant General.
ii
TABLE OP CONTENTS
Chapter 1. General. Paragraphs Page
Section I. General 1-7 1
II. Elements of data 8 7
III. Linear speed method 9-25 12
IV. Angular travel method 26-34 19
Chapter 2. Position Finding, Fire Control, and
Gunnery.
Section I. Position finding 35-37 25
II. Determination of altitude 38-44 29
III. Prediction; future position 45-53 35
IV. Mechanical solutions 54—61 40
V. Firing data 62-68 56
VI. Data transmission systems 69-77 61
VII. Application of firing data to
guns. . 78-80 67
VIII. Classes, types, and methods of
fire 81-82 69
IX. Exterior ballistics 83-88 71
X. Errors and probabilities 89-91 84
XI. Preparatory fire 92-136 90
XII. Fire for effect 137-139 119
XIII. Spotting and adjustment of fire. 140-154 122
Chapter 3. iNSTRUMENts and Accessories for
Antiaircraft Guns.
Section I. Directors 155-162 146
II. Height finders and altimeters 163-189 174
III. Observation instruments 190-199 197
IV. Lewis chart 200-203 213
V. Crichlow slide rule 204-207 219
VI. Fuze setters 208-212 225
VII. Data transmission 213-218 231
VIII. Stereoscopic training instru-
ments 219-222 238
Chapter 4. Orientation, Synchronization, and
Application of Calibration Cor-
rections.
Section I. General 223-225 243
II. Orientation 226-230 244
in. Synchronization 231-235 249
IV. Application of calibration cor-
rections 236-239 251
Chapter 5. Target Practice; Organization and
Duties of the Record and the
Range Sections.
Section I. Target practice 240-241 253
II. Record section 242-245 254
III. Range section 246 258
Chapter 6. Reference Data.
Section I. Symbols 247 260
II. Illustrative problems 246-254 263
III. Ballistic tables : 255-256 288
IV. Firing tables (extracts) 257 313
V. Derivation of formulas 258-260 351
VI. Additional references 261-262 360
Index 361
in
FM 4-110
COAST ARTILLERY FIELD MANUAL
ANTIAIRCRAFT ARTILLERY
GUNNERY, FIRE CONTROL, AND POSITION FINDING
(The matter contained herein supersedes chapter 1, part two, and
Tables J, K, L, and M, chapter 2, part three, Coast Artillery Field
Manual, Volume II, February 1, 1933.)
CHAPTER 1
GENERAL
Section" I. General
II. Elements of data
III. Linear speed method
IV. Angular travel method
Section I
GENERAL
■ 1. Scope. — This manual treats of the theory and practice of
gunnery, fire control, and position finding for antiaircraft
artillery guns. A knowledge of the fundamentals of exterior
ballistics and gunnery as covered in PM 4-10 will be helpful
in understanding similar fundamentals as applied to anti-
aircraft gunnery. Pertinent definitions and symbols should
be studied and a thorough understanding should be had of
the picture in space of the various elements of data.
B 2. Basic Assumption. — The design of present fire-control
instruments and present fire-control methods for antiair-
craft artillery guns are based on the assumption that the tar-
get will fly in a straight line, at a constant speed, at a con-
stant altitude, or with a constant change of altitude during
the time required to determine and apply data, fire the gun,
and during the time of flight of the projectile. This assump-
tion is based principally on a consideration of the possible
courses of action open to the individual pilot. The direction
of flight is largely subject to his control, and there is no
Paragraphs
1-7
8
9-25
26-34
I
2-3 COAST ARTILLERY FIELD MANUAL
definite assurance that he will continue to fly a straight
course. At any given instant the pilot has several choices of
action open to him. He may turn to the right or left or con-
tinue straight ahead; he may dive, climb, or continue at the
same altitude; or he may reduce or increase the speed, or
continue at the same speed. He may follow any one or a
combination of these courses. There is no method by which
his actions may be reliably anticipated. Within limits, how-
ever, the chances of a turn to the left or to the right, a dive
or a climb, or a decrease or increase in speed are about equal.
It can, therefore, be assumed that the average of all choices
open to the pilot is that he will follow a rectilinear course
during the period indicated in the basic assumption until he
is aware that he is being fired upon. This assumption is
further justified by the fact that the normal targets for anti-
aircraft artillery guns are bombardment and observation avi-
ation. These types of aircraft are not only less maneuverable
than the smaller and lighter types, but the successful ac-
complishment of their missions generally requires rectilinear
flight, particularly near the objective. While errors in pre-
diction due to the basic assumption are to be expected, these
errors, in the long run, will be smaller than if any other course
were predicted. Furthermore, when the target does not ad-
here to the assumed conditions, the resulting prediction error
can often be corrected by an adjustment of basic data.
■ 3. Antiaircraft vs. Aircraft. — Referring to the diagram-
matic representation of the capabilities of present-day anti-
aircraft weapons (fig. 1), some conclusions may be drawn as
to the normal targets for such weapons. First, as aircraft
may operate at any altitude below their service ceiling, the
general rules are:
a. All types of hostile aircraft within limiting range of any
antiaircraft weapon are normal targets for that weapon and
continue to be until they are destroyed, out of range, or a
target presenting a greater threat appears.
b. Whenever different types of hostile aircraft approach
simultaneously, the primary targets for all antiaircraft
weapons are those types of aircraft, within limiting range,
which are capable of inflicting the greatest damage upon the
ground establishments being defended. It should be kept
2
gunnery, etc., antiaircraft guns 3
constantly in mind that the application of general rules must
always be guided by common sense and in this instance by
what is termed in military phraseology as the “tactical
demands of the moment.”
c. Pursuit airplanes are designed principally for air combat.
However, they can be used to attack troops and their trans-
portation. They are characterized by great speed and maneu-
verability and small vulnerability, hence they are not con-
sidered as normal targets for antiaircraft guns except when
flying in large formations at a suitable altitude.
d. Observation airplanes are designed to conduct air recon-
naissance (visual and photographic) , observe artillery fire,
and provide liaison. They may operate singly or in groups
at altitudes best suited for the accomplishment of the
mission.
e. Light bombardment airplanes are designed primarily
for attacking light material objectives and troops. They
will probably operate at altitudes from 1,500 to 24,000 feet.
3
3-5
COAST ARTILLERY FIELD MANUAL
/. Dive bombers are designed for attacking material objec-
tives. A dive is generally made at an angle of about 70°
and is started at altitudes above 12,000 feet, if possible. The
bombs are released and the airplane pulled out of the dive
before it enters the zone of small-arms fire — that is, 1,500
feet altitude.
g. Medium and heavy bombardment airplanes are designed
primarily for attacking heavy material objectives. They may
operate at altitudes from 1,500 to 24,000 feet.
h . It will therefore be concluded that normal targets for
antiaircraft guns are bombardment and observation aviation.
Normal targets for the automatic weapons are all types of
aviation encountered at low and medium altitudes.
■ 4. Antiaircraft Artillery Development. — Characteristics
of the various types of antiaircraft weapons are:
Materiel
' Type of
mount
!
Firing
table,
muzzle
velocity
(ft/sec)
1
Horizon-
tal 1 range
(yds)
Vertical *
range
(yds)
Rate of
fire
(rds/min)
Fixed
2,700
ll f 100
9,800
25
3" A A gun
Mobile
2,700
11, 100
9, 800
25
3" A A gun
Trailer
2,600
7, 700
7, 570
15
90-mm gun
Mobile
2,800
12, 600
11,000
17
105-mm gun
Fixed
2, 800
! 13, 100
12, 300
15
37-mm gun
Trailer
2,700
3,500
3,500
120
.50 cal. machine gun
Tripod
2,700
1,800
1,800
500
.30-cal. machine gun..
Tripod
2,600
800
800
i
600
i Range limited by maximum fuze range or tracer burn-out point.
■ 5. General Characteristics of Aerial Targets. — As a
logical approach to the problems of position finding, data
computation, and firing which confront the antiaircraft
artilleryman, a more detailed examination of the capabilities
of the various types of airplanes is of interest. As a target,
the characteristics of an airplane which particularly interest
the artillerymen are speed, service ceiling, maneuverability,
and vulnerability. From an examination of “All the World’s
4
GUNNERY, ETC., ANTIAIRCRAFT GUNS
5-6
Aircraft” by Jane, considering all types of aircraft, it appears
that the artillerymen must be prepared to fire at aerial tar-
gets whose combined capabilities will cover the following wide
ranges:
a. Speed (normal) , 60 to 350 miles per hour,
b. Altitude, 25 to 35,000 feet.
c. Maneuverability:
(1) Change in speed, from 50 percent to 150 percent of nor-
mal cruising speed.
(2) Climb, 100 to 2,500 feet/minute.
(3) Dive, up to 40,000 feet/minute.
(4) Change direction:
90° in less than 15 seconds.
180° in less than 30 seconds.
d. Vulnerable area, very small and normally considered to
be engines, fuel tanks, and personnel.
■ 6. Antiaircraft Gunnery Problem. — a. Prom the capabili-
ties of military aircraft listed in paragraph 5, it may be con-
cluded that time is the basis of the antiaircraft gunnery prob-
lem. Consideration of a few specific examples will strengthen
this conclusion. The results of the following computations
are approximate:
(1) A bombing airplane flying a straight line course at a
constant altitude of 15,000 feet with a constant speed of 250
miles per hour will enter the field of fire of a 3” antiaircraft
gun at a horizontal range of 9,350 yards. If the airplane pro-
ceeds directly over the battery, it will remain in the field of fire
for 2.5 minutes.
(2) The same airplane flying at a constant altitude of 3,000
feet directly over the battery will remain in the field of fire of
the 37 -mm gun for 0.91 minute.
(3) If the airplane is flying at an altitude of 1,500 feet or
less directly over the battery it will remain in the field of fire
for the 37-mm gun for 0.94 minute and in the field of fire of
the caliber .50 machine gun for 0.46 minute.
(4) A dive bomber commencing its dive at 12,000 feet and
leveling off at 1,500 feet altitude will remain in the field of
fire of a 37-mm gun for 0.61 minute and in the field of fire of
the caliber .50 machine gun for 0.28 minute.
5
!
6-7 COAST ARTILLERY FIELD MANUAL
(5) The above times are the optimum and will rarely be
realized, as such factors as increase in speed and altitude,
multiple targets, and displacement of guns from the defended
area will tend to decrease the time available to fire.
b. Reviewing briefly the cycles of operation in firing a gun
at a moving naval target, it will be recalled that a “dead time”
of from 20 to 40 seconds can be tolerated without material
loss in accuracy for position finding and data calculation, due
to the comparatively slow movement of the target. Mani-
festly, such a “dead time” interval cannot be tolerated in
firing at a moving aerial target. It must be reduced or
entirely eliminated. Ideally, the operations of position finding
and data calculation should be instantaneous and continuous.
c. The time factor also exerts a marked influence upon the
methods of solving the problem. Referring to the specific
examples given in a above, a simple calculation will show that
in (1) the airplane will pass through a vertical angle of about
2,200 mils measured at the gun in 2.5 minutes, or an average
angular travel of about 14 mils per second, with a maximum
rate of about 25 mils per second; in (2) the average angular
travel rate is about 48 mils per second and the maximum rate
about 124 mils per second; in (3) the average angular travel
rate is about 51 mils per second with a maximum of 244 mils
per second for the 37-mm gun and 95 mils per second average
rate with a maximum of 244 mils per second for the caliber
.50 machine gun.
d. A consideration of the mechanical principles involved
will demonstrate that none of the current fire-control equip-
ment for antiaircraft guns is mechanically capable of operat-
ing when the angular travel of the target varies between such
wide limits. (The rate varies between 0 mil and 250 mils or
more per second.) In addition, the relatively heavy guns are
not flexible enough to use the data, if such data were calcu-
lated. The 37-mm gun and the caliber .50 machine gun,
which have sufficient flexibility to operate at high angular
velocities, have been developed to fire on the low-altitude,
high-speed airplanes using different methods of computing
and applying the firing data.
■ 7. General Doctrines of Antiaircraft Fire. — a. Considera-
tion of the relative capabilities of aircraft and antiaircraft
6
GUNNERY, ETC., ANTIAIRCRAFT GUNS
7-8
artillery leads to some definite conclusions regarding the
solution of the antiaircraft artillery gunnery problem.
(1) The relatively high speed of airplanes and the “fleeting
moments” available' for firing dictate that position finding
and data computation must be rapid, approaching as an ideal,
the instantaneous and continuous application of firing data
to the weapons employed, with a projectile meeting a target
the instant it comes within limiting range.
(2) The small vulnerable area presented by an airplane
target dictates first that position finding and data computa-
tion be accurate, and second, since a great many shots fired
in a minimum time increase the probability of hitting, that
weapons be fired at the maximum practicable rate,
(3) The wide variation of angular travel rate, coupled with
the mechanical limitations of both the fire-control equipment
and guns, necessitates that a different solution of the problem
be used for low-altitude, high-speed aircraft.
b. In its essential features, the problem of firing at an air-
plane is the same as firing at any moving land or water tar-
get. In its details, it is more complex, due to the greater speed
of the airplane and its ability to move in three dimensions.
In all cases it is desired to make the projectile meet the target
at some point in space. In antiaircraft-gun firing, the small
vulnerable area presented by an airplane target makes it
desirable to cause the projectile to burst, not upon impact as
with seacoast artillery, but on or just short of the expected
position of the target in order to increase the probability of
hitting. The elementary problem consists of predicting the
future location of the target on the basis of its behavior dur-
ing some interval of time just prior to the prediction, and
calculating data necessary to pass a trajectory through this
point.
Section II
ELEMENTS OP DATA
■ 8. Methods of Computing Firing Data. — a. Firing data
may be computed by two different methods — the linear speed
method and the angular travel method. At present the
linear speed method has superseded the angular travel
method. However, at some future date it is entirely possible
7
GUNNERY, ETC., ANTIAIRCRAFT GUNS
8
A p
AX or
X tp sin. @
or
Sg X tp COS 0
Ro
R p
s g
Sg COS 0
or N-S rate
S g sin 0
or E-W rate
}
}
Sg X tp
e
To
Tp
y 0
y P
Azimuth of target at present position (r 0 ).
Azimuth of target at future position (T v ) .
East-west component of travel of target during time
of flight of projectile.
North^south component of travel of target during
time of flight of projectile.
Horizontal range to target at present position (T 0 ) .
Horizontal range to target at future position (T p ).
Ground speed of target.
North-south component of ground speed of target.
East-west component of ground speed of target.
Linear travel of target in horizontal plane during
time of flight.
Angle between vertical planes containing course of
target and north-south axis of data computor.
(Never greater than 90°. )
Present position of target at instant of firing.
Future or predicted position of target.
Time of flight to future position of target.
East-west component of horizontal range to present
position.
East-west component of horizontal range to future
position.
North-south component of horizontal range to pres-
ent position.
North-south component of horizontal range to future
position.
9
COURSE OF TARGET
8
COAST ARTILLERY FIELD MANUAL
10
MS CD fcq to ^ to b b
J J v * / | <Q| <Q ‘Q’QtiOS y O B O s - tt a
GUNNERY, ETC., ANTIAIRCRAFT GUNS
8
xt p
t p cose 1
or l
-S travel J
t p sine 1
or l
-W travel j
Azimuth of target at present position (T 0 ).
Azimuth of target at future position (T p ) .
Firing azimuth, angle of train of gun.
Slant range to present position of target.
Slant range to future position of target.
Angular height of target at present position.
Angular height of target at future position.
Altitude of present position of target.
Altitude of future position of target.
Quadrant elevation.
Superelevation under existing conditions.
Horizontal range to present position of target.
Horizontal range to future position of target.
Ground speed of target.
Linear travel of target in horizontal plane during
time of flight.
North-south component of travel of target during
time 6f flight of projectile.
East-west component of travel of target during time
of flight of projectile.
Angle between vertical plane containing course of
target and vertical plane containing north— south
axis of the computor. (Never greater than 90°. )
Present position of target at instant of firing.
Future or predicted position of target.
Time of flight to future position of target.
11
8-10
COAST ARTILLERY FIELD MANUAL
that the angular travel method may replace or supplement
the linear speed method, and for this reason the angular
travel method is included in this manual.
b. The basic elements of firing data and the corresponding
symbols for each of the two methods are defined and dis-
cussed in sections III and IV. Certain elements of data are
applicable to both methods, even though they are discussed
under the section heading of either linear speed method or
angular travel method. A consolidated list of symbols, with
definitions, is located for convenience in paragraph 247.
Section III
LINEAR SPEED METHOD
■ 9. General. — Figures 2 and 3 show graphically the ele-
ments of data for the linear speed method.
■ 10. Location of Point in Space (T). — a. A point in space
(D , without reference to its direction from an observer on
the ground, may be located by the solution of a right triangle
in which one acute angle and one side, or any two sides, are
known. Thus in figure 4, if any two of the four elements of
the triangle shown are given, the point T may be located.
Figure 4. — Right triangle in space.
b. Altitude is used as the basic linear measurement for
reasons enumerated in paragraph 37.
c. The sights on the gun or the position-finding instru-
ments are directed on the point in space. The vertical angle
12
GUNNERY, ETC., ANTIAIRCRAFT GUNS
10-12
thus obtained (angular height) combined with the measured
altitude of the point will determine the horizontal range to
the point (T) . In practice this is done by some type of
mechanical calculating device.
d. To and T v are, respectively, the present position of the
target (at instant of firing) and the future (predicted) posi-
tion of the target.
■ 11. Angular Height. — (<=). — There is an angular height
corresponding to each of the two positions of the target (To
and T v ) . It is obvious that, considering an airplane moving
in space with reference to a point on the ground, the angular
height of the airplane will vary from instant to instant for
nearly all conditions of flight. The most notable exceptions
are those when the target flies at a constant altitude on the
circumference of a circle whose center is directly above the
observer, or dives or climbs along the line of position.
a. Present angular height (e 0 ) . — This is the angular height
of the target at the instant the gun is fired.
b. Future angular height (e P ). — This is the angular height
of the target in its future position; that is, the point where
it is predicted to be at the end of the time of flight.
■ 12. Altitude of Target ( H ) . — Corresponding to each of the
positions of the target To and Tv are the altitudes of these
points (all altitudes are based on a horizontal plane which
passes through the data computor) called Ho and H P , respec-
tively. Unless the target is executing a dive or a climb, these
two quantities are equal.
a. Present altitude (Ho). — Data computors are supplied
with the altitude obtained from one of three sources: estima-
tion, two- station altimeter system, or self-contained range
finder or height finder.
b. Future altitude (H P ) . — Originally the problem of deter-
mining future altitude (H P ) was ignored by the assumption
that the airplane did not change altitude during the time of
flight of the projectile. The latest data computors, however,
have made provision for shallow dives and climbs by the air-
plane. Based on a rate of change of altitude obtained either
by estimation or by use of some mechanical device, the data
computor predicts the future altitude (H P ) and calculates
firing data for this altitude.
244637 ° — 40 -
2
13
13
COAST ARTILLERY FIELD MANUAL
■ 13. Superelevation (<£sa) . — a. Definition. — A projectile does
not move in a straight line in the direction and elevation in
which it is fired, but describes a curve. Superelevation is
that part of the quadrant elevation which allows for the
curvature of the trajectory and represents the combined effect
of ballistic conditions and gravity in deflecting the projectile
downward from its line of departure.
b. Factors affecting superelevation. — (1) The curvature oi
the trajectory is dependent upon the initial direction of the
projectile, for the forces which act upon it exert their effect
according to the relation between the direction of motion of
the projectile and the direction in which the resultant force
acts. Thus a projectile fired straight up meets with forces
acting in a direction different from the direction of the forces
which will act on a projectile fired at a comparatively low
angle of departure.
(2) The superelevation necessary to cause a trajectory to
pass through a particular point in space is dependent also
upon the muzzle velocity of the projectile. If the muzzle
velocity developed is less than the assumed (firing table)
muzzle velocity, then for a given quadrant elevation, the
range and altitude attained at the end of a given time of
flight will be less than those shown by the firing table. Thus
for a particular horizontal range and altitude, if the muzzle
velocity were less than the firing table muzzle velocity, the
superelevation necessary to cause a trajectory to pass through
the predicted position would be greater than if the assumed
muzzle velocity were developed.
(3) For a given point, atmospheric conditions will affect
the amount of superelevation which must be given to the gun.
The wind which is blowing may accelerate or retard the
projectile. The existing density may increase or decrease the
range, as may also the temperature elasticity effect of the
atmosphere.
(4) Furthermore, the condition of the materiel will directly
affect the superelevation which must be given to the gun. A
new gun will fire with a greater velocity than an old one, and
as the gun wears, in order to obtain the same range, a greater
elevation must be given to the gun.
14
GUNNERY, ETC., ANTIAIRCRAFT GUNS
13-14
(5) Summarized, the superelevation which must be applied
to the gun is dependent upon —
(a) The position of the target.
(b) The existing atmospheric and ballistic conditions.
c. Superelevation value. — If the atmospheric and ballistic
conditions enumerated in b above were constant, then for any
particular horizontal range and altitude, superelevation would
be a constant value. But for varying atmospheric and ballis-
tic conditions, superelevation will have different values. In
order to distinguish between these two, the symbol 4> s is used
to designate the superelevation under firing table conditions,
and the symbol (psa to designate the superelevation under
conditions actually existing.
d. Firing table superelevation (<f>s) . — (1) Firing tables give
the superelevation in table B using fuze setting and quadrant
elevation as arguments. In table A, which uses time of flight
and quadrant elevation as arguments, the superelevation can
be obtained by subtracting angular height from quadrant ele-
vation. Extracts of tables A and B from Firing Tables
3 AA-J-2a and 3 AA-O-1 are found in paragraph 257.
(2) This value of <p s is used for the purpose of constructing
curves or cams or graduating drums in data computors. It is
subject to correction for the variation between existing
conditions and the firing table conditions.
e. Superelevation under nonstandard conditions (<psa ) . —
(1) When conditions existing at the time of firing vary from
firing table conditions, then the firing table data must be cor-
rected. The correction depends upon the effects of the varia-
tions in conditions.
(2) The vertical pointing correction (<T 2 ) is a correction of
the superelevation made necessary by variations between
standard and actual conditions. The factors affecting 02 are
discussed in paragraph 29b.
Thus, under actual conditions —
4> = e p ~ (- <ra,
and since <t> sa =<t>s±<r 2 ,
4> = ± <t>sa
■ 14. Fuze Range (F) . — a. From an examination of tra-
jectory chart (fig. 23 or 24), it is evident that by changing
15
14
COAST ARTILLERY FIELD MANUAL
the quadrant elevation ( 0 ) the trajectory can be passed
through any point in space within range. All that remains
to be done is to burst the projectile at some definite position
along the trajectory. This is done by means of the time
fuze. In other words, by varying the quadrant elevation ( 0 )
and the fuze range (F), the projectile can be made to burst
at any particular point in space within range. Fuze range
can therefore be defined as the fuze setting necessary to
burst the projectile at a particular point along the trajectory.
Fuze range for any particular point can be ascertained by
reference to either the trajectory chart or firing tables for
the particular gun and ammunition used. The data com-
putor calculates the fuze range to the future position (T P ) .
b. Nonstandard atmospheric and ballistic conditions affect
the shape of the trajectory (due to changes in superelevation,
see par. 13c) passing through a particular point in space.
Therefore the time of flight and consequently the fuze range
to the particular point will vary with the atmospheric and
ballistic conditions. Certain ammunition now in general use
in antiaircraft artillery is equipped with a 21 -second powder
train time fuze. The fuze is graduated in terms of fuze
range from 0 to 21.2. Theoretically each of the whole
divisions represents 1 second time of burning, but actually it
does not. As a result of experimental tests and firings, the
time of fuze burning (which is actually the time of flight ( tp ) )
for different fuze ranges and quadrant elevations has been
computed and tabulated. These same data are also shown
graphically on the trajectory chart. These tests have also
demonstrated that at least three physical factors affect the
burning of a powder train time fuze.
(1) Pressure under which it burns . — Since the air pressure
decreases as the altitude increases, the time of burning will
vary with the altitude attained by the projectile. (It will
also vary with the atmospheric density. This effect of density
on fuze burning is discussed in paragraph 86c.) A specific
example from the firing tables will show how much of a dif-
ference altitude makes on the time of burning of the fuze.
Referring to table XIX, paragraph 257, using as arguments
F=13, and 0=700 mils; t P = 12.68 seconds, and the altitude
of the burst is 3,223 yards. Using as arguments F=13, and
16
GUNNERY, ETC., ANTIAIRCRAFT GUNS
14-15
0=1,500 mils; f P =14.96 seconds and H— 6,189 yards. A dif-
ference of 2,966 yards in altitude has increased the time of
burning of the fuze for the same fuze setting 2.28 seconds.
( 2 ) Temperature of the fuze . — While the temperature of
the fuze affects its rate of burning, the magnitude of this
effect has not been determined satisfactorily.
(3) Speed of rotation of the projectile. — The speed of ro-
tation, or spin of the projectile, has an effect on the rate of
burning of the fuze. It has been found by experiment that
there are limits of rate of spin beyond which powder-train
fuzes may not be expected to function except with extreme
inaccuracy and unreliability. ,
c. Prom the above discussion it will be seen that the fuze
range varies according to the ballistic and atmospheric con-
ditions of the moment, with the altitude of the burst, and
with the quadrant elevation of the gun. If we assume certain
values for H and 0 , we select a certain point in space. This
same point can be identified equally as well by a combination
of (H P and Rp) , or (e P and t v ) . H v and Rp are used in the
M4 director to determine the fuze range (F) .
d. Mechanical time fuzes will ultimately replace the
powder train time fuze. They are graduated in terms of fuze
range from 0 to 30 seconds. The factors which affect the 1
functioning of the powder train time fuze do not have any
effect on the mechanical time fuze. Consequently, F equals t v
in the mechanical time fuze.
■ 15. Azimuth of Target (A) . — For each position of the
target, there is a horizontal angle called the azimuth of target
(A) . This angle is measured in a clockwise direction from a
reference axis to the horizontal projection of the target. The
reference axis is usually made to coincide with either grid
north or true north. The azimuths of the target at each of
the two positions of the target To and T P are called, respec-
tively, A 0 and A v .
a. Azimuth of target at present position (Ao). — A 0 is the
azimuth of the target at the instant the gun is fired,
b. Azimuth of target at future position (Ap) . — A v is the
azimuth of Tp . It is the azimuth at which the burst should
meet the target.
17
16-23
COAST ARTILLERY FIELD MANUAL
■ 16. Firing Azimuth ( A } ) . — A/ is the azimuth at which the
gun is laid in order that the burst will occur at Tp. A/=A P ±
52. The factors affecting 5 2 are discussed in paragraph 28b.
■ 17. Horizontal Range (R) . — For each of the positions of
the target, there is a corresponding horizontal range. The
horizontal ranges to T 0 and Tp are called, respectively,
Ro and Rp.
■ 18. Ground Speed of Target (Sg ) . — Ground speed of target
is the velocity of the target expressed in distance per interval
of time, usually yards per second. The distance is measured
in the horizontal plane.
■ 19. Time of Flight (t P ) . — tp is the time in seconds that it
will take the projectile to reach the future position (Tp) .
For the same point, it will vary depending upon the combina-
tion of gun and ammunition and the atmospheric and ballistic
conditions of the moment.
■ 20. Slant Range to Target (D) . — For each position of the
target in space, the distance measured from gun to target in
the inclined plane is called the slant range to target. For
each position of the target To and T Pt there is a corresponding
slant range called Do and Dp, respectively.
■ 21. Quadrant Elevation (0 ). — 0 is the elevation at which
the gun is laid in order that the trajectory will pass through
the future position. 0 is a function of Hp and Rp.
■ 22. Xo and Yo. — The horizontal range to the present posi-
tion of the target is resolved into a component in the E-W
direction (called Xo) and a component in the N-S direction
(called Yo) . It will be seen that X 0 and Yo are the coordinates
of the present position of the target using as reference axes,
the E-W and N-S directions. The gun is considered as being
at the origin.
■ 23. E-W and N-S Rates. — The continuous tracking of the
target establishes an instantaneous rate S g . This rate is re-
solved into a component in the Er-W direction (called E-W
rate=Sg sin 0) , and a component in the N-S direction (called
N-S rate=Sg cos 0) . These rates are the instantaneous rates
of change of X 0 and Y 0 .
18
GUNNERY, ETC., ANTIAIRCRAFT GUNS
24-28
■ 24. E-W and N-S Travel (A X and A Y) . — The E-W and
N-S rates multiplied by the time of flight, give the travel of
the target in the E-W and N-S directions during the time of
flight of the projectile.
A J£=E-W rat eXt p =Sg sin OXfp
A Y— N-S rateXfp=<Sg cos QXtp
■ 25. X v and Yp . — If the E-W and N-S travel of the target are
added algebraically to the coordinates of the present position
of the target, we have the coordinates of the future position of
the target X v and Y p .
X P =Xo± A X
Yp=Yo ± A Y
Section IV
ANGULAR TRAVEL METHOD
■ 26. General. — Figures 5, 6 , and 7 show graphically the
basic elements of data for the angular travel method.
■ 27. Location of a Point in Space. — The method of locating
a point in space is the same as in the linear speed method.
However, the data computor determines the slant range
(Do) instead of the horizontal range ( R 0 ) .
■ 28. Lateral Deflection Angle (5) . — The lateral deflection
angle is the angle by which the gun must lead the airplane
laterally in order that the projectile meet the target at the
predicted point (T P ). 5 is the difference between the firing
azimuth ( A /) and the present azimuth ( A 0 ) . It consists of
the algebraic sum of the components, principal lateral deflec-
tion (Si) and the lateral pointing correction ( 82 ) .
a. Principal lateral deflection (Si). — Si is the lateral lead
necessary to compensate for the travel of the target during
time of flight of the projectile. It is a variable whose value is
dependent upon direction of course of target, speed of target,
time of flight of the projectile, e 0 and e P , and the value of the
principal vertical deflection angle ( 01 ).
b. Lateral pointing correction ( 82) . — 82 is the lateral lead
necessary to compensate for effects other than travel of the
target. It is the algebraic sum of three variable quantities,
the lateral arbitrary adjustment correction ( 82 a), lateral
19
28
COAST ARTILLERY FIELD MANUAL
GUN
horizontal projection
Figure 5. — Elements of data, angular travel method (horizontal
projection) .
A p Azimuth of target at future position (T p ) .
A 0 Azimuth of target at present position (T 0 ).
Af Firing azimuth.
ap Angle of approach at future position (T p ) .
ao Angle of approach at present position (T 0 ) .
p Wind -fire angle.
5 Lateral deflection angle.
Principal lateral deflection angle.
5 2 Lateral pointing correction.
d 2 a Lateral adjustment correction (arbitrary) .
5 2 <i Lateral pointing correction due to drift.
$ 2W Lateral pointing correction due to cross wind.
R p Horizontal range to target at future position ( T p ) .
R 0 Horizontal range to target at present position ( T 0 ) .
S g Ground speed of target.
SgXt p Linear travel of target in horizontal plane during time of
flight,
T p Predicted position of target (future position) .
T 0 Present position of target (instant of firing).
t p Time of flight to future position of target (T p ) .
20
VERTICAL PROJECTION
(Visualized) airplane approaching directly over the battery
GUN
Figure 6. — Elements of data, angular travel method (vertical
projection) .
D p Slant range to target at future position ( T p ).
D 0 Slant range to target at present position (T 0 ) .
ep Angular height of target at future position (T p ) .
6 0 Angular height of target at present position (T 0 ).
H Altitude of target.
0 Quadrant elevation.
0s Superelevation under firing table conditions.
0 sa Superelevation under actual conditions.
Rp Horizontal range to target at future position (T p ).
R 0 Horizontal range to target at present position ( T Q ) .
S g Ground speed of target.
SgXt p Linear travel of target in horizontal plane during time of
flight.
<n Principal vertical deflection angle.
cf2 Vertical pointing correction.
<j2 a Vertical adjustment correction (arbitrary) .
e-id Vertical pointing correction due to density.
a2 V Vertical pointing correction due to muzzle velocity,
c t 2W Vertical pointing correction due to range wind.
T v Predicted position of target (future position).
T 0 Present position of target (instant of firing) .
t p Time of flight to future position of target (T p ) .
21
28
COAST ARTILLERY FIELD MANUAL
22
GUNNERY, ETC., ANTIAIRCRAFT GUNS
28-32
pointing correction due to cross wind (fcw) , and lateral point-
ing correction due to drift (Sad).
■ 29. Vertical Deflection Angle (<r) . — The vertical deflec-
tion angle is the angle (exclusive of superelevation) by which
the gun must lead the target vertically in order that the
projectile meet the target at the predicted point (T P ). It is
the algebraic sum of the principal vertical deflection (<n) and
the vertical pointing correction (rc) .
a. Principal vertical deflection (a ) . — <71 is the vertical lead
necessary to compensate for the travel of the target during
time of flight of the projectile. This variable is dependent
upon the direction of the course of the target, speed of the
target, time of flight of the projectile, eo and e p , and value of
the principal lateral deflection angle (5/).
b. Vertical pointing correction ( 0 - 2 ). — a 2 is the vertical lead
necessary to compensate for effects other than travel of the
target. It is the algebraic sum of four variable quantities,
vertical arbitrary adjustment correction ( 02 a ) , vertical point-
ing correction due to range wind (<T 2 w ) , vertical pointing cor-
rection due to variation in muzzle velocity (wv ) , and vertical
pointing correction due to variation of atmopsheric density
(<*2 a) .
■ 30. Angle of Approach (a) . — For each of the two positions
of the target, To and T v , there is a corresponding angle of
approach called ao and a P , respectively. The angle of ap-
proach in each case is the acute angle between the horizontal
projections of the course of the target and line of position.
■ 31. Wind-Fire Angle (/3 ). — 0 is the horizontal angle
measured between the vertical planes containing the axis
of the bore and the ballistic wind. It is obtained by sub-
tracting Af from A^. Aw, the azimuth of the ballistic wind,
is the direction from which the wind is blowing. Add 6,400
mils to A w> if necessary, in order to avoid a negative value
of /3.
■ 32. Angular Velocity (2). — This element of data is not
shown in the figures. It is the angle swept over by the target
per unit of time. In the operation of tracking, the data com-
putor resolves the angular velocity ( 2 ) into two components
23
32-34
COAST ARTILLERY FIELD MANUAL
(2 e ) which is the rate of change in angular height and (2 a )
which is the rate of change in azimuth.
B 33. Altitude (H) . — Unlike the linear speed method, the
angular travel method formulas developed to date are based
on the assumption of constant altitude of the target. As a
result H P always equals H 0 .
B 34. Elements Similar to Linear Speed Method. — The fol-
lowing elements of data are identical with those discussed
under the linear speed method (sec. Ill) : Azimuth of target
(A 0 , A P ) ; position of the target ( T 0 , T P ) ; slant range to target
(Do, Dp) ; angular height (eo, e P ) ; time of flight ( tp ) ; ground
speed of target (Sg) ; quadrant elevation (</>) ; superelevation
( <psa ) ; fuze range ( F ) ; and firing azimuth ( Aj ).
24
CHAPTER 2
POSITION FINDING, FIRE CONTROL, AND GUNNERY
Paragraphs
Section I. Position finding 35- 37
II. Determination of altitude 38- 44
III. Prediction; future position 45- 53
IV. Mechanical solutions j. 54- 61
V. Firing data 62- 68
VI. Data transmission systems 69- 77
VII. Application of firing data to guns 78- 80
VIII. Classes, types, and methods of fire 81- 82
IX. Exterior ballistics 83- 88
X. Errors and probabilities 89- 91
XI. Preparatory fire 92-136
XII. Fire for effect. __ 137-139
XIII. Spotting and adjustment of fire 140-154
Section I
POSITION FINDING
■ 35. General. — Position finding is the process of determining
the position of a target in space with reference to the battery
and the determination of a future position of the target. In
paragraph 7, it was emphasized that position finding should
be accomplished instantaneously and that the small vulner-
able area presented by an airplane demands the greatest
accuracy in observation and in the calculation of firing data.
■ 36. Use of Instruments. — a. In proceeding to study the
aspects of position finding by instrumental observation, it is
well to recall that all observation instruments used for pre-
cise measurements are essentially the same as the surveyor’s
transit, which measures horizontal and vertical angles. A
primary requirement for accuracy with such instruments is
that the angles they measure are truly vertical and truly
horizontal. The observing instruments used in the Coast Ar-
tillery Corps are so constructed that this requirement for
accuracy is satisfied by leveling. While the actual process of
leveling may vary with different instruments, the principles
are identical, and the procedure will usually be apparent
25
36-37
COAST ARTILLERY FIELD MANUAL
fit
from an examination of the instrument or by consulting the
handbook accompanying the instrument.
b. The location of the target with reference to the gun
or observer requires the measurement of angles from very
definite reference axes or reference planes. Therefore, as a
general rule, all instruments must be oriented or so pointed
that the horizontal angles measured will be in terms of angu-
lar units (azimuth) from an arbitrarily chosen reference di-
rection. For uniformity, the reference direction, or direction
of zero azimuth, is customarily chosen as north. As in the
case of leveling, the actual methods of orienting may vary,
but the procedure will usually be apparent. In addition, it
is essential that vertical angles be measured from a horizontal
plane. Therefore instruments must be adjusted or the scale
which indicates the vertical angle must read zero when the
line of sight is truly horizontal. The procedure in adjusting
an instrument varies with different instruments and will not,
as a rule, be readily apparent; hence a handbook must be
consulted or competent assistance must be obtained.
c. Instruments are generally quite rugged in construction,
but they must be carefully handled and should not be sub-
jected to unnecessary shocks, jars, or strains. Screws, hand-
wheels, and other moving parts should never be forced if
they do not operate freely. Instruments are provided with
weatherproof covers, packing boxes, carrying straps or han-
dles, and other impedimenta for protection against weather
and to facilitate careful handling. To avoid scratching the
surfaces of lenses, prisms, and other optical elements, they
should be cleaned only with a soft linen cloth or with optical
paper especially furnished for the purpose. Instruments
should be disassembled under the supervision of a competent
technician.
■ 37. Target Location. — a. With the foregoing in mind, the
position-finding problem and means and methods employed
in its solution will now be considered. The accurate location
of a point which is inaccessible to the observer presents the
usual triangulation problem. Referring to figure 8, it is clear
that a properly oriented instrument, continuously directed
at the target, will continuously and instantaneously furnish
an azimuth ( Ao ) and an angular height (e 0 ).
26
GUNNERY, ETC., ANTIAIRCRAFT GUNS
37
27
Figure 8. — Location of an airplane target; present position (T 0 ).
37
COAST ARTILLERY FIELD MANUAL
b. In order to solve the right triangle GToN (fig. 8) , it is
necessary that one angle and one side be known. e Q is in-
stantly and continuously available at the data computor. H
or R must be determined in order to solve the triangle.
c. In selecting the side of the triangle to be measured, brief
consideration of a specific example will be helpful. For an
airplane flying toward the observer at 300 miles an hour at
a constant altitude ( H ) of 10,000 feet, the horizontal range
( R ) will be changing uniformly at the rate of 150 yards per
second and the slant range (D) will be changing nonuni -
formly from slightly less than 150 yards per second to 0 yards
per second.
As the example assumes that the target was flying at con-
stant altitude ( H ) , there is no question as to the proper side
of the triangle to measure. However, before making a final
decision, the possibilities that a target will not fly at constant
altitude (H) should be examined. The modern bombing air-
plane is capable of climbing, fully loaded, at a rate of about
8 yards per second. Compared to the rate of change in the
horizontal ( R ) or slant ( D ) ranges, this rate of change in
altitude (H) appears insignificant. Considering the possibil-
ity of a negative change in altitude (H) , or “dive,” dive bomb-
ers are suitable targets for automatic weapons, their suit-
ability as gun targets being limited to that interval of time
just preceding the “dive,” The M4 director is capable of com-
puting firing data for a target whose altitude is changing at
a rate of not more than 50 yards per second.
d . Thus it is concluded, first, that the physical limitations
of both the instruments and the operators make it desirable
that the side of the triangle which changes at the slowest rate
be selected for measurement; and second, that the capabilities
of the normal targets for antiaircraft guns (military bombing
and observation airplanes) are such that the altitude (H)
“leg” of the triangle actually may change the least rapidly.
e. Having decided that H is the logical side of the triangle
to measure, we can proceed with the determination of the
present position of the target. We have three elements avail-
able, Ao, e 0 , and H. The present position of the target may be
located by the coordinates Ao, R 0 , and H; or A 0) e 0 , and D 0 ; or
Xo, Yo , and Ho.
28
GUNNERY, ETC., ANTIAIRCRAFT GUNS
37-40
/. When eo is less than +10°, the calculation of data is
more accurate if D is the measured side of the triangle. In
this case, the slant range to the target (Do) is determined by
the height finder and H 0 is computed by the director. Do is
assumed to be equal to Ro and the present position of the
target is located by the coordinates A 0> Ro, and H 0 ,
Section II
DETERMINATION OF ALTITUDE
B 38. General, — a. There are two general systems of in-
strumental determination of altitude — the two-station system
and the single -station system. In our service the altimeter,
M1920, is used in the two-station system and a stereoscopic
height finder is used in the single -station system.
b. Regardless of the method of altitude determination used,
it is of primary importance that the data are accurate. The
first determination should be obtained in a minimum of time
after the assignment of a target, and successive determina-
tions should be made as rapidly as possible.
B 39. Single- Station System. — The single-station system
employs an instrument which is entirely self-contained. The
unit consists of the following principal parts:
a. A self-contained stereoscopic range or height finder
mounted on a cradle and tripod in order to enable it to be
traversed and elevated as necessary.
b. Two auxiliary sighting systems for the trackers, who
assist the observer by keeping the height finder directed at
the target.
c. A data transmission system for instantaneously trans-
mitting to the director the determined range or altitude.
d. A target designating system — that is, electrical trans-
mission of Ao and e 0 from the director to the height finder —
to insure that both instruments are on the same target.
B 40. Principle of Stereoscopic Height Finder. — Stereo-
scopic height finding is based on the faculty of the eyes to
determine when two objects (target and reticle) are in the
same distance plane. This faculty is aided in the height
finder by increasing the effective base line of the eyes to the
244637 *»■
29
40-43
COAST ARTILLERY FIELD MANUAL
length of the height finder and increasing the sharpness of
vision by the magnifying power of the lenses of the instru-
ment. In the height finder, the adjustment necessary to move
the target image to the target reticle distance plane is a
measure of the range to the target. The instrument can
convert this range to altitude. (See TM 4-250.)
B 41. References to Stereoscopic Height Finding. — Further
detailed information on the height finder Ml will be found
in section II, chapter 3, and in the handbook Height Finder
Ml, issued with the instrument. For information on stereo-
scopic training devices, see section VIII, chapter 3.
■ 42. Two -Station System. — The two-station system of alti-
tude determination employs one optical instrument at each
end of a measured base line. The instrument contains charts
anH mechanical devices for the rapid and accurate solution
of triangles. Communication by telephone must be main-
tained between the two instruments during the determina-
tion of altitudes. The accurate determination of altitude is
dependent upon the accurate operation and orientation of
the instruments.
B 43. Two-Station Principles. — a. Consider the triangle
AB'B " (fig. 9) in the vertical plane. Designate the base line
as b, the altitude as H, the angles at B ' and B" as 01 and 0 2 ,
respectively.
A A
Figure 9. — Determination of altitude (two stations) .
30
GUNNERY, ETC., ANTIAIRCRAFT GUNS
43
By simple trigonometry it follows that —
Example a
Li=H cot <f>\
L 2 = H cot 0 2
b = L\ — L2
= ff (cot 0i — cot 0 2 )
Example b
L\ = H cot 4 > i
L% = H cot (180° — 0 2 )
= —H cot <t>2
b=Li + L 2
~H (cot </>i — cot 0 2 )
H
H=
cot 01 — cot 02 ~~ cot 01 — cot 02
Expressed logarithmically,
log ff=log b — log (cot 0i — cot 02)
Therefore by placing an instrument at each end of a measured
base line (b) and measuring the vertical angles, the altitude
( H ) to a point in the vertical plane which contains the base
line is readily computed. The necessary data are, first, that
the length of the base line (b) is known, and second, that the
angles 01 and 02 are measured (as indicated in fig. 9 ,
0 i interior and 02 exterior), in the vertical plane which in-
cludes the station at each end of the base line. It should be
noted that the altimeter computes altitude (H) only for
points in the same vertical plane as both stations. Manifestly,
it will seldom occur that an airplane target will be found
directly overhead. Hence the instruments must be so con-
structed as to permit accurate observation for any location.
b. In figure 10 , let B' and B" represent positions occupied
by instruments at the ends of a horizontal base line of known
length (b). B'c and B"d are both perpendicular to B'B'\
They are horizontal axes for planes which may be rotated
about them, B'c serving as an axis for the plane B'egc, and
B"d serving as an axis for plane B"egd. The intersection of
these two planes is a horizontal line; and, if both planes con-
tain the same point in space, this line will contain that point
and will be a certain distance above the horizontal plane con-
taining the base line. For any given base line, this distance
above the horizontal plane containing the base line depends
on the angles formed by the rotated planes with the hori-
zontal. The planes having been so rotated, lines of sight may
be moved in these planes until they are on the same point in
31
43
COAST ARTILLERY FIELD MANUAL
space. Being on the same point in space and lying in their
respective planes, they must intersect on the line (ridge)
where the planes intersect.
9
c . The two-station system makes use of the principle just
described in determining the altitude of a target. It consists
of two instruments (altimeters) , one to be used at each end of
a base line. Each instrument is capable of being oriented,
thus establishing the axes B'c and B"d, as shown in figure 10 .
The line of sight has one motion about a horizontal axis per-
pendicular to the base line and a second motion about an axis
at all times perpendicular to the rotated planes B'egc or
B"egd. Thus, in following the target, each instrument is
establishing the angle between its rotated plane and the hori-
zontal plane of the base line. These rotated planes intersect
in a horizontal line through the target. All points on this line
are at the same altitude above the horizontal plane B'cdB
If, then, the altitude of any point of this line through the tar-
get above the horizontal plane is determined, the altitude of
the target is known. In a above we have solved the triangle
in the vertical plane containing the base line. The formula
developed,
log H= log b — log (cot 0 i — cot 02 )
is true for all values of b, 0i, and 02. It should be noted that
02 is the exterior angle at B" and 01 is the interior angle at
B f . The actual construction of the instruments and the
operation thereof are covered in section II, chapter 3 .
32
GUNNERY, ETC., ANTIAIRCRAFT GUNS
43
d. In the preceding discussion the base-end stations are at
the same elevation. The expression for altitude as given above
will not hold when this condition does not exist. Consider the
situation as shown in figure 11. Assume a target flying at
2,000 yards altitude (H) directly toward the battery in the
vertical plane of the altimetric base line. The base line (b)
is 2,000 yards, with B ' at the battery and B" 200 yards above
the battery.
3 2 /
Figure 11. — Problem in determination of altitude.
In the same manner it can be shown that the altitudes
computed by the altimeter will be
Point 2, 2,000 yards. Error 0
Point 3, 1,895 yards. Error —105 yards
33
43-44
COAST ARTILLERY FIELD MANUAL
Thus it will be seen that the error is neither constant in
amount nor in direction and varies with the position of the
target.
e. There is no provision on the altimeter, M1920, for making
a mathematically accurate correction for the error introduced
when the B f and B " stations are not at the same level; hence
the application of an approximate correction must be resorted
to. In the example given (fig. 11), it will be noted that the
line joining the two stations makes an angle with the hori-
zontal whose tangent is equal to
difference in elevation
length of base line
tan e=
200
2,000
0.100
e=100 mils
If the vertical angles read at each station are reduced by one-
half this amount (50 mils) and again substituted in the
fomula for the following values of altitude (H) will be
computed
Point 1, 1,920 yards.
Point 2, 1,900 yards.
Point 3, 1,895 yards.
Realizing that 1,900 yards represents the altitude (H) of the
target above the midpoint of the line joining B' and B", it is
clear that a correction of one- half the angular height (e)
from B' to B ", applied to each instrument, will provide a
reasonably accurate computation of altitude ( H ) for all posi-
tions of the target, with a small constant error of one- half
the difference in elevation between B" and B', which can be
removed by a flat scale correction. The method of applying
corrections for the difference in elevation of B' and B " sta-
tions is discussed in paragraph 188.
■ 44. Comparison of Single- Station and Two-Station Sys-
tems. — a. Availability of instruments . — The present two-sta-
tion altimeter, M1920, is an adaptation of a World War in-
strument. It is available in considerable quantities, and addi-
tional instruments can be procured quickly at a relatively low
cost. The stereoscopic height finder, as an antiaircraft
instrument, is a post-war development in this country, is diffi-
cult to manufacture, and is costly.
34
GUNNERY, ETC., ANTIAIRCRAFT GUNS
44-45
b. Accuracy . — Theoretically, the two-station system is the
more accurate. Practically, the necessary “cramping” of
scales to reduce the size of instruments and unavoidable per-
sonnel errors in operation offer little choice in accuracy
between the two systems under normal conditions of opera-
tion.
c. Installation and control . — With respect to installation
and control, the stereoscopic height finder is superior to the
two -station system. It can be placed in operation much more
quickly than the two-station system and operates under the
direct control of the battery commander. The two- station
system requires the establishment of a base line and the in-
stallation and maintenance of telephone communication.
The lack of direct control over the distant station introduces
an element of uncertainty as to whether both stations will
“track” the same target in those situations where a number
of potential targets are in the field of fire.
d. Transportation . — The 4-meter base stereoscopic height
finder is a large bulky instrument weighing about 2,200 pounds
when packed and requires wheeled transportation for move-
ment over any considerable distance. The two- station, sys-
tem, including two altimeter instruments, telephones, and
field wire, has about one-fourth the weight and may be
“broken down” into loads convenient for handling.
e. Training of personnel . — The two- station system offers
advantages over the stereoscopic height finder with respect to
training of personnel. The required proficiency for altimeter
operators is quickly reached, and no special qualifications for
the operators are required. Proficiency, once attained, will
seldom suffer appreciably through lack of continuous train-
ing. In contrast, stereoscopic observers must be carefully
selected, carefully trained, and their proficiency maintained
by continuous drill and practice.
Section III
PREDICTION; FUTURE POSITION
■ 45. Definitions. — a. Prediction is the process of deter-
mining the location of the target at some future instant based
on the past performance of the target.
35
45-47
COAST ARTILLERY FIELD MANUAL
b. Future position of the target is that position in space at
which it is expected the target will arrive at the end of the
time of flight of the projectile.
■ 46. The Prediction Problem. — In paragraph 37, the meth-
ods of locating the present position of the target were ex-
plained. Briefly the present position may be located by cer-
tain combinations of the following elements: A 0> H, X Q > Y 0 ,
to. Do, and Ro , all of which are either instantly available by
the operation of tracking or are computed by some mecha-
nism. The performance of the target is measured at the
present position, and based on these data, performance of the
target during time of flight of the projectile is predicted. The
target occupies the present position only instantaneously.
The relations between the various elements enumerated above
exist only at that moment and are different from those exist-
ing the instant before and the instant after. As the data
computor measures the performance at a certain instant,
the prediction is based on what the plane is doing at that
moment. If, for instance, the plane is flying on a rectilinear
course, the prediction is made along the course extended in
the same direction. If, however, the plane is flying a curvi-
linear course, the situation is different. Data computors can-
not predict a curved course. All predictions are made along
a straight line. Therefore, all predictions made on a curvi-
linear course will be along the tangent to the course at the
present position of the target.
H 47. Methods of Prediction. — There are two general meth-
ods of predicting the location of the future position of a
target; the angular travel method and the linear speed
method. As the names imply, the predictions of data com-
putors which employ the angular travel method are based
upon the observed angular speed of the target, while the pre-
dictions of data computors which employ the linear speed
method are based on computed values of the target’s ground
speed and direction of flight. The standard antiaircraft di-
rector, M4, employs the linear speed method of prediction.
However, some older types of directors employ the angular
travel method of prediction. The design of future directors
may be based on either method.
36
GUNNERY, ETC., ANTIAIRCRAFT GUNS
48-49
■ 48. Angular Travel Method. — The basis of the angular *
travel method is the measurement of the instantaneous angu-
lar speed or velocity of the target in azimuth and in eleva-
tion, and the multiplication of these instantaneous angular
velocities by the time of flight. The Quantities obtained by
these multiplications will be the approximate lateral and ver-
tical deflection angles. When suitable correction factors are
introduced in the products, the principal lateral and vertical
deflection angles will be obtained. The final form in which
these predictions are utilized in pointing the gun depends
upon the method of pointing used.
■ 49. Angular Travel Error. — The multiplication of in-
stantaneous angular velocity by time of flight instead of aver-
Figure 12. — Vertical angular travel error.
age angular velocity by time of flight, or the solution of an
equation which, in effect, accomplishes this, results in the
determination of an approximate deflection angle Ox or 5 X )
and the introduction of an error. This error is called the
angular travel .error. Referring to figure 12, consider as a
specific example that an instantaneous vertical angular ve-
locity has been measured at the point a , and that multiplica-
tion by the time of flight (£) has resulted in a line of direc-
tion through the point b, the arc a-b representing the angular
travel of a target (vertically) during the time of flight. If
this is correct, the target must be traveling on the arc of a
37
49-50
COAST ARTILLERY FIELD MANUAL
c great circle at constant speed. However, the basic assumption
made in antiaircraft gunnery is that the target moves in
rectilinear flight. Therefore the path a~c represents the
actual travel of the target during the time of flight (f), and
the true line of direction should be through the point c.
Hence, the prediction must be refined to correct for the
angular travel error which is introduced by multiplying the
angular velocity at the point a, which differs materially from
that at the point c } by the time of flight. The correction may
be accomplished in three general ways. If the instantaneous
angular velocity (2) is multiplied by the true time of fight
(t P ), first, a correcting multiplier may be used; or, second,
a correction term of proper value (negative or positive) may
be added to the result ; and, third, the instantaneous angular
velocity (2) may be multiplied by a fictitious time of flight
(£') factor. Any one of these methods may be adapted to
mechanical processes.
Certain courses exist where either one or both of the angu-
lar velocities are constant, for instance, a plane diving directly
at the battery. But, it will be found that in nearly all condi-
tions of flight, both the lateral angular velocity and the verti-
cal angular velocity vary continuously, thereby introducing
angular travel errors.
■ 50. Principal Lateral Deflection Angle (Si). — The prin-
cipal lateral deflection angle (5i) is the horizontal angle,
measured at the gun position, through which the target will
move in the time intervening between the firing of the gun
and the arrival of the target and projectile at the future
position. The magnitude of this angle is subject to exact
mathematical determination under the basic assumptions of
target flight. The general expression for this value is as
follows:
sin <5i = 2 a
sin e p
tj) .
sin e 0
COS €p
COS €p
where 2 a (the instantaneous lateral angular velocity of the
target in its present position) is expressed in radians per
second. It is to be noted that the value of Si depends upon
the size of the principal vertical deflection angle as will be
seen from the appearance of eo and e p above. Similarly, it
38
GUNNERY, ETC., ANTIAIRCRAFT GUNS
50-52
will be found that the value of the principal vertical deflection
angle is dependent upon lateral deflection. Thus, the equa-
tions for Si and for <n are simultaneous equations, neither of
which may be solved without the other. The derivation of
the above formula is found in paragraph 258.
■ 51. Principal Vertical Deflection Angle (o-i). — The prin-
cipal vertical deflection angle Ui) is the vertical angle, meas-
ured at the gun position, through which the target will move
during the time intervening between the firing of the gun and
the arrival of the target and the projectile at the future
position. The magnitude of this vertical angle, like that of
the principal lateral deflection angle, is subject to exact
mathematical determination. The general expression for
this value is as follows:
sin (7i = 2 c £psm e p t . 5i .
— -sin Si tan — sin e 0 cos e v
sin e 0 2
where 2 e (the instantaneous vertical angular velocity of the
target at the present position) is expressed in radians per
second. It should be noted that the expression for the value
of the sine of <n is made up of two parts. The first,
represents the product of future time of flight and the
instantaneous vertical angular velocity corrected for the major
part of the angular travel error (since it is multiplied by the
ratio of
sin e v \
sin e 0 /
The second part of the expression for sin <n is called the
complementary term, since it varies with the value of lateral
deflection. The sign of this term is negative when the sign
of tJi is positive and vice versa, but the effect of the comple-
mentary term is always to decrease the angular height to the
future position regardless of the sign of <n. The derivation of
the above formula is found in paragraph 258.
■ 52. Use of Si and <tu — The values of Si and <n determined by
the formulas in paragraphs 50 and 51 above are used in two
39
52-54
COAST ARTILLERY FIELD MANUAL
different ways depending upon the method of pointing. In
case 1 V 2 pointing (par. 78) 5i and n are the principal deflec-
tions which are set on the sights of the guns. With 81 and <n
only set on the sight and the sight of the gun tracking the
target, the axis of the bore is pointed at the future position of
the target (Tp) .
In case III pointing (par. 78), Si and <n are added alge-
braically to A 0 and e 0 in order to get Ap and <?p. Tp is located
then in terms of Ap, e P , and H.
■ 53. Linear Speed Method. — a. As used in our service, the
linear speed method is based upon the continuous measure-
ment of the ground speed ( S g ) of the target and its direction
of flight. As in the angular travel method, the present posi-
tion of the target (To) is determined by the continuous track-
ing of the target thereby measuring A 0 and e 0 , and the meas-
uring of the altitude (H) 1 R 0 is computed mechanically from
the data e 0 and H. To is then located to scale using the polar
coordinates Ao and Ro. These polar coordinates are converted
to rectangular coordinates Xo and Yo. (See figs. 2 and 3.)
b. A device measures the instantaneous rates of change of
Xo and Yo. These rates are the E-W and N-S rates. The
E-W and N-S rates are multiplied by the time of flight (tp)
to the future position (T P ) giving the E-W travel (AX) and
the N-S travel (AY) during the time of flight. AX and AY
are added algebraically to the coordinates of the present posi-
tion Xo and Yo giving X v and Y v . (See figs. 2 and 3.) Xp
and Yp are converted to polar coordinates A P and R P . Thus
T P is located in terms of Ap . , R v , and Hp.
Section IV
MECHANICAL SOLUTIONS
■ 54. General. — Mechanical computing devices are not un-
common; slide rules, adding machines, and cash registers
are in everyday use. It is possible to obtain either a graphical
or mechanical solution, or both, for almost any law of mathe-
matics. Mechanical computing devices obtain answers very
rapidly and in some cases instantaneously. This section
considers the mechanical computing devices employed in the
M4 director.
40
GUNNERY, ETC., ANTIAIRCRAFT GUNS
55
■ 55. Variable Speed Drive. — a. The variable speed drive is
also known as the ball and disk integrator. It is used in the
standard director —
(1) To perform multiplication or division.
(2) To change linear distance to rotary motion.
(3) As a variable speed drive.
b. The variable speed drive consists primarily of a flat disk
(iW), a cylinder (R), and two steel balls (N) mounted in a
carriage one over the other and in contact with the disk and
cylinder. The disk is rotated at a given angular velocity (co).
Rotation of the disk is transmitted through the steel balls to
the cylinder. (See fig. 13.)
Figure 13. — Variable speed drive.
c. The operating principle of the variable speed drive is:
the angular velocity of the cylinder is proportional to the
angular velocity of the disk (to) and to the displacement of
the steel balls (r) from the center of the disk; that is,
Angular velocity of cylinder =
Angular velocity of disk
X displacement of balls
from center of disk
radius of cylinder
co times r
constant
41
55
COAST ARTILLERY FIELD MANUAL
Referring to figure 13, if the rotation of the disk ( M ) is in
the direction shown, the rotation of the cylinder ( R ) will be
shown. If the displacement of the balls (r) is zero, that is
the balls are at the center of the disk (Af) then
Angular velocity of cylinder —
%
« times 0
constant
= 0
If the balls are moved to the left side of the disk (AO , the
rotation of the cylinder ( R ) will be in the direction opposite
to that shown.
d. In the M4 director, the automatic prediction mechanism
uses a variable speed drive to perform division. The disk is
made to revolve at an angular velocity proportional to the
reciprocal of the time of flight
The displacement of the
balls (r) is made proportional to prediction ( AX , AY, or AH).
Then the
Angular velocity of cylinder = —- X prediction X
But rate =
t v
distance
time
constant
Therefore the angular velocity of cylinder is proportional to
the rate (either E-W, N-S, or altitude).
e. The automatic prediction mechanism also uses a varia-
ble speed drive to convert linear distance to rotary motion,
(w) must be constant. If the disk is driven by a constant
speed motor, (w) is constant, r is made proportional to the
quantity which is to be converted from a linear distance to
a rotary motion, the reciprocal of the time of flight
Then the
Angular velocity of cylinder —
constant X
constant
That is, the angular velocity of the cylinder is proportional
to the reciprocal of the time of flight (t P ) .
Likewise in the ballistic wind mechanism of the M4 director,
r is made proportional to the E-W or N-S component of the
42
GUNNERY, ETC., ANTIAIRCRAFT GUNS 55-56
ballistic wind. Then the angular velocity of the cylinder is
proportional to the E-W or N-S component of the ballistic
wind.
/. The range rate and altitude rate drives are used to sup-
plement the manual operation of matching pointers in the
M4 director. The disk is driven by a constant speed motor.
The angular velocity of the cylinder is therefore proportional
to the displacement of the balls. By adjusting the displace-
ment, the operators can make either Ro or Ho change at a
certain specified rate, or at a rate so as to keep the dials con-
tinuously matched. Such an operation can be done manually,
but a power drive has the advantage of resulting in a smoother
rate of change.
■ 56. Differential Gears. — a. The differential provides a
method of combining two motions into one resulting motion
which is the algebraic sum of the other two motions.
b. Essentially, a differential consists of three shafts inter-
connected by a train of gears. Figure 14 shows schematically
what happens in a differential. Motion is imparted to shafts
A and B. These motions are combined and result in the
motion of the housing, which in turn is taken off by the shaft
C. Any two of the shafts may be used for the input of data
and the output will come out on the third shaft.
SHAFT
w SHAFT
/ (
HOUSING
( S
LN
"t
SHAFT C
Figure 14. — Differential action.
c. The principle of the differential is best known in its
application to the automobile. The same action takes place
in the differentials of a director as in the differential of a
car. All differential actions can be classified in three groups
as follows:
43
56
COAST ARTILLERY FIELD MANUAL
Input
Output
1
Direction * and ve-
locity of shaft A i
Direction * and ve-
locity of shaft B
Direction * and veloc-
ity of shaft 0 .
i
1
1 Adding
Counterclockwise w j
revolution.
1
Clockwise <*> revolu-
tion.
Counterclockwise
w+ft) revolution.
2~
2 Canceling.
Clockwise « revolu-
tion.
Clockwise to revolu-
tion.
Stationary.
3 Equating..
Clockwise 2 w revolu-
tion.
Clockwise revolu-
tion.
Clockwise 2u— w revo-
lution. 2
*The direction of rotation is as viewed looking down each shaft toward the differ-
ential in figure 14.
d. The adding differential, as the name implies, combines
two motions so that the resulting motion is the algebraic
sum. For example, when the director is in action, the azi-
muth transmitter is constantly positioned according to Au
Any dA correction must be applied in such a way that it will
not disrupt this flow of data. A differential is inserted in the
system. The input of the differential is Af and dA. The
output is
Af±dA.
e. The canceling differential functions so as to keep the
output zero. In figure 14, if shaft A is turned four revolu-
tions clockwise, shaft C will turn. Now, if shaft B is turned
four revolutions clockwise, shaft C will return to its original
position. In other words, the output of the differential is
zero.
/. The equating differential takes two motions (rates),
compares them, and passes the difference to the output shaft.
When the two motions are equal, the difference is zero, and
therefore the output shaft will be stationary.
g. The same differential may perform any one of the three
operations enumerated above. Figure 15 shows the differen-
tial used in the M4 director. The input and output of the
differential are shaft (A-B) and gears D and F.
44
GUNNERY, ETC.* ANTIAIRCRAFT GUNS
57
Figure 15. — Differential.
■ 57. Three Dimensional Cams. — a. A cam is defined as a
plate, cylinder, or solid having a curved outline or groove,
which rotates or translates about an axis and by its motion
gives motion to another member or follower in contact with it.
b. Cams are used in the standard director for two different
purposes :
(1) The e 0 cam solves for the horizontal range to the pres-
ent position ( R 0 ) using Ho and e 0 to position it.
(2) The ballistic cams solve for i, e, and F using H P and
Rp to position them. tv
c. Any particular point on the surface of the e 0 cam repre-
sents a point in space whose coordinates are R 0 and H 0 .
The lift of the cam follower or cam pin — that is, the distance
of the point of the follower from the reference surface — is
made proportional to the angular height (e 0 ) of the point
whose coordinates are Ro and Ho. The cam is rotated accord-
ing to Ho and translated according to Ro. The follower is.
constrained by slides so as to have only one motion along its.
axis. In operation, the cam is first rotated until positioned
in Ho. The cam is translated until e 0 measured from* the:
cam is equal to measured by the elevation tracking tele-
scope. The distance that the cam has been translated is
proportional to Ro. (See fig. 16.)
244637° — 40-
4
45
57-58
COAST ARTILLERY FIELD MANUAL
Co DIALS
j INCREASING
ANGULAR
HEIGHT <€ 0 >
6 0 CAM
ANGULAR]
HEIGHT
<€q>
(FROM
TELE-
SCOPE)
RANGE (R 0 )
(FROM RANGE]
DRIVE)
ALTITUDE
(FROM ALTITUDE
DRIVE)
Figure 16 . — eo cam.
d. The ballistic cams are mechanical firing tables. A sepa-
rate cam is necessary for each element 0 , and F, but for
ease of construction and operation, the three are mounted as
an integral unit. Any particular point on the surface of a
ballistic cam represents a point in space whose coordinates
are H v and R P . By reference to firing tables, we can find
the values of and F for any point in space whose coordi-
nates are Hp and R P . The lift of each cam follower, that is,
the distance from the point of the follower to the reference
surface, is proportional to the values of <P, and F for the
particular values of H v and R P . The followers are constrained
by slides so as to have only one motion along their axes. The
cams are rotated in Rp and translated in H v . (See fig. 17.)
■ 58. Coordinate Conversion Mechanism.— a. Figure 18 illus-
trates the principle of the coordinate conversion mecha-
nism. The present position of the target is located by polar
coordinates A 0 and R 0 . The rectangular coordinates Xo and
Yo are measured by the displacement of the E-W and N-S
slides from the N-S and E-W axes.
b. The actual mechanism (figs. 19 and 20) used for the
conversion of coordinates employs the same principle illus-
trated in a above.
46
58
COAST ARTILLERY FIELD MANUAL
(1) To reproduce horizontal range to scale, a disk having
a spiral groove is used. The center of the disk represents the
gun position while the pin in the groove represents the target
position. (See fig. 19.) The radial distance from the center
of the disk to the pin represents the horizontal range to the
target. To reproduce the target azimuth, an azimuth disk
N
having a radial slot is placed next to the range disk so that
the disk centers are common and the radial slot in the azi-
muth disk carries the target position pin and slide. By hold-
ing the azimuth disk stationary and turning the range disk,
the target position pin is moved radially in or out along the
slot in the azimuth disk. If only the azimuth disk moves, the
pin swings about the disk center and at the same time slides
48
58
COAST ARTILLERY FIELD MANUAL
along the radial groove. A differential is inserted in the
drive between the two disks so that a change in azimuth ro-
tates both disks the same amount. Because of this, a change
in azimuth does not change the horizontal range. Thus it is
seen that by rotating the range disk and azimuth disk the
V type
Figure 20. — Slide mechanism for coordinate conversion.
target position pin is located by polar coordinates A 0 and Ro
in the case of the present position disks, and A p and Rp in
the case of the future position disks.
(2) The target position pin engages a slide block (fig. 20).
The slide block is capable of two motions, one vertically on
50
GUNNERY, ETC., ANTIAIRCRAFT GUNS
58-59
the gibs (N-S or Yo) and the other horizontally. For the
horizontal motion (E-W or Xo ) the entire slide assembly in-
cluding the slide block and gibs rolls on the two V-type slide
rails. Fastened to the slide block is a rack which engages
with the long pinion. Fastened to the slide assembly is an-
other rack which engages with a pinion. The motions of
these two pinions are measured. The rate at which the pin-
ions are turning is the E-W or N-S rate. The amount that
the pinions have turned is Xo or Yo on the present position
disks and Xp and Y P on the future position disks.
■ 59. Automatic Prediction Mechanism. — a. Ordinarily the
equation for prediction is:
AX— E-W, rate X t v
A Y= N-S rate X t v
AH'— Altitude rateXf?
In the solution of the prediction problem by the M4 director,
it is more convenient to express the above equations in a
different form which is:
E-W rate — AATX^r
‘p
N-S rate = A VXr
t p
Altitude rate=AHX-^
b. In paragraph 58 it is stated that the rate of turning of
the pinions on the present position slides is the E-W or N-S
rate. This rate is known as the “observed rate.” In the alti-
tude prediction mechanism the observed rate is set up by
operation of the altitude rate drive. (See par. 55/.)
c. Figure 21 is a schematic diagram of an automatic predic-
tion mechanism. Start at the ~ cam in the lower left corner.
t P
The lift of the follower positions the ball carriage of the varia-
ble speed drive. According to paragraph 55e, the angular
velocity of the cylinder is proportional to This cylinder,
r p
revolving at a rate proportional to — , is driving the disk of
tp
another variable speed drive in the upper left corner. Assume
51
59-60
COAST ARTILLERY FIELD MANUAL
that the ball carriage has been displaced from the center a
distance which we will call a prediction. Then by paragraph
55d —
Angular velocity of the cylinder^predictionX ~r
t v
But by a above:
Prediction X 7 ~= rate (either E-W, N-S, or altitude) ,
T p
Under the above circumstances, the variable speed drive is
creating a rate which is called the ‘‘generated rate.”
d. If we can make the generated rate equal to the observed
rate, the displacement of the ball carriage is then propor-
tional to the true prediction. The observed rate and the
generated rate are the inputs of an equating differential. By
paragraph 56/, the equating differential compares the two
rates .and passes the difference out through the third or out-
put shaft. This output shaft of the equating differential
is geared to the ball carriage of the variable speed drive. If
the two rates (observed and generated) are not equal, the
difference coming out through the output shaft moves the
ball carriage and either increases or decreases the generated
rate. When the two rates become equal, the difference is
zero, and the output shaft is therefore stationary. The pre-
diction is zero when the ball carriage is over the center of the
disk. The amount that the output shaft of the equating dif-
ferential has turned in positioning the ball carriage in order
to equalize the rates is therefore proportional to the displace-
ment of the ball carriage and hence proportional to the
prediction.
fi 60. Ballistic Wind Mechanism. — a. The ballistic wind
causes the projectile to deviate from the normal trajectory.
(See par. 86d.) In the M4 director, the wind is considered
tc have moved the future (predicted) position by amounts
equal to the E-W and N-S components of the ballistic wind
multiplied by the time of flight. This correction for ballistic
wind is effected by correcting the generated rate in the auto-
matic prediction mechanism.
b. Figure 21- shows schematically the ballistic wind mecha-
nism. The components of the ballistic wind are obtained by
operation of the wind component solver (fig. 55). Setting
52
GUNNERY, ETC., ANTIAIRCRAFT GUNS
60
Figtjre 21. — Automatic prediction mechanism — ballistic wind
mechanism.
53
60-61
COAST ARTILLERY FIELD MANUAL
the value of the wind component on the wind dial causes
the ball carriage of the variable speed drive (on the right
side of fig. 21) to be displaced from the center an amount
proportional to that wind component. By paragraph 55e,
the angular velocity of the cylinder is proportional to the
wind component. This wind rate is added algebraically to
the generated rate by a differential before the generated
rate enters the equating differential (par. 5 6d) . The output
of the adding differential is therefore the generated rate ±
the wind component rate. Hence the wind correction is
included in the prediction.
c. The ballistic wind mechanism has another use in that it
supplies rates for static check problems. When the director
is stationary, the observed rate is zero and therefore the pre-
diction is zero. The ballistic wind mechanism can be used to
set up a rate in the automatic prediction mechanism which
will take the place of the observed rate. In figure 21 the
component rate passes through the adding differential to the
equating differential where it causes the prediction shaft to
turn, making a prediction and displacing the ball carriage of
the variable speed drive (upper left). A rate which is fed
into the adding differential is generated. When this gen-
erated rate is equal to the component rate, the rates will be
equated by the differential and no further output will enter
the equating differential to change the prediction. The gen-
erated rate is equal to the component rate. The wind dials
are graduated from 0 to 50 miles per hour. Target velocities
are greater than wind velocities, therefore problem velocity
dials (graduated from 0 to 200 yards per second) are mounted
adjacent to the wind dials. They are set by the same knob
as the wind dials but are used only when setting in problems.
In setting wind rates, the knob is restricted by a stop to ap-
proximately one revolution. In order to set target velocities,
the knob is pulled out to pass the stop.
■ 61. Movable Index Dial. — a. The movable index dial is a
means of adding one quantity to another algebraically. Fig-
ure 22 is a sketch of a spot dial on the M4 director. The
complete dial consists of two concentric rings about a central
disk, The outermost ring, with the words “TRIAL FIRE
CORR.” on it, is fixed. The second ring, called the movable
54
GUNNERY, ETC., ANTIAIRCRAFT GUNS
61
index, is capable of rotation in either direction by using the
movable index knob. The central disk is operated by the
spotting handwheel and indicates the correction applied.
b. Suppose that the movable index is moved to down
(minus) 10 as shown in the figure. If the indices are
matched as shown, there is a spot of down (minus) 10 in the
data computor although according to the spot dial and mov-
able index the correction is 0. This is the procedure followed
in making ballistic corrections before opening fire. (See par.
100.) If, as a result of firing, a correction of down (minus)
10 is ordered, the spot dial is turned by means of the spotting
handwheel so that it reads down (minus) 10 with reference
to the movable index. It will be noted that with reference
to the fixed index on the outer ring, the correction is down
(minus) 20. The device has added the two corrections alge-
braically. Its use eliminates mental addition by the operator
55
61-62
COAST ARTILLERY FIELD MANUAL
and thereby reduces the possibility of the occurrence of per-
sonnel errors.
Section V
FIRING DATA
■ 62. General. — a. Instruments used for the computation of
antiaircraft artillery firing data are automatic in their action
and the necessary firing data are obtained without reference
to printed tables or charts. Firing table and trajectory chart
data must be available for the designing of instruments and
computations incident to calibration corrections and to trial
fire. An understanding of the use of firing tables and trajec-
tory charts is essential in connection with the conduct of
antiaircraft fire, including the preparation and observation
of fire.
b. Trajectories are calculated for a gun of given charac-
teristics, developing a stated or assumed muzzle velocity, and
firing a projectile with a given ballistic coefficient. In other
words, each combination of gun and ammunition has its own
characteristics. Therefore , me must use the firing tables ,
trajectory chart, and ballistic cams pertaining to the particu-
lar combination of gun and ammunition being used.
c. Firing tables and trajectory charts are available for use
as follows :
Firing tables
and trajectory
chart No.
Nor-
mal
MV
Pate 1
Caliber
of gun 1
Projectile and fuze
3 AA-I-2
2,400 j
1
December 1928.
3" |
Shell, HE, Mk. I; fuze Mk. III.
Shrapnel, Mk. I; fuze Mk. III.
3 AA-J-2
2,600 ,
October 1928.. -
3".
Shell, HE. Mk. I; fuze Mk. III.
Shrapnel, Mk. I; fuze Mk. III.
3 AA-K-2
2,800
February 1929..
3"— j
Shell HE, Mk. IX; fuze Mk. HI.
3 AA-L-1
2, 600
2,800 ,
October 1928.
3" . . i
Shell, HE, Mk. IX; fuze Mk. III.
Shell, HE, Mk. IX; fuze M2.
3 AA-N-1
August 1929.
3" ,
8 AA-O-1
2, 700
April 1939
3 "
Shell, HE, M42; fuze M43.
Shell, HE, M38; fuze M2.
j
105 AA-E-l. _j
i
2,800
Not available
for general
circulation.
105-mm .
i
105 AA-C-2. J
75 M-l |
2,800
do
August 1930...
105-mm.
75-mm__
Shell, HE, M38; fuze Mk. IIIAI.
Shell, HE, Mk, III.
56
GUNNERY, ETC., ANTIAIRCRAFT GUNS
63-64
■ 63, Firing Table Assumptions. — Firing tables are prepared
by the Ordnance Department for each type of gun and am-
munition under a set of conditions arbitrarily assumed as
standard. Their enumeration will serve to acquaint the
reader with the more important factors which affect the
trajectory.
Standard conditions.
Muzzle velocity (MV) (as listed in the table) .
Wind (W) , none.
Air density at the battery, 59° F. and 29.53" of mercury.
Air saturation, 78 percent. (525.9 grains per cu. ft.)
Temperature of air at battery, 59° F.
Temperature of powder, 70° F.
Weight of projectile (as listed in table) .
In addition, a standard atmosphere aloft is assumed; that is,
atmospheric temperature and density vary with altitude (H)
in a linear relationship. Drift ( 62 a) and lateral and vertical •
jump are determined experimentally.
■ 64. Contents of Firing Tables. — a, The present standard
firing tables are published in book form. The first section
gives general information pertaining to the gun and carriage
and the projectile and fuze. It also contains a detailed expla-
nation of the tables and of the meteorological message.
b. Part 1 of the tables contains charts and tables applicable
to all combinations of projectile, fuze, and powder charge, ,
and is the same in all antiaircraft artillery firing tables.
c. Part 2 consists of a number of sections, each of which
gives data pertaining to a particular combination of projec-
tile, fuze, and powder charge. This part of the firing tables
includes the following:
(1) Trajectory data.
(2) Fuze setter data.
(3) Drift in yards and in mils.
(4) Probable error —
(a) In time of flight in seconds.
(b) Along the trajectory in yards.
(c) In plane of the trajectory in yards in direction normal
to the trajectory.
(d) In deflection in yards,
57
64-66
COAST ARTILLERY FIELD MANUAL
(5) Differential effects on horizontal range, altitude, and
angular height due to —
(a) Change in angle of elevation.
( b ) Change in muzzle velocity.
(c) Rear wind.
id) Change in air density.
(e) Weight of the projectile.
if) A decrease of one division in corrector setting.
(6) Differential effects on deflection in yards and mils due
to cross wind.
(7) Differential effect on time of flight in seconds due to a
decrease of one division in corrector setting.
d. The effect of both vertical and lateral jump is included
and combined with other elements in the tables and does not
appear as a separate effect.
e. It should be noted throughout the differential variations
listed in the firing tables that the algebraic signs, where given,
are those for effects and not for corrections; further, that the
signs for drift effects apply to panoramic sights in which the
deflection scale readings increase as the line of sight is turned
to the right. These sights are not used on antiaircraft artil-
lery guns and care should be taken to apply the correction for
drift effects in the proper direction.
f. Extracts from Firing Tables 3 AA-J-2a and 3 AA-O-l
are given in paragraph 257.
■ 65. Trajectory Charts. — The trajectories plotted on the
charts, together with the associated time of flight and fuze
curves, the range and altitude components, and the quadrant
elevation and angular height data, represent the results of the
calculation of the trajectories in air for the guns and the
ammunition named under the assumed standard conditions.
The charts are constructed to show only that part of each of
the trajectories which is included within the maximum time
of burning or setting of the particular fuze used. Figures 23
and 24 show trajectory charts for Firing Tables 3 AA-J-2a
and 3 AA-O-l.
■ 66. Corrections for Nonstandard Ballistic and Atmos-
pheric Conditions. — Since ballistic cams in the data computer
are constructed from data contained in the firing tables (par.
57 d) it is obvious that the data from the instrument will be
58
ALTITUDE (Y) IN YARDS
lrilllllssllK!li
! B?aBi arjggggSBSiSS88S§^I
BaK gaasasassjig^^ssss
TRAJECTORY AND FUZE SETTER CURVES
« for
— 3 A.A.GUNS —
W9l7A2,MI9l7A3 t MI9l7MIA2 J W/9/7WM3,W9/7M// ( M/925M/ l M2,*f
AND M4.
A A SHELL M 42 FUZE M43 M.V.2700FS .
A.P.G. DEC. 1938.
MAXIMUM RANGE I4200YDS. )
TIME OF FLIGHT (M A X. RANGE) 6 MSEC. ^
. MAX.ORDINATE , 10 IOO YDS.
TIME OF FLIGHTtMAXORD.) 38.21 SEC.
TA
rnmmmi
Nil
■ill
lain
iwiiiEaiii
000 5000 6<
Ran GE in YARDS
Figure 24. — Trajectory chart 3 AA-O-1.
244637° — 40 (Face p. 58) No. 2
GUNNERY, ETC., ANTIAIRCRAFT GUNS
66-67
the same as that which could be extracted from the firing
tables. Therefore these data will be correct only when the
conditions, as enumerated in paragraph 63, are standard.
This will rarely, if ever, be the case. The variation of the dif-
ferent elements from standard conditions must be determined
and corrections for their effect applied. The muzzle velocity
<MV) to be expected may be determined approximately by
studying the results of previous firings and by applying the
effect of a difference in powder temperature from standard.
The variation from standard in the weight of a projectile is
determined at a glance from markings on the projectile. The
actual conditions of the atmosphere remain to be determined.
® 67. Meteorological Message. — a. The determination of the
atmospheric conditions seldom devolves upon the battery
commander. They are determined by other agencies and the
information is furnished in the form of a coded meteorological
message as indicated in the following example:
Coded message
Translation
MFS MFS
20570
Meteorological message from station FS 2— A A fire. 05— altitude
of station 500 feet. 70— temperature at station 70° F.
No.
Zone
Altitude
in feet
Direction
of ballistic
wind in
mils from
north
Speed of
wind in
m.p. h.
Density
in per-
cent of
normal
0241698
0
0
2,400
16
98
1231798 1
1
600
2,300
17
98
2221898 1
2
| 1,500
2,200
18
98
3211898
3
3,000
2,100
18
98
4211998
4
„ 4,500
2, 100 !
19 |
98
5202099
5
6,000 |
2,000
20 |
99
6202099
6
9,000 j
2,000
20 |
99
7192199
7 |
12,000
1, 900
21
99
8182299
8
15,000
1,800
22
99
9182200
9 :
18,000
1,800
22
100
b . All measurements are made at the meteorological sta-
tion, and if the location of the firing battery differs in alti-
tude, suitable corrections must be made. Azimuth of the
wind is always that from which the wind is blowing. The
groups of figures for each zone contain data for ballistic
59
67-68 COAST ARTILLERY FIELD MANUAL
wind and ballistic density. The term “ballistic” signifies a
wind and density equivalent in effect to the sum of the winds
and densities actually encountered up to the indicated alti-
tude. Use the group of the meteorological message of which
the altitude is nearest to, but not less than, the altitude of the
target. Therefore, if a target at 13,000 feet altitude is being
fired upon, only the group “8182299” need be decoded.
■ 68. Corrected Firing Data. — a. The effect of variations
from standard conditions may be illustrated by a specific
eXample - Present Future
Assume : position position
Altitude (H) (yards) 4, 200 4 , 200
Angular height <e) 672 820
Horizontal range (R) 5, 400 4, 035
Quadrant elevation ( 0 ) 900
Time of flight (t v ) 13. 1
Fuze range <F) 12 . 7
Muzzle velocity (MV) 2,500 f/s (previous firings).
Temperature of powder, 70° F.
Azimuth (Ap) of target from battery, 1,800 mils.
From the preceding meteorological message for zone 8 — •
Wind azimuth (Aw) 1,800 mils.
Speed 22 m. p. h.
Density 1 % (decrease)
Referring to firing table extracts in paragraph 257, and
trajectory chart, figure 23, the effects of these conditions on
the path of the projectile are readily listed as follows:
.
Effect
Condition
Horizontal j
range
Altitude
Muzzle Velocity (MV) 50 f/s decrease (cams cut for
«
2,550 f/s)
-50 (AEv)
-64 (AH t )
Temperature of powder 70° F _
0
0
Wind. Head wind 22 m. p. h
Note. — F rom the azimuth of the target and the
azimuth of the wind there is no cross-wind effect.
-73 <A7?«,)
-16 (AH W )
Density 1 percent decrease.
1 +13
j
+16
Total
-110 (AR)
-64 (AH)
60
GUNNERY, ETC., ANTIAIRCRAFT GUNS 68-70
To correct for these effects, the gun must be pointed in eleva-
tion so that the trajectory will pass through a point whose
coordinates are
Uncorrected coordinates, future Horizontal range Altitude
position 4, 035 (R) 4, 200 (H)
Correction 110 (dR) 64 (dH)
Corrected coordinates 4, 145 4, 264
Which requires, from the trajectory chart, the following ap-
proximate firing data:
Quadrant elevation (</>) 898 mils
Fuze (F) 13.0
The only lateral effect on the trajectory from the conditions
given is that of drift ( 82 a) 7 mils right. To correct for this,
the gun must be pointed 7 mils to the left of the target, or at
1,793 mils azimuth.
b. With this convincing example of the necessity for cor-
recting firing data, the question will naturally arise as to
how the instantaneous and continuous calculation and ap-
plication of these corrections may be incorporated with the
mechanically computed uncorrected firing data. It will be
found that methods exist in the calculation and application
of corrections, ranging from the roughest approximations,
applied manually and periodically, to the mechanically com-
plex methods of instantaneous and continuous calculation
and application. The method of applying corrections for
nonstandard conditions is fully explained in paragraph 100 .
Section VT
DATA TRANSMISSION SYSTEMS
■ 69. General. — There are three standard data transmission
systems in use in the antiaircraft artillery at the present time;
the telephone, the mechanical flexible cable, and the self-
synchronous alternating current system.
■ 70. Telephone. — The present standard field telephone is
the EE- 8 . It is a highly efficient type of local battery tele-
phone and is designed to be used with field telephone wire.
It is used where necessary to transmit data over distances
244637° — 40 5 61
70-73
COAST ARTILLERY FIELD MANUAL
that are too great for the other two systems to operate satis-
factorily; that is, distances in excess of 500 yards in the case
of the A. C. system and 100 feet in the case of the flexible
shaft system. It has the disadvantage that transmission of
the desired data is not instantaneous and is subject to error.
■ 71. Mechanical Flexible Shaft System. — This system con-
sists of a piece of stiff steel wire encased in a flexible metal
housing. It is similar to the flexible shaft that connects the
drive shaft of an automobile to the speedometer. The system
transmits data instantaneously but has the disadvantage that
it may be used for short distances only. It is relatively inex-
pensive and simple.
■ 72. A. C. Self -Synchronous Data Transmission System. —
This system is used to transmit data from the director to the
guns of a gun battery. It is completely self -synchronous and
transmits data instantaneously. A power plant which fur-
nishes 110 -volt, 60-cycle, single-phase alternating current is
required to operate the system. Multiconductor cables, con-
nected by junction boxes, transmit the data and the power.
Electrical data transmitters are included in the director;
electrical data receivers are attached to the guns. The M3
and M4 systems, which are practically identical, are the
present standard systems.
■ 73. Theory of Operation of A. C. Data Transmission
Systems. — a. The transmission of data is accomplished in
the following manner: In figure 25, let Pt and Pr be two
similar coils of wire connected in parallel to a 110-volt, single-
phase, A. C. line. These coils are fixed with respect to a
frame. Let St and Sr be two similar coils mounted on shafts
in such a manner as to allow them to rotate in the frame.
The alternating current in Pt and Pr will induce alternating
voltages in the coils St and Sr, but these coils are so con-
nected that these voltages are opposite to each other. Since
all parts are similar and similarly positioned, the voltages
are also equal. The voltages therefore cancel each other and
there is no current in the series circuit connecting coils
St and Sr. Suppose, however, that the coil St is rotated in
some manner, the angle of rotation being proportional to
62
GUNNERY, ETC., ANTIAIRCRAFT GUNS
73
the data that it is desired to transmit. The similarity of
position between the coils Pt and St and Pr and Sr is now
destroyed, and the voltages induced in coils Sr and St will
not be equal. A current will therefore flow in the series
circuit connecting coils St and Sr . This current produces a
torque which tends to rotate both St and S r . St, however,
is held by the mechanism which caused its initial rotation
so that only Sr is free to rotate. Sr will rotate as long as
there is a torque on it, and there will be a torque on it as
long as there is current through it. When Sr assumes the
same angular position with respect to Pr that St has with
respect to Pt, the induced voltages will again be equal and
opposite and therefore no current will flow. This angular
position will be a position of stable equilibrium for the coil Sr,
and the angle turned into St will be reproduced by Sr rot at*
SHAFT
SHAFT
ST SR
Figure 25. — Simple transmitter and receiver.
ing through the same angle. In this system, the coil desig-
nated by the subscript “t” acted as the transmitter, since it
was mechanically rotated proportionally to the data to be
transmitted, while the coil designated by the subscript “r”
acted as the repeater, since it “repeated” the angle set into
the transmitter. Obviously, the two could have been inter-
changed.
b. The above simple system has the serious disadvantage
of having “dead points” at which the magnitude of the
induced voltage is always zero. To eliminate these “dead
points,” the coils St and Sr are replaced by three coils each.
The three coils are placed 120° from each other and con-
nected in “Y” connection as shown in figure 26.
c. It is seen from the above (fig. 25) that the transmitter
and repeater may be identical in every detail. In practice,
however, slight differences exist between these units.
63
73-75
COAST ARTILLERY FIELD MANUAL
(1) The transmitter is made physically larger than the
repeater so that several repeaters may be positioned by one
transmitter.
(2) The repeater is provided with an oscillation damper
to prevent oscillation about the equilibrium point.
Figure 26. — Principle of the self-synchronous A. C, data transmis-
sion system.
■ 74. Single Operation. — In a system consisting of a single
transmitter and repeater, the units are connected as shown
at the top of figure 27. The two primary windings are excited
from a common source of 110-volt, single-phase, A. C. (or
from the same phase, in the case of a multiphase supply) and
the rotor windings are connected phase for phase. Figure 27
also shows the developed torque, excitation (primary) cur-
rent, and induced (secondary) current from various angles of
relative displacement. The torque is zero for both 0° and
180° displacement. For the 180° position, however, both the
primary and secondary currents are a maximum, and this is
a position of unstable equilibrium. The repeater will never
operate of its own accord in this position, but will always
synchronize when the primary windings are excited. Thus,
on the resumption of power after an interruption, the units
will automatically synchronize themselves.
■ 75. Multiple Operation. — a. In a system consisting of a
single transmitter and two or more repeater units, the oper-
ation is, in general, the same as the single operation. There
are, in addition, several features to be noted. The torque
angle characteristics for single operation given in figure 27
are dependent on the size of the transmitter and receivers.
If a given size is taken as standard, then the torque developed
by that size transmitter or repeater may be considered as the
standard torque. If two repeaters are operated from one
64
GUNNERY, ETC., ANTIAIRCRAFT GUNS
75
transmitter of the same size as the repeaters, the torque, de-
veloped in each repeater at any given angular displacement,
will be only % of the standard torque. In general, the
developed torque, Tr, will be
T r
2 T
n+1
where r= standard torque
n=number of repeaters
In order to bring this developed torque up to the standard
torque, the transmitters are usually made larger than the
repeaters.
Figure 27. — Approximate characteristics of A. C. synchronous units-
65
75-76
COAST ARTILLERY FIELD MANUAL
b. If the load (friction, inertia) on the separate repeater
units differs, the lightly loaded units will help the transmitter
to keep the more heavily loaded units in proper synchronism,
and much greater than standard torques may be developed
in the more heavily loaded unit. This is accompanied, how-
ever, by an increase in the size of the displacement angle of
the entire system. Therefore, if the rotation of a single
repeater is opposed by inertia or friction, all other repeaters
in the same circuit have a displacement error greater than
normal.
■ 76. Effect of External Voltage and Impedance. — The
torque on the coils St and Sr, in figure 25, arises from the
interaction of the magnetic fields due to the current induced
in St and Sr and the current in Pt and Pr.
a . External 'voltage, — The effect of voltage changes is then
obvious.
E
Since I where
E p = voltage impressed on P t (or P r )
Z p — external impedance of circuit-]- internal impedance of P t
or P r — constant
Ip = current in P t or P r ,
we see that the torque will decrease as Ep decreases. It is
desirable, therefore, to maintain an equal voltage (110 volts)
on both transmitter and repeater primaries. In order to
accomplish this, an autotransformer or tapped resistor is
included with the generating unit to step up or lower the
voltage at the remote units, thus compensating for the differ-
ences in line drop and equalizing the voltages at the trans-
mitter and repeater primaries.
b. External impedance . — The torque depends also on the
current in the secondary windings. This current will be
r E, t —E sr
Is— 2 t +z' + Z per phase ’ where
(Est— Esr) = net induced voltage per phase
(Zst~{~Z$r) =impedance of the windings
(Ze)~ external impedance due to the connecting wires
The term Ze affects the phase of the currents in the second-
aries, and the greater the value of Z e the less the current,
66
GUNNERY, ETC., ANTIAIRCRAFT GUNS
76-78
hence the less the torque. When Z e becomes comparable with
{Z s t+Zsr) serious difficulties may arise. For this reason it is
highly desirable to keep the resistance of the connecting lines
as low as possible, and keep this resistance the same for all
of the secondary windings.
■ 77. Data Transmission for Antiaircraft Batteries. — Three
sets of data must be supplied to an antiaircraft gun; eleva-
tion, azimuth, and fuze range. The mechanisms by which
these data are determined are not pertinent to this section.
It is sufficient to state that in the standard data computors,
the three sets of data are supplied automatically and continu-
ously, and that the gun is kept laid in azimuth and elevation
by the matching of the mechanical gun indices with the data
pointers. Similarly, the fuze setter is kept set by matching its
mechanical fuze-setting index with the transmitted data in-
dicated by the fuze setter receiver’s pointer. The electrical
transmission of altitude from the stereoscopic height finder
and the target designating system (par. 39 d) are also in-
cluded in the system.
Section VII
APPLICATION OF FIRING DATA TO GUNS
■ 78. General. — a. Firing data for antiaircraft firing includes
data for pointing the gun and data for setting the time fuze
so that the projectile will hurst at the future position of the
target.
b. Pointing the gun includes the application to the gun of
the direction and elevation data required to cause the trajec-
tory to pass through the target. The form in which these data
must be furnished depends upon the method of pointing
employed.
c. There are four general methods of pointing guns :
(1) Case L — In which the direction and quadrant elevation
are both given by means of the sight.
(2) Case /%. — In which the direction is given by the sight
and the quadrant elevation is given by a combination of the
sight and an elevation scale or graduated drum.
67
78-80
COAST ARTILLERY FIELD MANUAL
(3) Case JL — In which the direction is given by the sight
and the quadrant elevation is given by means of an elevation
scale or graduated drum.
(4) Case 111 . — In which the direction is given by means of
an azimuth scale and the quadrant elevation is given by means
of an elevation scale or graduated drum.
d. Case 1% pointing is no longer a standard method and no
further discussion of it will be made. Case II has never been
used with antiaircraft firings.
e. The two remaining methods, case III and case I, are
described in paragraphs 79 and 80.
H 79. Case III Pointing. — a . The elements of firing data for
case III pointing are firing azimuth (4/) , quadrant elevation
(0) > and fuze range (F ) , Each of these elements of data is
determined by the data computor and transmitted continu-
ously and electrically to the guns. The gun is properly pointed
when the operating personnel elevate and traverse the gun
and operate the fuze setter so that the mechanical pointers of
the receivers coincide with the electrical pointers.
b. Transmission of data by telephone or word of mouth for
case III pointing is possible, but this process is so slow that its
use is precluded except as an emergency method, and then its
use should be confined to guns not equipped with sights.
When sights are available and an electrical data transmission
system is not installed or is not in serviceable condition, case I
pointing is employed.
H 80. Case I Pointing. — a. In paragraph 156 it is stated that
the director M4 is provided with a means of determining data
for case I firing. It is necessary that the guns be equipped
with sights to use this method. At present, sights are not
standard equipment on the guns. In the future such equip-
ment may become available. Case I pointing will then, in all
probability, be used only as an emergency system of fire
control.
b. The elements of firing data for case I pointing are lateral
deflection, vertical deflection, and fuze range. Each of these
elements is determined by the director and transmitted by
telephone to the guns. At the guns, these data are set on the
appropriate dials. The gun is then properly pointed when the
gun pointer tracks the target with his telescope. It should be
68
GUNNERY, ETC., ANTIAIRCRAFT GUNS
80-82
noted that there is no provision for incorporating dead time
in the computation of data by the director M4. Consequently,
when case I pointing is used the data are only approximate.
Section VIII
CLASSES, TYPES, AND METHODS OP FIRE
® 81, General. — Antiaircraft artillery gunfire is divided and
subdivided into classes, types, and methods as shown on p. 70.
■ 82. Definitions. — The following definitions apply to the
classes, types, and methods of fire:
a. Preparatory fire. — Fire that is conducted for the purpose
of determining or verifying corrections to firing data.
b. Calibration fire. — Preparatory fire having for its purpose
the determination of the separate corrections to be applied
to the individual guns of a battery in order to cause the bursts
to occur in a definite pattern in the sky.
c. Trial fire. — Preparatory fire having for its purpose the
determination of corrections for the battery as a whole to
compensate for deviations not corrected for in the normal
operations of data computation.
d. Verification fire. — Preparatory fire having for its pur-
pose the test of the mechanical adjustment of all guns and
fire-control equipment of the battery and of the accuracy of
the corrections determined as a result of calibration fire and
trial fire.
e . Salvo fire. — Fire in which the guns of the battery fire
one after another in order, as Nos. 1, 2, 3, and 4.
/. Fire for effect. — Any fire conducted against a hostile
target.
g. Continuously pointed fire. — Fire in which the fire-con-
trol devices are directed on the target and the data vary
continuously with the position of the target.
h. Barrage fire. — Fire having for its purpose the placing
of a curtain or barrier of fire, executed on predetermined
firing data, across the probable course of enemy aircraft.
i. Continuous fire. — Fire conducted at the normal rate
without interruption.
69
70
GUNNERY, ETC., ANTIAIRCRAFT GUNS
82-84
j . Volley fire . — Fire in which each gun of the battery fires
a specified number of rounds at the maximum rate without
regard to the other guns of the battery.
Section IX
EXTERIOR BALLISTICS
■ 83. General. — a. In the preceding sections, the funda-
mental operations of locating an airplane target and calcu-
lating firing data have been presented. Despite the care with
which the firing data are calculated and the guns pointed,
it should not be expected that all projectiles fired from a gun
will strike the target. It becomes necessary to investigate
more thoroughly the factors which affect the path of a pro-
jectile. The solution of the various problems may then be
approached with greater understanding.
b. The solution of these problems involves the application
of principles of gunnery, which is defined as “the art and
science of firing guns.” Application of the principles of gun-
nery has for its purpose the reduction or elimination of the
effect of those factors which cause a projectile to deviate
from its intended path. This section presents a consideration
of these factors, together with the methods which have been
evolved for solving the various antiaircraft gunnery problems.
■ 84. Definitions. — Ballistics is defined as “the science of
the motion of projectiles.” It is divided into two main parts —
interior ballistics and exterior ballistics.
a. Interior ballistics is the study of the motion of the pro-
jectile while still in the bore of the gun, together with the
chemical and physical phenomena which cause and attend
this motion. It provides a determination of the relationship
between the projectile, powder, and gun, and the velocity
of the projectile and corresponding powder gas pressures at
any point in the bore, with particular reference to the muzzle
velocity and maximum pressure. Its chief application is
found in problems of design and manufacture.
b. Exterior ballistics is the study of the motion of the
projectile after it has left the gun. Its practical application
is in the calculation of trajectories, construction of firing
tables, and computation of other data essential to the solu-
71
84—85
COAST ARTILLERY FIELD MANUAL
tion of gunnery problems. It is the basis of the art of gun-
nery and therefore of prime importance to the artilleryman.
■ 85. Standard Trajectory. — a. The antiaircraft artillery-
man must be provided with accurate information for every
point of a considerable arc of the trajectory with particular
emphasis upon the time element. Only a portion of the tra-
jectory, principally the ascending branch, is useful due to the
time limitation of a fuze. The elements of primary impor-
tance to the antiaircraft artilleryman are illustrated in fig-
ure 28. Although the useful portion of a trajectory might
be extended by increasing the time of burning of the fuze,
it is well to point out that there is a practical limit which
must be established.
of Burst)
Of Flight
#ango
E /UOUTY
Figure 28. — Elements of a trajectory (antiaircraft guns).
b. The simplest problem of the trajectory is the hypothet-
ical case of a projectile fired “in vacuo.” Considering that
the projectile leaves the gun with a known velocity (v) and in
a known direction, there being no force, except gravity, act-
ing upon it after it leaves the gun, the equation of its path
reduces to that of a simple parabola. (See fig. 29.) The
coordinates of the point P are:
x—OM cos cos 0
y=OM sin <p—MP—Vt sin 0™ 1 / 4 gt 2
(fjr—acceleration due to gravity)
(£~time of flight)
The equation of the parabola is:
gx 2
y—x tan 0 — :
2V 2 cos 2 0
74 #6 FT
72
GUNNERY, ETC., ANTIAIRCRAFT GUNS
85
The equations for x and y above may be expressed as simul-
taneous differential equations as follows:
di =
V cos cf>
cPx
d**
= 0
dy^
dt
■V sin 4> — gt
d 2 y_
dfi 6
Figure 29. — Trajectory in vacuo.
c. Under normal conditions, when a projectile leaves a gun,
it is acted upon by two forces, the force of gravity and the
resistance of the air. This latter force is usually called the
“retardation” and is very complex. It will be recalled that a
rotating motion is imparted to the projectile while it is in
the bore of the gun due to a twist in the rifling, for the prin-
cipal reason of insuring stability in flight. This rotating
motion has a decided effect upon the air resistance. When a
projectile leaves a gun, it possesses a certain amount of kinetic
energy which must be partially expended in overcoming air
resistance as follows:
(1) Displacement of a volume of air from the path of the
projectile.
(2) Skin friction between the surface of the projectile and
the particles of air.
(3) Formation of eddy currents around the projectile.
(4) Formation of a partial vacuum in rear of the projectile.
(5) Wave motion set up in the air by the projectile.
(6) Gyroscopic wobbling.
d. Resistance of the air operates to change all the char-
acteristics of the “trajectory in vacuo.” Application of the
natural laws of “applied mechanics” has been proved by ex-
periment to be inadequate in calculating the trajectory in
free air. The retardation force due to air resistance is con-
sidered as dependent upon —
73
85
COAST ARTILLERY FIELD MANUAL
(1) The relative velocity between projectile and air, which
takes into consideration the motion of the air (wind).
(2) The condition of the air, which takes into considera-
tion such factors as temperature, pressure, saturation, and,
from these, density.
(3) (a) The size, weight, and shape of the projectile.
These characteristics of the projectile are combined to fa-
cilitate calculations and expressed by a single number called
the ballistic coefficient” (C) , which is considered as a meas-
ure of the power of the projectile to overcome air resistance.
The value C is
0 =—
id 2
where tv is the weight of the projectile in pounds; d } the di-
ameter in inches; i, the coefficient of form.
( b ) The value of i is determined empirically and referred
to an arbitrarily chosen standard shape of projectile which
is assigned a coefficient of X.
e. The calculation of trajectories is performed by the Ord-
nance Department. The standard equations of “applied me-
chanics,” having proved inadequate, are supplemented by
empirical formulae which have been derived as a result of
experimental firings. The equations of the trajectory in air
which are used are as follows :
d 2 x
dt%=- vE cos 0
d 2 y „ .
_ = _v£ sin <j> -g
where v represents the velocity of the projectile; g, the accel-
eration due to gravity; E, a function of the retardation, R f
(E=R/v ) .
Note. — Compare the above formulae with the simultaneous dif-
ferential equations in b above, which are the equations of the
trajectory “in vacuo.”
The retardation factor R is determined from the empirical
formula
p vG(v)H(y)
r C
in which
74
GUNNERY, ETC., ANTIAIRCRAFT GUNS
85-86
G(t;), read the “G-function of v” represents the retarda-
tion of a standard projectile (C=l), and is obtained from
ballistic tables;
H(y ) , read the “H-function of y” is a function of the
height of the projectile above the muzzle of the gun and intro-
duces into the value of R the change in density of the air
with altitude, H(y)=e~ h y, where e— 2.7182, the base of Na-
perian logarithms, ^—altitude, and ft=constant; C is the
ballistic coefficient.
Formerly, these were solved by the laborious processes of
numerical integration. They are now solved by a computing
machine known as a differential analyzer, which reduces the
time required for the solution of complex differential equa-
tions, in some cases, from a matter of days to a matter of
a few minutes.
/. Starting with an initial set of conditions — that is, ballis-
tic coefficient, muzzle velocity, and angle of departure — the
antiaircraft trajectory is computed, taking successive points,
each of which corresponds to a certain time of flight. The
trajectory thus calculated is known as a standard trajectory.
The calculation of the standard trajectory is the primary
problem in ballistics.
H 86. Differential Effects. — a. General . — Trajectories are
computed for standard conditions, but seldom, if ever, will
the artilleryman find standard conditions existing at the
time of firing. Therefore the secondary problem in ballistics
is to determine the effect of variations from these standard
conditions. The Ordnance Department calculates the effects
of variations from standard conditions wherever they are of
sufficient magnitude to be appreciable. These calculations
are included in the firing tables in the form of “differential
effects tables” (par. 257) . The mathematical equations from
which these effects are calculated are quite complex and
generally only first-order effects are considered. First-order
effects are linear in nature, that is, they may be represented
by a straight line. If at a specific point on the trajectory an
increase of 10 f/s in muzzle velocity increases the horizontal
range attained by a projectile by 25 yards, a decrease of
10 f/s will decrease the range by the same amount, and a
change of 100 f/s in either direction will be ten times that
75
86
COAST ARTILLERY FIELD MANUAL
for a 10 f/s change. A detailed study of these effects is of
the utmost importance since most of the gunnery problems
which confront the antiaircraft artilleryman arise from the
deviation of a projectile from its standard trajectory.
b. Muzzle velocity. — (1) A point on the trajectory chart,
3 AA-J— 2a (fig. 23), at a horizontal range of 4,740 yards
Figube 30. — Differential effect line — muzzle velocity.
and an altitude of 3,223 yards, is arbitrarily selected. The
trajectory through this point may be plotted from data
contained in table XIX of the extracts of Firing Tables
3 AA-0-2a, paragraph 257. From table XXII, paragraph 257,
data may be obtained for plotting a straight line through
this point which represents the differential effects due to a
change in muzzle velocity. The situation is illustrated in
76
GUNNERY, ETC., ANTIAIRCRAFT GUNS
86
figure 30. This is a graphic representation of information
contained in the firing table. If a projectile were fired under
standard conditions, it should be expected to burst at the
point #=4,740, H= 3,223. If the muzzle velocity changed
and all other conditions remained unchanged, it would burst
somewhere along the differential effect line. It should be
carefully noted that a variation from standard muzzle velocity
changes the altitude, horizontal range, and angular height
of the expected point of burst, but does not change the time
of flight or the quadrant elevation.
(2) The causes of variations from standard muzzle velocity
are numerous, but those of principal interest to the artillery-
man are erosion of the gun and varying temperatures of the
powder charge. Antiaircraft guns are classified as high-
velocity guns, and their accuracy life may be considered as
much shorter than that of guns ordinarily used for firing at
land or water targets. For example, a certain combination
of gun, projectile, and powder charge might be designed to
develop a muzzle velocity of 2,600 f/s and would normally be
expected to develop this velocity. However, the wear or ero-
sion in a gun is directly proportional to the number of rounds
fired from it; hence a decrease in developed muzzle velocity
may be expected to accompany continued firing, even though
identical projectiles and powder charges are used. Antiair-
craft guns use fixed ammunition, and in calculating standard
trajectories a powder temperature of 70° F. is assumed.
Variations from this temperature result in appreciable
changes in developed muzzle velocity.
c. Ballistic density . — (1) Continuing consideration of dif-
ferential effects in the vicinity of the point H= 3,223,
#= 4,740, the effects of a variation in ballistic density from
standard will be found in table XXII, paragraph 257, and
may be represented graphically as shown in figure 31. A
projectile fired under standard conditions should be expected
to burst at the point #=4,740, 3,223. With a variation
in ballistic density, all other conditions remaining standard,
it should burst somewhere along the differential effect line,
which results in a change in the altitude, horizontal range,
and angular height of the expected burst.
(2) The standard ballistic density is based upon a tem-
perature of 59° F., a barometric pressure of 29.53 inches of
244637 ° — 40 -
6
77
86
COAST ARTILLERY FIELD MANUAL
mercury, and a saturation of 78 percent. It is also assumed
to vary in a standard manner with altitude above the ground.
Wide variations in ballistic density are to be expected over
an extended period of time. Normally, the changes over
brief periods of time will be small.
||
■
■
i
u
IBS
rmm
P
Hgfl
HS
Ip
■
■
n
1
1
Snlnl
Figure 31. — Differential effect line — ballistic density.
(3) In addition to the effect of density on the trajectory
as shown in (1) above, density materially affects the time of
burning of powder-train fuzes. Part 1GB, page 7, of Firing
Tables 3 AA-J-2a shows graphically the effect of density on
the time of burning. These effects are measured along the
trajectory, a greater than normal density causing the time
of burning to decrease. Figure 31 shows both effects of
density, The vectorial sum of the effects of a 10-percent
78
GUNNERY, ETC., ANTIAIRCRAFT GUNS
86
variation in density (ballistic and burning) is also shown in
figure 31. In practice, the effect of variations in muzzle ve-
locity and density are averaged. (See par. 97ft.)
d . Ballistic wind.— (1) Standard trajectories are computed
under the assumption that there is no wind, a condition
which will seldom, if ever, confront the artilleryman. The
effect of wind upon a projectile depends upon the direction of
the wind (Aw), the velocity of the wind ( W ) , the direction of
the plane of fire (At) , and the time of flight (£) , For con-
venience, the wind is resolved into two components as illus-
Figtjre 32. — Vector diagram of ballistic wind.
trated in figure 32. Considering for the moment only the
effect of a range wind, a differential effect line may be plotted
(fig. 33) from information contained in Table XXII, para-
graph 257, in the same manner as those for variations from
standard muzzle velocity and density.
(2) A projectile fired under the standard conditions of no
wind should be expected to burst at the point R =4,' 740,
ff=3,223. The effect of a range wind is to cause the burst to
occur somewhere along the differential effect line for wind,
thus changing the altitude, horizontal range, and angular
79
86
COAST ARTILLERY FIELD MANUAL
height of the expected burst. As a general rule, the direction
and velocity of the ballistic wind are not subject to rapid
changes, but the effect of the wind depends upon the direction
of the target from the gun, and hence is subject to very rapid
changes in the case of an airplane target.
iMI
□
■
■
PPP
wm
Wcm
BO AH W/HD
l
= |
K
■
( 606
<?> 700
t '-1268
Vo-2600
■
6*595
<t>HO0
t*/? 68
Vo* 2600
Dmsity-ioo
l
!2
l
EE-
l
■■■■VfVllI
■aalllllll
lillillll
W 46
iiniiiii
W 47i
//ob/zobtal
iiniiiii
} 0 4Bt
j?AN6£
lillillll
'0 49i
iiniiiii
10 50 1
iliiiiiii
'0
Hi
Figure 33. — Differential effect line — ballistic wind.
e. Quadrant elevation and fuze setting. — (1) The effects
of two other variations are of importance; a change or an
error in setting quadrant elevation on the gun, or the fuze
range on the projectile. These effects are illustrated in
figure 34. It will be noted that a change in fuze setting moves
the burst along the trajectory and a change in quadrant ele-
vation moves the burst along the 0 line. In either case the
altitude, horizontal range, and angular height of the expected
80
GUNNERY, ETC., ANTIAIRCRAFT GUNS
86
burst are changed. Note that differential effect lines for
these elements, taken from data contained in Table XXII,
paragraph 257, provide very close approximations of the
trajectory and 4 > line in the vicinity of the point under
consideration.
(2) Errors in quadrant elevation usually arise from some
maladjustment or malfunctioning of materiel. However, the
iaUl
1
1
99
99
99
^ n
■
|R|
■
H9
■
9
9
■
■
on
H
p
9
■
9
B
9
H
g
i
9
9
1
1
9
9
9
9
■
9
191
H
9
mm
99
mm |
99
Figure 34. — Differential effect lines — quadrant elevation and fuze
setting.
time of burning of a powder train fuze is affected by a num-
ber of factors, among which are —
(a) Atmospheric pressure under which it burns.
(£>) Temperature of the fuze.
(c) Speed at which it is rotating while burning.
81
86
COAST ARTILLERY FIELD MANUAL
(3) Not infrequently a difference in time of burning will
be noticed between fuzes of different manufacture or different
lots made by the same manufacturer. Conditions of storage
sometimes affect the rate of burning of the powder train.
The mechanical fuze is unaffected by these factors.
f. Altitude . — Although this element, strictly speaking, per-
tains solely to the position -fin ding problem, the effect of
change of altitude upon the position of the burst is of interest.
The change in the position of the burst is effected through a
change in the calculated firing data, which is based upon
the elements of the target’s position. As illustrated in figure
35, a change in altitude (AH) with no change in angular
height will move the expected point of burst along the line of
position.
82
GUNNERY, ETC., ANTIAIRCRAFT GUNS
86-88
g. The differential effects due to the earth’s rotation and
variations in weight of projectile, which are of consider-
able magnitude in firing long-range seacoast guns, are not of
particular importance in antiaircraft gunnery problems.
Variations in air temperature affect density and power
temperature corrections.
■ 87. Cross Wind and Drift Effects. — a. The resolution of
the effect of ballistic wind into two components, a range com-
ponent and a deflection component, is discussed in paragraph
86cZ. The deflection component of the wind manifestly causes
a deviation of the projectile from its standard trajectory in
direction (azimuth) . In figure 32 it is clear that the deflection
component of the wind will tend to carry the projectile to the
left. The angular deviation will be proportional to the veloc-
ity of the deflection component, time of flight of the projectile,
and quadrant elevation at which the projectile leaves the gun.
Differential effect tables for cross wind will be found in the
firing tables as in the case of the range wind component. The
magnitude of the cross wind component depends upon the
azimuth of the target and will vary quite rapidly in the case
of an airplane target.
b. Drift is the horizontal angular deviation of the projectile
from its plane of departure from the gun, caused by the rota-
tion of the projectile and the resistance of the air. It varies
with time of flight and quadrant elevation. Tables containing
values of drift are contained in firing tables. (See table XX,
par. 257.)
■ 88. Danger Space of Shell Bursts. — o. The danger space
resulting from the burst of a 3" antiaircraft high- explosive
shell has been f ound to have a shape approximating the shape
generated by the revolution of the area, shown in figure 36,
about its long axis. It resembles a mushroom. This danger
space has been determined by experiment and represents the
volume which is filled with shell fragments of sufficient size
and velocity to secure penetration of an arbitrarily chosen
standard material.
b. The dimensions of this danger space are of importance
in solving gunnery problems related to securing “hits” on a
moving airplane target. It is to be noted that projectiles
83
88-89
COAST ARTILLERY FIELD MANUAL
bursting beyond the target are ineffective. For effectiveness
projectiles must burst at the target or just short of it.
Figure 36. — Danger space of 3" antiaircraft shell burst.
Section X
ERRORS AND PROBABILITIES
■ 89. Dispersion and Errors. — a. In section IX, the more
important reasons for the deviation of a projectile from its
standard trajectory are briefly analyzed. During the discus-
sion, the behavior of only a single projectile was considered.
Let it now be assumed that a very large number of shots, each
with the same fuze setting, is fired from a gun which is care-
fully pointed at the same azimuth and elevation for each shot
fired and that, as far as can be determined, standard condi-
tions prevail for each shot fired. Experience has shown that
these shots will be scattered in range and in direction, later-
ally and vertically. This scattering is called “dispersion”.
The shots may be expected to arrange themselves about a
definite point, called the “center of dispersion”, in a manner
which may be approximately predicted mathematically. The
center of dispersion will not necessarily coincide with the
point at which fire is directed, and its location can never be
determined precisely as it is the mean point of burst of an
infinite number of shots. The mean point of burst of a
finite number of shots is called the “center of burst”.
b. The factors which prevent all projectiles from bursting
at the same point and which cause that point to deviate
from the intended target are known as “errors”. A complete
explanation of the causes of errors or the mathematical
theory underlying them is not within the scope of this man-
ual. However, it may be said that the laws of probability
84
GUNNERY, ETC., ANTIAIRCRAFT GUNS 89
and the theory of errors as applied to seacoast artillery firing
(PM 4-10), apply with equal force to fire against aircraft.
The essential difference lies in the fact that in seacoast artil-
lery, dispersion in a horizontal plane only is considered while
in antiaircraft artillery it is necessary to consider a disper-
sion in volume. Errors are divided into two general classes:
(1) Accidental errors are those errors which cause a dis-
persion of shots about the center of burst. Accidental errors,
such as those arising from inaccurate or careless operation
of fire-control instruments, inaccurate pointing of guns, or
backlash in the mechanism may be largely eliminated through
careful training of the operating personnel and careful ad-
justment of matdriel. Indeterminate accidental errors are
caused by round- to -round variations in the characteristics
of the materiel, such as variations in the shape and surface of
projectiles and relative location of their centers of gravity and
variations in the action of the gun and carriage. It is because
these indeterminate errors are sometimes compensating and
at other times additive, that dispersion occurs. The disper-
sion of a particular gun is referred to as its armament error.
(2) Systematic errors are those errors which cause the
center of burst to deviate from the point being fired on. Sys-
tematic errors arising from sources which are known and
understood, such as known variations from standard muzzle
velocities, densities, or ballistic winds, are calculable and may
be almost completely eliminated by the application of methods
described below. Indeterminate systematic errors such as
those which arise from an empirical determination of atmos-
pheric conditions and the disregard of second and higher
order differential effects, added to those determinate errors
which cannot be eliminated, are responsible for the deviation
of the center of burst from the point being fired on. The
elimination of this latter class of errors is probably one of
the most difficult problems confronting the antiaircraft artil-
leryman. No complete solution has been found as yet, ap-
proximate methods being resorted to as will be shown later.
c. If a very large number of shots are fired from an anti-
aircraft gun at a fixed point, they will be dispersed about the
center of burst in range along the trajectory, and in deflection
both laterally and vertically. The dispersion can be repre-
sented graphically by a geometrical figure which may be
85
89-90
COAST ARTILLERY FIELD MANUAL
called a dispersion volume. If each of the three dimensions is
divided into eight equal parts, it will be found that the points
of burst will be arranged about the center of burst as indi-
cated by the approximate percentage figures given in figure
37. The dispersion volume may be divided into zones, later-
ally, vertically, and in range, within which 50 percent of the
shots fired will burst. (The 50 percent zones are shown in
figure 37.) It should be noted that each of the faces shown
in the geometrical figure corresponds to the dispersion ladder
as applied to seacoast artillery.
■ 90. Probability. — a. The discussion of dispersion has been
based upon the assumption that a very large number of shots
Figure 37. — Dispersion volume.
is fired. The artilleryman must constantly deal, however,
with a relatively small number of shots. It is necessary to
consider the shots actually fired as samples from a larger
group and to resort to a branch of mathematics called “Prob-
ability,” which deals with the likelihood that a situation con-
cerning which information is not complete will occur. For
example, since the dispersion volume (fig. 37) provides an
indication of where 50 percent of the shots fired may burst,
a reasonable conclusion is that any single shot fired has an
even chance of bursting within a 50 percent zone. Also, con-
sidering the smaller number of shots as a sample of a larger
group, a reasonable assumption is that half the shots fired
will burst within a 50 percent zone.
86
GUNNERY, ETC., ANTIAIRCRAFT GUNS
90
b. The physical dimensions of the dispersion volume are
subject to variations which depend upon the time of flight
to, and quadrant elevation of, the point at which the gun is
being fired. These dimensions are determined at the proving
grounds, as a result of a limited number of shots fired at
various points, and tabulated in firing tables in the form of
probable errors in yards along the trajectory, in deflection
laterally, and in deflection vertically. A probable error is
defined as “the error which is as likely as not to be exceeded,
a value which, in the long run, will be exceeded one -half the
time, and not exceeded one-half the time.” By referring
to the diagram of the dispersion volume (fig. 37), it will be
seen that a probable error is one -half of the width of the
50 percent zone.
c. (1) There are several features of the theory of errors
and laws of probability as applied to antiaircraft firing that
are of particular importance. When the deviations of shots
from the target can be measured, the most probable center
of burst is determined by taking the algebraic mean of such
deviations. It will frequently happen, particularly when fir-
ing at a rapidly moving target, that it will be impracticable
to measure deviations. In such a situation sensings may
be obtained and advantage may be taken of a rule of prob-
ability which states: “The most probable position of the
center of impact (or burst) is that which, in a large number
of trials, would produce in the same ratio those outcomes
which have been observed.” For example, consider that of
four shots fired from an antiaircraft gun, three were seen to
burst “short” of the target and one “over.” Under the law
given, the relative frequency of shorts and overs observed is
assumed to be the same as if a very large number of shots
had been fired; that is, 75 percent short and 25 percent over.
The center of burst must be short of the target, since, if it
were at the target, 50 percent of the shots would have burst
on each side. In the problem given 75 percent burst short
of the target, and since it is assumed that 50 percent burst
short of the center of burst, 25 percent must be assumed to
have burst between the center of burst and the target.
Therefore the most probable position of the center of burst
is one probable error short of the target. It must be kept
in mind, however, that in making use of this law the behavior
87
90 COAST ARTILLERY FIELD MANUAL
of a limited number of shots will not always agree with that
of a very large number.
(2) To locate the center of dispersion and to know it as
such would require the firing of an infinite number of shots,
a task impossible of accomplishment. However, it should be
clear that the center of burst determined from even a small
number of shots is a more reliable indication of the center of
dispersion than that determined by any individual shot, but
for any number a probable error exists in locating the center
of dispersion. This error may be determined in a simple
manner from the equation
where
Eve is the probable error in location of the center of
dispersion,
E P is the probable error of a single shot, and
n is the number of shots.
Consider, for example, that the firing table probable error
along the trajectory for a given point is 50 yards. The follow-
ing table shows the probable error in location of the center
of dispersion (along the trajectory) for various numbers of
shots fired:
No. of shots (ft) 1 2 3 4 5 6 8 12 16
E vc 50 35 29 25 22 20 18 14 12
Thus it will be seen that the error, E pc , is halved by firing four
shots instead of one, but that it is necessary to fire twelve
more in order to again halve the error. 50 percent of the
error introduced by assuming the center of burst as the
center of dispersion is eliminated by basing the determination
of the center of burst on four rounds.
(3) By applying the rules of probability, it is possible to
calculate the chances of securing a burst at a target. For
example, assume that the dispersion volume illustrated in
figure 37 is based upon firing table data for 0=700 and F=13.
Consider a target whose center coincides with the center of
burst and whose dimensions are 20 yards along the trajectory,
15 yards laterally, and 18 yards vertically. It can be shown
that the probability of securing a burst in this small volume
is approximately 0.03, which means that of 100 shots fired at
88
GUNNERY, ETC., ANTIAIRCRAFT GUNS
90-91
this target, three might be reasonably expected to burst in
this small volume.
(4) The dispersion volume illustrated in figure 37 includes
100 percent of all shots fired. This is a close approximation
of the mathematical laws. However, about 1 percent of a
very large number of shots may be expected to burst more
than four probable errors from the target. In firing a smaller
number of shots, there is no assurance that this small per-
centage will not occur early in the series. If such shots did
occur and were taken into consideration in determining the
center of burst of a small group of shots, they would exert an
undue influence on the calculations. Hence it is considered
sound practice, to disregard wild shots, which are defined as
those which burst more than four probable errors from the
center of burst.
(5) One of the hypotheses of a rule of accidental errors is
that “Plus errors and minus errors occur with the same fre-
quency in a large number of trials and hence have equal
probabilities.” An example of the application of this rule
will be found in the operation of laying a gun in elevation with
a quadrant. It is unlikely that a gun can be set precisely
at the same elevation on two successive trials. However, a
justifiable assumption may be made that the average setting
of a large number of trials will be the true elevation, as plus
and minus errors occurring with the same frequency tend to
compensate each other.
■ 91. Application. — a. The ultimate object of all artillery fire
is to hit the target. The foregoing discussion has indicated
that gunnery is not an exact science. However, armed with
the knowledge that errors do exist in firing and that they
tend to follow certain rules, the artilleryman may act to reduce
or eliminate them as far as possible. The principal problems
in gunnery are concerned with the elimination of errors in
firing. The solution of such problems involves the eliminating
of determinate errors, reducing dispersion, and placing the
center of impact on the target and keeping it there.
b. The procedure may be divided into two phases. In the
first phase, by careful preparation, which includes the test and
adjustment of all materiel, thorough training of personnel,
and preparatory firings, determinate errors may be largely
89
91-92
COAST ARTILLERY FIELD MANUAL
eliminated and disperson reduced. In the second phase, fire
is directed at the target and the compensation for indeter-
minate errors which cause a deviation of the center of impact
from the target is undertaken. This latter problem is the
more difficult of solution.
c. (1) Preparatory fire is usually directed at fixed points in
space under conditions which permit the maximum degree of
accuracy in determining errors. The elimination of errors is
undertaken by applying corrections to firing data.
(2) Fire for effect is directed at airplane targets which
move at high speed. This situation does not permit a deter-
mination of errors and the application of corrections with a
degree of accuracy comparable to that for preparatory fire,
since the conditions under which shots are fired are continu-
ally and rapidly changing. However, since the accuracy of the
rules of probability increases with the number of shots fired,
the solution of the problem is aided by the fact that generally
the fire of more than one gun is directed at the target. The
solution is further aided by maintaining the highest rate of
fire, consistent with accuracy, from all guns, since by so doing
an approximation results of the condition that all shots should
be fired under conditions as nearly identical as possible.
Section XT
PREPARATORY FIRE
■ 92. Preparation of Fire. — Careful preparation of fire is
essential for all types of artillery. Preparation for fire against
aerial targets is more difficult and complex than for other
types of targets since the antiaircraft problem is one of three
dimensions. It is important that this preparation is made
carefully and accurately because of the short time the target
can be engaged and the difficulty of fire adjustment. Further-
more, the pilot of an enemy airplane can be expected to
maneuver as soon as he sees the first burst. As the adjust-
ment of fire on a maneuvering target is even more difficult,
every possible effort will be made to place the first bursts on
the target. Preparation of fire includes —
a. Training of personnel.
b. Test, adjustment, and check of materiel.
90
GUNNERY, ETC., ANTIAIRCRAFT GUNS
92-94
c. Test and adjustment of pointing system.
d. Preparatory fire.
■ 93. Trial Fire. — a. All fire-control instruments are de-
signed on the basis of firing table data which assume the
existence of standard conditions. The purpose of trial fire
is to determine the magnitude of the errors, due to unknown
causes, and apply corrections to firing data in such a manner
that the center of burst will be moved onto a point called the
trial shot point ( TSP ) .
b. The corrections for errors determined as a result of trial
fire should be —
(1) Equally effective in all parts of the field of fire.
(2) In such a form that they can be applied to any fire-
control system in use.
(3) Applied to correct the basic cause of the error. The
correction should not cause the data computor to make an
error in the calculation of basic data.
c. Extended investigation of all the known methods of de-
termining and applying trial fire corrections has been con-
ducted in the past. None of the methods proved entirely
satisfactory. The method described in paragraph 107 is
theoretically sound and gives good results.
d . The frequency with which trial fire is conducted will
depend upon the tactical situation, availability of suitable
meteorological data, and knowledge possessed by the battery
as to performance of the materiel.
■ 94. Trial Shot Point.— a. The trial shot point C TSP) is a
definite fixed point in space at which trial shots are fired.
The location of this point is determined by its angular height,
horizontal range or altitude, and azimuth.
b. While any point within effective range of the materiel
might be selected as a trial shot point, trial fire usually is
conducted at one of the following points:
TSP No. 1
Firing table
<£
e
H
JR
1 - _ _
3 AA-J-2a
700
13
m
3, 223
4,740
2
3 AA-J-2& -
700
7
661
2,213
2, 914
3 . -
3 AA-J-2a
500
13
403
2,154
5, 153
4
3 AA-O-1—
900
15
814
1
5,095
4, 957
91
95-96 COAST ARTILLERY FIELD MANUAL
B 95. Materiel Preparations — Trial Fire, — Emplacement of
the guns is discussed in FM 4-125. Necessary steps for the
preparation of materiel for firing are listed in FM 4-120.
See Technical Manuals or Ordnance Department pamphlets
pertaining to the materiel in question for the methods by
which the tests and adjustments to the guns and mounts are
made. The methods of making the tests and adjustments to
the instruments are explained in sections I, II, and III,
chapter 3. Orientation and synchronization are discussed
in chapter 4.
■ 96. Selection of Trial Shot Point (T&P). — a. Choice of
the trial shot point to be used is governed by the gun and am-
munition being used, visibility, ceiling, and expected altitude
and course of enemy targets. TSP No s. 1, 2, and 3 are for
use with 3'' AA shrapnel, Mk. I (FT 3 AA-J-2a), MV, 2,600
i/s . TSP No. 1 is at medium altitude and range and is the
TSP most commonly used. TSP No. 2 is at a shorter range
and lower altitude and is used when the visibility does not
permit observation at either of the other points. TSP No. 3
is at a longer range and lower altitude than TSP No. 1 and
should be used in preference to TSP No. 2 when the ceiling is
not high enough to observe TSP No. 1. TSP No. 4 is for use
with 3" AA shell HE, M42 (FT 3 AA-O-1), MV, 2,700 i/s;
other suitable points may be selected.
b. (1) The choice , of a suitable azimuth is governed by the
following considerations:
(a) Safety of the field of fire.
(b) Visibility from the distant (O 2 ) station.
(c) Accuracy of observation from O 2 .
( d ) Probable direction of approach of enemy targets.
(2) The second consideration must be borne in mind par-
ticularly when there are a number of clouds below the TSP.
While there may be perfect visibility from the battery position
(Oi), a cloud may obscure the TSP from O 2 . In order to
comply with the third consideration, the azimuth of the TSP
should be selected so that the horizontal projections of the
lines of sight from Oi and O 2 to the TSP will intersect at an
angle of approximately 90°.
c. Trial fire is not restricted to the four points selected in
paragraph 94, TSP Nos. 1, 2, and 3 were selected as the
92
GUNNERY, ETC., ANTIAIRCRAFT GUNS
96-97
result of numerous test firings, and consequently should be
used except when unusual conditions justify the selection of
a different point. Trial shot charts must be constructed from
firing -table data for the TSP selected.
H 97. Construction of Trial Shot Chart.— The following
problem illustrates the method of constructing a trial shot
chart:
a. Assume TSP No. 4.
0=900 m R= 4,957 yards
F=15 H= 5,095 yards
FT=3 AA-O-1 e= 814 mils
MV =2,700 f/s
b. Plot the point for F=15 (the TSP) on cross-section
paper at F=4,957 yards and H= 5,095 yards as shown in
figure 38.
c. Extracting from tables K-2 and K-3, Firing Tables 3
AA-O-1 : At F=15 and 0—900, a minus 0.1 of a unit fuze range
change has the following effects:
A R— —24 yards
A H= —17 yards
Multiplying these effects by 10, we get the effect of —1 unit of
fuze range change or A R= —240 yards and A H= —170 yards.
Plot a point on the chart (fig. 38) 240 yards to the left and 170
yards below the point F=15. Join this point with the TSP
and extend the line an equal amount on the other side of the
TSP. Subdivide the above line into 10 equal segments on
each side of the TSP and label as shown in the figure. This
line is the trajectory.
d. Extracting from tables E-l and E-2, Firing Tables 3
AA-O-1: At F=15 and 0—900, a +10 mils change in 0, has
the following effects:
AR= — 57 yards
AiJ= +54 yards
Multiplying the above figures by 3, we get the effects of +30
mils change in 0 or A — 171 yards and A H= +162 yards.
Plot a point on the chart 171 yards to the left and 162 yards
above the TSP. Join this point with the TSP. Extend the
244637°— 40 7
93
97
COAST ARTILLERY FIELD MANUAL
line below the trajectory. Subdivide into equal segments and
number as shown. This is the <f> line.
e. Extracting from table B, Firing Tables 3 AA-O-1: At
F=15 and 0—900, e=814 mils.
Through the TSP draw a straight line, making an angle of
814 mils with the horizontal. This is the line of position.
/. On the left edge of the chart draw the altitude correction
scale in yards. The scale is the same as the vertical scale of
the chart.
g. Determine the altitude correction percent scale as fol-
lows: Altitude %Xaltitude= altitude of TSP. In the case of
TSP No. 4— Altitude=4riF-
VO ti
For example: when %H= 96% ( — 4%)
altitude^ —5307 yards.
.96
Calculating for different %H and tabulating :
96%
-4%_.
Altitude (yds.)
— 5307
101%
1 %—
Altitude (yds.)
— 5045
97%
— 3%_.
_ _ 5253
102%
2% —
— 4995
98%
-2%..
5199
103%
3% —
_ 4947
99%
- 1 %-
_ __ 5146
104%
4% —
4899
100%
0%-
__ 5095
Plot the above altitudes on the left of the chart and label
each according to the percent as shown in figure 38. The
units of this scale are not equally divided.
h. Extracting from tables F-l and F-2, Firing Tables 3
AA-O-1: At F — 15 and 0—900, a —100 i/s change in MV , has
the following effect:
AR = — 145 yards
AH— —185 yards
Multiply each of the above effects by 1.25. Then AH = —181
yards and AH— —231 yards. These are the effects for —125
f/s change in MV. Extracting from tables 1-1 and 1-2, FT 3
AA-O-1: At F=15 and 0=900, a +10% change in density has
the following effects:
A R— —193 yards
AH= —228 yards
94
95
97-98
COAST ARTILLERY FIELD MANUAL
Averaging the effects for —125 f/s and +10 percent change
in density,
A R= —187 yards
A H= —230 yards
Plot a point on the chart 187 yards to the left and 230 yards
below the TSP. Join this point with the TSP and extend the
line an equal amount on the other side of the TSP. Divide
the line into 10 equal segments on each side of the TSP and
label as shown. This line is the MV — density line on which
—125 f/s MV is equivalent to +10 percent change in density.
■ 98. Data for the Oi and O 2 Stations. — a. In order to
measure the deviations of the bursts from the TSP , it is
necessary that the instruments be laid on the TSP selected.
The various angles and distances concerned in computing
the Oi and O 2 data are shown in figure 39. The problem
is to determine the azimuth and angular height of the TSP
from each observing instrument. Figure 40 shows the two
triangles which must be solved.
TSP
Figure 40. — Triangles solved in determining O x and 0 2 data.
They can be solved by trigonometric formulas. Two rapid
methods have been developed to solve the problem:
(1) The Lewis chart.
(2) The Crichlow slide rule.
b. The successive steps to be followed when using the Lewis
chart method are tabulated and an illustrative problem is
given in paragraph 248.
c. The successive steps to be followed when using the Crich-
low slide rule method are tabulated and an illustrated prob-
lem is given in paragraph 249.
VERTICAL PROJECTION
96
GUNNERY, ETC., ANTIAIRCRAFT GUNS
99-100
■ 99, Pointing Observation Instruments — Trial Fire. — a.
Bilateral observation. — The observation instruments deter-
mine the deviations of a burst from the TSP at which they are
directed. The necessity for accurate pointing of the instru-
ments is obvious, since errors in pointing will result in erro-
neous deviations. Both the Oi and O 2 instruments must be
accurately leveled and oriented. After a TSP is selected, the
data for the O 2 instrument (A 2 and e 2 > are telephoned to the
O 2 station, where they are used to point the instrument at the
TSP . As the Oi instrument is generally at the battery posi-
tion, it is customary to transmit the Oi data ( Ai and ei) orally
to the operator, who then points the instrument at the TSP .
b. Unilateral observation. — One observation instrument
located at the Oi (battery position) station is used. It is set
up, oriented, and pointed at the TSP in the same manner as
the Oi instrument described in a above. In addition, the
height finder is pointed at the TSP with data furnished to the
Oi station corrected for parallax, if necessary.
H 100. Computing Ballistic Corrections — Trial Fire. — a. (1)
The actual MV of the guns will frequently differ from the
standard (powder tag MV) for the following reasons:
(a) Erosion of the bore and deterioration of powder.
(b) Ballistic density is nonstandard.
(c) Temperature of the powder is nonstandard.
(2) In addition, nonstandard ballistic density affects the
time of burning of powder train time fuzes.
b. The effects of the above factors, as given in firing tables,
are difficult to apply to the director. Tables which convert
the firing table data to a form readily applicable to the direc-
tor have been prepared. These tables are given in paragraph
256. Always apply ballistic corrections before firing.
c. All of the factors enumerated above, except time of fuze
burning, are reduced to an effect on MV and then added
algebraically to give the total MV variation.
d. Ballistic cams are cut for MV below standard because
such a value is closer to the average MV developed through-
out the life of the gun. In the M4 director, the cams are cut
for 2,550 f/s for shrapnel and 2,700 f/s for shell.
e. Variation in developed MV from that for which the bal-
listic cams are cut is determined either by the method de-
97
100
COAST ARTILLERY FIELD MANUAL
scribed in paragraph 135, or a value is assumed, based on such
factors as the powder tag MV and the previous number of
rounds fired from the guns. (Muzzle velocity decreases 3 f/s
for every 100 rounds fired.) This is the variation from the
MV for which the cams are cut,
(1) Effect on MV due to ballistic density is obtained from
table VIII, paragraph 256.
(2) Effect on MV due to temperature of powder is obtained
from table IX, paragraph 256.
/. The total MV variation is corrected for by a vertical
correction (applied to the vertical spot dial) and an altitude
correction (applied to the altitude spot dial). The amount
of the correction (dcp or dH 0 ) is obtained from the ballistic
tables, paragraph 256. These corrections ( d<p and dH ) are
tabulated for MV variations of 25, 50, 75, and 100 f/s. Select
the table closest to the total MV variation determined in e
above. Extract the correction from the table using the H
and F of the target as arguments. (In the case of trial fire,
use the H and F of the TSP.)
g. The ballistic correction for time of burning of powder
train fuzes due to ballistic density is extracted from either
table I or II, depending upon whether the ballistic density
is above or below normal. The tables give the correction to
fuze (applied to the fuze spot dial) in corrector divisions for
a ±10 percent change in density. Smaller percent changes
are proportional. Enter the proper table using H and F as
arguments and take the proportional amount of the correc-
tion tabulated. (In case of trial fire, use H and F of the
TSP.) This correction is not applied when using mechanical
fuzes.
h. The ballistic corrections obtained in f and g above are
independent of any other corrections which may be applied.
In other words, such corrections as trial fire corrections, cor-
rection for constant fuze error, and adjustment corrections
(sec. XIII) are made in addition to the ballistic corrections.
The ballistic corrections, as examination of the tables will
disclose, change as the H and F of the target vary.
i. Ballistic corrections are applied before firing trial shots.
They are also applied before fire for effect. The proper alti-
tude and fuze range ( H and F) determine the proper correc-
tions. (See illustrative problem, par. 250.)
98
GUNNERY, ETC., ANTIAIRCRAFT GUNS
101
■ 101. Setting Trial Shot Data in Director. — a. The suc-
cessive steps to be followed in determining the corrected
firing data depend upon the type of data computor being
used. In general, as the data computors turn out data based
on standard conditions (par. 66), it is necessary to correct
for nonstandard conditions. Corrections are made on the
data computor for as many of the nonstandard conditions as
are known and which are capable of correction. The succes-
sive steps to be followed in the M4 director are as follows:
(1) Be sure that the data computor is leveled and oriented,
and that the synchronization has been checked. (See ch. 4.)
Check to see that the proper ballistic cams are in place.
(2) Set in the necessary parallax. If no parallax is neces-
sary, check to see that there is no parallax set in the data
computor. (See par. 159.)
(3) Traverse the data computor until the present azimuth
dials indicate the azimuth of the TSP.
(4) Elevate the telescopes of the data computor until the
€ 0 dials indicate the angular height of the TSP.
(5) Set the altitude of the TSP on the H dial.
(6) Using the wind component solver mounted on the left
side of the data computor, determine the N-S and E-W com-
ponents of the ballistic wind obtained from the meteorological
message.
(7) Set the components of the ballistic wind obtained in
(6) above on the wind rate dials. A ballistic wind from the
NE has a north and an east component. Set the north com-
ponent on the scale marked “north” and the east component
on the scale marked “east.” Likewise a ballistic wind from
the SW has a south and a west component which are set on
the scales marked “south” and “west.”
(8) Determine the ballistic corrections for the TSP. (See
par. 100 and illustrative problem, par. 250.)
(9) Apply the ballistic corrections determined in (8) above
to the spot dials. The corrections are d<p and dH. A dF
correction is necessary if a powder train time fuze is being
used. If no correction to a particular element is needed, be
sure that particular spot dial is set at zero.
(10) Obtain the drift for the TSP from the firing tables.
Add this value, with sign as shown, to -j-10 when firing
shrapnel, and to +7 $ when firing shell. The result, with
99
101-102
COAST ARTILLERY FIELD MANUAL
sign as determined, is the net drift correction which is applied
to the dA spot dial. (The director makes a fiat drift correc-
tion of — 10 mils when firing shrapnel and —7 mils when
firing shell.)
(11) Turn on the power.
(12) Match the e 0 dials by the Ro handwheel. Check to be
sure that the range rate dial is set at zero. Observe the
present horizontal range counter. If it moves, there is a
range rate set in. Adjust the range rate knob until the
counter does not creep.
(13) Set the altitude rate dial at zero and operate the alti-
tude follow-up motor for a short time so as to remove any
altitude prediction which may have been left in the data
computor. The altitude prediction motor should be turned
off during the firing of trial shots.
(14) Corrected firing data are now available at the guns
which can be laid for firing at the TSP by matching the
pointers at the guns.
b. Methods of determining the corrected firing data for
other types of directors are found in handbooks pertaining
to the particular instrument.
■ 102. Firing Trial Shots. — a. The gun selected to fire the
trial shots must be prepared as outlined in paragraph 95
before firing the trial shot problem.
b . The matching of the elevation and azimuth pointers
should be checked after the gun is loaded for each round.
The setting 1 of the fuze on each projectile should be checked
against the fuze range as determined by the data computor.
It must be remembered that a calibration correction to the
fuze (par. 239) on the gun firing the trial shots will cause
the fuze setting on the projectile to vary by the amount of
the calibration correction. The rounds should be fired with-
out loss of any more time between rounds than is necessary
to observe the bursts accurately, record the deviations, and
perform the duties incidental to firing.
c. Normally, not less than five trial shots are fired, all from
one gun of the battery. The shots upon which corrections are
based must be normal rounds. Rounds that result in abnor-
mal deviations because of defective fuzes or other reasons
should be disregarded. Therefore, prior to firing the trial
100
GUNNERY, ETC., ANTIAIRCRAFT GUNS
102-103
shots from mobile guns in a new position, one or more rounds
should be fired from each gun in order to settle the mounts.
N 103. Observing Bursts and Determining CB — Trial Fire. —
It is of primary importance that the deviation of the center
of burst (CB) of the trial shots be determined with the great-
est accuracy practicable. There are two methods of observing
the trial shot bursts and determining the coordinates of the
CB; unilateral observation and bilateral observation. The
first is the simpler but is less accurate ; the second, while more
accurate, requires the use of an observation base line. Bilat-
eral observation should be used when practicable.
a . Unilateral observation. — (1) Unilateral observation is
frequently necessary when sufficient time for the establish-'
ment of a base line does not exist. Because of the expected
frequency of such situations in time of war, this method, while
less accurate, is of no less importance than the bilateral
method.
(2) The Ch instrument and the height finder are pointed,
using the angular height and azimuth of the TSP.
(3) The following data must be recorded for each shot:
Data .
Altitude of burst
Angular height of burst 1
Lateral deviation of burst]
Source
Height finder.
B. C. telescope, Ml.
(4) When the data pertaining to all the trial shots have
been obtained, they are averaged to determine the location of
the CB. The angular height and altitude of the CB are suffi-
cient data to locate the CB on the trial shot chart.
b. Bilateral observation. — (1) Bilateral observation should
be used whenever time and other conditions permit. The
location of the O 2 station must be known. It can be deter-
mined either from a survey or from an accurate large-
scale map.
(2) For operation of the bilateral system, two battery com-
mander’s telescopes Ml (or instruments of equal accuracy and
utility), must be available; one at the Oi station (battery
position) and the other at the O 2 station (flank position) .
The spotting telescope on the M4 director can be used at the
Oi station in lieu of a separate instrument. In general, the
101
103-104
COAST ARTILLERY FIELD MANUAL
distant station O 2 should be located so that the horizontal
projection of the angle O 2 TO 1 is approximately 90°, T being
the trial shot point and Oi the battery station.
(3) The Oi and O 2 instruments are pointed on the TSP
using data determined by one of the two methods outlined in.
paragraph 98.
(4) The following data must be recorded for each shot:
Data : Source
Vertical deviation of burst Oi instrument
Lateral deviation of burst Oi instrument
Range deviation of burst (in mils) O 2 instrument
(5) When the deviations of all the trial shots have been
obtained, they are averaged to determine the lateral and ver-
tical deviations of the CB as determined at the Oi position
and the range deviation of the CB as determined at the O 2
station. With these data, the location of the CB may be deter-
mined from the Crichlow slide rule or the Lewis chart.
■ 104. Conversion of Deviations to Horizontal Plane —
Trial Fire. — The observation instruments at Oi and O 2 meas-
ure the lateral and range deviations, respectively, of the burst
from the TSP in the inclined plane. Before we can use the
deviations of the CB, we must measure these angles in the
horizontal plane because the Lewis chart and the Crichlow
slide rule solve the horizontal triangle. (See par. 98.) These
deviations must be multiplied by the ratio
slant range 1
horizontal range cos e
This conversion can be done by means of the Crichlow slide
rule by following the instructions printed on the face of the
slide rule. Another method is to use the graph shown in
figure 41. A larger chart is furnished with each set of Lewis
charts. It is used as follows: Select the curve on this chart
whose value equals the lateral deviation in the slant plane.
Mark the point where this curve crosses the horizontal line
whose ordinate equals the angular height of the TSP from
the observing station. The abscissa of the point just deter-
mined is the lateral deviation in the horizontal plane. Ver-
tical deviations are never converted to the horizontal plane.
102
GUNNERY, ETC., ANTIAIRCRAFT GUNS
105
■ 105. Plotting CB on Trial Shot Chart — Bilateral Ob-
servation. — It is necessary to determine the horizontal range
to the CB from Oi before the CB can be plotted on the trial
ahoibh a>/nnDNv
shot chart. This range can be determined by means of either
the Crichlow slide rule or the Lewis chart.
a. Crichlow slide rule method . — Examination of figure 42
will show that the angles used in solving the horizontal tri-
103
105
COAST ARTILLERY FIELD MANUAL
angle Ox — CB — 0 2 are the interior angle on the right and
the exterior angle on the left end of the base line. Using the
rules given in paragraph 207, right deviations are added to
and left deviations are subtracted from the Ox and 0 2 angles
to the TSP to get the new Oi and 0 2 angles to the CB. Devi-
ations are first converted to the horizontal plane. The new T
angle is the difference between the new Oi and 0 2 angles.
The horizontal triangle Ox — CB — 0 2 is to be solved for the
horizontal range O t to CB. Set the arm “S” of the Crichlow
slide rule to the value of the new 0 2 angle to CB on scale D .
N N
Figure 42. — Determining the Oj and 0 2 angles to CB.
Without moving the arm “S,” set the arm “L” to the value of
the new target angle (T) (interior angle at CB) on scale D.
Without changing the angular displacement between the
arms “S” and “L,” set the arm “S” to the length of the base
line on scale E. Under the arm “L” on scale E read the hori-
zontal range Oi to CB.
b. Leans chart method . — Examination of figure 42 shows
that the angles used in solving the horizontal triangle
Oi — CB — 0 2 with the Lewis chart are one interior and one
exterior angle. Using the rules given in paragraph 203, right
104
altitude cowecriON per cent
GUNNERY, ETC., ANTIAIRCRAFT GUNS
105-108
deviations are added to and left deviations subtracted from
the Oi and 0 2 angles to the TSP to get the new Oi and Os
angles to the CB. Deviations are first converted to the hori-
zontal plane. The CB is plotted with the new Oi angle to CB
as abscissa and the new 0 2 angle to CB as ordinate on the
Lewis chart. Mark the point CB. Place the log range scale
on the vertical line passing through CB with the base line
length in line with the zero ordinate line of the chart. Oppo-
site CB read the value of the horizontal range Ox to CB on the
log range scale. (See also fig. 92.)
c. Plot the CB on the trial shot chart as follows: Draw a
vertical line on the chart through the abscissa equal to the
horizontal range Oi to CB. Draw a line parallel to the line
of position through the point on the 0 line corresponding
to the observed vertical deviation of the CB. The inter-
section of these two lines is the CB. Mark it so on the trial
shot chart. (See fig. 43.)
Note.- — In drav/ing the trial shot chart for a trial shot problem
only the 0 line and the line of position need be shown.
■ 106. Plotting CB on Trial Shot Chart — Unilateral Ob-
servation. — Draw a horizontal line on the trial shot chart
through the ordinate equal to the altitude to the CB. Draw
a line parallel to the line of position through the point on
the 0 line which corresponds to the observed vertical devia-
tion of the CB. The intersection of these two lines is the CB.
Mark it so on the trial shot chart.
■ 107. Determining Trial Shot Corrections. — a. Paragraphs
105 and 106 describe the methods of plotting the CB on the
trial shot chart.
b. The trial shot corrections are determined as follows:
The observed vertical deviation of the CB with the sign re-
versed is the d<p correction. Draw a line through the CB
parallel to the 0 line until it intersects the line of position.
From this intersection draw a horizontal line to the left until
it intersects the %H scale. This intersection with the %H
scale is the %H correction. (See fig. 43 and illustrative prob-
lem, par. 251.)
■ 108. Determination of Lateral Correction From Trial
Fire. — The observed lateral deviation of the CB from Oi,
105
108-111
COAST ARTILLERY FIELD MANUAL
converted to the horizontal plane, with the sign reversed is
the lateral id A) correction.
■ 109. Removal of Ballistic Corrections. — a. Prior to the
firing of trial shots ballistic corrections were placed on the
spot dials of the director (par. 101a(9)>. These corrections
were based on F and H for the TSP and therefore are not
applicable to a target appearing at a different F and H. The
ballistic corrections (exclusive of ballistic wind corrections)
are removed after trial fire is completed because it is easier
and less conducive to errors to apply an entirely new correc-
tion than to correct a correction already applied to the
director. (See illustrative problem, par. 252.)
b. In paragraph 101a(10), it is stated that prior to the
firing of trial shots a dA spot was placed on the spot dial
of the director in order to refine the flat correction for drift.
This correction is made only so that the CB will be as close to
the TSP as possible. The lateral correction (par. 108) deter-
mined from trial fire corrects for all variations except drift.
It would be unwise to attempt to refine the drift correction at
other points than the TSP, especially since the drift correc-
tion incorporated in the director is an average value selected
for the portion of the field of fire where targets are most
likely to be encountered. Consequently the dA spot (applied
before trial fire for the refinement of the drift correction)
is removed after firing the trial shots and only the dA as a
result of trial shots is used to open fire for effect.
■ 110. Application of Trial Shot Corrections. — a. Regard-
less of the method used, the trial fire corrections determined
are d<f>, dA, and %H. The corrections, d<t> and dA, can be
applied to the spot dials as soon as determined. %H cannot
be applied to the spot dial because it is a percentage correc-
tion. When the altitude of the target is determined, dH
is computed (dH=%HXH) and applied to the spot dial.
b. Figure 22 shows the vertical spot dial (d<p ) . The other
spot dials are similar. The trial fire correction is set on the
spot dial by turning the spotting handwheel until the proper
value is opposite the movable index.
■ 111. Records. — a. Each time a trial shot problem is fired
the following records should be kept:
(1) Meteorological message.
106
GUNNERY, ETC., ANTIAIRCRAFT GUNS
111-112
(2) Ballistic corrections applied.
(3) Deviations of the CB.
(4) Location of TSP .
b. These data are necessary for the determination of the
fuze error and the developed muzzle velocity. (See par. 133.)
■ 112. Summary of Trial Shot Firing. — The process of firing
trial shots and determining corrections therefrom may be
briefly summarized as follows :
a. Complete all materiel preparations as outlined in para-
graph 95.
b . Select a trial shot point and decide upon a suitable
azimuth for the TSP .
c. Compute the data to point the Oi and O 2 instruments
at the TSP , using either the Lewis chart or the Crichlow
slide rule, and the proper firing tables.
d. Orient the observing instruments at the Oi and O 2 sta-
tions and point each instrument at the azimuth and eleva-
tion of the TSP.
e. Compute the ballistic corrections for the TSP . (See
par. 100.)
/. Compute the corrected firing data by the procedure
tabulated in paragraph 101.
g. Fire five shots (or more if necessary to obtain five nor-
mal rounds) with the gun set on these data, checking the
laying of the gun and setting of the fuze before each round
is fired,
h. Observe the firing of each shot, using the most accurate
method available. The vertical (above or below) and lateral
(right or left) deviations of each burst are measured at the
Oi station. The range deviation (over or short) of each
burst is measured at the O 2 station. Compute the average
vertical and lateral deviations from Oi and the average range
deviation from O 2 in order to determine the deviation of the
CB from the TSP .
i. Convert only the lateral deviation of the CB from Oi
and the range deviation of the CB from O 2 (both observed
in the slant plane) to deviations in the horizontal plane,
using the conversion chart (fig. 41) or the Crichlow slide
rule.
107
112-113
COAST ARTILLERY FIELD MANUAL
j. Determine the horizontal range to the CB from Oi,
using either the Crichlow slide rule or the Lewis chart.
k. Plot the CB on the trial shot chart, using the observed
vertical deviation of the CB and the horizontal range to CB
from Ou (See par. 105.)
L The d <p correction is the observed vertical deviation with
sign reversed. Scale the %H correction from the trial shot
chart.
m. The lateral ( dA ) correction is the observed lateral
deviation of the CB (corrected to the horizontal plane) with
the sign reversed.
n. Remove the ballistic corrections and the dA spot (re-
finement to the drift correction) applied prior to the firing
of the trial shots. The ballistic corrections will be reapplied
as soon as F and H for the target can be determined.
o. Apply the trial shot corrections d<p and dA determined
in l and m above to the spot dials of the director. The %H
correction is applied to the dH spot dial as a flat correction
as soon as the altitude of the target is determined.
p. Keep a record of the meteorological message, ballistic
corrections, and deviations of the CB for future reference.
q. If unilateral observation was used, vary the above pro-
cedure as follows:
(1) In h, the altitude of the burst is measured by the height
finder instead of measuring the range deviation from O 2 .
(2) In k, plot the CB on the trial shot chart, using the ob-
served vertical deviation of the CB and the altitude of the
CB. (See par. 106.)
■ 113. Calibration Fire. — The purpose of calibration fire is
to determine from the relative location of the centers of burst
of the several guns of a battery the corrections which must be
applied to each gun in order to obtain either a center of burst
common to all guns of the battery or an arbitrary pattern of
bursts. Calibration fire is undertaken upon receipt of new
guns and when analysis of the results of fire indicates that
the former calibration corrections are no longer effective.
Calibration corrections, when determined, are recorded and
applied to the individual guns and are not changed until
superseded by corrections determined at a later calibration
108
GUNNERY, ETC., ANTIAIRCRAFT GUNS 113-122
firing. Since the corrections are applied to the individual
guns, the corrections must be in terms of A, 0 , and F.
■ 114. Materiel Preparations — Calibration Fire. — The same
materiel preparations as are outlined in paragraph 95 for trial
fire must be completed prior to calibration fire.
■ 115. Removal of Previous Corrections on Guns. — It is
never a good policy to correct a correction if it can be avoided.
Consequently all corrections are removed from the guns before
conducting calibration fire. The calibration corrections com-
pensate for factors which are causing the guns to shoot an
undesirable pattern in the sky.
■ 116. Selection of the Calibration Point. — The choice of
the calibration point is governed by the same considerations
as the choice of the TSP (par. 96). TSP No. 1 or No. 4 is
recommended as the calibration point unless circumstances
prevent their use.
■ 117. Computation of Oi and O 2 Data. — The computation of
the data for the Oi and O 2 stations is exactly the same as
described in trial fire. (See par. 98.)
■ 118. Pointing Observation Instruments — C alibration
Fire. — See paragraph 99 for information concerning the
pointing of observation instruments.
■ 119. Computing Ballistic Corrections — Calibration Fire.—
The same procedure as outlined in trial fire, paragraph 100,
is followed.
■ 120. Computing Corrected Firing Data.- — The same pro-
cedure as outlined in trial fire, paragraph 101, is followed.
■ 121. Firing a Settling Shot. — A settling shot should be
fired by each gun prior to the calibration firing so as to settle
the gun.
■ 122. Firing Calibration Fire. — Five rounds should be fired
from each gun. The matching of the elevation and azimuth
pointers is verified after each gun is loaded for each shot. The
fuze setting of each projectile is checked against the fuze
range as determined by the director. The guns are fired alter-
nately so that changing conditions affect all guns in a similar
manner. Only sufficient time to insure the accurate pointing
244637 ° — 40 -
-8
109
122-126 COAST ARTILLERY FIELD MANUAL
and leveling of the guns and the accurate observation and
recording of the bursts from Ox and O 2 is allowed to elapse
between rounds. If for any reason any of the bursts have
abnormal deviations, that particular round is disregarded and
additional rounds are fired so as to have recorded data for
five normal shots from each gun.
■ 123. Observing Bursts and Determining CB — Calibration
Fire. — Bilateral observation should always be used for cali-
bration fire. If time and other considerations prohibit bilat-
eral observation, the firing of calibration fire should be de-
deferred until bilateral observation can be obtained. (See
par. 103b for data to be recorded at each station.) The de-
viations of all the shots for each gun are averaged to get the
deviations of the CB for each gun.
■ 124. Conversion of Deviations to the Horizontal Plane —
Calibration Fire. — The deviations of the CB measured in
paragraph 123 are in the inclined plane. Use the conversion
chart (fig. 41) or the Crichlow slide rule to convert the lateral
deviation from Oi and the range deviation from O 2 to the
horizontal plant. (See par. 104.)
■ 125. Plotting CB of Each Gun on Trial Shot Chart. —
Using the same methods outlined in paragraph 105, plot the
center of burst for each gun on the trial shot chart. Identify
each CB with the gun which fired it by the notation CB1, CB2,
CB3, and CB4. (See fig. 97.)
Note. — In preparing a calibration chart only three lines need be
shown, the < f > line, the line of position, and the trajectory.
■ 126. Parallax Corrections. — a . Calibration corrections
which cause the fire of the battery to converge in one part of
the field of fire will cause it to diverge an equal amount when
firing in the opposite direction. Hence, it is common prac-
tice to apply calibration corrections so that the guns shoot
parallel. In this way, the danger volume of the battery is
increased since the guns are, under service conditions, em-
placed some distance apart; the flat calibration corrections
will hold equally well in all parts of the field of fire.
b. The CB’ s should make a pattern in the sky which will
have the shape and dimensions of the lay-out of the guns on
the ground. The calibration corrections to each gun must be
110
GUNNERY, ETC., ANTIAIRCRAFT GUNS
126-127
based on the deviation of each CB from points displaced
laterally and in range from the common point T\ ( T ' is
the point in space at which the director and the observation
instruments at Oi and O 2 are pointed.) These displacements
from T f are equal respectively to the lateral and range dis-
placement of each gun from the center of the square which
the guns form on the ground. The computation of calibra-
tion corrections is greatly simplified if the plane of fire is
taken along one of the diagonals of the square. The director
is placed at the center of the square for calibration fire.
Figure 44. — Battery emplacement.
■ 127. Plotting Calibration Point for Each Gun on Trial
Shot Chart. — a. Figure 44 shows a typical battery emplace-
ment. Assume TSP No. 1 is used as the calibration point and
that the plane of fire is along the diagonal of the square
through gun No. 4. The trial shot chart being a vertical
plane through the calibration point, the vertical and range
deviations but not the lateral deviations can be plotted. The
calibration point for each gun (Cl, C2, C3, and C4) will have
the same relative locations around the point T f as the guns
have around the center of the square. Cl and C3 will there-
fore be coincident with T f . As guns Nos. 2 and 4 are dis-
placed minus and plus 35 yards in range from the center of
111
127-129 COAST ARTILLERY FIELD MANUAL
the square, C2 and C4 will be displaced minus and plus 35
yards along the horizontal line through T'. (See fig. 45.)
b. The lateral deviations of each calibration point from T’
(they cannot be shown on the trial shot chart) are computed
as follows : 35 yards at 4,740 yards range subtends an angle of
OC
~~ mils, equals 7 mils approximately. Therefore the lateral
displacements of the individual calibration points will be Cl
left 7 mils, C2 line, C3 right 7 mils, C4 line.
■ 128. Target Practice Conditions. — Under target practice
conditions the guns may be emplaced so close together that
we can ignore the parallax corrections in computing the cali-
bration corrections. In this case the points Cl, C2, C3, and C4
coincide with T\
■ 129. Calibration Corrections Using Trial Shot Chart. — a.
Figure 45 shows a trial shot chart on which CB4 and C4 only
have been plotted. Through CB4 draw a line parallel to the
<f> line. Through C4 draw a line parallel to the trajectory.
The distances, which are the d<p and dF corrections, are shown
in figure 45. These distances are measured by the scales
superimposed on the <P line and the trajectory of the trial
shot chart. As CB4 is below the line parallel to the trajectory
through C4, the d<p correction is plus. As C£4 is short of C4,
the dF correction is plus.
b. To compute the dA correction, subtract the lateral
deviation of CB4 as observed from Oi (converted to the hori-
zontal plane), from the lateral parallax correction of C4
(which in paragraph 127b was shown to be line for the bat-
tery emplaced as shown in figure 44) . In this particular case,
the observed lateral deviation of CB4 with sign reversed is
the dA correction. If the deviation of No. 1 gun were left
( — ) 10 niils as spotted from the Oi station, the dA correction
would be — 7 — ( — 10) =4-3 mils. Similarly, if the deviation of
No. 3 gun were right (4-) 2 mils as spotted from the Oi
station, the dA correction would be 4-7— (4-2) =4-5 mils.
(See fig. 45.) These computations should always be checked
by drawing a figure.
c. Repeat the above computation for each gun.
d. If we applied the calibration corrections as computed
above to the individual guns, we would then have the guns
112
GUNNERY, ETC., ANTIAIRCRAFT GUNS
129
VERTICAL CALIBRATION CORRECTIONS.
LATERAL CALIBRATION CORRECTIONS
*1 =-7-(-IO) = +
*3 =»7-(+2) = +5iA
Figure 45.- — Plotting individual calibration points and center of
burst for each gun on the trial shot chart.
113
129-130
COAST ARTILLERY FIELD MANUAL
shooting the correct pattern in the sky and in addition the
center of the pattern would be' at the TSP. It will be found
that such corrections would be relatively large on each gun
because they would include corrections normally made by
trial fire corrections.
e. In paragraph 93b(3), it is stated that the corrections
should not cause the director to make an error in basic data.
Changing the fuze range violates this consideration because
it changes the time of flight of the projectile. In making
calibration corrections, we knowingly violate this considera-
tion because there is no alternative. We can keep the result-
ing error to the minimum, however, by selecting the base
piece with a view to insuring small fuze corrections. For ex-
ample, suppose the fuze corrections determined were No. 1,
+2; No. 2, +4; No. 3, +4; and No, 4, +6. It is obvious that
with either No. 2 or No. 3 gun as a base piece only two guns
will require corrections and these will be small and of oppo-
site sign. If either No. 1 or No. 4 is taken as the base piece,
there will be three corrections all of the same sign and one
correction much larger than the others.
f. A base piece is selected whose fuze corrections, when
subtracted from the fuze correction of the other guns of the
battery, will cause the least amount of fuze change. The
calibration corrections for the guns are determined by sub-
tracting all of the calibration corrections for the base piece
from the respective calibration corrections for the other guns.
Note that by following this procedure the calibration correc-
tions applied to the base piece are zero. It will be seen that
when done in the above manner the calibration corrections
move three of the guns with respect to the fourth or base
piece. The desired pattern is obtained
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