Document text
MHI
Copy 3
ibuau^ FM 4-112
WAR DEPARTMENT
COAST ARTILLERY
FIELD MANUAL
ANTIAIRCRAFT ARTILLERY
GUNNERY, FIRE CONTROL,
POSITION FINDING,
AND HORIZONTAL FffiE,
ANTIAIRCRAFT AUTOMATIC
WEAPONS
(CASE I FDUNG)
August 22, 1942
FM 31-15
C 2
BASIC FIELD MANUAL
OPERATIONS IN SNOW AND EXTREME COLD
FM 31-15, September 18, 1941, is changed as follows :
■ 60. Because carbon dioxide is exhaled from the lungs, it is
not advisable to sleep with the head completely covered. Even
in the severest cold the nose and mouth should be uncovered.
[A. G. 062.11 (9-22-42).] (C 2, Sept. 29, 1942.)
By OEDEK OF the Secbetaby or War :
WAB DEPARTMENT,
Washington, September 29, 1942.
G. 0. MARSHALL,
Chief of Staff.
Official :
J. A. ULIO,
Major General,
The Adjutant General.
487422°— 42
U. S PRINTING OFFICE : 1942
FM 4-112
COAST ARTILLERY
FIELD MANUAL
ANTIAIRCRAFT ARTILLERY
GUNNERY, FIRE CONTROL, POSITION
FINDING, AND HORIZONTAL FIRE,
ANTIAIRCRAFT AUTOMATIC WEAPONS
(CASE I FIRING)
UNITED STATES
GOVERNMENT PRINTING OFFICE
WASHINGTON : 1942
WAR DEPARTMENT,
Washington, August 22, 1942.
FM4-112, Coast Artillery Field Manual, Antiaircraft Artil-
lery — Gunnery, Fire Control, Position Finding, and Horizontal
Fire, Antiaircraft Automatic Weapons (Case I Firing), is
published for the information and guidance of all concerned.
[A. G. 062.11 (6-5-42).]
By order op the Secretary of War:
G. C. MARSHALL,
Chief of Staff.
Official:
J. A. ULIO,
Major General,
The Adjutant General.
Distribution:
R and HI (2) ; Bn and H 4 (3) ; IBn and H 4 (10) ;
IC 4 (25) .
(For explanation of symbols see FM 21-6.)
n
TABLE OF CONTENTS
Chapter 1. General. Paragraphs Page
Section I. General 1-5 1
H. Antiaircraft automatic weapons
problem 6-11 3
III. Gun pointer control 12-17 6
IV. On carriage sight control 18-24 9
V. Off carriage sight control 25-32 11
VI. Director control 33-38 13
Chapter 2. Dispersion and hit expectancy.
Section I. Dispersion 39-44 16
II. Hit expectancy 45-47 25
Chapter 3. Calculation of leads.
Section I. Elements of data 48-53 28
II. Firing tables 54-57 35
ni. Methods of lead calculation 58-64 41
Chapter 4. Lead curves and charts.
Section I. Lead curves and lead charts for
constant altitude courses 65-67 76
II. Lead charts for dive targets 68-72 83
Chapter 5. Lead characteristics 73-80 102
Chapter 6. Horizontal fire.
Section I. General 81-82 130
II. Antimechanized defense 83-86 130
III. Assault of fortifications 87-88 138
IV. Engagement of water-borne tar-
gets 89-91 139
V. Lateral leads and lead charts 92-95 141
Chapter 7. Observation and adjustment of fire.
Section I. Methods of observation 96-99 151
II. Individual tracer control 100-101 157
III. Central tracer control 102-106 159
IV. Fire adjustment 107-109 161
V. Data transmission 110-113 165
Chapter 8. Range section 114-116 168
Chapter 9. Training.
Section I. General 117-120 173
II. Training of gunners and gun
pointers 121-123 174
IH. Training of adjusters and spotters 124-127 176
IV. Tracer control trainer 128-133 180
V. Subcaliber firing 134 196
Appendix I. Glossary of symbols, automatic weapons 197
II. Lead charts 199
III. Use of Ml (Crichlow) slide rule 206
IV. Drill table for control equipment set Ml 211
Index 217
III
FM 4-112
1-2
COAST ARTILLERY FIELD MANUAL
ANTIAIRCRAFT ARTILLERY
GUNNERY, FIRE CONTROL, POSITION FINDING, AND
HORIZONTAL FIRE ANTIAIRCRAFT AUTOMATIC
WEAPONS (CASE I FIRING)
(This manual supersedes EM 4-112, July 12, 1940.)
CHAPTER 1
GENERAL
Section I. General
II. Antiaircraft automatic weapons problem
III. Gun pointer control
IV. On carriage sight control
V. Off carriage sight control
VI. Director control
Section I
GENERAL
■ 1. Scope. — This manual treats of the theory and practice of
gunnery and Are control for antiaircraft artillery automatic
weapons when firing by gun pointer and central control
methods. The fundamentals of exterior ballistics and gun-
nery as covered in chapters 1 and 2, FM 4-110, should be
carefully studied to acquire a thorough understanding of the
general antiaircraft problem. Pertinent definitions and sym-
bols which appear in FM 4-155 and appendix I of this manual
should also be studied. A clear understanding should be had
of the picture in space of the various elements of data. Case
III firing (firing by director control) is completely covered
in FM 4-113.
■ 2. General Missions. — a. The primary mission of antiair-
craft artillery automatic weapons is to attack all enemy air-
craft within range, particularly low-flying airplanes, to destroy
them, to cause them to abandon their missions, or to decrease
the efficiency of their operations. These aerial targets, either
low-level or diving, are the most dangerous of all aircraft to our
Paragraphs
1-5
&-11
12-17
18-24
25-32
33-38
1
2-4
COAST ARTILLERY FIELD MANUAL
personnel and materiel. They strike suddenly, swiftly, and
with deadly effect if unopposed. It is difficult to obtain warn-
ing of their approach as they invariably use some form of
cover such as the sun, clouds, trees, or hills in order to get
near their objective unseen and unidentified. The only effec-
tive defense against such aircraft is to destroy them in such
numbers that the objective to be gained by their attack is
not worth the cost.
6. The contingent mission of antiaircraft artillery auto-
matic weapons is defense against mechanized vehicles, and
other ground, water, or air -borne targets, for fire against
which the characteristics and fire control methods of anti-
aircraft artillery automatic weapons are particularly suitable.
■ 3. Types of Weapons. — The weapons designed or adopted
for this general mission are —
a. Small arms. — These include rifles and automatic rifles
which fire solid ball ammunition. Such weapons by them-
selves cannot be considered adequate for local defense, but
should always be used to supplement machine-gun fire.
b. Machine guns. — These include caliber .30 and caliber .50
machine guns which fire solid ball and tracer ammunition.
Such weapons are suitable for local defense or as training
weapons. They may also be used for the defense of very small
objectives, but consideration must be given to their limited
range and effectiveness.
c. Automatic cannon. — These include guns of the 20-mm,
37-mm, and 40-mm type that fire high-explosive projectiles
with a tracer element and point-detonating fuze, and armor-
piercing shot for use against armored vehicles. Such pro-
jectiles are highly destructive to airplanes, but hits must be
obtained to accomplish the mission as detonation is by contact
with the target. To be effective, this type of antiaircraft
weapon depends on its ability to open fire quickly, its high rate
of fire, and rapid adjustment of fire by observation of tracers.
■ 4. Basic Assumptions. — Effective fire with present antiair-
craft automatic weapons equipment is limited by ballistic and
gunnery factors to targets within approximately 3 seconds'
time of flight of the projectile. The only basic assumption
necessary is that the target will fly in a straight line at a
2
ANTIAIRCRAFT AUTOMATIC WEAPONS
4-6
constant speed during this time of flight. The flight of even
the latest high-speed aircraft will usually conform to this
assumption.
■ 5. Importance. — The study of gunnery and fire control for
antiaircraft automatic weapons is of special importance for
the following reasons:
a. All military units armed with suitable weapons are
responsible for their own local antiaircraft defense. They
will use all their small arms for this purpose, but machine
guns fired by individual tracer control will be their primary
defense.
o. The short time available for opening and adjusting fire
with these local defense machine guns requires the individual
gunners to be expert in target identification, estimation of
certain elements of data, and adjustment of fire by obser-
vation of the tracer stream.
c. In antiaircraft automatic weapons units, the individual
gun is usually the fire unit. This places the responsibility
for fire control upon the enlisted men of the section. The
training of these enlisted men will be the greatest problem
of the antiaircraft automatic weapons commander.
d. Some, if not all, data for the fire control of antiaircraft
automatic weapons must be estimated. Rapidity of opening
fire and adjustment require that these estimates be almost
instinctive. This can be accomplished only by careful study,
understanding of the problem, and training.
Section II
ANTIAIRCRAFT AUTOMATIC WEAPONS PROBLEM
■ 6. Targets. — The primary target for antiaircraft automatic
weapons — the low-flying airplane — is the most versatile of all
targets. It not only can move in three dimensions at the will
of its pilot, but it also can accomplish its mission in a number
of ways and in a very brief period of time. If unopposed, the
low-flying airplane can accomplish almost any military mis-
sion except that of actually occupying territory. Even this
can be accomplished by landing of parachute or air-borne
troops. The inability of pursuit aviation and antiaircraft
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COAST ARTILLERY FIELD MANUAL
guns of larger caliber to combat successfully the low-flying
airplane has been demonstrated many times. The barrage
balloon is an excellent defense in special situations, but the
antiaircraft automatic weapon still remains the best all-
around defense against such targets.
■ 7. Element op Time. — The most important factor in the
antiaircraft automatic weapons problem is time. The high
speed of the target and its ability to use cover for its approach
require that it be quickly taken under fire as soon as observed
and identified. This is necessary in order to give sufficient
firing time to insure hits before the aircraft can complete
its mission or get out of range. Also, continuous and rapid
changes in time of flight and angular travel cause rapid
changes in the basic firing data. If a low-level (crossing-
constant altitude) target traveling 300 miles per hour passes
400 yards from a gun at the midpoint of its course, its angular
velocity in azimuth 10 seconds before it reaches the midpoint
will be 23 mils per second; at the midpoint, this angular
velocity will be 365 mils per second. On such a course the
leads will change as much as 40 mils per second. The target
should be kept under fire at least 10 seconds, and it will nor-
mally take an additional 10 seconds to identify the target,
obtain firing data, and open Are. In this total time of 20
seconds, assuming a reasonable target speed of 300 miles per
hour, the target will have traveled 3,000 yards or nearly 2
miles. If the target is coming directly at the gun, the range
will change from 2,000 yards to 500 yards in 10 seconds. In a
70° dive this target will change altitude from 5,000 feet to 900
feet in 10 seconds. All of these rapid changes in basic ele-
ments must be considered in selecting any method of fire
control. As these rapid changes practically preclude the ac-
curate measurement of all data, at least some of the data
must be estimated.
■ 8. Ballistic Factors. — a. Any gun that will meet the re-
quired conditions of flexibility and high rate of fire will either
be of small caliber or decidedly heavy and complicated. Up
to the present time only small caliber guns have met these
conditions satisfactorily.
b. Two of the principal ballistic factors acting upon auto-
4
ANTIAIRCRAFT AUTOMATIC WEAPONS 8-10
matic weapons projectiles are the propelling charge and the
ballistic coefficient. The area weight relationship is included
in the ballistic coefficient.
( 1 ) The procedure of manufacture is not sufficiently precise
to load 'each projectile case with exactly the same amount
of propelling charge. Thus, the initial velocities caused by a
difference in loading may vary as much as 150 foot-seconds.
(2) The present type of small caliber projectiles has very
poor ballistic qualities as compared with larger caliber projec-
tiles. Practical limitations on the accuracy of manufacture
cause individual projectiles to have different ballistic coeffi-
cients. The rapidity with which a projectile loses initial
velocity is partially a function of the relationship between
the weight of the shot and its air resistance. An examination
of the firing tables will show that small caliber projectiles
lose their velocities faster than large caliber projectiles (see
fig. 2) .
c. The difference in time of flight from round to round at a
given range directly affects the accuracy of fire at that range
when firing at a high speed target. Therefore, the accuracy
required to get a satisfactory percentage of hits cannot be
expected except for a small proportion of the ground impact
range of an antiaircraft automatic weapon.
■ 9. Gunnery Factors. — The necessity for flexibility and
speed requires that observation and adjustment be practi-
cally instantaneous. Adjustment of fire, based on observa-
tion of tracer ammunition, is the best way to accomplish
this. It is a known fact that as the range increases, the diffi-
culty of tracer observation increases. The longer the time of
flight, the greater will be the probability of the target chang-
ing its course and speed such as to render fire adjustment
ineffective. Moreover, the longer the range, the smaller the
angular errors that can be absorbed by the size of the target.
The objective of gunnery for automatic weapons is to obtain
at least one hit on each target in the shortest time possible.
■ 10. Summary of Problem. — The antiaircraft automatic
weapons problem may be summarized as follows:
a. The versatility of the target requires an accurate, flex-
ible, and high velocity gun with a high rate of fire.
5
10-13
COAST ARTILLERY FIELD MANUAL
b. Fire control must be simple, rapid, and accurate.
c. As fire must be destructive, high-explosive projectiles
should be used.
d. Effective fire is limited to short ranges by the ballistic
limitations of small projectiles and gunnery factors of the
problem.
e. Observation and adjustment, to be effective, must be
limited to short times of flight.
■ 11. Possible Solutions of Problem. — a. Gun pointer con-
trol, in which the gun pointer or pointers have entire charge
of Are control.
b. On carriage sight control, where the sight or sights
on the gun are controlled from a position on the gun car-
riage.
c. Off carriage sight control, where the sight or sights on
the gun are controlled from a position some distance from
the gun.
d. Director control, where there are no sights on the gun
and the pointing of the gun is controlled remotely from a
director.
Section m
GUN POINTER CONTROL
■ 12. General. — The gun pointer or pointers open fire with
an estimated lead and control the fire. They can do this
by using either forward area sights or individual tracer con-
trol. This form of control, especially with machine guns,
gives extreme flexibility, as the gun is normally free mounted,
and allows each gun to be its own fire unit.
■ 13. Forward Area Sights. — Such a sight usually has the
forward element so designed that leads can be obtained by
tracking the target off center on this element. Initial leads
are obtained by estimation of course and speed of target.
Such a sight is essential if tracers are not available and can
well be used at all times to obtain initial leads. Adjustment
can be carried on by continuous estimations or by tracer con-
trol. A gunner who thoroughly understands the leads and
6
ANTIAIRCRAFT AUTOMATIC WEAPONS
13-15
the possibility of such a sight can get good results at the
shorter ranges.
■ 14. Individual Tracer Control. — Without the use of sights,
the gun pointer opens fire by leading the target the esti-
mated correct number of target lengths, and swinging with
it as in wing shooting. He then adjusts his fire by observa-
tion of the tracer stream as one would direct a stream of water
from a hose. Such a method of fire control is the simplest
as well as the quickest to use. All antiaircraft automatic
weapons troops should have some training in the use of
individual tracer control regardless of their type of weapon,
for often this simple method will be the only one available.
With the proper training and high morale of these gun
crews, this method will prove effective against airplanes com-
ing directly at them, and on crossing targets at short ranges.
■ 15. Advantages. — a. Gun pointer control is the simplest
and most rapid method of fire control. For that reason it
must always be considered as an available emergency
method. When not on the alert and when the guns must
be manned with the fewest possible number of gunners, this
method can be exercised quickly and with the fewest men.
b. Forward area sights are essential when tracer ammuni-
tion is not available. A gunner who thoroughly understands
the leads and the possibility of such a sight can get results.
c. Forward area sights where two gun pointers are required
have proved more successful than individual tracer control.
With two gun pointers the problem of selecting a point of
aim on the forward element of the sight is simplified. The
lateral pointer has only to judge the speed and the angle
of approach to estimate fairly accurately the lateral lead
required. The vertical pointer can with fair accuracy esti-
mate the vertical lead by the range and the clock hour of
approach. With a clock face forward element on the sight,
this latter estimation is fairly simple.
d. Forward area sights are the most simple forms for anti-
mechanized firing. The target is picked up easily and quickly
and rarely lost due to the sight. For speed of getting on
target the forward area sight is the best type delevoped to
date.
7
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COAST ARTILLERY FIELD MANUAL
e. Individual tracer control can be very effective at short
ranges and for coming targets. It is probably the best type
of control for close-in fighting with antiaircraft machine
guns. Given ball, armor-piercing, and tracer ammunition
that have very nearly the same ballistic qualities, machine
gun fire can be very effective against airplanes within 500
yards of the gun (slant range) .
/. Individual tracer control is the only method of fire
control that can be used at night, unless targets are suf-
ficiently illuminated to use sights. It frequently happens
that airplanes can be seen close in at night by their exhaust
or due to moonlight, but not sufficiently to use sights. Trac-
ers from other guns passing near the airplane or the air-
plane's own guns firing will often give sufficient indication
of its position to allow effective firing with individual tracer
control.
g. The advantage of full automatic fire can be obtained
with individual tracer control. The volume of fire thus
obtained in some measure makes up for its lack of accuracy.
Where firing time is extremely short, such as where a fast
airplane sneaks in close before being identified, this quick
volume of fire offers the best hope of success.
■ 16. Disadvantage. — a. Gun pointer control is the least
accurate method of firing. For that reason its use should
be considered only as an emergency method for antiaircraft
automatic weapons units. For all troops it can be considered
the primary method of fire control for purely local defense,
that is, for firing on aerial or. ground targets coming directly
at the unit itself with obvious intent to strafe or bomb the
unit.
b. The use of gun pointer control places the whole burden
of fire control on the gunner. It must be realized that, in
fact, he acts in the capacity of range section and gun sec-
tion combined. His responsibility includes estimating leads,
operating the gun, and controlling the fire. His knowledge
must include leads, materiel, ammunition, and observation
and adjustment of fire. The selection of soldiers for this
position must be made with the greatest care and consider-
ation for their natural ability.
8
ANTIAIRCRAFT AUTOMATIC WEAPONS
16-19
c. When using forward area sights, both leads can seldom
be correct at the same instant.
d. When gun pointers also control the fire, it is very difficult
for them to track a fast target smoothly. Therefore, the
tracer stream is not steady, and observation is very uncertain
and difficult.
e. Gun pointers are invariably bothered, both in pointing
and in observation, by vibration, smoke, and flash of the firing
gun. Frequently they will lose the target and are forced to
cease firing to pick it up again. This decreases both the accu-
racy and the volume of fire.
/. Effective fire cannot be expected beyond 500 yards using
gun pointer control. This is mainly due to poor observation,
and the size of the target at longer ranges cannot absorb
even a small proportion of the errors in pointing.
■ 17. Summary. — Gun pointer control can be considered —
o. The principal method for local defense machine guns.
b. An emergency method of fire control for all antiaircraft
automatic weapons.
c. Effective only within 500 yards.
d. The most flexible and rapid method of control and there-
fore desirable in close-in defense.
e. Sufficiently effective for antimechanized defense.
Section IV
ON CARRIAGE SIGHT CONTROL
■ 18. General. — This method uses sights on the guns which
can be set to the required lateral and vertical leads. The
leads are set from a position on the carriage, either by estima-
tion of leads or by means of a simple computer using esti-
mates of various elements of the course arid speed of the
target. By the latter method either a simple linear speed or
angular travel director mounted on the gun carriage can be
used for the computation.
■ 19. Lead Control. — The gun pointers have only to track
the target with their sights, and the sights are controlled
from a position on the carriage by another man who esti-
9
19-23
COAST ARTILLERY FIELD MANUAL
mates and sets the leads. Adjustment of fire is continuous
by observation of the tracer stream.
■ 20. Course and Speed Lead Computer. — A small, simple
linear speed lead computer is mounted directly on the car-
riage. It automatically sets the sights at the proper leads
when certain elements of data are set into the computer.
These elements include speed of target, range, angle of dive,
and direction of flight. This method has been used fre-
quently by European armies. Tests by our service have not
been satisfactory, and present policy is to discontinue further
experiments.
■ 21. Angular Travel Lead Computer. — This method em-
ploys the angular travel principle of lead computing. Con-
tinuous tracking of the target by the gun pointers set hori-
zontal and vertical rates into a simple computer mounted
in the gun carriage. The only remaining element needed
is time of flight to the future position. This must be esti-
mated and set in the computer by the adjuster, who then
adjusts fire by observation of the tracer stream.
ffl 22. Advantages. — a. All such methods of fire control are
utilized to get on a target and open fire quickly. The guns
can go into action quickly from the traveling position, as
they should require no bore sighting or orientation.
b. Accuracy is much greater than for gun pointer control.
Specialized personnel do the estimating, observation, and
adjustment. The improved accuracy tends to make this
method effective at longer ranges than is possible with gun
pointer control.
c. Each gun can be used as a separate fire unit without
increasing the personnel required. More vital points and
a larger area can be covered with at least some fire.
d. The method should be satisfactory for antimechanized
firing.
■ 23. Disadvantages. — a. Such methods of fire control are not
practical except for cannon type automatic weapons or
multiple mounts. Normally, it requires two gun pointers.
b. Too many estimations are required for lead control, and
10
ANTIAIRCRAFT AUTOMATIC WEAPONS 23-26
the course and speed lead computers ; and adjustments must
be made in terms of two or more elements of data.
c. Accurate and steady gun pointing Is difficult due to vibra-
tion of the mount, smoke, and flash of firing.
d. Observation of the tracer stream is difficult from a
position on the gun carriage. The adjuster is also bothered
by vibration, smoke, and flash of firing.
e. The use of sights limits such a method of fire control
to daylight or where targets are illuminated at night.
■ 24. Summary. — a. On carriage sight control does not offer
the flexibility of gun pointer control but is more accurate.
b. Gun pointers and adjusters on the gun carriage are
badly handicapped by vibration, flash, and smoke of a con-
tinuously fired automatic gun.
c. The method depends to a great extent on estimations
which can seldom be accurate.
d. Reports from the present war indicate that it is not
entirely satisfactory.
Section V
OFF CARRIAGE SIGHT CONTROL
■ 25. General. — This method of fire control is similar to on
carriage sight control except that the control, either by lead
estimations or by lead computer, is located at some distance
from the gun. This requires a data transmission system to
transmit leads to the sights on the gun.
■ 26. Central Tracer Control. — The fire control system for
a platoon of Browning machine guns, caliber .50, M2, water-
cooled, mounted on antiaircraft machine-gun mounts, caliber
.50, M2, or a platoon of two 37-mm antiaircraft guns M1A2
on carriages M3 is called the automatic gun, antiaircraft,
control equipment set Ml, or the central tracer control. It
consists of movable sights on the guns that can be set to
desired leads. These leads are set on a centrally located
control box and are transmitted to the sights mechanically by
a system of flexible cables. This cable is a simple and trouble-
free method of transmission for distances up to 100 feet. In-
itial leads are estimated by the adjusters located at the con-
11
26-30
COAST ARTILLERY FIELD MANUAL
trol box, and adjustment is continuous, based on observation
of the tracer stream. Lateral and vertical leads are set
independently.
■ 27. Remote Control. — Observation of the tracer stream is
greatly facilitated, especially at the longer ranges, if the
lateral and vertical adjusters are considerably separated and
placed in a more suitable position to observe lateral or ver-
tical deviations. To use such a system would require a more
flexible transmission system than the present mechanical
system. Electrical transmission has been tried with excel-
lent results, but the ballistic and gunnery limitations of anti-
aircraft automatic weapons now make it appear that such a
method of fire control would not be entirely justified.
H 28. Oriented Charts. — A form of lead computer which con-
sists of curves of computed leads has been experimented with
in connection with the central tracer control equipment.
This is similar to the course and speed lead computer in that
all elements of the target's course and speed must be esti-
mated in order to select the proper lead curve to follow. Ad-
justment must be made by jumping from one curve to an-
other, as deviations of the tracer stream are observed.
H 29. Lead Computer. — Lead computers similar to those de-
signed for use on the gun carriage will -give more accurate
results when taken off the gun and placed nearby. These
compute the required leads and transmit them to the gun
sights through the control box. The control box of the cen-
tral tracer control equipment is made to receive such data,
combine it with adjustments, and transmit the corrected lead
to the gun sights. Such computers have been tried but so far
have never given consistent results. Here, as in so many other
methods of fire control, there are too many estimations to be
made and too many possibilities of errors in transmission
and gun pointing to take full advantage of the accuracy of
a lead computer.
H 30. Advantages. — a. The off carriage method of Are control
allows the firing of two or more guns together as a fire unit,
thereby increasing the volume of fire and improving observa-
tion of fire.
12
ANTIAIRCRAFT AUTOMATIC WEAPONS
30-33
b. Such a method gives the best observation of the tracer
stream, therefore the best opportunity to adjust fire con-
tinuously.
c. Except in distant remote control, the transmission sys-
tem is simple, trouble-free, and requires no electricity for
operation.
d. Accuracy of the fire unit is greatly increased.
■ 31. Disadvantages. — a. Such a method of Are control re-
quires additional equipment and personnel.
b. It requires bore sighting and synchronizing to bring all
guns of the fire unit to fire together.
c. It does not eliminate the errors of gun pointing.
d. Flexibility of the fire unit is greatly decreased.
e. Consistent hitting on each target has not been obtained,
while a high percentage of hits has been obtained on a series
of targets.
■ 32. Summary. — a. Central tracer control has proved much
more effective than either gun pointer control or on carriage
sight control.
b. The inherent errors of gun pointing will not allow full
advantage to be taken of lead computers or of continuous
observation and adjustment.
c. Such a system, while gaining somewhat in accuracy, loses
considerable in flexibility. It requires more materiel and per-
sonnel as well as more time to set up and go into action.
Section VI
DIRECTOR CONTROL
B 33. General. — It is an acknowledged fact that a director
can track the present position of a target much more accu-
rately than can be done with sights on the gun. To take
advantage of this accuracy, the gun must be remotely con-
trolled from the director. The final degree of accuracy of this
method of fire control can therefore be separated into the
accuracy of the gun and ammunition and the accuracy of the
computed leads. The ballistic and gunnery factors of anti-
aircraft automatic weapons limit the accuracy of the gun to
short ranges. Thus the director, in addition to being rugged,
473316° — 42 2
13
33-36
COAST ARTILLERY FIELD MANUAL
simple, and rapid of operation, should compute leads to an
accuracy within the limitations of accuracy of fire. Within
these limitations the director can be of the approximate angu-
lar travel type or of an exact angular travel or linear speed
type.
■ 34. Approximate Director. — a. An approximate director
based on the angular travel principle is more feasible than
any other type. It requires only the measurement of both
horizontal and vertical angular travel and their multiplica-
tion by a time of flight to give approximate leads. For short
times of flight these leads would be sufficiently accurate. The
errors would be absorbed by the size of the target. The prin-
cipal requirements are smooth rates and accurate tracking.
i>. The present standard director is the director M5, which
is based on the angular travel principle. This director is
used with the 40-mm antiaircraft gun on the carriage M2
and the 37-mm antiaircraft gun on the carriage M3A1. The
director tracks the target in present position, computes the
leads and superelevation, and transmits future azimuth and
future quadrant elevation to the gun. The director M6 is
identical with the director M5 except that it is designed to
be employed with British equipment. (See FM 4-113.)
■ 35. Exact Director. — The British Vickers and the M4 are
such directors. It is possible that this type could be built
to compute leads with sufficient rapidity for use with anti-
aircraft automatic weapons. However, such a director would
not be simple or rugged. It is also doubtful if such a degree
of accuracy is required by small caliber guns, due to their
inherent ballistic limitations.
■ 36. Advantages. — a. More accurate tracking can be accom-
plished with a director.
b. More accurate leads can be computed.
c. Control and adjustment of fire can be in terms of one
element, either range or time of flight.
d. Such a system will give a better chance of obtaining
a hit on each target.
e. Such a system should give better results at longer
ranges than any other system.
14
ANTIAIRCRAFT AUTOMATIC WEAPONS
37-38
■ 37. Disadvantages. — a. The disadvantages of director con-
trol are the loss of time in getting on the target and obtaining
smooth rates.
b. Additional equipment and personnel are required, espe-
cially electrical equipment with its possible failure under
field conditions.
c. Accurate orientation and trial shots are required.
d. Such a method usually cannot make use of the full rate
of fire of automatic weapons.
■ 38. Summary. — The many variations in the antiaircraft
automatic weapons problem practically prevent the use of
one method of fire control that will give the best results under
all conditions. Some form of tracer observation is the only
method that will give sufficient speed and continuous adjust-
ment. Individual tracer control must always be considered
an available emergency method of fire control, and all fire
units must be trained to use it. Regardless of the equipment
in use and the method of fire control, a complete knowledge
of the fire control problem, leads, their characteristics for
type courses, and the variation of the several elements of
these courses should be acquired by all antiaircraft automatic
weapons personnel.
15
39-40
COAST ARTILLERY FIELD MANUAL
CHAPTER 2
DISPERSION AND HIT EXPECTANCY
Section I. Dispersion
n. Hit expectancy.
Paragraphs
39-14
45-47
Section I
DISPERSION
■ 39. General. — a. Standard methods of fire control for
antiaircraft automatic weapons depend upon the observation
of tracer bullets for the adjustment of fire. To assist in ob-
serving these tracers, and to insure a reasonable percentage
of hits when fire is adjusted, the cone of fire which they
form must be as small as possible. This requirement is par-
ticularly important at the longer ranges.
b. Spreading of the cone of fire is caused by dispersion.
Many factors enter into dispersion. These factors are erratic
gun pointing, vibration of the gun and mount, variations in
muzzle velocity between shots from the same gun and be-
tween guns, and poor bore sighting and synchronization of
the fire-control system. Most of these factors can be elim-
inated or their effect greatly reduced by careful training and
proper care and use of equipment.
■ 40. Gun Pointing. — a. Gun pointing is the basic factor in
the reduction of dispersion when firing using forward area
sights or individual tracer control. If the gun pointing is
erratic, all other efforts to reduce dispersion will be of little
or no value.
b. Gun pointing is particularly important in the case of
machine guns since one gunner points both laterally and ver-
tically with a free, mounted gun. The following steps must
be taken to insure smooth tracking by machine gunners:
(1) Machine gunners are selected whose eyes are not sensi-
tive to smoke, atmospheric conditions, flash, and glare. They
must have the strength to manipulate readily the gun and
16
ANTIAIRCRAFT AUTOMATIC WEAPONS
40-41
mount and should be mentally and physically well coor-
dinated.
(2) The back rests and the distance of the gun trun-
nions above the ground should conform to the stature of the
gunners. The gunners should also be provided with a firm
and level footing.
(3) The gunners should receive training in the tracking
of high speed aerial targets to accustom their muscles to
function smoothly and instinctively during rapid movements
in direction and elevation.
(4) The gunners should receive training in firing on high
speed aerial targets to accustom them to the shock, smoke,
and flash of firing and to the vibration of the mounts.
c. Gun pointing for the 37-mm gun, while not quite as im-
portant as in the case of machine guns, is still vital to the
problem of dispersion. Gun pointers move the gun in azi-
muth and elevation by means of handwheels. The following
steps must be taken to insure smooth tracking by the gun
pointers:
(1) Gun pointers are selected whose eyes are not sensi-
tive to smoke, atmospheric conditions, flash, and glare. They
should be mentally and physically well coordinated.
(2) They should receive training in the tracking of higU
speed aerial targets to accustom them to the operation of
the handwheels to accomplish rapid movements in direction
and elevation.
(3) They should receive training in firing on high speed
aerial targets to accustom them to the shock, smoke, and flash
of firing and to the vibration of the carriages.
(4) The above remarks will also apply to the 40-mm gun
when using forward area sights.
■ 41. Vibration of Mount or Carriage. — a. The high rates
of fire of caliber .50 machine guns and 37-mm and 40-mm
guns causes the mount or carriage to vibrate continually
while the gun is being fired. This vibration makes accu-
rate gun pointing difficult.
b. (1) The vibration of the antiaircraft machine gun mount
can be reduced appreciably by adjusting the rate of fire of
the gun by means of the oil buffer as described in FM. 4-135.
17
41-42
COAST ARTILLERY FIELD MANUAL
Each individual gun will be found to have its own cyclic
rate at which vibration is least. This rate should be deter-
mined and then maintained.
(2) On the M2 mount a recoil mechanism is provided
to reduce the vibration of the mount. Required adjustments
to this mechanism are made as prescribed in FM 4-135.
c. The carriages for the 37-mm and 40-mm gun are much
steadier than the machine gun mount. The only method
of reducing vibration is to keep all moving parts in good
operating condition and the length of recoil properly adjusted.
■ 42. Variation in Time op Flight. — a. General. — When fir-
ing at fixed or slowly moving targets, moderate variations in
time of flight normally have only a minor effect on the fall
of the shots. However, as the target speed is increased, the
resulting dispersion becomes more serious and causes the
cross-section of the cone of fire to change from a circle to
an ellipse with the longer axis in the direction of flight of
the target. This can best be illustrated by a problem. Con-
sider a target moving at right angles to the line of fire at
150 yards per second. Assume that two bullets were fired
at this target at the same instant and that one of them
took 0.10 second longer to reach the target than the other.
(Such an assumption is reasonable. A difference in time of
flight of 0.10 second is caused at midrange (1,000 yards) by
a variation in muzzle velocity of 170 feet per second.) During
this 0.10 second the target will have moved 15 yards. Assum-
ing that these two bullets would have struck the same vertical
line in a stationary target, they will make holes 15 yards
apart in the target traveling at 150 yards per second. On
most automatic weapon targets, both shots could not have
been hits. When a series of shots is fired at normal rates,
this dispersion is apparent to the adjusters and spotters,
causing a widening of the cone of Are and resulting in poor
observation and adjustment of Are.
6. Variations from round to round. — (1) Variations in time
of flight from round to round of a particular type and lot of
ammunition are caused principally by slight differences in the
rounds, which cause variations in the developed muzzle veloc-
ity. These differences may be of considerable magnitude.
18
ANTIAIRCRAFT AUTOMATIC WEAPONS
42
Tests of the velocities of 10 shots fired consecutively from a
single caliber .50 machine gun barrel have shown variations
of more than 100 feet per second.
(2) Small differences in the time of flight of ball and tracer
ammunition also exist at most ranges. Complete data on
these differences are not available at this time. Present prac-
tice is to disregard the differences in these two types of ammu-
nition. This problem applies only to machine guns, since all
37-mm or 40-mm antiaircraft ammunition is tracer ammuni-
tion.
(3) Round to round variations in muzzle velocity, both
within types and between ball and tracer, are a characteristic
of the ammunition and cannot be corrected for by the using
personnel.
c. Variations among guns. — (1) Differences in time of flight
among guns are caused chiefly by differences in the muzzle
velocities developed by the individual barrels of those guns.
For a particular barrel and ammunition the muzzle velocity
depends mainly upon the amount that the bore has been
eroded, particularly that portion at the breech end of the
barrel. Due to the high rate of fire of antiaircraft automatic
weapons, the barrels erode rapidly. For example, available
data indicate that, under average conditions of firing, the
barrel of a caliber .50 M2 machine gun will be eroded suffi-
ciently to cause a loss of approximately 200 feet per second
in muzzle velocity by the time that 3,000 to 3,500 rounds have
been fired. At the maximum rate of fire (600 rounds per
minute) this represents only 5 to 6 minutes of continuous fire.
Similarly, erosion in the barrel of a caliber .30 machine gun
causes a loss of about 160 feet per second in muzzle velocity by
the time 5,000 rounds have been fired. This represents 9 to 11
minutes of continuous fire. Data on erosion of the 37-mm
guns are limited, but loss in muzzle velocity appears to be
negligible during the first 1,000 rounds, although after about
1,200 rounds have been fired loss in muzzle velocity increases
rapidly.
(2) (a) The best method for determining the loss of
muzzle velocity of machine-gun barrels is to gage the advance
of the forcing cone and the wear of lands at the breech.
Breech bore gages have been developed for both caliber .30
19
42
COAST ARTILLERY FIELD MANUAL
and caliber .50 machine guns but normally are not Issued to
antiaircraft artillery units. However, bullet seating gives
a fair approximation of this gaging and therefore of the
muzzle velocity to be expected.
(b) A simple gage for determining bullet seating may be
made by fastening a stiff wire or rod to the base of a bullet
of the proper caliber. Insert the bullet in the breech of a
new barrel and scribe a mark on the rod or wire flush with
the face of the breech. Mark this point 1.9 inches for the
caliber .30 gage and 3.0 inches for the caliber .50 gage. With
this mark as a starting point, lay off on the rod or wire a
scale graduated in tenths of an inch, continuing the scale
outward 1.5 inches (caliber .30) or 4.0 inches (caliber .50)
from the mark. Each inch line should be marked to show
the number of inches from the rear face of the bullet to that
line. The wear of a barrel is then determined by dropping
the gage into the breech end of the bore and reading the
value on the scale at the point flush with the rear end of the
barrel.
(c) Where no gage (manufactured or improvised) is avail-
able, a loose bullet may be carefully dropped, point first, into
the breech end of the barrel and the distance from the rear
face of the bullet to the rear face of the barrel then measured
while the barrel is held vertically with the breech up. The
bullet should always be dropped the minimum distance pos-
sible, and care should be taken to avoid pressing on the bullet
when measuring the bullet seating.
(d) Having determined the bullet seating of a barrel, the
chart in figure 1 is entered to obtain the variation in muzzle
velocity which may be expected. For example, a reading
of 5.5 inches' bullet seating for a 45-inch caliber .50 barrel
indicates a muzzle velocity of about 90 foot/seconds below
firing table MV and of about 190 foot/seconds below that of
a new barrel.' Similarly a reading of 2.5 inches' bullet seating
for a caliber .30 barrel indicates a muzzle velocity of about
50 foot/seconds below firing table MV and of about 150 foot/
seconds below that of a new barrel.
(e) So far as the question of dispersion is concerned, as
long as all barrels of a fire unit show approximately the
same amount of wear, variation in muzzle velocity from stand-
20
ANTIAIRCRAFT AUTOMATIC WEAPONS
42
01
z
21
42-43
COAST ARTILLERY FIELD MANUAL
ard will have little effect as the guns will still shoot together.-
(See eh. 5 for the effect on computed leads.) This desirable
condition can be maintained by frequently checking bullet
seating and matching the barrels in sets having approxi-
mately the same bullet seating. An examination of the
curves in figure 1 shows that to keep the muzzle velocities of
the different barrels within about 50 feet per second of each
other, the values of bullet seating should be within 1 inch
of each other for caliber .50 machine guns and 0.5 inch of
each other for caliber .30 machine guns.
(3) In the case of the 37-mm antiaircraft gun, no tested
method of determining tube (barrel) erosion employable by
using personnel has been developed. Therefore an attempt
should be made, when practicable, to fire the guns so that
the total number of rounds fired will be approximately the
same for both guns of the fire unit. This should give ap-
proximately uniform wear for both guns since the rate of fire
is not as variable as, and is much lower than, that of machine
guns.
M 43. Spreading the Guns. — a. When used in connection with
antiaircraft automatic weapons, the term "spreading the
;guns" means the adjusting of the sighting systems of fire
unit so that when certain leads are set on the control box lead
dials, the corresponding leads set on the gun sights will vary
.slightly from gun to gun. For example, in a machine gun
platoon with the lateral lead dial of the control box set at
normal (see par. 26) , the lateral leads for guns Nos. 2 and 3
might be 0; that for gun No. 1, plus 2; and that for gun No. 4,
minus 2. Similar spreading vertically can be accomplished.
b. The purpose of spreading the guns is to enlarge the cone
of fire so as to increase the volume of the space in which hits
can be expected.
c. There are three important reasons why spreading the
guns is unsound.
(1) Effective fire from automatic weapons can be ob-
tained consistently only when the maximum possible volume
■of fire is placed on the target. Even under ideal conditions,
the dispersion of automatic weapons fire at moving targets
is such as to permit only a small percentage of hits on the
22
ANTIAIRCRAFT AUTOMATIC WEAPONS
43-44
target. Spreading the guns will increase this dispersion still
further, resulting in even fewer hits.
(2) The enlargement of the cone of fire will increase the
difficulty of observing and adjusting fire. This will normally
result in an additional reduction in the percentage of hits
obtained.
(3) Although spreading of the guns can usually be accom-
plished during target practice, it cannot be successfully ac-
complished, so far as lateral leads are concerned, under
service conditions. The guns are intended for use in all-
around Are. Guns spread laterally at one point are corre-
spondingly converged if they are traversed 3,200 mils. There-
fore, the spreading of the guns is accomplished for only a
part of the field of fire.
■ 44. Synchronization of Fire-Control System. — a. The
synchronization of the fire-control system (central control
only) is the adjustment necessary to insure that the desired
lateral and vertical leads, when set on the control box, will
be set on each gun. This synchronization must be performed
each time the materiel is set up in firing position. When the
materiel is in position for some time, the synchronization is
performed daily, or more often if necessary.
b. The first step in synchronization of the system is the
adjustment of the control box. To accomplish this, the
control box having been set up, turn the adjusting knobs
until the lead adjusting indexes read zero. When this has
been done, see that the lead indexes are at normal (300
for machine gun units, 500 for 37-mm gun units) . If they
are not, remove the covers from the input couplings and
rotate the couplings until the lead indexes are properly set.
Then replace the coupling covers, checking to see that the
lead adjusting indexes and lead indexes have not been moved.
After the adjustment is completed, the coupling covers must
not be removed unless specifically authorized. Set the trans-
mitted lead indexes at normal by turning the lead hand-
wheels.
c. The second step in the synchronization is the hooking
up of the flexible shafts. The control box having been ad-
justed as described in b above and the guns bore sighted as
23
44
COAST ARTILLERY FIELD MANUAL
described in FM 4-135 (machine guns) or PM 4-140 (37-mm
guns) , hook up the required number of flexible shafts from
the output couplings of the control box to the correspond-
ing couplings (lateral or vertical) of the sighting systems
(see b above) .
d. When the system has been connected, set various leads
on the lead dials of the control box and check them against
the readings of the counters on the sighting system of the
guns. At least one reading on each side of normal should be
checked for both the lateral and vertical sight mechanisms.
e. (1) If the readings checked as described in d above
agree in each case, the synchronization of the system is com-
pleted.
(2) If the readings of one of the counters are con-
sistently in error by a few mils plus or minus, the system
must be resynchronized. To do this, return the correspond-
ing lead index (lateral or vertical) of the control box to its
normal reading and remove the flexible shaft from the cou-
pling of the part of the sight mechanism to which the counter
is attached. Recheck the bore sighting, making the necessary
adjustments as described in PM 4-135 or FM 4-140. When
the system is again connected recheck the synchronization
as described in d above.
(3) If, after the system is connected, one of the counters
fails to turn when the corresponding lead handwheel is op-
erated, some part to the sight mechanism is probably broken
or damaged. In this case it will usually be found that the
flexible shaft is broken. Return all parts of the system to
normal, replace the flexible shaft with a new shaft, and
recheck the synchronization as described in d above.
/. (1) The vertical lead flexible shafts may be broken if
an attempt is made to turn the vertical lead handwheel on
the control box so as to set a positive vertical lead on the
gun sights when the 37-mm gun is depressed below about 15°.
Therefore, before the cables are connected to a gun sighting
system, be sure that the gun is elevated above 15°. There-
after, keep the guns elevated above 15" whenever the system
is connected except when they are depressed for a specific
purpose, in which case care must be taken to insure that the
24
ANTIAIRCRAFT AUTOMATIC WEAPONS
44-45
control box is not operated. This precaution is necessary
because when the gun is depressed to zero, the sights can be
depressed only about 50 additional mils before they hit the
sight brackets. This precaution does not apply to the M2
machine-gun mount.
(2) (a) Even though the 37-mm guns are partly elevated, if
the gun sighting systems were to be connected to the- control
box when the vertical counter on a sighting system has a
reading which differs considerably from that of the vertical
lead index of the control box, an extreme vertical lead may
later be set on the sighting system resulting in the same diffi-
culty as described in (1) above.
(b) Under similar conditions, the front sight of the M2
machine-gun mount may be damaged at any angle of ele-
vation.
(c) Therefore, always insure that the lead counters or
indexes on the sighting systems and the indexes on the con-
trol box are at the same readings before hooking up the
flexible shafts.
(3) Forcing of lead handwheels may cause damage to the
control set or to the sight mechanism. Pointer matchers
must be cautioned never to put excessive pressure on the
lead handwheels. If a handwheel is hard to turn, they must
stop and determine the cause. Possible causes are sights
or the transmitted lead indexes coming up against a stop,
accumulation of dirt blocking the movement of the sight,
kinked flexible shaft, or burs on gears of the control box.
Section n
HIT EXPECTANCY
■ 45. Test of Dispersion of Free Mounted Gun. — a. To
determine the minimum dispersion (maximum percentage
of hits) to be expected with a free mounted automatic
weapon, tests have been conducted with a caliber .50 machine
gun, mounted on an M2 mount, firing on a stationary target.
The hits obtained on the target and on the B9 silhouette may
be summarized as follows:
25
45-47
COAST ARTILLERY FIELD MANUAL
Range in yards
Percent holes
in target
Percent hits
on B9 sil-
houette
800..
1,300.
1,800.
98
70
50
43.8
20.0
10.6
b. The percentage of holes in the various parts of the
target were not in accordance with the distribution which
could be expected from the laws of probability. This was
probably due to the constant shifting in the point of aim that
a free mounted gun will always produce when firing. Ex-
perience has shown that an experienced machine gunner
firing a caliber .50 machine gun can barely keep a high speed
target in view in ring sight that subtends 10 mils, which in-
dicates that the total dispersion of gun pointing is about 10
mils. This minimum error represents 3 yards at 300 yards'
range, 6 yards at 600 yards' range, and 18 yards at 1,800
yards' range.
c. The number of rounds per unit of area within the cone
of Are at 1,800 yards is % of that at 600 yards and %e of that
at 300 yards. This clearly indicates that the percentage of
hits should decrease markedly' as the range is increased. This
assumption is supported by the test described in a above.
■ 46. Relative Frequency of Hitting Laterally and Verti-
cally. — Accurate data are lacking on whether most shots
from automatic weapons miss the target laterally or verti-
cally. Such factors as variations in the rate of change of
leads, reversal of rates from increasing to decreasing (or from
decreasing to increasing) , relative ability of the lateral and
vertical adjusters and pointer matchers at the control box,
the speed of the target, the shape of the cone of fire, and the
shape of the vulnerable area of the target complicate the
problem. A reliable answer to the question cannot be given
until the results of a number of complete dispersion tests
against fast-moving targets are available.
■ 47. Relation of Remaining Velocity to Time of Plight. —
Figure 2 shows the rapidity with which a 37-mm projectile
26
ANTIAIRCRAFT AUTOMATIC WEAPONS
47
loses velocity. At 3 seconds' time of flight the velocity of a
37-mm projectile has dropped to 1,300 foot-seconds from an
initial muzzle velocity of 2,500 foot-seconds. At 5 seconds it
has dropped to approximately 1,050 foot-seconds. Figure 2
illustrates that, with a given muzzle velocity, time of flight
is not only a function of range but also a function of the
remaining velocity of the projectile. Thus, it can be under-
stood that the more effective fire must be restricted to the
very short times of flight.
500 TOOO 1500 2000 2500 3000 3500 4000
SLANT RANGE IN YARDS
( • 600 [HI
Figure 2. — Relation of remaining velocity to time of flight.
27
48
COAST ARTILLERY FIELD MANUAL
CHAPTER 3
CALCULATION OF LEADS
Paragraphs
Section I. Elements ol data
II. Firing tables
III. Methods of lead calculation
48-53
54-57
58-64
Section I
ELEMENTS OF DATA
■ 48. General. — a. An analysis of gunnery for antiaircraft
automatic weapons includes careful study of leads and their
characteristics for representative type target courses and
speeds. This is true whether forward area sights, computing
sights, tracer control, oriented charts for dive targets, or di-
rector control is the means of fire control.
b. If the fire of antiaircraft automatic weapons is to be
successfully adjusted by observation of tracers, the tracer
stream must be kept at least in the immediate vicinity of the
target. To accomplish this, approximately correct leads must
be continuously applied to the guns. Since no satisfactory
lead computer is at present available (except in the case of
director-controlled automatic weapons) for determining the
leads which should be applied to the guns, dependence must
be placed on the estimation of leads both for determining
initial leads and for anticipating the rates of change in the
required leads throughout the course of the target. These
changes in the leads are at rates which vary constantly dur-
ing the course. Leads must be calculated for use in con-
structing lead charts in order to enable personnel responsible
for the application of these leads to become familiar with the
approximate leads required for various types of target
courses. .
c. Only target courses which are rectilinear and are flown
at constant speeds can be calculated readily. These courses
are divided, with respect to the target's course and the gun
position, into two general types, coming courses and crossing
courses. Each of these types of courses is further subdivided
into constant altitude courses and diving courses. The
28
ANTIAIRCRAFT AUTOMATIC WEAPONS
48-49
method of calculating leads for courses In each of these
classifications is discussed separately in section III.
d. In this text all calculations of leads for crossing courses
are based on left to right courses, and all lateral leads are
right leads. The data for right to left courses are calculated
and plotted in the same manner, in which case all lateral
leads would be left leads.
■ 49. Coming-Constant Altitude Course. — A typical set-up
in the vertical plane for a coming-constant altitude course
is given in figure 3. This figure shows the basic elements of
data for such a course and should be thoroughly understood
before proceeding with the computation of leads. (For the
prescribed symbols used with antiaircraft automatic weapons
see appendix I.)
COURSE OF
TARGET
HORIZONTAL
PROJECTION
OF COURSE
OF TARGET
to Angular height of target at present position (T ) .
eji Angular height of target at future position (T v ) .
Jl Altitude of target.
^ s Superelevation under firing table conditions.
Jj Horizontal range to target at present position (T ).
B Horizontal range to target at future position (T v ).
S g Ground speed of target.
S g X t P Linear horizontal travel of target during time of flight.
— ... ... _ —
1 m
T
ox
Midpoint — position of target where e=90°.
Present position of target (instant of firing) .
Predicted position of target (future position) .
Time of flight of projectile to future position of target (T v )
Principal vertical lead' angle.
Vertical lead.
.figure 3. — Elements of data for coming-constant altitude course
(vertical plane containing gun, T , T v , and T m ) .
473316° — 42 3 29
49-51
COAST ARTILLERY FIELD MANUAL
■ 50. Coming-Diving Course. — A typical set-up in the ver-
tical plane for a coming-diving course is given in figure 4.
The basic elements are the same as those for a coming-
constant altitude course except for the following:
Add y Angle of dive.
For H substitute —
H m Altitude of target at midpoint (T m ).
H Altitude of target at present position (T ).
H„ Altitude of target at future position (T p ).
Figure 4. — Elements of data for coming-diving course (vertical
• plane containing gun, T , T p , and T m ).
. 9 51. Crossing-Constant Altitude Course. — A typical set-up
in spaqe for a crossing-constant altitude course, showing the
basic elements of data, is given in figure 5.
■ 52. Crossing-Diving Course. — A typical set-up in space for
a crossing- diving course is given in figure 6. The basic ele-
ments are the same as those for a crossing-constant altitude
course, with the following exceptions:
7 . Angle of dive, measured from the horizontal.
La Horizontal distance from present position of a dive
target to the objective.
Lm Horizontal distance from the midpoint to the objective
of a dive target.
For H substitute:
Hm Altitude of target at midpoint (2V) .
30
ANTIAIRCRAFT AUTOMATIC WEAPONS
51-52
COURSE OF
TARGET
-Sgtp-
.Tp
oo Angle of approach at present position of target (T ) .
ao Angle of approach at future position of target (T v ) .
D m f n Minimum slant range. (For constant altitude courses
D m Slant range to midpoint of course (T m ).
D Slant range to target at present position (T ).
D p Slant range to target at future position (T p ).
e Angular height of target at present position (T ).
e Angular height of target at future position (T v ).
H Altitude of target.
L a Distance from midpoint of course (T m ) to present position
(T ) in horizontal plane.
£„ Distance from midpoint of course (T m ) to future position
(T v ) in horizontal plane.
d, s Superelevation under firing table conditions.
R m Minimum horizontal range or horizontal range to target
at midpoint of course (T m ).
R Horizontal range to target at present position (T ).
B v Horizontal range to target at future position (T v ) .
S g Ground speed of target.
S g X t p Linear horizontal travel of target during time of flight.
T m Midpoint — position of target where o =90°.
T Present position of target (instant of firing) .
T Predicted position of target (future position).
t v Time of flight to future position of target (T v ) .
Figure 5. — Elements of data for a crossing-constant altitude course.
31
52-53
COAST ARTILLERY FIELD MANUAL
Ho Altitude of target at present position (To).
Hp Altitude of target at future position (T P ).
■ 53. Definitions and Symbols. — a. Angle of approach
(o). — (1) Angle of approach is the acute horizontal angle
between the plane of position and the vertical plane contain-
ing the course of the target (never greater than 90°).
(2) The symbol for the angle of approach at the present
position of the target is «o.
Figure 6. — Elements of data for crossing-diving course.
(3) The symbol for the angle of approach at the future
position of the target is a v .
(4) On a coming course, a is always zero.
(5) The gun-objective-target angle is the horizontal angle
between the vertical planes containing the target's course
and the gun-objective line.
b. Target position (T) . — (1) T designates the position of
the target at some particular instant.
(2) The position of the target at the instant of firing is
called the present position of the target and is represented
by the symbol To.
(3) The position of the target at which it is predicted the
projectile will meet the target is called the future position
of the target and is represented by the symbol T p .
HORIZONTAL PROJECTION
OF COURSE OF TARGET
OBJECTIVE
32
ANTIAIRCRAFT AUTOMATIC WEAPONS
53
(4) The position of the target when the angle of ap-
proach equals 90° is called the midpoint of the course and
is represented by the symbol Tm. On coming courses, Tm
is directly over the gun, that is, « equals 90°.
c. Slant range. — (1) Slant range is the distance from the
gun to the target measured along the line of position.
(2) The slant ranges to each of the positions of the target,
To, T P and Tm, are represented by the symbols Do, Dp, and Dm,
respectively.
(3) Dmin is the symbol for the minimum slant range to
the target. In constant altitude courses the minimum slant
range is at the midpoint of the course, and Dmin=D m .
d. Horizontal range (R). — (1) Horizontal range is the dis-
tance from the gun to the projection of the target position
in the horizontal plane.
(2) The horizontal ranges to each of the positions of the
target, To, Tp, and Tm, are represented by the symbols Ro, R P ,
and Rm, respectively.
(3) On coming courses Rm is equal to zero.
e. Angular height (e). — (1) Angular height is the vertical
angle measured from the horizontal to the line of position.
(2) The angular heights to To and Tp are represented by
the symbols eo and «p, respectively.
/. Altitude (H). — (1) Altitude is the vertical distance to
the target from the horizontal plane through the gun.
(2) The altitudes to each of the positions of the target,
To, T P , and Tm are represented by the symbols H , Hp, and
Hm, respectively.
(3) For constant altitude courses Hm=H =H P , and the
altitude is represented by the symbol H.
(4) For diving courses —
Ho=H m ± (L tan7) (crossing)
or Ho=H m ±(Ro tatiy) (coming).
H v =Hm± (L p tan7> (crossing)
or Hp— H m ±(Rp tany) (coming).
g. Horizontal distance along course (L) . — (1) The hori-
zontal distance from the midpoint (Tm) to the present posi-
tion of the target (To) is represented by the symbol Lo.
33
53
COAST ARTILLERY FIELD MANUAL
(2) The horizontal distance from the midpoint (T m ) to
the future position of the target (T P ) is represented by the
symbol Lp.
(3) The horizontal distance from the midpoint (Tm) to
the objective of a dive target is represented by the symbol Lm.
(4) The horizontal distance from the present position of
a dive target (To) to the objective is represented by the
symbol La.
Note. — Values of L„ and Z.„ are considered plus when measured
In the direction of flight and minus when measured in the oppo-
site direction.
h. Superelevation (0 S ). — (1) Superelevation is that part
of the quadrant elevation which compensates for the curva-
ture of the trajectory. It is the amount that the axis of the
bore must be pointed above the line of position to the future
position of the target (T P ) in order that the trajectory will
pass through the target at that point. Values of supereleva-
tion are obtained from firing tables.
(2) Superelevation is always a plus value and is added,
algebraically to the principal vertical lead angle to obtain
the vertical lead.
i. Time of flight (t v ) . — Time of flight is the elapsed time
in seconds for the projectile to travel, from the gun to the
future position of the target (T P ). It is represented by the
symbol tp.
j. Ground speed (S g ) . — (1) The ground speed of the target
is the velocity of the target with respect to the ground. It
is measured by determining the rate of travel in the hori-
zontal plane of the projection of the target in that plane.
In calculation it is always expressed in yards per second.
Miles per hour divided by two represents yards per second
with sufficient accuracy for calculation. Ground speed is
represented by the symbol Sg.
(2) The symbol for speed of the target along its path
is S. It may be expressed in miles per hour or in yards per
second.
(3) For diving courses, S g —S cos y.
k. Lateral lead (Sl). — Lateral lead is the angle in the
slant plane of the lateral sight by which the gun must lead
the target to cause the projectile and target to meet. It is
34
ANTIAIRCRAFT AUTOMATIC WEAPONS
53-54
the algebraic sum of the principal lateral lead angle (Si and
any necessary pointing correction (82) . The pointing correc-
tion (S2) is not considered in the calculation of leads. How-
ever, this correction does exist but it is included and applied
by the adjuster. (This element of data is not shown in figs. 7
and 8.)
I. Vertical lead («,) . — Vertical lead is the angle by which
the gun must lead the target vertically in order that the
projectile will meet the target at the future position. It is
measured in the vertical plane containing the axis of the
bore of the gun and is the algebraic sum of the principal
vertical lead angle (01), the superelevation dps), and any nec-
essary pointing correction (0-2). The pointing correction
(0-2) is not considered in the calculation of leads. However,
this correction does exist but it is included and applied by
the adjuster.
m. Principal lateral or vertical lead angle (5i or 01). — (1)
The principal lateral (or vertical) lead angle is the lead
angle necessary to compensate for the travel of the target
during the time of flight of the projectile.
(2) The principal lateral lead angle is represented by the
symbol 81.
(3) The principal vertical lead angle is represented by the
symbol <n.
n. Angle of dive (7). — (1) Angle of dive is the vertical
angle between the course of the target and the horizontal.
(2) The projection of the angle of dive on the vertical
plane containing the gun and the future position of the
target (T v ) is represented by the symbol yv.
Section n
FIRING TABLES
■ 54. General. — a. Firing tables are used to determine time
of flight (t p ) and superelevation (tf> s ) for the future position
of the target in computing leads. A discussion of these tables
therefore properly belongs in a study of lead calculation.
b. In addition to their use in determining tp and <p s , firing
tables are employed to determine differential effects of varia-
35
54-55
COAST ARTILLERY FIELD MANUAL
tions from the standard conditions on which the firing tables
are based and other trajectory data.
c. (1) The standard conditions on which firing tables are
based are —
(a) Muzzle Velocity (MV) — as listed in the table.
(b) Wind — none.
(c) Air density at the battery — that for a temperature of
59° P., a barometric reading of 29.53 inches of mercury, and
air saturation of 78 percent (525.9 grains per cubic foot) .
(d) Air temperature at the battery — 59° P.
(e) Powder temperature — 70" P.
(/) A standard atmospheric structure aloft is assumed;
that is, atmospheric temperature and density vary with alti-
tude in a particular manner.
(2) Variations from these assumed conditions will affect
the behavior of the projectile. In firing tables for anti-
aircraft automatic weapons, these variations from standard
conditions are listed in terms of their effects on supereleva-
tion and time of flight, except in the caliber .30 tables, where
the effects are given in terms of range, altitude, and angular
height.
d. A list of the standard firing tables pertaining to a partic-
ular weapon will be found in the Standard Nomenclature
List published by the Ordnance Department.
■ 55. Contents of Firing Tables. — The present standard
firing tables are published in book form. The first section
(introduction) contains general information pertaining to
the gun and projectile, and a detailed explanation of the
tables and of the meteorological message. Subsequent parts
of the tables give the following data:
a. Trajectory data (horizontal range, altitude, angular
height, and superelevation) , using quadrant elevation and
time of flight as arguments.
b. Time of flight and superelevation, using horizontal range
and altitude (and, in addition, in firing tables for the 37-mm
or 40-mm guns, slant range and angular height) as argu-
ments.
c. (1) Differential effects on superelevation and time of
flight due to 100 f/s decrease in muzzle velocity, 10 percent
36
ANTIAIRCRAFT AUTOMATIC WEAPONS
55-56
decrease in density, and 10 mph rear wind, using horizontal
range and altitude as arguments.
(2) Differential effects on lateral lead due to 10 mph cross
wind, using horizontal range and altitude as arguments.
d. In each firing table, a trajectory chart is included. This
chart shows in- graphical form the relationship of altitude
and horizontal range, quadrant elevation, time of flight, and
angular height.
■ 56. Determination of Time of Flight and Supereleva-
tion. — a. Time of flight and superelevation under standard
firing table conditions are normally extracted from the firing
tables, using Rp and Hp (or H) as arguments. In the case of
tables for the 37-mm or 40-mm guns, Dp and e p may also be
used as arguments, the choice of arguments to be used being
dictated by convenience. For example, since time of flight
is virtually constant for a certain slant range, regardless of
angular height, tedious interpolation may often be eliminated
by using Dp and e p as arguments to extract tp. In either
case, however, values obtained should be the same.
6. (1) Having selected the proper table, the procedure is
to read under the correct value of altitude (or angular height)
and opposite the correct value of horizontal (or slant) range
the time of flight in seconds (or superelevation in mils) .
(2) Example: What are the superelevation and time of
flight under standard conditions for the points (H P =800,
Kp=1,000) and (e P =500, Dp=l,200) , when firing a 37-mm gun
M1A2, using fixed HE shell M54? (Use FT 37-AA-N-2.)
(a) Entering table lb, opposite 1,000 yards horizontal range
and under 800 yards altitude is found the time of flight, 1.95
seconds.
(6) Entering table Ic, opposite 1,000 yards horizontal
range and under 800 yards altitude is found the supereleva-
tion, +13.4 mils.
(c) Entering table Id, opposite 1,200 yards slant range
and under 500 mils angular height is found the time of flight,
1.79 seconds.
(d) Entering table Ie, opposite 1,200 yards slant range
and under 500 mils angular height is found the superelevation,
+13.8 mils.
37
56-57
COAST ARTILLERY FIELD MANUAL
Tabulation
Given
Tables used
( p (sec)
$i (mils)
H„=800__
.R„=1,000.
E P =500..
J>p=1,200.
lb and Io.
•Id and Ie.
1.95
1.79
+13.4
+13.8
■ 57. Corrections for Variations From Standard Condi-
tions. — a. Where it is desired to obtain superelevations and
times of flight corrected for nonstandard conditions, it is
necessary to add algebraically to the superelevation and time
of flight for standard conditions the corrections for the effects
of the variations from standard conditions as shown in the
firing tables.
b. Following is an example of the proper method to employ
in obtaining corrected superelevation and time of flight for
a particular point in space when firing a 37-mm gun M1A2,
using fixed HE shell M54, under nonstandard conditions.
Given: Determine data for the point R P = 1,800 yards, Hp—
600 yards. Assume nonstandard conditions:
Developed muzzle velocity 2,600 f/s.
Air density--. 95 percent.
Rear wind 30 mph.
Cross wind 30 mph (right to left).
The firing table to be used is FT 37-AA-N-2, which is based
on a muzzle velocity of 2,500 f/s. Note that the values given
in the differential effects tables are effects and not corrections.
Solution:
(1) Muzzle velocity. — (a) The developed muzzle velocity is
100 f/s greater than standard. Turn to table Ila in the firing
tables. This table is for the effect on superelevation of a
decrease in muzzle velocity of 100 f/s. To obtain the effect
of a 100 f/s increase in muzzle velocity, reverss the sign of
the effect.
38
ANTIAIRCRAFT AUTOMATIC WEAPONS
57
(b) Entering the table, opposite 1,800 yards horizontal
range and under 600 yards altitude, the value —2.5 mils is
obtained. Changing the sign as mentioned above, the effect
on superelevation of an increase of 100 f/s in muzzle velocity
at the point selected becomes +2.5 mils. Enter this value
in the tabulation below.
(c) In a similar manner enter table lib to obtain the effect
of the assumed muzzle velocity on time of flight. The value
(with sign changed as above) is +0.15 second. Enter this
value in the tabulation.
(2) Air density. — (a) Turning to tables nc and Hd, they
are found to show the effects for a decrease in air density
of 10 percent. The assumed air density is 95 percent or a
decrease from normal of 5 percent. Therefore, the effects
taken from tables lie and lid will be correct in sign but must
be divided by two to obtain the required value.
(b) Enter table lie. Opposite 1,800 yards horizontal range
and under 600 yards altitude is the value +1.5 mils. Divid-
ing this by two, the effect on superelevation of the assumed
air density is found to be +0.8 mil. Enter this value in the
tabulation.
(c) In a similar manner the value +0.07 second is ob-
tained from table lid as the effect on time of flight of the
variation in air density. Enter this value in the tabulation.
(3) Rear wind. — (a) Turning to tables He and Ilf, they
are found to show the effects for a rear wind of 10 mph. Since
the assumed rear wind is 30 mph the values found in the
tables must be multiplied by three to determine effects of a
rear wind of this velocity.
(b) Enter table He. Opposite 1,800 yards horizontal range
and under 600 yards altitude is found the value —0.7 mil,
which is the effect on superelevation of a rear wind of 10
mph. This value is multiplied by three and the product,
—2.1 mils, entered in the tabulation.
(c) In a similar manner the value +0.03 second is obtained
from table Ilf as the effect on time of flight of the variation
in rear wind. Enter this value in the tabulation.
39
57
COAST ARTILLERY FIELD MANUAL
Tabulation
Assumed condition
Tables used
Effects on
(mils) t P (seconds)
+100 f/s, MV
—5 percent density.
30 mph rear wind...
Total effects...
Ha, lib.
lie, lid.
He, IIf_.
+2.5
+0.8
-2.1
+1.2
<t>. (mils)
t p (seconds)
Total corrections for nonstandard conditions. . . _ _
+26.1
-1.2
+24.9
or +25
+3.28
-0.25
+3.03
(4) Correction for cross wind. — (a) In table Ilg the effect
of cross wind on the lateral lead is given directly in mils.
The table is made up for a cross wind of 10 mph. For a
cross wind of 30 mph the value taken from the table must be
multiplied by three to determine the effect of a cross wind
of this velocity.
(b) Entering the table opposite 1,800 yards horizontal
range and under 600 yards altitude, the effect on lateral
lead is found to be 7.8 mils (without sign) . Since the wind
is from right to left, the trajectory is moved to the left, the
effect is L 7.8 mils, and the correction is R 7.8 mils. If the
computed lead is in reference numbers such as appear on the
lead dials of the control box, the correction is added alge-
braically to it. In cases where leads are given as left or
right by the actual number of mils, the correction would be
subtracted from a left lead and added to a right lead.
c. (1) Under service conditions it will be impracticable to
determine corrections for nonstandard conditions for the
specific course to be fired on. However, if the lead values for
points on type courses have been computed previously, both
for standard conditions and selected nonstandard condi-
tions, and lead curves plotted to show the relationships of
40
ANTIAIRCRAFT AUTOMATIC WEAPONS 57-59
these leads, an estimate of the approximate average change
in leads required as the result of a specific nonstandard con-
dition can be made.
(2) Wind corrections normally are not practicable for a
crossing course as the wind components vary continuously
throughout the course at a rapid rate. Possible exceptions
are courses at the longer ranges, particularly those which
approximate coming courses.
Section III
METHODS OP LEAD CALCULATION
■ 58. General. — a. Antiaircraft automatic weapons pointed
by central control use sights to point the gun in elevation
and direction. The sight is mounted directly on the gun or
carriage and traverses and elevates with the gun. Appli-
cation of the required leads is accomplished by shifting the
line of sight (of the sight) from a line parallel to the axis
of the bore by an angular amount equal to the required leads.
The shifting of the line of sight is done by means of tangent
screws or by rotating the sighting elements.
b. Leads must be calculated for the future position of the
target (T P ) where tp and <t>s are applicable. Future posi-
tions are selected at convenient distances along the course
of the target (usually in even hundreds of yards to facilitate
use of the firing tables), and from them the corresponding
present positions as well as the leads are calculated.
■ 59. Definitions of Leads. — a. Positive lateral leads. — (1)
A positive (+) lateral lead is one where the gun points
ahead of the target.
(2) An increasing positive (+) lateral lead is one where
the gun continues to point farther ahead of the target with
each succeeding increment of time.
(3) A decreasing positive (+) lateral lead is one where
the gun (pointing ahead of the target) continues to point
closer to the target with each succeeding increment of time.
b. Negative lateral leads. — These are leads in which the
gun points behind the target. Naturally, they are never used
in the automatic weapons gunnery problem whether increas-
ing, decreasing, or static.
41
59-61
COAST ARTILLERY FIELD MANUAL
c. Positive vertical leads. — (1) A positive (+) vertical lead
is one where the gun points above the target.
(2) An increasing positive (+) vertical lead is one where
the gun continues to point farther above the target with
each succeeding increment of time. (It is rarely obtained
in automatic weapons fire.)
(3) A decreasing positive (+) vertical lead is one where
the gun (pointing above the target) continues to point closer
to the target with each succeeding increment of time.
d. Negative vertical leads. — (1) A negative (— ) vertical
lead is one where the gun points below the target.
(2) An increasing negative (— ) vertical lead is one where
the gun continues to point farther below the target with each
succeeding increment of time.
(3) A decreasing negative (— ) vertical lead is one where
the gun (pointing below the target) continues to point closer
to the target with each succeeding increment of time.
e. Zero vertical leads. — A zero vertical lead occurs when a
decreasing positive lead changes to an increasing negative
lead.
■ 60. Data Required for Calculation of Leads. — a. To cal-
culate leads for a course, the following basic data are
assumed:
(1) Minimum horizontal range or range to midpoint (R m ) .
(2) Altitude at midpoint (flm).
(3) Ground speed of target (.Sg).
(4) Various future positions of the target (T P ) along the
course are selected by assuming values of Lv or R v .
(5) Angle of dive (7) .
b. In addition, certain data are extracted from firing
tables :
(1) Time of flight to future position (t P ).
(2) Superelevation to future position (0 S ) .
■ 61. Coming-Constant Altitude Courses. — a. In the com-
putation for coming courses, there are no lateral leads, since
the angle of approach of the target is 0. Only the vertical
leads are computed.
b. Although the only true coming courses are those
where the target comes directly toward the gun position
42
ANTIAIRCRAFT AUTOMATIC WEAPONS
61
(iJ™=0) , all crossing courses with an R m less than 100 yards
are considered to be coming courses. The lateral leads are
small until the target is very close and then they change so
rapidly that even if a gun could follow the target, it would
be impossible to transmit the rapidly changing lead to the
sights. Also the vertical leads for these courses are prac-
FrGTTRE 7. — Vertical lead, coming-constant altitude course.
tically the same as for a true coming course of the same
altitude and speed.
c. Figure 7 represents the pictorial view of the approaching
leg of a coming- constant altitude course. The formula for
vertical lead for a true coming-constant altitude course is —
Referring to figure 7, it is obvious that the lead necessary
to cause the projectile to meet the target at T P is merely
the angular difference between eo and *p, added algebraically
to the superelevation. Note that the principal vertical lead
43
61
COAST ARTILLERY FIELD MANUAL
angle (*?— e , or <n) is always positive on the approaching
leg of a coming- constant altitude course, and is always
negative on the receding leg of such a course. Supereleva-
tion is always positive.
d. (1) To compute the leads for a type course, the altitude
and ground speed of the target are assumed, and various
future positions of the target are selected in terms of Rp.
The maximum value of Rp on either the approaching or
receding leg will depend on the maximum range of the
armament. Leads may be calculated at 100- to 400-yard
increments, depending upon the maximum range and desired
accuracy for plotting the lead curve. The approaching leg
and receding leg may be calculated on one form, using a large
increment for Rp, or a small increment may be used to com-
pute only the approaching or receding leg. The computation
for each selected future position then consists of determining
the following:
«p from Rp and H.
Ro from R v and Sgtp.
«o from Ro and H.
ah from e p> eo, and <ps.
Note. — If corresponding values of B„ on the approaching leg and
. on the receding leg are selected, the work required to determine
cp, t p , and S will be reduced.
(2) The above computations can be rapidly performed by
using the Ml (Crichlow) slide rule. Calculation Form No.
1 (/ below) is a convenient form for use when this slide
rule is employed.
e. To calculate the vertical lead:
(1) Enter the selected values of Rp on line 1 of the form.
(2) Extract from the proper firing tables the times of
flight and the superelevations for each selected future posi-
tion, using H and Rp as arguments. Enter the times of flight
(nearest hundredth of a second) and the superelevations
(nearest mil) on lines 3 and 8, respectively, of the form.
(3) Multiply each time of flight by the assumed ground
speed in yards per second and enter the results (to the nearest
yard) on line 4. It may be desired to perform the multipli-
44
ANTIAIRCRAFT AUTOMATIC WEAPONS
61
cation of Sg and t P on the Ml (Crichlow) slide rale. Set the
long arm (L) to the assumed Sg in yards per second on scale
E, and move the short arm (S) to the index of scale E.
Without changing the angle between the arms, shift (L) until
(S) is set to the first time of flight on scale E and read under
(L) the value of Sgtp on scale E. Still without changing the
angle between the arms, continue to set (S) to times of flight
and read values of Sgt P under (L) for each R P .
(4) Add to (approaching leg) or subtract from (receding
leg) line 1 the values in line 4 to obtain values of Ro. Enter
these values on line 5.
(5) Compute the values of e p for each selected future posi-
tion, using the slide rule. Set long arm (L) on the larger
value, R v or H, on scale E, and set the short arm (S) on the
smaller of the two' values, R P or H, on scale E. Without
changing the angle between the two arms, move (L) until
(S) is on the index of scale E, and read the value of under
(L) on scale C. Note that scale C has two sets of readings.
If if is less than R P , read the smaller angle. If H is greater
than Rp read the larger angle. Enter the values of e P on
line 2 of the form.
(6) Compute the value of e for each present position
corresponding to a selected future position, using the slide
rule. This is done as described in (5) above, except that
Ro is substituted for R P . Enter the values of *o on line 6.
(7) Subtract each value of « from the corresponding value
of e p to obtain values of n. Enter these values on line 7.
(8) Add lines 7 and 8 algebraically to obtain values of
n. Enter these values on line 9.
/. If it is desired to calculate the leads with an ordinary
slide rule or calculating machine, the form shown below
must be changed to show the functions of the angles. By
using the Crichlow slide rule the angle is found directly,
whereas on an ordinary slide rule or calculating machine the
trigonometric function of the angle is found. The angle
then will be found by referring to tables of natural trigono-
metric functions. Leads for coming courses can also be
measured graphically.
478316°— 42 4
45
61
COAST ARTILLERY FIELD MANUAL
6*3 «
o S co
§
H
M (1)
o o
+ 1
05
r
-H
II
■a
+
46
ANTIAIRCRAFT AUTOMATIC WEAPONS
62
■ 62. Coming-Diving Courses. — a. Figure 8 represents a pic-
torial view of the approaching leg for a coming-diving course.
Figure 8. — Vertical lead coming-diving course.
As in the coming-constant altitude course, the formula for
vertical lead for a coming-diving course is —
ox — cp- — eo-f"0s
b. For courses where the target is diving at a point in rear
of the gun position, the value e P — e will be positive on the
47
62
COAST ARTILLERY FIELD MANUAL
approaching leg and negative on the receding leg. For courses
where the target is diving at a point in front of the gun posi-
tion, the value *p— e will always be negative. For courses
where the target is diving directly at the gun position,
e„— eo=0, and <tl=<I>s. As in the case of the coming-con-
stant-altitude courses, the superelevation is always positive
and is added algebraically to ep — e .
c. (1) The leads for coming- diving courses can be com-
puted in a manner similar to that for coming-constant alti-
tude courses, but with the addition of one other factor, the
angle of dive (7) . Hm and Sg are assumed, as well as 7, and
as before, various future positions of the target are selected
in terms of Rp. If actual speed of the target (S) is given,
ground speed (.Sg) may be determined by the formula S g =S
cos 7. " The computation for each selected future position
then consists of determining the following:
Hp from Hm, R P , and 7.
c P from Rp and Hp.
Ro from Rp and S g t p .
Ho from Hm, Ro, and 7.
«o from Ro and Ho.
ah from ej>, e , and 0s.
(2) The computations can be rapidly performed by using
the Ml (Crichlow) slide rule. Calculation Form No. 2 is a
convenient form for Use when this slide rule is employed.
d. To calculate the vertical lead:
(1) Enter the selected values of Rp on line 1 of the form.
(2) Determine the values of R P tan 7 for each future
position, using the slide rule.
(a) If 7 is greater than (>) 800 mils, set the long arm (Z,)
to the value of 7 on the outer set of figures (tangents) of
scale O, and the short arm (S) on the index. Without chang-
ing the angle of displacement between the two arms, move
(£) until (S) is set to the value of Rp on scale E, and under
(Zi) read the value of R v tan 7 on scale E.
48
ANTIAIRCRAFT AUTOMATIC WEAPONS
62
(b) If 7 is less than (<) 800 mils, set (L) on the index,
and (S) to the value of y on the inner set of figures (co-
tangents) of scale C. Without changing the angle of displace-
ment between the two arms, set (S) to the value of R P on scale
E, and under (L) read the value of R P tan y on scale E. En-
ter these values on line 2.
(3) Determine the values of Hp for the selected future
positions, by adding to (approaching leg) or subtracting from
(receding leg) Hm the values of Rp tan y on line 2. Enter
these values on line 3.
(4) Extract from the proper firing tables the times of flight
and the superelevations for each selected future position,
using Hp and R P as arguments. Enter the times of flight
(nearest hundredth of a second) and the superelevations
(nearest mil) on lines 5 and 12, respectively, of the form.
(5) Multiply each time of flight by the assumed ground
speed in yards per second, and enter the results (to the near-
est yard) on line 6. It may be desired to perform the multi-
plication of S g and t P on the Ml (Crichlow) slide rule. In
this case all settings are made and read on scale E. Set the
long arm (L) to the assumed Sg in yards per second, and the
short arm (S) to the index. Without changing the angle
between the arms, shift (L) until (S) is set to the first time
of flight, and read under (L) the value of S g t P . Still without
changing the angle between the arms, continue to set (S) to
times of flight, and read values of Sgt P under (L).
(6) Add to (approaching leg) or subtract from (reced-
ing leg) the values of Rp (line 1) the values of S g t p (line 6)
to obtain values of Ro. Enter these values on line 1.
(7) Determine the values of Ro tan y for each required
present position in the same manner that values of Rp tan 7
were determined in (2) above, except that R is substituted for
R P , Enter the values obtained on line 8.
(8) Determine values of H for each required present posi-
tion by adding to (approaching leg) or subtracting from
(receding leg) Hm the values of R tan 7 on line 8. Enter
these values on line 9.
49
62
COAST ARTILLERY FIELD MANUAL
Sit
° g"
Lfl'
&3W
50
ANTIAIRCRAFT AUTOMATIC WEAPONS
a
7
so
03 d
ft} jsw
° !3 «
s
Eh
3
-H
ftj
-H
51
62-63
COAST ARTILLERY FIELD MANUAL
(9) Compute the values of ep for each selected future
position, using the slide rule. To do this, set the long
arm (L) on the larger value, Rp or Hp, on scale E, and the
short arm (S) on the smaller value, Rp or Hp, on scale E.
Without changing the angle between the two arms, move (L)
and (S) until (S) is on the index of scale E, and read the
value of ep under (L) on scale C. Note that scale C has two
sets of readings. If Hp is less than Rp, read the smaller
angle. If Hp is greater than Rp, read the larger angle. En-
ter the values of ep on line 4.
(10) Compute the values of e for each present position
corresponding to a selected future position, using the slide
rule. This is done as described in (9) above, except that
Ro and Ho are substituted for Rp and Hp, respectively. Enter
the values of e on line 10.
(11) Subtract each value of e from the corresponding
value of %> to obtain values of <n (or e P — e ). Enter these
values on line' 11.
(12) Add lines 11 and 12 algebraically to obtain values of
oh. Enter these values on line 13,
■ 63. Crossing-Constant Altitude Courses. — a. When com-
puting leads for a crossing-constant altitude course, both
vertical leads and lateral leads must be determined. Figure
9 represents the approaching leg of a crossing-constant alti-
tude course. The formulas for computing the leads for such
a course are —
Sl (lateral lead=sin -i s ^" sina P .
Do
cl (vertical lead)=f sin -^ 9tp cos gpSinei ' }+</>,.
The various steps required to develop these formulas for a
point on the approaching leg of the course are shown in
figures 9, 10, and 11®. These formulas are also correct for
the receding leg of the course.
b. To derive the lateral lead formula:
(1) Referring to figure 9, the right triangle, To'-Gun-A, is
constructed by extending Rp beyond T P '. (The location of
Tp' is determined by dropping a vertical line from Tp until it
52
ANTIAIRCRAFT AUTOMATIC WEAPONS
63
intersects the ground. Likewise, TV is located by dropping a
vertical line from To until it intersects the ground.) Draw
a line from To' perpendicular to Rp extended. The intersec-
tion is marked A. In the right triangle To'-Tp'-A, the side
To'-Tv (which is the hypotenuse of the triangle) is equal
to Sgtp. The angle To'-Tp'-A is equal to a p . Hence the side
To'-A is equal to S g tp sin op.
(2) Prom (1) above, the horizontal triangle To'-A-Tp' has
been constructed. Referring to figure 10, simply lift this
Figure 9. — Crossing-constant altitude course.
horizontal triangle vertically, superimposing To' on To, and
Tp' on Tp. The point To" will be vertically above A and at
the same altitude as To and Tp. The side To'-A has already
been found equal to Sgtp sin a P . Therefore, the side To-To"
also equals S g t P sin op. It is also evident from the figure, and
true, that the side T "-T P lies in the same vertical plane as
the vertical triangle, Gun-Tp-Tp'.
(3) As lateral leads are measured in the slant plane, it Js
only necessary to calculate the slant plane angle, 2V-Gun-
To", which is the lateral lead (8l).
53
63
COAST ARTILLERY FIELD MANUAL
(4) From the right triangle, To— To"— Gun, Si^sin- 1
Sgtp sin ap
Do
c. To derive the vertical lead formula:
(1) In figure 11® the side A-p' in right triangle
To' — Tp' — A is equal to Sgtp cos a P ; and the side To"—T P (of
Figure 10. — Lateral leaa In slant plane, crossing-constant altitude
course.
triangle To— To"— Tp) =A— Tp'=S g tp cos ap, because similar
sides of equal triangles are equal.
(2) Referring again to figure 10, in the right triangle
To— Gun— To", the side Gun— To" equals Do cos 5l.
(3) The angle To"— Gun— T P , lying in the vertical plane
through Tp and the Gun, is oi, as shown in figure 11®.
(4) oi is found by the law of sines. In the triangle
sin o-i sin To"— Tp— Gun
-Gun,
Sgtp COS ap Do COS Sl
54
ANTIAIRCRAFT AUTOMATIC WEAPONS
63
(a) Angle of To"— T P ~ Gun=180°— e p .
(b) Sin (180°— « P )=sin e P (the sine of the supplementary-
angle is equal to the sine of the angle itself) .
(5) As in the case of coming courses, <n,=<ri+<t>s. n is
always positive on the approaching leg and negative on the
receding leg. <t>s is always positive and is added algebraically
to 01.
d. (1) To compute the leads for any one course, the alti-
tude, ground speed of the target, and minimum horizontal
range (Rm) of the course are assumed. Various future posi-
tions of the target are selected in terms of L v . For conven-
ience in computation, it will be found advantageous to select
values of H, Rm, and Lp in even hundreds of yards and values
of S g in even tens of yards per second. The computation for
each selected future position consists of determining t v , a v , Do,
ep and <ps and substituting them in the lead formulas to obtain
Sl and o-l.
(2) As in the case of coming courses, computations are
facilitated by the use of the Ml (Crichlow) slide rule. Cal-
culation Form No. 3 is a convenient form for. use when this
slide rule is employed.
e. To calculate the lateral lead:
(1) Enter the selected values of Lp on line 1 of the form.
The values of Lp should be determined in the same manner
as the values for Rp on the coming courses in paragraph
61d(l).
(2) Using the slide rule, determine the values of a P for the
selected future position. For each position, set the long
arm (L) to the larger value, Rm or Lp, on scale E, and the
short arm (S) on the smaller value, R m or Lp, on scale E.
Without changing the angular displacement, move (D until
(S) is on the index of scale E, and read the value of ap under
(L) on scale C, reading the greater angle if Rm is greater than
L P and the smaller angle if Rm is less than Lp. Enter values
a P on line 2.
(c) Thus,-
sin <n sin <fr
Sgtp COS ap Do COS Sl
(<2) Therefore <n=sin- i:
Sgtp COS ap Sin Cp
Do COS Sl
55
63
COAST ARTILLERY FIELD MANUAL
® Principal vertical lead angle and superelevation under firing
table conditions, crossing-constant altitude course.
1. Plot L p (lina IJogoinst Dp (line 5)
2. Enter with L (Hne8) ond read
value Dp. Record In line 10
Read 1045
PLol
TV
982
Plot Dp =982
I
K
F
\
Read 925'
7
f
■n
D
r
■a
>-
c
O
I-
1 Enter with 870 1
1°
lo
1?
1 a
l_l
1 O
10-
A
<*
n
lo
lo
■00
1°-
Enter with 73<
Y
L in YARDS
-
APPROACHING L
EG II 1 II 1
RECEDING LEG
600
© Relationship of L to D.
Figure H.
56
ANTIAIRCRAFT AUTOMATIC WEAPONS
63
(3) Using the slide rule, determine the values of Rp for the
selected future positions. For each position, set the long arm
(L) to Rm on scale E, and the short arm (S) on the index
of scale E. Without changing the angular displacement of
the arms, move (L) until (S) is on the value of a P (line 2) on
scale D and read the value of Rp under (L) on scale E. Enter
values of Rp on line 3.
(4) Using the slide rule, determine the values of e P for the
selected future positions. Proceed as in (2) above, substitut-
ing H for Rm and Rp for Lp. Enter values of ep on line 4.
(5) Using the slide rule, determine the values of Dp for
the selected future positions. Proceed as in (3) above, sub-
stituting H for Rm and e p for ap. Enter values of Dp on line 5.
(6) Enter the firing tables with Dp and ep (or H and Rp) as
arguments, and extract values of tp and <ps for each selected
future position. Enter the values of tp (nearest hundredth
second) and <ps (nearest mil) on lines 6 and 16, respectively.
(7) Multiply each time of flight by the assumed ground
speed of the target in yards per second, and enter the results,
to the nearest yard, on line 7. It may be desired to perform
the multiplication of Sg and tp on the slide rule. Set the
long arm (L) to the assumed Sg in yards per second on scale
E, and the short arm (S) on the index. Without changing
the angle between the arms, shift (L) until (S) is set to
the first time of flight and read under (L) the value of S g t P .
Still without changing the angle between the arms, continue
to set (S) to times of flight, and read values of Sgtp under (L) .
(8) Add to (approaching leg) or subtract from (receding
leg) the values of L P (line 1) the value of S g t P (line 7) to
obtain values of L corresponding to each value of Lp. Enter
these values on line 8.
(9) Using the slide rule, determine the values of Sgtp
sin ap for the selected future positions. For each position,
set the long arm (L) to Sgtp on scale E, and the short arm
(S) to the value of ap (line 2) on scale D. Without changing
the angular displacement of the arms, move (L) until (S)
is on index of scale E, and read the value of Sgtp sin op under
(L) on scale E. Enter these values on line 9.
57
63
COAST ARTILLERY FIELD MANUAL
M ^ TO
"2 a a
« 5^
= O C.2
M 02
m^&3
ECO
ft} tfj&i
IN
02
ft: few
o
EC!
03
03
O H <fl
^ .s
to-
1 cs
I
\
58
ANTIAIRCRAFT AUTOMATIC WEAPONS
63
Q, 0>
+ 1
«8
^■3
= 1
o p
.S3
5 S
^■3
3 §
CO
3|
cm PQ
03 CD
0*3
M 02
59
63
COAST ARTILLERY FIELD MANUAL
(10) Determine graphically the value of D for each value
of Dp in the following manner. Plot on cross-section paper,
as shown in figure 11©, to any convenient scale, values of Dp
(line 5) as ordinates against the corresponding values of Lp
(line 1) as abscissas. With a French curve, draw a smooth
curve through the plotted points. Then from this curve, sub-
stituting Do for Dp and Lo for hp, read the values of Do cor-
responding to values of Lo shown on line 8. Enter these
values on line 10.
Note. — The relationship of L to X> Is the same for a given point on
the course regardless of whether the point represents To or Tv.
(11) Using the slide rule, determine Sl for each future
position. For each position, set the long arm (L) on the
value of Do on scale E, and the short arm (S) on the value
of Sgtp sin ap on scale E (line 9). Without changing the
angular displacement of the arms, move (L) until (S) is
on the index of scale E, and read under (L) the value of
Sl on scale D. (See appendix III for procedure on reading
mil angle values on the D scale of the Crichlow slide rule.)
Enter these values on line 11. They are the required lateral
leads.
/. To calculate the vertical lead:
(1) Using the slide rule, determine the value of S g t P cos ap
for each future position. For each position, set the long
arm (L) to the value of Sgtp on scale E and the short arm
(S) on the value of ap (line 2) on scale B. Without changing
the angular displacement between the arms, move (L) until
(S) is on the index of scale E, and read Sgt P , cos ap under (L)
on scale E. Enter values of Sgt v cos ap on line 12.
(2) Using the slide rule, determine values of S g t P cos ap
sin ej, for the required future positions. Proceed as in e(9)
above, substituting Sgtp cos ap for S g t P , and e p for ap. Enter
values of Sgtp cos a P sin e P on line 13.
(3) Using the slide rule, determine values of Do cos Sl for
the required future positions. Proceed as in (1) above, sub-
stituting Do for Sgtp, and Sl for a P . Enter values of Do cos
Sl on line 14.
(4) Using the slide rule, determine values of o-i for the
required future positions. Proceed as in e(ll) above, sub-
60
ANTIAIRCRAFT AUTOMATIC WEAPONS
63-64
stltuting Do cos Si for Do, and S g t P cos up sin ep for S g t P sin a v .
Enter values of n on line 15. oi is plus on the approaching
leg and minus on the receding leg.
(5) Add values of n (line 15) and <p s (line 16) algebraically
to obtain values of ox. Enter these values on line 17.' They
are the required vertical leads.
■ 64. Crossing-Diving Courses. — o. As in the case of crossing-
constant altitude courses, both lateral and vertical leads
FtGUKE 12/ — Crossing-diving course.
must be computed for crossing-diving courses. The compu-
tation is similar to that for crossing-constant altitude courses.
One additional factor, angle of dive, must be considered and
Hm assumed instead of H.
473316°— 42-
61
64
COAST ARTILLERY FIELD MANUAL
b. Figure 13 represents the approaching leg of a crossing-
diving course. The formulas for computing the leads for
such a course are —
Si (lateral lead) =sin -1 ^^°°* .
, j.- i n ~j\ / ,Sgtp tan 7 sin (ep : ¥ya\ , ,
ah (vertical lead) = ( s i n - 1 . — — — — ) +^ s -
V sm yvDo cos «, /
c. To determine the lateral lead:
(1) The formula for lateral lead for a crossing-diving
course is identical with, and developed in the same manner as,
the formula for lateral lead for a crossing-constant altitude
course.
(2) The various steps required to develop the vertical lead
formula for a point on the approaching leg of the course are
shown in figures 13 to 17, inclusive. These formulas are also
correct for the receding leg of the course.
d. To derive the vertical lead formula:
(1) Referring to figures 13, 14, and 15, the difference in
altitude between To and T P is S g t P tan 7, which is equal to the
line To~C.
(2) By actual construction the side To"— B is made equal
to the side To— C.
(3) Therefore, the side To"— B=S g t p tan 7.
(4) By construction the side B — Tp=the side A— Tp'.
(5) The side A— T P ' is equal to S g t P cos op.
(6) Therefore the side B—T p =S g t p cos a P .
(7) Referring to figure 13, simply connect the two points
To" and T P with a line. This line then becomes the projec-
tion of the target's course on to the vertical plane through
the gun and T P . The angle formed, T "—T P —B, is the pro-
jection of the angle of dive (7) on to this vertical plane. This
new angle, T "—T p —B, is called yv, and is always greater
than 7 because, as both of these latter angles subtend the
same vertical distance, the side To"—T P is shorter than the
side To— T p .
62
ANTIAIRCRAFT AUTOMATIC WEAPONS
64
(8) In the right triangle T a "—T v —B,
iT "—B
7t;=tan ■
Tp—-B
Fiqidke 13. — Crossing-diving course, approaching leg.
(9) Substituting, 7»=tan-i^i55_I
Sgtp COS a»
(10) In the same triangle, the sin yv—
(11) The side T v ~T a "=^£JmJl.
sin 7»
, side To"~B _
side T P — To"
Sgtp tan 7
side Tp—To"
63
64
COAST ARTILLERY FIELD MANUAL
To
- t- „ \ x
\
Figuee 14. — Determination of y v , crossing-diving course.
(12) Then in the vertical triangle Gun— T p — To", ai may
be found by the law of sines.
(13) Thus sin °f angle Tp— Gun— To"
side T "—T v ~
sin of angle To"— Tp— Gun
side Do cos Sl
(14) The angle Tp— Gun— To" is n, since it is the vertical
angle between To" (the projection of To on the vertical
plane through the Gun— T P line) and Tp.
(15) Angle To"— T v — Gun is equal to 180° — (angle
N-Tp— To").
(16) Angle N— Tp— To"= (angle N—Tp—B)— (angle
To" — T P — B) .
64
ANTIAIRCRAFT AUTOMATIC WEAPONS
10" B
He. o/
Fiotoe 15. — Determination of cross-diving course.
(17) The angle N— T P — B=e p .
(18) The angle To"—T P — B=7».
(19) Thus, angle W— Tj>— To"=ep— 7».
(20) Therefore, angle To"— T v — Gun=180"
(21) Sin 180°— (eu— 7»)=sin (e r — 7»).
sin o-i sin Up—jv)
(22) Therefore,
Sgtp tan 7 Do cos Sl
sin 7t>
(23) ^sin- 1 gg^ tan if (ep-7,).
sin 7d Do cos . St
- (e p — 70) .
65
64
COAST ARTILLERY FIELD MANUAL
1 I
_ T « _ .Sg»p-1an V
'0 'P~ : — r;
sin V v
Piguke 16. — Determination of T p obtuse angle for crossing-diving
courses, approaching leg.
(24) <ri.=<n+<ps, as can be seen from figure 17. <n is posi-
tive ( + ) when ej> is greater than 70. Somewhere on the ap-
proaching leg, c P equals 7». At this point <n=0 (zero) . As
the target continues on its course, yv becomes greater than
e P , and 01 is then negative (— ).
(25) To summarize:
o-i is — when ep<yv J
(b) <n is always minus (—
(26) Superelevation (<ps)
added algebraically to <n.
on the approaching leg.
) on the receding leg.
is always positive (+>, and is
66
, ANTIAIRCRAFT AUTOMATIC WEAPONS 64
Figure 17. — Determination of ox. approaching leg.
e. (1) To compute the leads for any one course, the alti-
tude to the midpoint of the course, the ground speed of the
target, the minimum horizontal range, and the angle of dive
are assumed. If actual speed of the target is assumed, S g is
obtained by the formula S g =S cos 7. Various future positions
of the target are selected in terms of Lp. For convenience in
computation, it will be found advantageous to select values
of Hm, Rm, and Lp in even hundreds of yards and values of Sg
(or S) in even tens of yards per second. The computation for
each selected future position consists of determining t v , <m,
Do, ej>, 7B, and 0s and substituting them in the lead formulas
to obtain Sl and n.
(2) As in the case of other types of courses, computations
are facilitated by the use of the Ml (Crichlow) slide rule.
Calculation Form No. 4 is a convenient form for use when
this slide rule is employed.
67
64
COAST ARTILLERY FIELD MANUAL
/. To calculate the lateral lead:
(1) Enter the selected values of L? on line 1 of the form.
(2) Using the slide rule, determine the values of o P for the
selected future positions. For each position, set the long arm
(L) to the larger value, Rm or Lp, on scale E, and the short
arm (S) on the smaller value, Rm or Lj>, on scale E. Without
Figure 18. — Crossing-diving course, receding leg.
changing the angular displacement, move (L) until (S) is on
the index of scale E, and read the value of a v under (L) on
scale C. Read the greater angle if Rm is greater than Lp, and
the smaller angle if Rm is less than Lp. Enter values of op
on line 2.
(3) Using the slide rule, determine the values of Rv for
the selected future positions. For each position, set the
long arm (L) to the value of Rm on scale E, and the short
arm (S) to the index of scale E. Without changing the an-
68
ANTIAIRCRAFT AUTOMATIC WEAPONS
64
gular displacement of the arms, move (L) until (S) is on the
value of a P on scale D, and read the value of Rp under (L) on
scale E. Enter values of Rp on line 3.
(4) Using the slide rule, determine the value of L p tan y
for the selected future positions. Enter these values of L v
tan 7 on line 4.
(a) If 7 is greater than 800 mils, set the long arm (L) to
the value of 7 on the outer set of figures (tangent) of scale C,
and the short arm (S) on the index. Without changing the
Figure 19. — Determination of 01, receding leg.
angular displacement between the arms, move (L) until (S)
is set to the value of Lp on scale E, and under (L) read the
value of Lp tan 7 on scale E.
(b) If 7 is less than 800 mils, set (L) to the index, and (S)
to the value of 7 on the inner set of figures (cotangent),
scale C. Without changing the angular displacement between
the arms, move (L») until (S) is set to the value of Lp on
scale E, and under (L) read the value of Lp tan 7 on scale E.
(5) Add to (approaching leg) or subtract from (receding
leg) Hm the values of Lp tan 7 to obtain values of Hp for each
69
64
COAST ARTILLERY FIELD MANUAL
selected future position. Knter these values of Hp on line 5.
(6) Using the slide rule, determine the values of e P for the
selected future positions. Proceed as in (2) above, substitut-
ing Hp for Rm, and Rp for hp- Enter values of ep on line 6.
(7) Using the slide rule, determine the values of A> for the
selected future positions. Proceed as in (3) above, sub-
stituting Hp for Rm, and ep for op. Enter values of Dp on
line 7.
(8) Enter the firing tables with Dp and e P (or Hp and Rv)
as arguments, and extract values of tp and 4>s for each se-
lected future position. Enter the values of tp (nearest
hundredth second) and <t>s (nearest mil) on lines 8 and 22,
respectively.
(9) Multiply each time of flight by the assumed ground
speed in yards per second, and enter the results, to the
nearest yard, on line 9. It may be desired to perform the
multiplication of S g and tp on the slide rule. In this case
all settings are made and read on scale E. Set the long
arm (L) to the assumed Sg in yards per second on scale E,
and the short arm (S) on the index of scale E. Without
changing the angle between the arms, shift (L) until (S)
is set to the first time of flight and read under (L) the
value of Sgtp. Still without changing the angle between the
arms, continue to set (S) to times of flight, and read values
of Sgtp under- (L) on scale E.
(10) Add to (approaching leg) or subtract from (receding
leg) the values of Lp (line 1) the values of Sgtp (line 9) to
obtain values of Lo corresponding to each value of Lp. Enter
these values on line 10.
(11) Using the slide rule, determine values of Sgtp sin ap
for the selected future positions. For each position, set the
long arm (L) to Sgtp on scale E, and the short arm (S) to the
value of a P on scale D. Without changing the angular dis-
placement of the arms, move (L) until (S) is set to the
index, scale E, and under (L) read the value of Sgtp sin a P
on scale E. Enter these values on line 11.
(12) Determine graphically the value of Do for each value
of Dp in the following manner. Plot on cross-section paper,
to any convenient scale, values of D p (line 7) as ordinates
against the corresponding values of Lp (line 1) as abscissas.
70
ANTIAIRCRAFT AUTOMATIC WEAPONS
64
With a French curve, draw a smooth curve through the
plotted points. Then from this curve, substituting Do for Dp,
and Lo for Lp, read for values of Lo (line 10) the corresponding
values of Do. Enter these values on line 12.
(13) Using the slide rule, determine Sl for each future
position. For each position, set the long arm (L) on the
value of Do on scale E, and the short arm (S) on the value
of Sgtp sin a P on scale E. Without changing the angular
displacement of the arms, move (L) until (S) is on the index
of scale E, and read under (L) the value of Sl on scale D.
Enter these values on line 13. They are the required lateral
leads. (See appendix III for notes on use of the Crichlow
slide rule.)
g. To calculate the vertical lead:
(1) Using the slide rule, determine the values of S g t v tan y
for the selected future positions. Proceed as in b(4) above,
substituting Sgtp for Lp. Enter values of Sgtp tan y on
line 14.
(2) Using the slide rule, determine the value of Sgtp cos a P
for each future position. For each position, set the long
arm (L) to the value of Sgtp on scale E, and the short arm
(S) to the value of a P on scale B. Without changing
the angular displacement between the arms, move (L) until
(S) is set on the index of scale E, and read Sgtp cos <* P
under (L) on scale E. Enter values of Sgtp cos a p on line 15.
(3) Using the slide rule, determine the values of yv for
the selected future positions. Proceed as in b(2) above,
substituting Sgtp tan 7 for R m , and Sgtp cos a P for hp. Enter
values of yv on line 16.
(4) Add to (receding leg) or subtract from (approaching
leg) the values of ep the corresponding values of yv to obtain
values of Up^fyv). Enter these values on line 17 without
sign.
(5) Using the slide rule, determine the values of Sgtp
tan 7 sin Up^Fyv) for the selected future positions. Proceed
as in b(ll) above, substituting Sgtp tan 7 for S g t P , and
(ep±7») for a P . Enter the values of Sgtp tan 7 sin (e p ±y v )
on line 18. (See appendix in.)
(6) Using the slide rule, determine the values of Do cos Sl
for the selected future positions. Proceed as in (2) above,
71
64
COAST ARTILLERY FIELD MANUAL
substituting Do for S g t P , and Sl for ap. Enter the values of
Do cos Sl on line 19.
(7) Using the slide rule, determine the values of Do cos Sl
sin 7c for the selected future positions. Proceed as in b(ll)
above, substituting Do cos Sl for Sgtp, and 70 for ap. Enter
the values of Do cos Sl sin yv on line 20.
(8) Using the slide rule, determine the values of <n for
the required future positions. Proceed as in b(13) above,
substituting Do cos Sl sin y v for Do, and Sgtp tan 7 sin
(e p ± 70) for Sgtp sin ap. Enter values of a\ on line 21. Note
i7uif itfte »aZ«e of 01 is positive if «p is greater than yv, and
negative if e p is less than yv on approaching leg, and is also
negative on the receding leg. (See appendix HI.)
(9) Determine values of <tl for each future position by
adding 01 and 4>s algebraically. Enter values of ox on line 23.
h. If it is desired to calculate the leads with an ordinary
slide rule or calculating machine, the calculation form must
be changed to show the functions of the various angles com-
puted. The angle then can be found by referring to tables
of natural trigonometric functions.
72
ANTIAIRCRAFT AUTOMATIC WEAPONS
64
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Solution by Crichlow slide rule
Read
under
L on
Assumed or selected
6
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— on receding leg
o
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73
COAST ARTILLERY FIELD MANUAL
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j Solution by Crichlow slide rule
Read
under
L on
Firing tables with Hp and R p or D p
and E v
Scale E
+ on approaching leg
— on receding leg
Scale E
Plot a curve of D p against L p and read
D from the curve for values of L
Scale D
Scale E
Turn
both
until
S is at
Line 8
Scale E
Index
Scale E
Index
Scale E
W
«??
CO
Set S at
Index
Scale E
Line 2
Scale D
Line 11
Scale E
Index
7 (cot)
Scale C
Set L at
8, Scale
Line 9 i
Scale E 1
Line 12
Scale E
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Index
oc
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ANTIAIRCRAFT AUTOMATIC WEAPONS
64
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75
65
COAST ARTILLERY FIELD MANUAL
CHAPTER 4
LEAD CURVES AND CHARTS
Paragraphs
Section I. Lead curves and lead charts for constant altitude
courses 65-67
II. Lead charts for dive targets 68-72
Section I
LEAD CURVES AND LEAD CHARTS FOR CONSTANT
ALTITUDE COURSES
■ 65. General. — a. Chapter 3 described the methods of cal-
culating the leads for future positions of the target on various
types of courses. To put the leads in a satisfactory form for
practical use, they must first be referred to the corresponding
present positions by constructing lead curves, and then the
data from a number of curves transferred to suitable charts.
These curves and charts can be used to familiarize personnel
with the initial leads and the rates of change of leads re-
quired for particular courses and can also be employed to
study the effect of variations in altitude, speed of the target,
and other basic elements of data on those same leads and
rates of change of leads.
b. The greatest value of lead curves and charts is for use
in the training of personnel of those antiaircraft automatic
weapons units which control fire with central control equip-
ment. However, they also are valuable when used in train-
ing personnel who normally fire with director control in the
use of emergency fire control methods, or for training per-
sonnel who fire by individual tracer control.
c. Neither lead curves nor lead charts are suitable for use
during service firing to obtain the required leads, although
they may be used to a limited extent during the early stages
of individual firing and preliminary platoon firing if desired.
Their main purpose is to familiarize the adjusters, prior to
actual firing, with the initial leads and the rates of change
of leads which will be required at various points along repre-
76
ANTIAIRCRAFT AUTOMATIC WEAPONS
65-66
sentative courses. However, adjusters should not be per-
mitted to continue to refer to these charts in determining
required leads.
■ 66. Lead Curves. — a. (1) In the computations of leads, the
present position corresponding to each selected future posi-
tion is determined in terms of either Lo (for crossing courses)
or Ro (for coming courses) . When constructing lead curves,
points are plotted in terms of these present position values,
Lo or jRo as abscissas and the corresponding lateral or vertical
leads as ordinates.
(2) The values of L and Ro are computed from the mid-
point of the course. Therefore, the midpoint of the course
is represented by the y-axis. For crossing courses this y-axis
is placed at the center of the plot, and values of Lo are meas-
ured left or right from this line. Negative values are meas-
ured to the left if the approaching leg of the course is to the
left of the midpoint and to the right if the approaching leg
is to the right of the midpoint. Positive values are laid off in
the opposite direction from negative values. As only the
approaching leg of a coming course is usually plotted, the
y-axis of the lead curve for this type of course is usually
placed at the edge of the plot. Values of Ro are measured
from this line.
(3) When all the points for a particular curve have been
plotted, the plotted points are connected by a curved line.
This curved line is the lead curve (lateral or vertical) for the
particular weapon, ammunition, and target course under
consideration.
b. If desired, two or more lead curves may be placed on the
same plot. These curves may. be the lateral and the vertical
lead curves for a particular course. Figure 20 is an example
of such a plot for a type crossing-constant altitude course
when firing a caliber .50 machine gun. Similarly, a series of
curves may be plotted for various target courses and speeds,
or for the various antiaircraft automatic weapons (see fig. 21) .
Such grouping of curves facilitates study of the manner in
which the leads vary when the basic elements of data or the
weapons or ammunition are changed.
c. For a discussion of lead curves see chapter 5.
473316°— 42 6 77
78
79
67
COAST ARTILLERY FIELD MANUAL
■ 67. Lead Charts. — a. Lead charts are constructed from a
series of related lead curves. Two types of lead charts have
proved particularly satisfactory, one for constant altitude
courses and the other for diving courses.
b. (1) The simplest and most practical form of lead chart
yet devised is that for crossing-constant altitude courses,
examples of which are illustrated in figures 22 and 23. One
chart is required for lateral leads and another for vertical
leads. Similar charts can be made for constant-altitude
coming courses.
(2) A chart for crossing-constant altitude courses is usually
prepared from a number of lateral (or vertical) lead curves
for the same weapon and the same altitude of course. If
desired, two target speeds can be represented. Several
courses can be shown, each having a different R m . The en-
tire chart is constructed to scale to assist personnel in visual-
izing the courses represented. The method of construction is
as follows:
. (a) Draw a vertical line through the center of the chart
to represent the line of midpoints of all courses. On this line
and near the bottom of the chart mark a point representing
the gun position. Through this point draw a horizontal line
across the chart. Mark off this line to the same scale as the
Lo scale of the lead curves, using 100-yard divisions. Mark
off to scale, from the gun position, along the line of mid-
points, distances equal to the R m s of the courses to be repre^
sented. Through each of these points draw a horizontal line
across the chart.
; !(&) Select a lead curve for the proper weapon, altitude,
and speed of target, and place it with the x-axis along the
line on the chart representing a course of that Rm and with
its; y-axis at the line of midpoints. Project the lead values
in : mils from the lead curve to the line on the lead chart.
This is done by marking on the lead curve the points of
intersection of the curve with horizontal lines from the scale
ofordinates and then dropping a vertical line to the line on
the chart from each of these points, and marking the point
where these vertical lines strike the horizontal line of the
lead chart. Each of these points must be clearly marked by
drawing a short vertical line above (or below) the horizontal
80
81
67
COAST ARTILLERY FIELD MANUAL
82
ANTIAIRCRAFT AUTOMATIC WEAPONS
67-68
line at that point. The distances between lines should
represent 1-mil differences except where they would be too
close to be identified, in which case 5-mil divisions are per-
missible. Every fifth mil line (see fig. 22) is a little longer
than the others and every tenth mil line (see fig. 23) is
labeled with its value. Any point where the lead changes
from increasing to decreasing, or the reverse, should be
clearly marked by labeling the mil line with the value, around
which is drawn a rectangle (see fig. 22) or other distinguish-
ing mark.
(c) A second lead curve for the same weapon, altitude,
and Rm of course but for a different speed of target can be
plotted on the same line of the chart by marking the mil
divisions below (or above) the line.
(d) In a similar manner all of the selected lead curves
can be transferred to the lead chart.
(e) If lines radiating from the point representing the gun
position are drawn across the chart at 200-mil intervals, they
will be found to assist greatly in orienting the chart when
it is desired to use it during the early stages of firing. These
lines indicate angles of approach.
(3) Lead charts for coming-constant altitude courses are
constructed in a similar manner. However, since no Rms
are involved, one chart can represent as many altitudes as
may be plotted on the chart. As in the case of the cor-
responding lead curves, the line of midpoints is at the edge
of the chart. Also, instead of drawing angles of approach,
angles of elevation are drawn at 200-mil intervals on the
chart.
Section II
LEAD CHARTS FOR DIVE TARGETS
■ 68. General. — a. These charts are practical for training
use against dive targets because a dive target must of neces-
sity fly a rectilinear course at more or less constant speed.
Three elements of data affect the leads. These are angle
of dive, gun-objective distance, and ground speed.
b. The effect of angle of dive (7) on vertical lead is small
even for large differences in the angle of dive. The rates
83
68
COAST ARTILLERY FIELD MANUAL
of change for lateral leads are not excessive and can be
estimated.
c. The variable gun-objective distance can be readily elim-
inated by selection of a suitable chart as soon as the gun-
objective distance is known.
d. Ground speed has little effect on rate of change of leads.
It has an effect on initial leads which is uniform, and which
can be readily estimated. (For lead charts see figs. 24
through 31.)
90°
GUN - 37 MM
0- MV=2500 f/»
FT - 37AA-N-2
MAXIMUM RANGE I.Vapprox so yds/sec
(PRESENT POSITION) V = to = 1245 mils
SCALE (YARDS)
O IOO iOO JOO 400 500 600 TOO 800 XoO
M - 1 1111 111
E • S B 10 IE 14 l« !•
SCALE (SECONDS)
D = OBJECTIVE
• - GUN POSITION
Figure 24. — Lateral lead chart, gun-objective distance 100 yards.
84
ANTIAIRCRAFT AUTOMATIC WEAPONS
68
Pigube 25. — Vertical lead chart, gun-objective distance 100 yards.
85
68
COAST ARTILLERY FIELD MANUAL
ANTIAIRCRAFT AUTOMATIC WEAPONS
68
ISO*
S g = APPROX. 80 YDS /SEC
V»:?0*=I2« MILS
SCALE . (YARDS)
O 100 tOO MO 400 100 MO TOO 000 tOO
!" 1 1 1 1 1 1 1 1 T
SCALE (SECONDS)
□ b OBJECTIVE
Figure 27. — Vertical lead chart, gun-objective distance 300 yards.
87
68
COAST ARTILLERY FIELD MANUAL
ANTIAIRCRAFT AUTOMATIC WEAPONS
68
68
COAST ARTILLERY FIELD MANUAL
MAXIMUM RANGE
(PRESENT POSITION)
LEGEND
GUN - 37 MM
MV= 2500 f/s
FT- 37AA-N-2
S= 300 MPH
Sg = APPROX. 50 YDS/SEC
y= 70"= 1245 MILS
SCALE (YARDS)
tOOZOO3O0 4OO90O6OO70O80O900
1 1 I I I I I I I H
2 4 6 10 12 '4 16 16
SCALE (SECONDS)
O • OBJECTIVE
• ■ GUN POSITION
Pigtjbe 30. — Lateral lead chart, gun-objective distance 1,000 yards.
90
ANTIAIRCRAFT AUTOMATIC WEAPONS
68
MAXIMUM RANGE /„'
(PRESENT POSITION) J
\ \ GUN
;A MV =
; N ft -
LEGEND
GUN - 37 MM
2500 f/s
37AA-N-2
S » 300 MPH
Sg= APPROX. 50 YDS/ SEC
V s 70°=I245MILS
SCALE (YARDS)
O 100 200 300 400 900 600 TOO 600 900
W I I I I I I I I
2 4 6 10 IE 14 16 IB
SCALE (SECONDS)
□ = OBJECTIVE
Figure 31. — Vertical lead chart, gun-objective distance 1,000 yards.
91
69-70
COAST ARTILLERY FIELD MANUAL
■ 69. Use of Lead Charts. — A set of lead charts (vertical and
lateral) for dive targets should be available to every Are unit.
The gun-objective distance is the principal controlling fac-
tor. The technique of dive targets indicates that approxi-
mately a 70° dive is the most practical angle of dive. Their
most practical speed has proved to be from 250 to 300 miles
per hour, or 125 to 150 yards per second of travel. Pour
charts should be available for gun-objective distances of 100,
300, 500, and 1,000 yards. If additional time is available two
additional charts may be calculated and plotted for gun-
objective distances of 200 and 750 yards. For discussion of
maximum range, see paragraph 70i.
■ 70. Calculation of Lead Charts. — a. Decide on the angle
of dive (7) and the most probable speed of the target.
b. Locate the gun with respect to the objective, such as
100 yards away, as shown in figure 32.
c. Using a sheet of paper, locate the objective in the center.
Draw a vertical line through the objective to both the top
and bottom margins of the sheet. On the lower side of the
objective, on the vertical line, locate (to the scale of the
drawing) the position of the gun. Call that portion of the
line, objective to gun, the zero orienting line. This line will
be seen as zero degrees (0°) in figure 32.
d. With the objective as a center construct radiating lines
every 30° from the orienting (zero degree) line. Label these
lines 30°, 60°, 90°, 120°, and so forth in a clockwise and coun-
terclockwise direction from the zero line. These lines repre-
sent typical courses that may be flown by dive bombers at-
tacking the objective.
e. (1) Calculate the R m for all courses from 30° to 150°.
Figure 32 shows this calculation for 30°, 60°, 120°, and 150°.
The Rm of a 90° course is the distance, gun-objective, while
on a 0° or 180° course, it is zero. It should be noted that the
Rm on the 120° and 150° course is laid out to a point on the
course extended through and beyond the objective.
(2) Rm is determined as follows: In the horizontal right
triangle O-G-MP, the side a is known (gun-objective dis-
tance) , and the angles O and G are known. Thus, the side
Rm can be calculated as follows: Rm=a sin 30°. The side g
92
ANTIAIRCRAFT AUTOMATIC WEAPONS
70
(objective-midpoint) may be calculated as: g=a cos 30°.
The same calculation is used to determine the 60°, 120°, and
150° radii.
/. (1) Calculate Hm of the same courses for which Rm
was determined. Figure 33 shows Rm and Hm. Hm is found
as follows:
(2) In the vertical triangle T-O-MP, angle O is equal to
70° (angle of dive), and angle T is thus equal to 20°. With
ieo*
0'.
Figure 32. — Lead chart showing construction of R m .
the side g determined as above, Hm=g tan 70°. This same
calculation is used to determine Hm for 60°, 120°, and 150°
courses. It should be noted that Hm on the 120° and 150°
courses is also laid out to a point on the course extended
through and beyond the objective. This position corresponds
473316°
93
70
COAST ARTILLERY FIELD MANUAL
to a minus (— ) Hm as shown in figure 33. (Minus Hm is
shown by construction and by arrow pointed downward on
the 120° and 150° courses.)
g. Calculate all leads using Calculation Form No. 2 for
coming-diving courses and Calculation Form No. 4 for cross-
1B0*
Figure 33.— Lead chart showing construction of Rm and Hm.
ing-diving courses, chapter 3. Two courses will be calcu-
lated as coming-diving courses (0° and 180°). Five courses
will be calculated as crossing-diving courses (30°, 60°, 90°,
120°, 150°).
Note. — In addition to these courses it will be necessary to cal-
culate the vertical and lateral leads for the 15° course because the
leads are changing very rapidly on this course. For the same rea-
son, the lateral but not the vertical lead must be calculated for the
165° course. However, these radii (15° and 165°) are used only as
construction lines and are not drawn in on the completed chart.
94
ANTIAIRCRAFT AUTOMATIC WEAPONS
70
h. (1) Continue the computation of leads according to the
form. For determination of value of line 12, Calculation
Form No. 4, first plot the Dp and Lp curves on a large sheet
of cross-section paper. A sheet 18 inches by 24 inches is con-
venient. Plot Dp as the ordinate to a scale of 1 inch=400
yards. Plot Lp as the. abscissa to the scale of 1 inch=200
yards. Connect all plotted points to construct Dp-L P curve.
Figure 34 illustrates the method of this plotting. On the
Dp-Lp plot above, consider Lo as abscissa and Do as ordinate.
With the values of plotted Dp and Lp, read values of Do from
the curves for the value of L . From Lo as abscissa, read ver-
tically to a point on the curve, then read D horizontally from
the ordinate scale.
i. In order to calculate the limit of maximum range, meas-
ured from the midpoint, Lp must be obtained. To secure
Lp read horizontally from the point on the ordinate scale
where A>=2,500 yards (a value which represents the approxi-
mate maximum slant range) . When the 2,500-yard Dp hori-
zontal line meets the curve, follow a vertical line to the
bottom of the chart and read Lp on the abscissa. Then cal-
culate Lo from the formula L =L P +Sgt P . To compute tp
enter firing tables with A>=2,500 yards as one argument and
the approximate value of e p at this point as the other
argument.
Note. — Greater and lesser values than 2,500 have been calculated
for D v on Form No. 4 with the corresponding angular height for
each. Thus, by Interpolation, an approximate value of ejJ when
Dp =2,500 may be determined.
j. As the objective of the diving target is known, it is
easier to estimate the course and future position of the
target along its line of dive by reference to this objective,
rather than to have the adjuster make an estimate of the
midpoint. Thus, leads are calculated as for an ordinary
diving course, using the distance Lo from the midpoint to
the present position of target, but leads are referred to the
objective by adding or subtracting the distance, midpoint-
objective, to the distance Lo. This gives the horizontal dis-
tance from the objective to the present position of the
95
70
COAST ARTILLERY FIELD MANUAL
target (T ). This distance, objective to present position of
target, is called La and is obtained from the formula —
in which
Z/ij=horizontal distance To-objective
Lm=horizontal distance MP-objective
It must be noted that —
Ld=L +Lm when |_TOG<90°
Ld=Lo when l_TOG=90°
Ld=Lo— Lm when \_TOG>90°
S fl *5l.3 YOS/.SEC
« ■ 70'
lp & Lo IN YARD S
Pigttre 34. — Plot of Dp and L p curves, gun-objective distance
500 yards.
96
ANTIAIRCRAFT AUTOMATIC WEAPONS
70
Calculation Form No. 4 is completed to determine the lat-
eral and vertical leads. It is recommended that all calcula-
tions and plotting for a course be completed before entering
on computation for the next course, provided that calcula-
tions and plotting are consistent.
k. (1) Lateral and vertical curves are then plotted against
Li, with the lead curves as the vertical scale and Ld as hori-
S fl =51.3 YOS/SEC
APPROACHING LEG
1600 1400 1200 1000 800 600 400 200
Ld IN YARDS
Figure 35. — Plot ot lateral lead curves against L d in yards,
gun-objective distance 500 yards.
zontal scale. A suitable scale for use in plotting Ld is 1
inch=2Q0 yards; and for leads, 1 inch=10 or 20 mils, depend-
ing on the range of variation of leads. Figures 35 and 36
illustrate the plotting of the leads against Ld.
(2) From these curves, values of La in yards for even 5-mil
and 10-mil increments of lead may be read.
(3) It should be noted that a projection of the target's
course in the vertical plane shows Rd (horizontal distance
97
70
COAST ARTILLERY FIELD MANUAL
from To to objective) for 0° course to be greater than Re.
for 180° course. Figure 37 indicates this difference. The
1600 1400 1200 1000 600 600 400 200 '
L d IN YAR0S
Figuee 36. — Plot of vertical lead curves against L d in yards, gun-
objective distance 500 yards.
formula for Ra is JJa=iJo±distance gun-objective, in which
Ro=Rv+Sgtv As will be seen from figure 37, the distance
gun-objective is added to R for 0° course. However, for a
98
ANTIAIRCRAFT AUTOMATIC WEAPONS
70
180° course, the distance gun-objective is subtracted, reducing
the value of Ra.
I. Plot on the chart the vertical and lateral leads in terms
of La in yards for each 5-mil increment. (It is more satis-
Sgtp = 246 YDS
180*
R d =500+403+246=1149 YDS.
R d =1278+246-500=1024 YDS.
SCALE IN YARDS
200 400 600 800 1000
1 l I ■ I ' I I I ' I
Figure 37. — Coming-diving target, vertical plane, gun-objective
distance, 500 yards.
99
70-71
COAST ARTILLERY FIELD MANUAL
factory to construct separate charts for vertical and lateral
leads.) Ld is measured along each ray to the scale of 1 inch=
200 yards. The initial lead (read as ordinate on lead-L<i
plot) is plotted on the proper ray at distance from objective
equal to value of Ld in yards (read as abscissa on lead-I«j
plot) . Similarly, enter lateral or vertical lead for each 5-mil
increment in terms of Ld. Complete the plotting of lateral
and vertical leads for all rays.
m. All points of equal lead on chart are connected to con-
struct isolead curves.
n. Lay off on each ray the limit of maximum range, ob-
tained as in i above. Connect with a smooth curve all of these
points.
o. Draw a circle around objective 100 yards in radius. Leads
have been computed for this area but are not plotted, for it
is assumed, in this study, that the dive target will level off
and pull out of dive when Hp is 1,000 feet. (See figs. 24,
through 31.)
p. As the 37-mm has a maximum elevation of only 85°, a
dead space exists over each weapon. The area of the dead
space depends on the value of Hm on the 0° ray. The 5°
angle (90°-85°) at the gun describes a circle of dead space in
the air. The radius of the circle equals the product of tangent
5° and Hm. This dead space circle above the gun is drawn in
on the chart. For gun-objective distance of 100 yards, the
area of dead space is relatively small, but for greater gun-
objective distances, this dead space area becomes increasingly
larger.
■ 71. Comparison of Charts, Varying Gun-Objective Dis-
tance. — Upon completion of all charts for gun-objective dis-
tance of 100 to 1,000 yards, it will be observed that an increase
in gun-objective distance has the immediate effect of making
the pattern of similar leads more intricate and complicated,
indicating a rapidly changing rate and consequently a more
difficult problem for the adjusters in making estimates of
leads. Consequently, it may be stated that if the tactical
situation permits, and if target is primarily the dive bomber,
a gun should be placed as near as possible to area being de-
fended (not closer than 100 yards) .
100
ANTIAIRCRAFT AUTOMATIC WEAPONS
72
■ 72. Application to Training of Personnel. — a. A careful
inspection of the lead chart for dive targets reveals a num-
ber of definite advantages and characteristics for getting a
stream of fire upon the target more speedily and in holding
it there during the course of the target. These charts are
to be used in training to familiarize the adjusters and gunners
with the leads at various angles of approach, angle of dive,
and speed. The chart offers a practical and useful means of
estimating an initial lead, rates of change of leads, and the
time in which the plane will be under fire. These advantages
may be realized for any possible line of approach of the dive
target.
b. Furthermore, such a chart becomes most profitable when
it is oriented for certain prominent features of the terrain
about the gun installation. It is suggested that these promi-
nent landmarks be indicated on the oriented lead chart.
Thus, the chart is oriented for a line of approach of the
plane over a schoolhouse, a hill, a church steeple, a high
tree, and so forth. The adjusters can readily apply accurate
initial and "following" leads just as soon as the target appears
over or near one of these terrain features. Personnel may
become familiar with rates of change of leads over oriented
course, the sign (+ or — ) of the leads, and the limit of time
in which the target will be subject to fire. Inasmuch as no
satisfactory diving target has as yet been developed for
actual firing practice, training of adjusters by using oriented
charts becomes especially advantageous.
101
73
COAST ARTILLERY FIELD MANUAL
CHAPTER 5
LEAD CHARACTERISTICS
■ 73. General. — From a study cf lead curves and charts for
various target courses and speeds, conclusions can be drawn
as to the general characteristics of leads required for
automatic weapons (see par. 59 for definitions).
a. Coming courses. — (1) On a true coming course, the
lateral lead is zero. Any place where Rm is equal to or less
than 100 yards, lateral lead is negligible and may be dis-
regarded so far as computed leads are concerned.
Note. — In actual firing a small lateral pointing correction may
be required for targets which do not pass directly over the gun
position.
(2) When the target is flying at a constant altitude, the
vertical lead curve is positive throughout the approaching
leg of the course. On the receding leg the lead curve ap-
proaches a straight line starting near the midpoint with a
large initial negative value. It remains negative throughout
the receding course except for a slight positive value far
out on the course beyond the range of fire.
&. Crossing courses. — (1) Lateral leads for right-to-left
courses are always to the left of the target, and for left-to-
right courses are always to the right of the target.
(2) On crossing courses the lateral lead starts with the
least positive lead on the approaching leg, reaches a maxi-
mum at approximately the midpoint, and then decreases on
the receding leg.
(3) Vertical leads are at their maximum positive value
at the start of the approaching leg and decrease positively,
pass through zero, and then increase negatively until the
target is well past the midpoint of the course, the rate of
change being very great. After reaching their maximum
negative value they decrease negatively, sometimes passing
through zero again and increasing positively before the target
passes beyond range.
102
ANTIAIRCRAFT AUTOMATIC WEAPONS
73-74
c. Lead characteristics. — The remainder of this chapter is
a discussion of lead characteristics for the 37-mm gun. The
characteristics for other automatic weapons are similar.
■ 74. Coming-Constant Altitude Courses. — a. The vertical
lead for coming-constant altitude courses is affected by two
Figure 38. — Variation in target speed, coming-constant altitude
course.
variable elements of data, target speed and altitude of the
target.
6. Prom figure 38 it can be seen that an increase in target
speed on a coming-constant altitude course causes a large
103
74
COAST ARTILLERY FIELD MANUAL
increase in the required initial vertical lead and an increase
in the rate of change of leads. The rate of change of leads
is increased as the slope of the lead curve becomes steeper.
c. Figure 39 shows that, as the altitude is increased, the
initial vertical lead must be increased. At the shorter ranges
PUN- 37 MM
MV - 2500 f/»
FT-37AA-N- 2
+ 100 s 9 " 110 VOS/SEC
Figure 39. — Variation in altitude, coming-constant altitude course.
the rate of change of leads is decreased as the altitude is
increased, but at the longer ranges the rates are nearly the
same. The rates are the same where the lead curves are
parallel to each other.
d. Note from both figures 38 and 39 that the extreme change
in leads from a large positive to a large negative value occurs
as the target passes overhead and thus makes any attempt
104
ANTIAIRCRAFT AUTOMATIC WEAPONS
74-75
to fire at that point of the course impracticable for several
seconds. Limitations of the gun mounts (maximum eleva-
tion of the 37-mm gun is 85° ; maximum elevation of machine
guns is 70° to 80°) also prevent fire on this part of course.
■ 75. Coming-Diving Courses. — a. (1) The vertical lead for
coming-diving courses is affected by three elements of data:
target speed, angle of dive, and the distance Hm.
(2) Three general situations must be considered: first,
where the target dives at the gun position; second, where the
target passes over the gun position while diving at a point
in rear of the gun; and third, where the target dives at a point
in front of the gun so that the gun must be fired across the
objective at the approaching target.
b. Figures 40 and 41 show that when the target dives di-
rectly at the gun position (ffm=0), the initial vertical lead
is small and decreases to zero at the theoretical conclusion
of the dive. In these courses, «p is always equal to e , there-
fore the vertical lead is equal only to superelevation.
These figures also show that there is very little change in the
lead for either a change in target speed or a change in angle of
dive when Hm is zero. With no lateral lead, and with ver-
tical leads small and changing slowly, this target is an ideal
automatic weapons target, providing the tactical situation
permits emplacement of the gun near the objective.
c. Figures 40 and 41 also show the effect of target speed
and angle of dive on vertical leads for courses having H ro =400
yards and Km=800 yards (objective in rear of gun). As in
the case of coming-constant altitude courses, an increase of
target speed increases the initial vertical lead and slightly
increases the rate of change of leads. As angle of dive is de-
creased, the initial vertical lead and rate of change of lead
increase somewhat. The sharp angle at which the leads
increase on the receding leg of the course shows conclusively
that any attempt to track on the target on this type of course
after it passes overhead is practically useless. Therefore a
decision may be made to put up a fixed or semifixed barrage
on the receding leg.
d. Figures 42 and 43 show the effect of changes in target
speed and angle of dive when the objective is in front of
105
75
COAST ARTILLERY FIELD MANUAL
APPROACHING LEG
RECEDING L EC
GUN - 37 MM
MV - 2500 f/s
FT- 37AA - N - 2
Y - 7 0°
" = 400 M P H
— — — - 200 MPH
' V*" H m « 800 YDS
H "> = «°0 YDS
- 1 o i \ \
\\\
-H m = 8.00 YDS
•Km =400 YOS
< -200
Figure 40. — Variation In target speed and In H m , comlng-dlving
course.
106
ANTIAIRCRAFT AUTOMATIC WEAPONS
75
+ 200
+ I 5 O
+ 100
+ 50
TAR OS
o o
O o
IO o
APPR AC H I N G LEG
GUN - 37MM
MV - 2 500 1/1
FT-37AA-N-
S - 400 CI PH
H m = =
Hid = 400 YDS= -■
I
Z
■15
o -200
250
RECEDING LEG
t^70"
I
I
I
U
II
II
u
U 50°
\» !/
-30
Figure 41. — Variation in angle of dive, coming-diving course.
107
75
COAST ARTILLERY FIELD MANUAL
the gun. In both cases the leads are smaller and change
less rapidly at the longer ranges. The initial vertical lead
becomes negative sooner as the target speed increases, but
rate of change of leads remains the same. All angles of
+ 30
APPROACHING LEG
Figure 42.— Variation in target speed, coming-diving course,
objective in front of gun.
dive from 30° to 70° require about the same initial vertical
lead, but rates of change of leads are greater as the angle
of dive is changed from 30° to 70°. Near the objective, the
leads are normally changing too rapidly to permit effective
fire.
108
ANTIAIRCRAFT AUTOMATIC WEAPONS
75-76
APPROACHING LEG
O O
O O
£- iso
GUN - 37 MM
-1 V - 2 500 f/s
FT— 37AA - N - 2
S- 400 M PH
Figure 43. — Variation in angle of dive, coming-diving course,
objective 400 yards in front of gun.
H 76. Crossing-Constant Altitude Courses. — The values of
three elements of data determine the lateral and vertical
leads for crossing-constant altitude courses. These are tar-
get speed, altitude, and horizontal range to the midpoint of
the course. Their effects on the lateral lead are shown in
figures 44, 45, and' 48. Their effects on the vertical lead are
shown in figures 48 to 52, inclusive.
a. Lateral lead. — (1) Figure 44 shows that an increase of
80 yards per second in target speed calls for a large increase
in the initial lateral lead and a small increase in the rate
of change of leads. The point of maximum lead with relation
to the midpoint of the course is not materially changed.
(2) Figure 45 shows that for both service and target prac-
tice speeds a change of 400 yards in altitude causes only a
small change in the initial lateral lead and almost no change
473316°— 42 8
109
76
COAST ARTILLERY FIELD MANUAL
1500 1000 500
APPROACHING LEG
0)200
2
L« IN YARDS
GUN - 37MM
MV - 2500 f/e -
' FT - 37AA-N-2
H— 600 YDS
R m — 1000 YDS
"1 1 1
500 1000 1500
RECEDING LEG
Figure 44. — Variation in target speed, crossing-constant altitude
course (lateral lead).
GUN - 37MM
MV-2500 f/s
FT-37AA-N-2
R m - <000 YDS
S fl -M50 AND 70 YDS/SEC
1500 1000
APPROACHING LEO
Figtjke 45.— Variation in altitude, crossing-constant altitude
course (lateral lead) .
110
ANTIAIRCRAFT AUTOMATIC WEAPONS
76
in the rate of change of leads. Particularly at service speeds,
the point of maximum lead occurs earlier on the course as the
altitude is increased.
(3) Figure 46 shows that for both service and target prac-
tice speeds, an increase (decrease) of 400 yards in horizontal
range to the midpoint causes a large increase (decrease) in
the initial lateral lead and a considerable decrease (increase)
GUN -37MM
MV - 2500 t/s
FT-37AA-N-2
PiGOBE 46: — Variation in horizontal range to midpoint, crossing-con-
stant altitude course (lateral lead) .
in the rate of change of the lead. The point of maximum lead
remains near the midpoint.
(4) Figure 47 shows how an incorrect estimation of angle
of approach (incorrect location of midpoint) causes gun to
shoot either ahead of or behind the target. If this error is
made, the only point at which the adjuster will be on the tar-
get will be at the midpoint. If the midpoint has been esti-
mated to the right, the gun will fire behind the target on
the approaching leg and ahead on the receding leg. The error
will be reversed if the midpoint is estimated to the left.
Ill
76
COAST ARTILLERY FIELD MANUAL
b. Vertical lead. — (1) Figure 48 shows that the vertical lead
becomes more positive on the approaching leg and more nega-
C0N-37MM
MV-- 2700 f/5
FT-37AA-N-I
eo
YAROS
1
16 00
Figure 47. — Effect on lateral lead of incorrect estimation of angle
of approach, crossing-constant altitude course.
-IOO
Figure 48. — Variation In target speed, crossing-constant altitude-
course (vertical lead) .
tive on the receding leg as the speed increases, thus making
the curve for the higher speed steeper.
(.2) Figure 49 indicates that an increase in altitude causes
a large increase in vertical lead (both positive and negative),
112
ANTIAIRCRAFT AUTOMATIC WEAPONS <JQ
and makes the curve steeper. The effect is the same as for
an increase in speed.
GUN~3?MM
MV-2500 »/i
FT-37AA-N-2
R m -IOOO YDS
S g -|50 YDS/SEC
Figure 49.— Variation in altitude, crossing-constant altitude course
at service speed (vertical lead).
I£0o
GUN-37MM
MV-2300 !/»
FT-37AA-N-S
R«l -1000 YDS
70 YDS /SEC
Figure 50.-Variation in altitude, crossing-constant altitude course
at towed target speed (vertical lead) .
(3) Figure 50 shows the same effects as in figure 49. It
is to be noted, however, that with a slower speed, the vertical
113
76
COAST ARTILLERY FIELD MANUAL
leads are smaller (both positive and negative) and the curves
are flatter.
(4) Figure 51 shows that as range to the midpoint (.Rm)
is decreased, the vertical lead is more positive on the ap-
proaching leg and more negative on the receding leg. Thus,
the greatest rate of change of leads will occur on targets
■v* I ISO
zopo
-150
Figure 51. — Variation in R m , crossing-constant altitude course
at service speed (vertical lead) . <
closest to the gun position, since the curve becomes steeper
as Rm is decreased.
(5) Figure 52 shows that the initial vertical leads are
nearly the same for all targets whose range to the midpoint
is between 600 and 1,400 yards. As the target approaches
the midpoint, the rate of change of the vertical lead is
greatest on the closer target; that is, the change in the
vertical lead is in inverse proportion to the change in Rm.
An increase in R m decreases the lead, makes it less positive
on the approaching leg and less negative on the receding
leg, thus making the curve for the greater Rm flatter. Close
114
ANTIAIRCRAFT AUTOMATIC WEAPONS
76
to midpoint (approaching) , curves pass through an identical
point.
(6) Figure 52 is similar to figure 51, except it is calculated
for approximately one-half the speed. The decrease in speed
to a
FiGtntE 52.— Variation In R m , crossing-constant altitude course
at towed target speed (vertical lead,) .
40
Figure 53. — Effect on vertical lead of Incorrect estimation of angle
of approach, crossing-constant altitude course.
lie
76-77
COAST ARTILLERY FIELD MANUAL
indicates a smaller initial vertical lead. However, the charac-
teristics of the curves are similar to those in figure 51. Gen-
erally, the rate of change of the vertical lead is also less at
the slower speed.
(7) Figure 53 shows how the incorrect estimation of the
angle of approach (incorrect choice of midpoint) causes the
trajectory to be below or above the target. If the midpoint
is incorrectly estimated to the left, the vertical lead will cause
the trajectory to be below the target during the approaching
leg and a considerable distance out on the receding leg. If
the midpoint were incorrectly estimated to the right, the
errors would be reversed.
■ 77. Crossing-Diving Courses. — The leads for crossing-
diving courses are affected by four elements of data. These
GUN — 37 M M
MV -2500 f/s
FT - 37AA -N-Z
R m - 1000 YDS
H m -0 YDS
r-70'
S = 400 HPH
S= 300 MPH
S= 200 MPH
z
z
a
.50 <
IN YARDS
1
2000
T
1
1000
1500
APPROACHING
I
500
•0 i-
i <
Piguke 54. — Variation in target speed, crossing-diving course
(lateral lead).
are speed of the target, altitude at the midpoint, range at the
midpoint, and the angle of dive. The effect of lateral lead
is shown in figures 54 to 57, inclusive. The effect on vertical
lead of changing elements of data is shown in figures 58 to
61, inclusive.
a. Lateral lead. — (1) Figure 54 shows how an increased
target speed increases the initial lateral lead. However, the
rate of change of the leads for these different speeds is fairly
uniform.
116
ANTIAIRCRAFT AUTOMATIC WEAPONS
77
(2) Figure 55 indicates that a difference in altitude at the
midpoint has little effect on either initial lateral lead or rate
of change. As the target reaches the midpoint, the leads
become erratic.
GUN - 37 MM
MV -2600 f/S
FT-37AA -N-2
R^, - 1000 YDS
S- 400 MPH
*-70"
+ 1200 YDS-—
+ 600 YDS
YOS;
- 600 YDS
r
500 500
L„ IN YARDS
Figure 55. — Variation in H m , crossing-diving course (lateral lead).
(3) Figure 56 indicates that as the range to the midpoint
increases, the initial lateral lead increases while the rate of
change is not seriously affected.
GUN - 37M M
MV-2500 f/5
FT-37AA-N-2
H„-0
S-400MPH
APPROACHING LEG
1500 1000 500
L„ IN YARDS
Piguke 56. — Variation in R m , crossing-diving course (lateral lead).
117
77
COAST ARTILLERY FIELD MANUAL
(4) Figure 57 shows how a variation in angle of dive has an
extreme effect on both initial lateral lead and the rate of
250
R^-1000 YDS
S - 400 M PH
L„ IN YARDS
- 1 1 1 1 1
2500 2000 1500 1000 500
APPROACHING LEG
Figure 57. — Variation in angle of dive, crossing-diving course
(lateral lead) .
change of lateral lead. This extreme effect is that as angle
of dive increases, the lead decreases and the curve becomes
flatter.
118
ANTIAIRCRAFT AUTOMATIC WEAPONS
77
b. Vertical lead. — (1) Figure 58 shows how an increase
in target speed increases the negative initial vertical lead
but the rate of change remains fairly constant.
APPROACHING LEG
2000 1500 1000 500
Figure 58. — Variation in target speed, crossing-diving course
(vertical lead) .
119
77
COAST ARTILLERY FIELD MANUAL
(2) Figure 59 shows how an increase in altitude of the
midpoint on a crossing-diving course causes the initial lead
to become less negative but the rate of change of leads is
not materially affected.
L IN YARDS
2000
1500 1000 500
APPROACHING LEG
+ 600 YDS
YDS
-600
500
RECEDING LEG
Figure 59. — Variation in H m , crossing-diving course (vertical lead).
(3) Figure 60 shows how an increase in horizontal range
to the midpoint causes vertical lead to become more nega-
tive. It also shows how a variation in horizontal range to
the midpoint causes a large difference in initial leads, while
the rate of change of lead is fairly uniform.
120
ANTIAIRCRAFT AUTOMATIC WEAPONS
77
APPROACHING LEG
1500 1000 500
Figure 60. — Variation in R m , crossing-diving course (vertical lead) .
121
77-78
COAST ARTILLERY FIELD MANUAL
(4) Figure 61 indicates that a variation in angle of dive has
a small effect on initial vertical lead. The rate of change
of these leads is fairly uniform except at the closer ranges.
+ 50
3000
Figure 61. — Variation in angle of dive, crossing-diving course
(vertical lead) .
■ 78. Differential Effects. — a. General. — The differential
effects from standard conditions (muzzle velocity, ballistic
density, and wind) are shown in the differential effects
tables of FT 37-AA-N-2.
b. Muzzle velocity. — Of the three conditions for which
differential effects are provided, muzzle velocity varies most
uniformly. It can be predicted fairly accurately before firing
122
ANTIAIRCRAFT AUTOMATIC WEAPONS
78
is to take place. Figures 62, 63, and 64 show that on both
coining and crossing courses, the effects of variations in
muzzle velocity are quite uniform throughout the course.
APPROACHING LEG
GUN - 1TMM
FT-57AA - N - 2
H - 600 YDS
Sg - 150 YDS / SEC
+ 50
YARDS
RECEDING LEG
Figure 62. — Variation in muzzle velocity, coming-constant altitude
course (vertical lead).
They indicate that for a 37-mm gun the lateral and vertical
leads, whether negative or positive, should be increased about
5 percent for each 100 foot-seconds decrease in muzzle
velocity.
123
78
COAST ARTILLERY FIELD MANUAL
GUN — 37 M M
FT-37AA-N-2
H-800 YDS
R„-IOOD_.YDS
JTSO YDS /SEC =
'[70- YDS/SEC"
2500 YDS—
L. IN
-V- V.
1500 1000
APPROACHING
SOO
LEG
— 1 1 1
500 1000 1500
RECEDING LEG
Figure 63.-
-Variation In muzzle velocity, crossing-constant altitude
course (lateral lead). .
2600 voT"
— iipa ros^" 2500 ,DS '
"oo"y§J- =
1500 1000
APPROACHING LEG
GUN -37MM
FT-37AA-N-2
H-800 YDS
R-,-1000 YDS
[fsO YDS /SEC
70 YDS/SEC •
RECEDING LEG
2600 Y 2goo yDg _j
"7400 1
FiGuiiE 64. — Variation In muzzle velocity, crossing-constant altitude
course (vertical lead).
124
ANTIAIRCRAFT AUTOMATIC WEAPONS
78
c. Ballistic density. — The effects of ballistic density as
shown in figures 65 to 67, inclusive, are not as uniform as
those of muzzle velocity. However, they indicate roughly
a 4-percent increase in leads for each 10-percent increase
APPROACHING LEO
GUM - 37 M M
MY " 2500 - f /,
FT-37AA-N-2
H - 800 - YDS
Sj - 150 YDS / SEC
+ 50
YAROS
RECEDING LEG
Figure 65. — Variation in ballistic density, coming-constant altitude
(vertical lead) .
in ballistic density. This approximation may be accepted
with considerable reliability. A series of calculations in
which are made such approximations of the effects of ballistic
density changes upon leads (applied in terms of percentage
effects on leads) conforms closely to computations of differ-
ential effects on times of flight and superelevations taken
473316°— 42 9
125
78
COAST ARTILLERY FIELD MANUAL
from firing tables. However, as data on ballistic density may
not be readily available to an automatic weapons platoon,
GUN - 37MM
MV- 250O f/s
FT - 37AA-N-Z
H-800 YDS
0OO_Y0S
150 YDS/SEC *
70 YDS/SEC *
1000 500
APPROACHING LEG
500 1000 1500
RECEDING LEG
Figure 66.— Variation in ballistic density, crossing- constant altitude
course (lateral lead).
- . JIO %
"90"%*
APPROACHING
T 1
2000 1500
+ 50
YARDS
RECEDING
500 1000
1000
GUN - 37MM
MV-2500 f/3
FT-37AA-N-2
H-SOO YDS
R ft."" l0 _9_0 YDS
150 YDS /SEC * ■
70 YDS/SEC •
S - P°
9 Ljo
90.°^ -j^*
"■"ho"*"
Figure 67. — Variation in ballistic density, crossing-constant altitude
course (vertical lead) .
the disregarding of this effect appears fully justified, except
in case of an extreme change, in which case a correction
126
ANTIAIRCRAFT AUTOMATIC WEAPONS 78-79
such as that above should be made. Such wide variations
will hardly be encountered in the continental United States.
If, in other latitudes, a variation of ± 10 percent in ballistic
density occurs, a flat correction to leads, as above, should
be applied.
d. Wind. — Wind effects as indicated by figure 68, where
usable, are so small as to make consideration of this condi-
tion a useless refinement of approximate data. As stated
in chapter 3, they cannot be used at all on crossing courses
except in a few special cases.
■ 79. Lead Corrections for Differential Effects. — a. Gen-
eral. — The following calculations indicate that corrections
for ballistic density, muzzle velocity, and powder tempera-
ture may be made after leads for standard conditions have
been calculated:
(1) Ballistic density.
10 percent increase=4 percent increase in leads.
10 percent decrease=4 percent decrease in leads.
(2) Muzzle velocity.
100 f/s decrease=5 percent increase in leads.
100 f/s increase=5 percent decrease in leads.
(3) Powder temperature. — The formula is: (temperature
of powder —70°) X proper MV factor for the gun being used.
A+l° P. change in powder temperature from the normal
70° F. gives a+MV in accordance with the table below.
A — 1° P. change reverses the sign of MV.
MV factor
Caliber .30 tracer, solid and AP shot=1.69 f/s
Caliber .50 tracer, solid and AP shot=1.80 f/s
37-mm shell and AP shot =1.62 f/s
40-mm shell and AP shot =1.77 f/s
b. Muzzle velocity correction. — Developed muzzle velocity
should be determined according to the following formula:
(1) Caliber .30 machine gun. — A new gun barrel measures
1.9 inches from the face of the breech to the back of the
projectile. A barrel measures 3.0 inches from the face of
the breech to the back of the projectile when 175 f/s muzzle
velocity has been lost, or when approximately 6,000 rounds
127
79
COAST ARTILLERY FIELD MANUAL
have been fired. Therefore, there is a loss of approximately
3 f/s muzzle velocity per 100 rounds fired.
(2) Caliber .50 machine gun. — A new gun barrel measures
3.0 inches from the face of the breech back to the pro-
APPROACHiNG LEG
UN - 3 7 MM
MV - 2 5 f/j
FT - 37AA-N-2
H-600 YDS
S J- ISO T0S/SEC
+ 30
YAP. S
RECEDING LEG
Figure 68. — Variation in wind velocity parallel to the trajectory,
coming-constant altitude course (vertical lead) .
jectile. Guns which have lost approximately 200 f/s muzzle
velocity measure 6.0 inches from the face of breech to the
back of the projectile. Therefore, there is an increase of
approximately 1.5 inches in breech gaging for each lOOf/s
loss of muzzle velocity.
(3) 37-m.m gun. — According to available information, this
gun loses 200 f/s muzzle velocity after approximately 3,000
128
ANTIAIRCRAFT AUTOMATIC WEAPONS
79-80
rounds have been fired. Thus, there is approximately a
6 f/s loss in muzzle velocity per 100 rounds fired.
c. Method of correcting leads. — (1) Determine the muzzle
velocity correction for powder temperature.
(2) Determine the muzzle velocity correction for barrel
wear.
(3) Add these two muzzle velocity corrections.
(4) Determine the lead correction percentage factor due
to change in muzzle velocity.
(5) Determine the lead correction percentage factor due
to change in ballistic density.
(6) Add these two factors algebraically.
(7) Correct the standard leads by applying this percentage
correction factor.
d. Methods. — In chapter 2 ballistic corrections were deter-
mined as a function of t v and <t>s. However, it is easier to
calculate leads for standard conditions and then make flat
percentage corrections for ballistic changes as shown above.
The latter method checks with sufficient accuracy against
the former method to be advantageously used, and it is thus
recommended.
■ 80. Summary. — The character of the automatic weapons
problem is such that a mastery of the fundamental charac-
teristics of lead curves and of the differential effects for
various types of courses is essential for the" delivery of effec-
tive fire. It is also of the highest practical importance for
officers and adjusters to realize that certain variables are
not as important as others. Ability to estimate quickly and
accurately the leads for a particular course should be instinc-
tive. Such ability can be developed only by the analysis of
lead curves and by experience. The expert "skeet" shooter
has learned from long experience at the sport the proper
lead to allow in order to hit the 25 "birds" from the various
shooting positions. The automatic weapons adjuster has a
more difficult problem in that he must not only learn the
value of the proper lead, but also must learn to take into
account the many conditions under which targets may ap-
pear, such as variations in altitude, speed, range, and angle
of dive.
129
81-83
COAST ARTILLERY FIELD MANUAL
CHAPTER 6
HORIZONTAL FIRE
Paragraphs
Section I. General
II. Antimechanized defense
III. Assault of fortifications
IV. Engagement of water-borne targets.
V. Lateral leads and lead charts
81-82
83-86
87-88
89-91
92-95
Section I
GENERAL
■ 81. General. — FM 100-5 states that the antiaircraft artil-
lery is so equipped that it can execute antitank and other
ground missions when necessary. Experience in the present
war indicates that these weapons are effective against mech-
anized targets and field fortifications. In addition > the
need for weapons with a relatively high muzzle velocity and
rate of' fire may require the assignment of antiaircraft artil-
lery to missions of defense against small, high speed, water-
borne targets.
■ 82. Tactics. — The details of the tactical employment of
antiaircraft automatic weapons against land and water-
borne targets are contained in FM 4-105.
B 83. General. — a. Accuracy of fire. — Although the mecha-
nized target has less speed and maneuverability than the air-
plane, when a mechanized attack does occur, the action is
fast, furious: and of short duration. All personnel must
realize that tanks will appear with little or no warning, and
must be engaged speedily. It is essential that initial fire be
accurate. If opening fire is inaccurate, the tank can easily
seek another avenue of approach or may retire to a defiladed
spot and neutralize the disclosed position. Also when anti-
tank positions are disclosed, they may be attacked by dis-
mounted parties.
Section II
ANTIMECHANIZED DEFENSE
130
ANTIAIRCRAFT AUTOMATIC WEAPONS 83-84
b. Ammunition. — Although HE shell can be used effec-
tively against some targets, armor-piercing ammunition will
be required against most armored vehicles. It is contem-
plated that all antiaircraft armor-piercing projectiles, ex-
cept the caliber .50, will be provided with a tracer element.
In the case of the caliber .50 machine guns, tracer ammuni-
tion is interspersed with armor-piercing to produce a tracer
stream. Muzzle velocities of armor-piercing ammunition
for antiaircraft artillery automatic weapons are shown below
and are the velocities developed by new guns:
Weapon
Ammunition
Muzzle
velocity
(f/s)
Caliber .50 machine gun _ _
Ml.- _
2,700
2,050
37-mm gun _ _ _ . . .
M59
Armor-piercing ammunition is also being developed for
the 40-mm gun.
■ 84. Characteristics of Targets. — a. General. — Mechanized
targets which the antiaircraft artillery automatic weapons
may be required to engage are —
(1) Heavy tanks (50 to 75 tons) . — These are suitable tar-
gets for the 3-inch and 90-mm guns, but normally are not
vulnerable to fire from 37-mm and 40-mm guns except at
very short ranges.
(2) Medium tanks (18 to 35 tons). — These are suitable
targets for 37-mm and 40-mm guns at ranges up to 500 yards.
(3) Light tanks and armored cars. — These are lightly
armored and are suitable targets for all antiaircraft artil-
lery automatic weapons of caliber .50 and above.
(4) Unarmored vehicles. — These are suitable targets for all
automatic weapons including small arms.
b. Vulnerability of tanks. — Tanks are most heavily armored
on turrets and the front of the vehicle. The most vulnerable
areas are the sides, bellies, tracks, and track suspension
mechanisms. Every effort should be made to engage tanks
so that these vulnerable points are brought under fire. To
131
84-85
COAST ARTILLERY FIELD MANUAL
accomplish this, flanking fire is preferable to frontal, and
plunging fire is least effective. It is not necessary to de-
molish a tank to put it out of action. Shell fragments and
small caliber bullets may penetrate vision slits or ports
and destroy the crew or essential tank mechanism. Even
a caliber .30 bullet fired into a turret juncture may jam
the turret and prevent accurate sighting of the tank guns.
At close range, small arms fire should be brought to bear
on the vulnerable points mentioned above.
■ 85. Technique. — a. General. — (1) In order to stop a tank
it must be hit with a force sufficient to penetrate the armor,
to demolish a vital part of the mechanism, or to kill the
crew. In order to obtain the first effective blow, accuracy
of initial fire is desired above all else.
(2) Prom a gunnery standpoint the accuracy of fire on a
moving tank is in part a function of the muzzle velocity and
the range at which the target is engaged. At short ranges
the maximum ordinates of trajectories of antiaircraft auto-
matic weapons is only a few feet. The target is usually high
enough to receive hits even though small errors are made
in range pointing, because of the flatness of the trajectory.
Moreover, the shorter time of flight results in a smaller lat-
eral lead. At longer ranges, not only are lateral leads greater,
but smaller errors in range pointing may result in complete
misses because of curvature of the trajectory.
&. Fire control. — (l) Power-trained 37-mm and 40-mm
guns can. be fired at ground targets with the same director
control used against airplanes. By changing the position of
the mechanical stops on the guns slightly, these guns can
be used effectively with director control. These stops must
be adjusted so the gun will cut out slightly below zero quad-
rant elevation; otherwise the gun is apt to cut out from
power control while firing at or near zero degrees. When a
power-controlled unit must suddenly engage a ground target,
director control will be used.
(2) When units are controlled with central tracer equip-
ment for antiaircraft fire, this same method may be used for
antimechanized fire if only a single target must be engaged.
Where more than one target must be engaged by the unit,
132
ANTIAIRCRAFT AUTOMATIC WEAPONS
85
direct pointing by the individual gunners will be resorted to.
This will be accomplished if the control box is set to normal
and each gun pointer leads his target the necessary amount.
(3) Compared to airplanes, the speed of mechanized tar-
gets is low and the ranges at which these targets are engaged
are short. Consequently, the leads required for fire against
mechanized targets are small enough to be estimated and
applied by the gun pointers.
(4) A discussion of the latter method, as it applies to the
different types of automatic weapons, is contained in c and
d below. All members of antiaircraft gun crews, including
ammunition details, should be so thoroughly trained in the
estimation of speeds and ranges, and the application of leads
for fire against mechanized targets, that they can perform the
duties of gun pointers under the stress of antimechanized
action.
c. Caliber .50 AA machine guns. — (1) Fire should not be
opened at ranges greater than 400 yards.
(2) At such ranges, the maximum ordinate of the trajec-
tory is less than 3 feet. As a result a flat correction for
superelevation (0 S ) may be applied and the sights themselves
will supply the correct angle of site. Before opening fire, a
vertical deflection of plus 3 mils should be set on the sights.
The target should be tracked for elevations on the line of the
top track housing.
(3) Lateral leads are best estimated in terms of target
lengths that is, the over-all length of the silhouette as seen
by the gunner, and are measured from the leading edge of the
target. The gun should be swung across the target and the
swing continued until the proper number of target lengths
lead has been taken. Fire is then opened and adjustment
made by individual tracer control.
(4) The following tables showing the proper aiming point
on the target or the correct lateral lead in target lengths
to hit the center of the target are presented as an aid for
training. It is not expected that these tables will be used
during actual fire because gun pointers should be so thor-
oughly drilled in their use that the application of correct leads
becomes a matter of second nature. Leads are always meas-
133
85 COAST ARTILLERY FIELD MANUAL
ured from the leading edge of the target. See paragraph 92
for a method of calculating the lateral leads.
LATERAL LEADS IN TARGET LENGTHS
Caliber .50 Ml ammunition (MV 2,700 f/s)
Target speed, 15 miles per hour
Target crossing perpendicular to line of site:
Range in yards
Target length
4 yards
6 yards
8 yards
100__.
Forward edge
Center... _._ ._
Center.
Forward edge.
Do.
Do.
200--.. —
do
Forward edge.
300
U
do
400
H-
U-
Target crossing at 45" to line of site:
Range in yards
Target length
4 yards
6 yards
8 yards
100
Center __. . -..
Center. _
Center.
Do.
Forward edge.
Do.
200. .
Forward edge
do
300
do
Forward edge.. .. ..
400
H-
do..-
Target speed, 30 miles per hour
Target crossing perpendicular to line of site:
Range in yards
Target length
4 yards
6 yards
8 yards
100
Forward edge _.
Forward edge ___
Forward edge.
Do.
M-
54
200
Vi
Vi -
300. _
1
H— -
400
1H— -
M — -
134
ANTIAIRCRAFT AUTOMATIC WEAPONS 85
Target crossing at 45° to line of site:
Range in yards
Target length
4 yards
6 yards
8 yards
100,.
Forward edge. . _.
Center.
Center.
Forward edge.
Do.
200
X
Forward edge.. . ...
300
K
H -
400
H
H - -
d. 37 -mm and 40-mm guns. — (1) Fire should not be opened
at ranges greater than 600 yards.
(2) At these ranges, as in the case of the machine guns,
the trajectory of even the M59 projectile (MV 2,050 f/s) is
Figure 69. — Correct pointing for range with M7 telescope. Hori-
zontal cross-hair on top track housing.
sufficiently flat to permit the use of a single correction for
superelevation (<f>s) for all ranges. Superelevation of +6 mils
should be applied and the horizontal cross-hair of the vertical
sight carried on the top track housing of the tank as shown in
figure 69.
(3) Lateral leads are estimated and applied by the gun
pointer as shown in figure 70. The following tables, similar
135
85
COAST ARTILLERY FIELD MANUAL
to those described in paragraph c(4) above for the caliber .50
machine guns, are presented as an aid for training:
LATERAL LEADS IN TARGET LENGTHS
37-mm M59 ammunition (MV 2,050 f/s)
Target speed, 15 miles per hour
Target crossing perpendicular to line of site:
Range in yards
Target length
4 yards
6 yards
8 yards
100.
200.
300.
400.
600..
600.
Forward <
— .do.-..
Center, _ .
Forward c
....do....
H
H -
%
Center.
Forward edge.
Do.
M-
Yi.
H.
Target crossing at 45° to line of site:
Range in yards
Target length
4 yards
6 yards
8 yards
100.
200.
300.
400.
600.
600.
Center
Forward edge.
_...do
a.—
H -
Vi -
Center. . _
Forward e
....do....
-..do....
Ji
X
Center.
Do.
Forward «
Do.
Do.
Yi.
Target speed, 30 miles per how-
Target crossing perpendicular to line of site:
Range in yards
Target length
4 yards
6 yards
8 yards
100..
200..
300.
400.
600.
800.
Forward edge.
1H-
2...
2H-
3H-
Forward (
H- -
%- -
IK
1H-
2
Forward e
Do.
Vi-
i.
136
ANTIAIRCRAFT AUTOMATIC WEAPONS
Target crossing at 45° to line of site:
85-86
Range in yards
Target length
4 yards
6 yards
8 yards
100
Forward edge
Forward edge
Center.
Forward edge.
Do.
Yi-
H.
%■
200
Yi.
....do
300
H
Yi
400
M
H
600
1H
l
600
2
iJi- — - -
Figure 70. — Correct lateral lead with M7 telescope. Lead measured
from leading edge of target.
(4) Fire will be adjusted by tracer control. Since dust
from the muzzle blast may obscure the target and interfere
with rapid adjustment of fire, all possible steps should be
taken to prevent this interference.
■ 86. Principles of Antitank Firing. — a. It is essential that
fire be held until targets are within the ranges discussed
previously for each weapon. Opening Are must be accurate,
for it is probable that once an antiaircraft artillery position
has been disclosed, no movement to alternate positions
can be made during that phase of the battle. The shorter
the range at which fire is opened the greater is the probabil-
ity of obtaining hits with the opening rounds.
137
36-88
COAST ARTILLERY FIELD MANUAL
b. Fire will be opened as prescribed by the platoon or fire-
unit commander for 37-mm and 40-mm guns. In general,
as many targets as possible within range will be engaged by
the guns of a fire unit. The fire of more than one gun on one
target will be ordered only when no other suitable target
presents itself for the second gun.
c. The crews of moving tanks are relatively deaf, and blind
except in a narrow sector to their front. These handicaps
should be exploited by the use of ambush wherever possible.
For example, three tanks which appear to be traveling a
course that will take them to the flank of a gun position
should be permitted to come almost abreast of the position
and the last tank in the column engaged first, then the
second in column; and, last, the first in column,
d. On the other hand, when tanks approach and threaten
a gun position, the tank which is most menacing (usually the
closest to the gun) should be fired upon until hit; then the
next nearest (or most menacing) should be fired upon.
It must be noted, however, that the most effective fire from
tank guns is obtained when firing from a halted tank. Con-
sequently, a halted tank that is firing upon the gun position
may be more menacing than a closer, moving tank.
e. When a tank has been stopped, one more round should
be fired into it before another target is engaged. However,
no effort should be made completely to destroy disabled tanks
as long as a mobile tank is within range or view, unless the
disabled tank is firing upon friendly troops.
Section m
ASSAULT OF FORTIFICATIONS
■ 87. General. — The targets which the antiaircraft artillery
automatic weapons may be required to engage are the ports
and embrasures of fortifications.
■ 88. Technique. — a. In the assault of a permanent fortifi-
cation, the mission of the antiaircraft artillery is to require
the defenders to keep ports closed and deny their use for
returning fire. This mission can be effectively accomplished
by 37-mm and 40-mm guns firing HE shell with supersensi-
138
ANTIAIRCRAFT AUTOMATIC WEAPONS
88-89
tive fuze. Where the actual destruction of smaller works
is required, direct fire by 3-inch and 90-mm guns firing
armor-piercing shot will probably be required. In either case
the problem involves direct laying on a stationary target,
and the comments made in paragraph 85 are appropriate for
this mission.
b. In order that opening rounds will fall near the target,
ranges should be determined as accurately as possible and
translated into vertical deflections and applied to the M7
sights of the automatic weapons. Since the effects of wind
and drift are usually negligible at short ranges, no lateral
corrections are indicated for opening fire. Adjustment of fire
will be as described in paragraph 85.
Section IV
ENGAGEMENT OF WATER-BORNE TARGETS
■ 89. General. — a. The employment of antiaircraft artillery
automatic weapons against water-borne targets may be nec-
essary due to the need for weapons with relatively high
muzzle velocity and high rate of Are which can be used against
high speed maneuvering, small water-borne targets. The
fact that our present antiaircraft materiel was not designed
for and is not basically suited for use against water-borne
targets must be borne in mind before a decision is reached
to employ these weapons on such missions.
6. (1) In approaching the problem of employment of anti-
aircraft artillery automatic weapons against water-borne
targets, it is necessary to consider the probable enemy target
and tactics. Due to the comparative newness of the motor
torpedo boat and the lack of information as to its employ-
ment, many assumptions will have to be made.
(2) It is visualized that motor torpedo boats will operate
in groups of about five. They will depend on their speed
-and maneuverability for protection against fire from shore
batteries. They will attempt an attack at high speed in or-
der to take advantage of the element of surprise.
(3) Motor torpedo boats have the following character-
istics :
(a) Length, from 55 to 100 feet.
(b) Width, from 13 to 20 feet.
139
89-91
COAST ARTILLERY FIELD MANUAL
(c) Speed, from 30 to 60 miles per hour.
(ci) Radius of action, up to 1,000 miles at reduced speed.
(e) Hull construction, almost entirely of wood.
(/) Low silhouette, about 10 feet above water line.
■ 90. Available Antiaircraft Artillery Weapons. — a. The
weapons to be considered for use against water-borne targets
are the 37-mm and 40-mm automatic weapons, with their
standard and emergency fire-control systems.
b. In general, the 3-inch or 90-mm antiaircraft guns should
be used for defense against motor torpedo boats. Although,
in some cases, the 37-mm and 40-mm guns may have sufficient
range capabilities for the purpose, their caliber is too small to
insure sufficient damage from one hit. The larger caliber
guns will permit firing at greater ranges, thus increasing the
time that the targets can be taken under Are, and will also
insure destructive effect from one hit. In addition, ricochet
bursts from the larger caliber guns may cause considerable
damage.
c. In general, two-gun fire units should be used. This is the
standard unit for the 37-mm gun with central tracer con-
trol. The 37-mm and 40-mm guns with director control
will have to fire as individual guns. Thus, they may engage
either one or two targets simultaneously.
■ 91. 37-mm and 40-mm Materiel. — a. General. — In general,
effective fire from the 37-mm and 40-mm automatic cannon
against motor torpedo boats can be obtained only by accu-
rate adjustment of fire. This adjustment is facilitated if
the rate of fire is held to about 60 shots per gun per minute,
using single shot operation instead of automatic fire. This
condition is believed to be true of each of the methods of
Are control discussed below.
b. 37-mm gun with control equipment set Ml. — In this
case a two-gun fire unit sited as low as feasible is used. It
will be found advantageous to site the control station above '
and in rear of the guns in order to make the determination
of overs and shorts easier. Initial lateral and vertical leads
must be estimated. These leads are altered by the control
station operators, based on their observation of the lateral
and vertical deviations of the splashes from the target. Fire
140
ANTIAIRCRAFT AUTOMATIC WEAPONS
91-92
will be relatively Ineffective beyond a range of 2,500 yards
because of the difficulty of sensing splashes correctly.
c. 37-mm and iO-mm guns with directors of Kerrison type
(M5 or M6). — The effective use of these directors requires
that the gun and director be sited as low as feasible. Fire
should not be opened beyond 2,000 yards' range because of
mechanical limitations of these directors. The range setter
should estimate and set into the director a slant range to-
ward which the target's course is tending and hold this value
until it is evident that either a hit is obtained or the slant
range set is obviously too long or too short.- The slant range
should be corrected then in bold steps of about 500 yards in
the indicated direction. It will be found that, because of the
height of the director, the range setter will rarely have an
unobstructed view of the target and must depend, in order
to adjust slant range, on the sensings of the overs and shorts
repeated to him by the trackers. Sensings of overs and
shorts are comparatively easy for the trackers since, in
general, the splash of a short will eclipse the target and the
splash of an over will silhouette it.
d. 37-mm and 40-mm guns using gun sights. — The same
method is employed using gun sights as is used with the
control equipment set Ml. However, both vertical and lat-
eral initial leads will be estimated and applied by the gun
pointers and adjusted in accordance with their observation
of the fall of shots. Generally, this method will be less
effective than either director or central tracer control and
should be resorted to only in the event that director control
cannot be used.
Section V
LATERAL LEADS AND LEAD CHARTS
■ 92. Lateral Leads. — a. When a mechanized target is mov-
ing perpendicular to the line of site, the value of the lateral
lead depends upon the travel of the target during the time
of flight of the projectile. The time of flight of a caliber .50
Ml projectile for a range of 100 yards is given on page 8 of
FT 0.50-AA-E-4 as 0.14 second. During this 0.14 second,
a mechanized target traveling at a speed of 15 miles per
473316°— 42 10 141
92
COAST ARTILLERY FIELD MANUAL
hour will move 0.14 second times 7.5 yards per second or
1.05 yards. If the forward edge of a 4-yard mechanized tar-
get were used as the aiming point, the projectiles would hit
the target about 1 yard from the front. The center of the
target would be used as the aiming point if the targets were
TANK AT INSTANT
OF FIRING
\ V \
TANK AT INSTANT
OF IMPACT
AIMING POINT
7/4 TARGET LENGTH
PATH OF
PROJECTILE I
1
1 \ ^
ujIuj
o|o
- -
-jl-l
. I
Figure 71. — Target crossing at 45° to line of site.
6 or 8 yards long. Similar calculations may be made for
200, 300, and 400 yards' range and the location of the aiming
point with respect to the target determined.
b. When a mechanized target is crossing at 45° to the
line of site, the value of the lateral lead depends upon the
lateral component of the travel of the target during the time
of flight of the projectile. In this case, the target length
142
ANTIAIRCRAFT AUTOMATIC WEAPONS
92-93
is the over-all length of the silhouette as seen by the gunner.
The time of flight of a caliber .50 Ml projectile for a range
of 400 yards is 0.51 second. During this 0.51 second, a mech-
anized target traveling at a speed of 15 miles per hour will
move 0.51 seconds times 7.5 yards per second or 3.82 yards.
If a lateral lead of Vt target length were taken on the leading
edge of the silhouette of tank as shown in figure 71, the path
of the projectile would be approximately through the center
of the target.
■ 93. Lead Charts. — a. Use. — A knowledge of the construcr
tion of lead charts, length and height of targets in terms of
mils, and the conversion of lead chart leads into leads in
terms of target lengths for horizontal fire will be of value
for the determination of the correct lateral and vertical leads
in terms of target lengths for any course and speed of the
target.
b. Basic assumptions. — The computation of lateral and ver-
tical leads for horizontal fire is a simple process of solving
right triangles and taking certain data out of firing tables.
Certain assumptions are made that are not exactly correct,
but which are so nearly correct that no error of any magni-
tude is introduced into the results by their acceptance. Such
errors are within the probable error of the guns.
(1) It is assumed that initial lateral lead will increase in
direct proportion to the increase in target speed up to 50
miles per hour.
(2) It is assumed that vertical lead is exactly equal to
superelevation for the horizontal range to the target, and
that it is not affected by speed.
(3) It is assumed that leads will be the same on both the
approaching and the receding leg of a crossing target.
c. Computation form. — The following form has been de-
vised for use in computing leads for horizontal Are. One
such form will be required to figure the lateral and vertical
leads for one target, for one speed, and for one range to mid-
point (Rm). The form itself is self-explanatory, as is the
method of making the computations with the Crichlow slide
rule.
143
93
COAST ARTILLERY FIELD MANUAL
144
ANTIAIRCRAFT AUTOMATIC WEAPONS
1.18
O
tH
CO
o
3
0.98
o
o
OS
CO
1, 012
OS
0. 85
OS
OS
1,286
CO
CO
0. 80
00
00
1, 586
^tj
CO
0.85
OS
1,260
CO
00
0.98
©
O
T}H
OS
00
OS
OS
1.18
CN
CO
s
o
From firing tables using R„
Scale B
+ on approaching leg — on receding leg
Scale i
ho
CD
« Wl
.a »
,Q d
»s
as
cs a
a°
°.»
o 1
c
<f> t — From firing tables using i? p
Line 4
Scale E
Index
Scale E
Index
Scale E
Rm or Lc
(smaller)
Scale E
Scale E
i
i
V.
*!
i
n
\
CO
41
h
4
n
>-)
00
It
•j
b
OS
145
94
COAST ARTILLERY FIELD MANUAL
■ 94. Construction of Lead Charts. — One very useful way to
construct lead charts is to plot and draw isolead curves of
the computed lead values. One chart will be constructed for
lateral and another for vertical leads. Vertical and lateral
leads are computed for one speed of target. Figures 72 and
CURVES of CONSTANT LATERAL LEAD — HORIZONTAL FIRE
37-mm GUN Speed 20m.p.h. F.T. 37AA-N-2
(Rm-ydsJ
Figure 72. — Lateral lead chart, horizontal fire.
73 illustrate lateral and vertical leads for a 20 mph
…[truncated]