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Distribution authorized to U.S. Gov't. agencies and their contractors; Administrative/Operational Use; Nov 1967. Other requests shall be referred to US Army Ballistic Research Lab., Aberdeen Proving Ground, MD.
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Army Armament R&D Ctr, Aberdeen Proving Ground, MD ltr dtd 20 Feb 1981
THIS PAGE IS UNCLASSIFIED

14A

REPORT NO. 1371
THE PRODUCTION OF FIRING TABLES FOR CANNON ARTILLERY

030

by

let

Elizabeth R. Dickinson

November 1967

This document is subject to special export controls and each transmittal to foreign governments or foreign nationals may be made only with prior approval of Commanding Officer, U.S. Army Ballistic Research Laboratories, Aberdeen Proving Ground, Maryland

U. S. ARMY MATERIEL COMMAND
BALLISTIC RESEARCH LABORATORIES
ABERDEEN PROVING GROUND, MARYLANP

Destroy this report when it is no longer needed. Do not return it to the originator.

....

.... .. .

i

The findings in this report are not to be construed as
an official Department of the Army position, unless so designated by other authorized documents.

SBALLISTIC

RESEARCG1 LAbUKA REPORT NO. 1371 NOVEMBER 1967

OIURES

THE PRODUCTION OF FIRING TABLES FOR
CANNON ARTILLERY Elizabeth R. Dickinson Computing Laboratory
This document Issubject to special export controls and each transmittal to foreign governments or foreign nationals may be made only with prior Sarpoval of Commanding Officer, U.S. Army Ballistic Research Laboratories, Aerdan Proving Ground, Maryland

RDT&E Project No. 1T523801A287 ABERDEEN P ROVING GROUND, MARYLAND

I

BALLISTIC

RESEARCH LABORATORIES REPORT NO. 1371

ERDickinson/sw Aberdeen Proving Ground, Md. November 1967

I I

THE PRODUCTION OF FIRING TABLES
FOR

CANNON ARTILLERY

SABSTRACT

This report describes in detail the acquisition and analysis of firing data as well as the conversion of the measured data to printed firing tables.

I,

3

3.

TABLE OF CONTENTS

ABSTRACT.......................................

......

3

I.

TABLE OF SYMBOLS AND ABBREVIATIONS ......... ... ............

7

II.

INTRODUCTION .......

....... ......................

. . .. 10

III. REQUIREMENT FOR A FIRING TABLE ...................

........

11

IV. ACQUISITION OF DATA FOR A FIRING TABLE .......

......

.... 12

A. Data for Velocity Zoning ....... ...........

.........

12

B. Data for Provisional Table ..... ..... ........

..... 15

C. Data for Final Table .....

...

. . .....

16

V. ANALYSIS OF RAW DATA ...............

... ..

21

A. Equations of Motion

. . . . . . . . . . . . . . 21

B. Drag Coefficient . . . . . . .

. ......

. 23

C. Reduction of Range Firing Data ...........

. 24

1. Preparation for Reduction for Ballistic Coefficient • 24

a. Formation of Points .......

. . . 24

b. Meterological Data

... . . . . .

. . 25

c. Muzzle Velocity . . . . . . . ........

.. 25

d. Means and Probable Errors, per Point

.

e. N-Factor . . . . . . . . .

..

.

. . 27
. . 28

f. Change in Velocity for a Change in Propellant

Temperature . . . . . . . . . . ........

31

g. Compensation for Rotation of Earth .. ....... ... 32

2. Reduction for Ballistic Coefficient . ......

32

a. Ballistic Coefficient and Jump . . .......

32

b. Change in Range for Change in Elevation, Velocity

and Ballistic Coefficient . . .........

40

4

I

TARBLE O1F rnNTRNTS (Ccntinued)

Page

c. Drift . . . . . . . . . . . . . . . . . . . . 40
II
d. Time . . . . . . . . . . . . . . . . . . . . . 41

3. Probable Errors, per Charge ...... ............ a. Probable Error in Range to Impact .....

.. 43 ....... 43

b. Probable Error in Deflection .... .........

.. 44

4. Fuze Data . . ..........

. . . . . . . . . . 45

a. Fuze Setting . . . . . . . . . . . . . . . . . . 45

b. Probable Error in Time to Burst . . . . . . . . .46

c. Probable Error in Height of Burst and Probable Error in Range to Burst .......... . 47
5. Illuminating Projectile . . . . . . . . . . . . . . . 47

VI. COMPUTATIONS FOR THE TABULAR FIRING TABLE . . . . . . . . . . . 50

A. Table A: Line Number . . .

.. . . 50

B. Table B: Complementary Range and Line Number .....

55

C. Table C: Wind Components ........

. . . . . 58

D. Table D: Air Temperature and Density Corrections . . . 58

E. Table E: Propellant Temperature . . . . . .

59

F. Table F: Ground Data and Correction Factors . .

59

G. Table G1 Supplementary Data ........

...

62

H. Table H: Rotation (Corrections to Range) ..

. . . 64

I. Table I: Rotation (Corrections to Azimuth) .

. ..

66

J. Table J: Fuze Setting Factors

.. ........

.67

K. Table K: AR, AH (Elevation) . . .....

. . ..

.

67

L. Table L: &R, AR (Time) ........

......

. 69

M. Table M: Fuze Setting . . .

. . . .....

. 70

5

TABLE OF CONTENTS (Continued)

r age

N. illuminating Projectile ....... .................

... 70

0. Trajectory Charts ...... ... ......................

72

VII. PUBLICATION OF THE TABULAR FIRING TABLE ...........

74

VIII. ADDITIONAL AIMING DATA ..............

....................

75

A. Graphical Equipment ...........

..................

.. 75

1. Graphical Firing Table .

..............

. 75

2. Graphical Site Table . . . . .....

...............

78

3. Wind Cards . . . . . . . . . . . . . . . . .

. 80

4. Graphical Equipment for Illuminating Projectiles . 84

B. Reticles and Aiming Data Charts . . . ..........

86

REFERENCES . . . . . . . . . . . . . .

. . . . . . 90

APPENDIX . . .

. . . . . .. 93

DISTRIBUTION LIST . . . . . . . . . . . . . . . . . . . . . I.1

p

6

AC
BRLESC
C CDC CS D

1. TABLE OF SYMBOLS AND ABBREVIATIONS
Azimuth correction for wind
Ballistic Research Laboratories Electronic Scientific Computer
Ballistic coefficient Combat Developments Command Complement~ary angle of site Deflection, drift

C

F

Fork

FS

Fuze setting

PSC

Fuze setting correction for wind

G

G~vre function

GFT

Graphical firing table

GST

Graphical site table

H "Heavy,

height

!

ICAO

International Civil Aviation Organization

J

Jump

KD

Di Drag coefficient

L

Latitude, lightweight, distance from the trunnion of

the gun to the muzzle

M

Mach number (velocity of projectile/velocity of sound),

MDP

Meteorological datum plans

MPT

Mean firing time

MLW

"Mean low water

I. IAaL6 U' SiThiOLS AND ABBREVIATiONS (uUiLiuuud)

MRT

Mean release time

MSL N-Factor

Mean sea level Factor for correcting the velocity of a projectile of
nonstandard weight

PE

Probable error

QMR

Qualitative materiel requirement

R

Range

RC

Range correction for wind

S

Spin

T

Observed time of flight, target

V

Velocity

VI

Vertical interval

Wh
W W
x W
z Z axpay a z
d Sg h n

Headwind
Tailwind Range wind
Cross wind
Deflection Accelerations due to the rotation of the earth
Diameter Acceleration due to gravity Height of the trunnions of the gun above mean low water Calibers per revolution, 1/n - twist in revolutions per
caliber
8

I

I. TABLE OF SYMBOLS AND ABBREVIATIONS (Continued)

s

Standard deviation

t

Computed time of flight

x

Distance along the line of fire

y

Height

z

Distance to the right or left of the line of fire

of ti.e line of fire

S

Chart direction of the wind

Azimuth of the wind

X1,2,3 0 p

Components of the earth's angular velocity Angle of elevation, angle of departure Air density as a function of height Angular velocity of the earth

Mil

Subscripts

First and second derivatives with respect to time

o

Initial value

n

Nonstandard value

s

Standard value

W

Final value

SAzimuth

9

II. INTRODUCTION

Ideally, a firing table enables the artilleryman to solve his fire

problem and to hit the target with the first round fired. In• the pre-

sent state of the art, this goal is seldom achieved, except coinci-

4 dently. The use of one or more forward observers, in conjunction with the use of a firing table, enables the artilleryman to adjust his fire

and hit the target with the third or fourth round fired.

It is, however, the ultimate goal of the Firing Tables Branch of

the Ballistic Research Laboratories (BRL) to give the artilleryman the

N-P

tool for achieving accurate, predicted fire.

This report is concerned with the steps involved in the production

;V

of a current artillery firing table. with principal emphasis on the

conversion of measured data to printed tables. No report has been published on the computational procedures for producing firing tables

since that of Gorn and Juncosa(I)* in 1954. As a new high speed compu-

ter, with a much larger memory, the Ballistic Research Laboratories

Electronic Scientific Computer (BRLESC), has been added to the compu-

ting facilities at BRL, the computation of firing tables has become

more highly mechanized than it was in 1954.

Ni description has been published of the process by which the

necessary data for a firing table are acquired. Thus, the purpose of

this report in two-fold: to update the work of Gorn and Juncosa, and

to trace the history of a firing table from the adoption of a new weapon

or a new piece of anmunition to the publication of a table for the use

of that weapon or ammuni.tion in the field.

*Superscriptnumbers in pare:itheses denote references which may be found

on page 90.

10

III. REQUIREMENT FOR A FTRTNC TARBL Whenever a new combination of artillery weapon and ammunition goes

into the field, a firing table must accompany the system. There is a

rather lengthy chain of events leading up to the placing in the field of a new weapon or a new projectile. Initially, the requirement for

such an item is written by the Combat Developments Command (CDC). The qualitative materiel requirement (QMR) set up by CDC is very detailed,

listing weight, lethality, transportability and many other attributes

as well as performance characteristics.

After the item has passed through the research and development

stage, it is subjected to safety, engineering and service tests.

When

all tests are passed satisfactorily, the item is classified as standard

and goes into production. As soon as the production item is available,

it and its firing table are released to troops for training. Thus as soon as a QMR is published, it is known that a firing table
will be ultimately required. In addition, a provisional firing table

will be needed to conduct the firings for the various tests of the item.

rI
I
IV. ACQUISITION OF DATA FOR A FIRING TABLE We acquire data for firing tables in several stages and for several purposes: to provide velocity zoning, to produce a provisional table and to produce a final table. A. Data for Velocity Zoning Velocity zoning can be defined as the establishment of a series of finite weights of propellant, called charges, which are to be used to deliver a projectile, by means of a given weapon system, to certain required ranges. Within each zone, or charge, an infinite variation of elevations permits the gunner to deliver the projectile at any range up to the maximum for that charge. Zoning gives flexibility to a weapon system. For a given projectile, fired from a given weapon, by means of a given propellant, the range of that projectile is a function of the elevation of the tube and of the amount of propellant used. For a given amount of propellant, maximum range is reached with an elevation in the neighborhood of 459. The maximum amount of propellant which can be used is governed by the chamber volume of the weapon and by the maximum gas
pressure which the weapon can safely withstand. It is the responsibility of the Firing Tables Branch of the Ballistic
Research Laboratories to zone artillery weapons. The zoning is done in such a way as to meet the criteria established by the qualitative materiel requirement. THE QMR establishes (1) either a maximum range or a maximum muzzle velocity, (2) a minimum range, (3) a low or high elevation criterion, or a mask clearance criterion, and (4) the amount of range overlap. These criteria will be discussed on the following page.
12

The first step in the zoning process is to compute a series of traJectories, all at an elevation of 450, at various muzzle velocities up to and including the maximum velocity. From these data a plot is then made of muzzle velocity versus range. The next step is determined by the criterion set up by the QMR in (3), above, with its three possibilities. (a) If the weapon is a gun, trajectories may be computed for various muzzle velocities, all at an elevation of 15*. (b) If the weapon in a howitzer, trajectories may be computed at various muzzle velocities, all at an elevation of 70. (c) For either type of weapon, however, a mask clearance criterion may be used. A mask clearance
requirement might be stated as: 300 meters at 1000 meters. In other words, all trajectories must clear a height of 300 meters at a distance from the weapon of 1000 meters. If this is the criterion established by the QMR, a series of trajectories is computed at various muzzle
velocities, all clearing a 300 meter mask at 1000 meters. Thus, depending on the requirements for the weapon system (150, 70"
or mask clearance), data are obtained for a second velocity-tange relationship. These values are plotted on the same graph with the 453 curve. By means of these two curves, zoning is now done graphically.
If the maximum rane has been established by military requirements, the horizontal line is drawn, between the two curves, that intersects the 450 curve at this range (Figure 1). This is the velocity for the zone with greatest range (highest charge). If, however, the maximum velocity has been established, the horizontal line is drawn that
The method by which trajeotories are computed is described in Section V.
13

I
r 1000-

""600

RANGE •Xi
MASK CLEARANCE:
300M AT IOQOM

CHG. 3

>
J

RANGE' Xt. Ix
I

N

ip

400

i0000

20000

RANGE (M)

"Figure1, Vetocity zoning for artillery weapons

30000

14

I
intersects the two curves at this velocity. This line's intersection with the 45*-curve will show the maximum attainable range. Usually, the QMR states that zoning must provide for a 10 percent range overlap between successive zones. This overlap is determined by computing 10 percent of the minimum range on the horizontal line, adding this to the minimum range and dropping a perpendicular from this point to the 45 0 -curve. From this point of intersection, a horizontal line is drawn to the other curve, determining the next lower charge. This process is continued until the minimum range, set by military requirements, is reached. The number of charges for a typical gun system is three; for a typical howitzer system, seven.
The tests that are conducted during the research and development stage of the item's existence are all fired with the charges established by this zoning. If the item is so modified that the zoning no longer satisfies the QMR, a new velocity zoning is established. Thus, at the end of the research and development stage, final zoning has been established. B. Data for Provisional Table
A firing table is basically a listing of range-elevation relationships for a given weapon firing a given projectile at a given velocity under arbitrarily chosen "standard" conditions. In addition, information is given for making corrections to firing data due to nonstandard conditions of weather and materiel.
This type of data is necessary for the conduct of safety, engineering and service tests of a weapon system, before it can be accepted and classified as standard. Hence a provisional firing table must be provided
15

rI
for firing these tests. The data for a provisional table are gleaned from all available firings during the research and development phase. These data do not come from a series of firings designed to furnish firing table data, hence the provisional table is at best as accurate an estimate as can be made of the range-elevation relationship of the system, and of the effects of nonstandard conditions. This type of table is adequate, however, for conducting the tests. C. Data for Final Table
A range firing program is drawn up and submitted, for inclusion in
the engineering tests, to the agency that will be conducting those tests. The program is so designed (Table I) that the range-elevation relationship with both standard and nonstandard material can be determined. Only two nonstandard conditions of material are considereds projectile weight and propellant temperature. The arbitrarily chosen "standard" propellant temperature for United Shates artillery chmunition is 70t Fahrenheit.
At the time of firing, pertinent observed data are recorded and forwarded to the Firing Tables Branch (Table II). From the firing and meteorological data obtained, corrections can be determined for nonstandard conditions of weather: wind velocity and direction, air temperature and density.
Because of the mission of an illuminating projectile, less accuracy of fire is required than with an HE projectile. A range firing progran for an illuminating projectile is, consequently, less extensive. A typical firing program is shown in Table I11.
16

Ts1, T. TNnirq1 Rqnnp Firing Prnarnm fnr HE Proiectiles
105mm Howitzer M108 firing
HE Projectile Ml

Elevation (degrees)

•. Qo Rounds

Condition

5

10

15

20

25

20

35

20

45

10

55

20

65

10

(Max. trail) -3

10

Std. wt. (33 Ibs), std. temp. (70*F).
Std. wt., 10 rds. at 70*, alternating w/10 rds. at 1250.
Std. wt., 10 rds. at 70', alternating w/10 rds. at 0*.
Std. wt., 10 rds. at 70°, alternating w11O rdu. at -40*.
Std. wt., std. temp.
Std. temp., 10 rds. of 32.5 lbs., alternating w/10 rds. of 33.5 lbs.
Std. wt., std. temp.
Std. wt., std. temp.

The above program of 120 rounds is to be fired for each of the seven charges with propellant M67i

17

p.
Table II. Complete Range Data for Artillery and Mortar Firing Tables
A. General Information 1. Weapon a. Complete nomenclature b. Length of tube, defined as distance from trunnions to muzzle 2. Projectile a. Complete nomenclature b. Lot number 3. Fuze a, Complete nomenclature b. Lot number 4. Propellant a. Complete nomenclature b. Lot number 5. Impact data* a. Land: height of impact area above mean low water or mean sea level b. Water: tide readings every hour-bracketing times of firing
B. Metro** 1. Metro aloft every hour - bracketing times of firing 2. Altitude of met station above mean low water or mean sea level
Impact data are not to be supplied for i~luminating sheZZ. Time to buret, range to buret and height of buret above MLW or MSL are required instead. *Metroreferenoed to the line of fire.
18

1

(Continued)
C. Round-by-Round Data 1. Date 2. Time of firing 3. Test round number and tube round number 4. Azimuth of line of fire 5. Height of trunnions above mean low water 6. Angle of elevation (clinometer), before and after each group 7. Charge number 8. Propellant temperature 9. Fuze Temperature (when applicable) 10. Projectile temperature (when applicable) 11. Projectile weight 12. Slant distance from gun muzzle to first coil, and between coils 13. Coil time 14. Time of Flight 15. Range 16. Deflection* 17. Fuze setting (when applicable)
Not required for il.uminating sheZl. 19

Trlp TYTT. Tynirel Ranne Firina for Illuminatina Prolectiles*
105tmw HowlLzer M108 firing
Illuminating Projectile M314

Charge
1 2 3

Elevation (degrees)

20

25

30

35

40

45

x

x

X

x

X

X

X

4

X

X

X

X

5

x

x

x

x

6

X

X

K

X

I

7

x

X

x

x

10 rounds are to be fired under each condition.

J

Al• oharges are not fired at all elevations, beoause low oharges will not fire the prodeatile to the requisite height (750 meters) at low elevations.
20
I1

I
V. ANALYSIS OF RAW DATA We- 1usL select the appropriate equations of motion and the appropriate drag coefficient in order to reduce the range firing data. A. Equations of Motion
The equations of motion, incorporating all six degrees of freedom of a body in free flight, have been programmed for the BRLESC and are used for the burning phase of rocket trajectories. (2) The procedure is a very lengthy one, however; even on the very high speed BRLESC, average computing time is approximately 4 seconds per second of time of flight. For cannon artillery tables, this computing time would be prohibitive. In preparing a firing table for a howitzer, we compute about 200,000 trajectories having an average time of flight of about 50 seconds. This would
mean approximately 10,000 hours of computer timel
In contrast, the equations of motion for the particle theory, which are currently used for computing firing tables for cannon artillery, use far less computer time: approximately 1 second per 160 seconds of time of flight. For the same howitzer table used as an example above, approximately 20 hours of computer time are required.
Although the trajectory computed by the particle theory does not yield an exact match along an actual trajectory, it does match the end points. For present purposes, this theory provides the requisite degree of accuracy for artillery firing tables. •This long oomputing time is for spinning projectiles. Machine time for
nonspinning or slowly spinning rockets and missiles is in the ratio of approximately 100 seconds per 60 seconds of time of flight. At the time of writing, a new procedure is evolving. Because it is expected that greater accuracy will be required in the future, the equations of motion, or three degrees of freedom, in a modified form have been developed. V(J When this new method has been fully programmed for BRLESC, all firing table work will be computed with the new equations.
21

describe the particle theory are referenced to a ground-fixed, right

hand, coordinate system. The equations of motion which are used in the

machine reduction of the fiting data are:

PVKD

_

WWx•) + ax

pVK

y---

y- g+a

r

•= - 0-V-K- • -W ) + a

C

Z z

where the dots indicate differentiation with respect to time, x, y and z * distances along the x, y and z axes,

p * air density as a function of height,

V a velocity,

K - drag coefficient, C * ballistic coefficient,

W• range wind

* cross wind

g& acceleration due to gravity

and ax, ay and az are accelerations due to the rotation of the

earth. For a given projectile, 1 varien with Mach number and with angle

of attack. The ballistic coefficient,, C, defined as weight. over diameter squared (W/d2 ) is a constant. However, for convenience in handling

data along any given trajectory, KD is allowed to vary only with Mach

number, and C becomes a variable. In other words, the K used is that. for zero angle of attack. In actual flight, drag increases with an

22

S
41
;4
-j

increase in angle of departure, due to large summital yaws at high angles. Thus, if KD is not allowed to increase with increasing angle, C will decrease in order to maintain the correct KD/C ratio. Up to an angle of departure of 450, however, sumnital yaws are so small that C is usually a constant for any given muzzle velocity. B. Drag Coefficient
Before any trajectories can be computed, the drag coefficient of the projectile must be determined. In the past, one of the Givre functions, (G, through G8 ) with an appropriate form factor, was used. Today, most of the firing table computations are made with the drag coefficient for the specific projectile under consideration.
If a completely new configuration is in question, the drag coefficient is usually determined by means of firings in one of the free-flight ranges( 4 05) of the Exterior Ballistics Laboratory. The drag data thus obtained are then fitted in a form suitable for use with the BRLESC(6)
Usually, the drag coefficient is determined rather early in the research stage. If the configuration is modified only slightly during its development, differential corrections can be applied to the original drag coefficient. For example, the effects of slight changes in head shape, overall length, boattail length or boattail angle can be quite accurately estimated, as these effects have been determined experimentally. (See references 7-14.) If a major modification is made to a projectile, such as a deep body undercut, a new drag curve must be determined experimentally.
23

C. Reduction of Range Firing Data Aii oD Lhe ruutudt £IL.L w.. . ..

.. ,_ ^Z-..,.. .e;._ .. . ..

handled at one time. The following description of the reduction of data

applies to one charge. Each charge is handled successively in exactly
the same manner. Because most of the parameters determined by the reduction of data are functions of muzzle velocity, judgment must be used

in correlating the values obtained for each charge, before the final
computations are made for the printed firing table.
"The following discussion is divided into two main sections: the

first describes computations preparatory to the reduction of data for the'ballistic coefficient, the second describes the reduction for the ballistic coefficient.
1. Preparation for Reduction for Ballistic Coefficient, a. Formation of Points. As shown in Table I (page 17), simi-
lar rounds, under similar conditions, are fired in groups of ten. Each group in designated as a point. As soon as raw data are received, the
instrument velocity of each round in a given point (supplied by the agency conducting the range firings) is plotted against its range. Any I~i. inconsistent rounds are investigated and, if a legitimate reason for doing so is discovered, are eliminated from any further computations.*

The remaining rounds constitute the point. All of the computations concerned with the reduction of the observed
data are machine computations, The only handwork is the plotting of rounds described here. PoeibZe reasone for eliminating a round include: inorrecot oharge, weight, or temperature.

24

for each round for use in the computation of muzzle velocity for the given round. Metro aloft is computed for each point for use in the computation of ballistic coefficient.
To compute metro aloft for any given point, linearly interpolated values, for even increments of altitude, are determined from the observed data. A linear interpolation factor is then computed, based on the mean release time of the given balloon runs and the mean firing time for the given point. This factor is used to weight the observed metro data at
the given intervals to obtain the metro structure to be used with the given point.
In Figure 2: MRT - mean release time, (release time + 1/2 ascension time) MFT - mean firing time, (mean of all rounds in the point) y - altitude, - range wind, Wz - cross wind, T - air temperature, p - air density.
Surface metro is computed in a similar manner, the .iinear factor being determined by using the release time of the given balloon runs and the firing time of each giver round.
c. Muzzle Velocity. The toordinates of the muzzle are the initial coordinates of each trajectory. At Aberdeen Proving Ground, the origin of the co-ordinate system is the intersection of a vertical
25

Balloon 1 Ba1lMlFoTn

Point 1

MRTl

M

Rjl.5MFT MRT2

Balloon 2 MRT2

Interpolated Metro Data
Yiq WxljO W lip Tlis Pl~
,

____
MMRRTT22 -- MMFRTTI

Interpolated Metro Data
Yis Wx21p W21, T21, p21
ii

Metro for Point 1
w e(Wxl1 + (1- e)(W12i)
wz* 8(WZl + (1 - e)(Wm2 1) T i a Ol(T1i + (1 - 0)(T21) pi - 8 (plj + (1 - 8)(p2j)

Figure 2. Metro structure for use with a given point 26

:1

1^thrcgh the trunne.Qf. ti g,.

a horizontal line established

by mean IOw water. The coordinates of the muzzle are, therefore:

x0 L cos~o

where

Yo h + L sin o L - distance from the trunnions of the gun to the
muzzle,

o0 angle of elevation of the gun, h * height of trunnions above mean low water.

After leaving the muzzle of the gun, each round (magnetized just prior to firing) passes through a pair of solenoid coils. These coils

are placed as close to the muzzle as possible without danger of their being triggered by blast or unburned powder. The time lapse as the

projectile travels from the first coil to the second is measured by a

chronograph; the distance from the muzzle to the first coil, and the

distance between coils are known. Using the equatiods of motion, an

estimated

C -

2 W/d (of the

individual

round)

and the

observed

metro,

we

can simulate the flight of the projectile. By an iteration process, a

muzzle velocity is determined for each round such that the time-distance

relationship given by the computed trajectory matches that measured by

the chronograph. d. Means and Probable Errors, per Point. For each point, the
mean and the probable error are computed for: range, muzzle velocity,

deflection, time of flight, height of impact, weight, time to burst (when appropriate) and fuze setting (when appropriate). For any given

set of data {x,} (1- 1, 2, 3... n), the mean,
n i.

i2l 27

p

Probable errors are computed Ir. two ways, by the root-mean-square method and by successive J-.fJerences. Both probable errors are printed,
S~A followed by the preferred (smaller) probable error.
Probable error by the root-mean-square method: PE - S (Kent-factor) (see Table IV)

where

S -

i ýxn

Probable error by successive differences:

PE .4769
Yn -l

where 6 - X, 1 "xx+ (Ui 1, 2, 3... n-1). a. N-Factor. One of the conditions that affect the range of

a projectile is its weight. Hence it must be possible to correct for a projectile of nonstandard weight.

Given some standard velocity, V., and some standard weight,

We, and assuming all deviations from standard weight to be small, we

can compute a number, N, such that !V

AW

Ws

where

AV - V5 - Vn AW We Wn

Subscript a - standard n - nonstandard

28

Table IV. Kent Factors
Computation of Probable Error (PE) by Standard Deviation (s) and Successive Differences (6)

where A - deviations from arithmetic mean, n - number of observations
Let s be the observed standard deviation, then the best estimate for the PE, i.e., such that average PE-- true PE, is given by

.6745 0 (•i•)e

PE

PE=--)1/02 1 2 2

See Doming and Birge, Reviews of Modern Physics Vol. 6, No. 3, July 1934, P. 128

xi PE/s

.2 PE/s

ni FE/2

ni

E/a

2 1.19,550 3 .93213
4 .84535
5 .80225 6 .77650 7 .75939
8 .74719 9 .73805 10 .73096 11 .72529 12 .72065 13 .71679 14 .71353 15 .71073
16 .70831 17 .70619 18 .70432 19 .70266 20 .70117

21 .69984 22 .6986
23 .69753
24 .69652 25 .69560 26 .69476
27 .69398 28 .69325 29 .69258 30 .69196 31 .69138 32 .69083 33 .69032 34 .68984
35 .68939 36 .68896 37 .68856 38 .68818 39 .68782

PE by successive differences -

.6745" -

40 .68747

41 .68715

42 .68684

43 .68655 44 .68627

45 .68600

46 .68574

47 .68550

48 .68527

49 .68504

50 .68482

51 .68462

52 .68442

53 .68423

54 .68404

55 .68386

56 .68369

57 .68353

58 .68337

E/-62

-V

.4769"-J

59 .68322 60 .68307
61 .68293
62 .68279 63 .68265 64 .68252 65 .68240 66 .68228 67 .68216 68 .68204 69 .68193 70 .68183 71 .68172 72 .68162
73 .68152 74 .68142 75 .68133
• .67449
.6

where 6 - differences between successive observation, n * number of observations

29

I

In order to determine N, 20 rounds (see Table I) at standard tem-

perature are fired at the same elevation and muzzle velocity. Ten of

these rounds, weighing less than standard, are fired alternately with

10 rounds weighing more than standard. The N-factor is computed from

these data using the followtag equation:

k

SAV AW

W

N -

i i

s

k k

V

where,

AV i VHi -VLi

AW WHi - WLi

and,

VUH = velocity of the ith heavy round

VLj velocity of the ith light round

*i weight of the ith heavy round
WLi * weight of the ith light round

The equation for computing N-factor was determined by a least

square* technique as follows: n

let,

G (N) - j{AVi" N g AWi})

thus, ii•

n

S().. [ {AV, - N,vAw}.i 'aAw] 0

i-

5W

Wa

n

N

i AV i

Vs

nVs i='l

AW

2

30

f. Change in Velocity for a Change in Propellant Temperature. As shown in Table I, range firings are conducted with rounds conditioned to various nonstandard propellant temperatures (-40*F, 0OF, 125 0 F) alternated with rounds conditioned to the standard propellant temperature (70*F). The following information can be obtained for a given pair of

points:

V?709 W70d; V-40a, W_-40 V7 0 *, W7 00 ; V 0o, WOO V7 00 1 W?0*; V.2,o' W1 2 5 °

where, V - velocity

W - weight. The V ci• and W. 's for all three firings are not necessarily

70

70

equivalent.

Since the weight for each.point is not necessarily standard,

the N-factor for each charge is used to strip out the effects of projectile weight. Oliven some velocity V7 0' some weight W7 0 , and some standard weight W, the standard V is computed.

Since, where,

AV N W AVV 7 - V
AW W .70 W,

7L)

then,
and

V 70W- V - N I (W700 W). V- 700/ [i- - (W- W7o 0)],

Thus all six points must be corrected for nonstandard projectile

weight. Then,
AV_4 0 o
""

V_4 Oe NV -4 ..

- Wo)

W

-40

VQO" .

( (W-- W

W

70

31

By the same process, a AV is computed for the OOF point and the

125*F point. A least squares technique is then used to compute a function AV a a (T - 700) + a 2 (T - 700)2
using the three given data points at -400F, O*F and 1250 F.

g. Compensation for Rotation of Earth. The final computations

to be made in preparation for determining the ballistic coefficient are

those to determine the coefficients used in the equations of motion to

compensate for the rotation of the earth.

X,= 2 0 coo L sina

X2 M 2 0 sin L Sa 2 fl coso , cos a

where,

n w angular velocity of the earth in radians/second

•

20 a .0001458424

L - latitude a azimuth of line of fire, measured clockwise
from North
In the equations of motions given on page 22:

ay = 1 ic

1

3

2. Reduction for Ballistic Coefficient.

a. Ballistic Coefficient and Jump. The raw data, including

metro, are by now processed; all parameters except the ballistic coeffi-

cient are now available for solving the equations of motion. The

available data are: elevation (0), drag coefficient (KD vs M), standard

weight and velocity, initial coordinates of the trajectory (xo, yo, zo),

32

I

'ancwn

%Wx

I

W

ai

-~nqt

and air temperature at even intervals of height], means and probable

errors (x , y , z, PE, PEV, PED, PET), time of flight, and the rota-

tional forces ( 1

22 '

3 3

An iterative process is used to determine the ballistic coeffi-

cient. As a first approximation, C is set equal to weight/diameter 2

By computing a trajectory to ground (y. - 0), the equations of motion

are solved for each point, using all the available data for the given

point. The computed range is then compared with the observed mean range

for the point. If the ranges do not match*, C is adjusted by plus or

minus C/16 (plus if the computed range is less than the observed range, minus if it is greater) and another trajectory is computed. If this new range does not match the observed range, another C is computed either

by interpolation (if the two computed ranges bracket the observed range)

or by extrapolation (if the two computed ranges do not bracket the ob-

served range). This process is repeated, always using the last two computed C's for the interpolation (or extrapolation), until the computed

range matches the observed range with the required tolerance. The final

C is called the ballistic coefficient from reduction (Cred)' As part of the same program, a change in range for a unit change

in C is computed fo-z use in future computations. To obtain this value,

AX/AC, a trajectory ie computed with

C - Cred + 2-8 Cred

resulting in a range value, X . Another trajectory is computed, with

*The present BRLESC progyram requires the ranges to matoh to I x 1o"
meters. 33

r

Il

S•reJ -

red

resnitring in a range value, X

2 x -x thus 4X- 1 2-7 Cred

As stated earlier, the C used in the muzzle vrlocity computations was merely C - W/d2 . If this C is in error by a significant amount,

the muzzle velocities computed using this C would also be in error.

At the time muzzle velocity was computed, two C's were used for

each round: C - W/d2 and C - 1.1 W/d2 . Hence two muzzle velocities

1I

2

were obtained for each round; V and V2.. Thus it was possible to com-

pute a change in velocity for a one percent change in ballistic coeffi-

cient.

dC . 1

I

where AV is the mcan of the absolute values: IV1 - V2 11

V1 and V9 are mean values for all rounds in the point, and C Sis corrected to standard weight.

The change in C for a one mil change in elevation, AC/49, is also computed in the reduction program. The Cred corresponds to the elevation,( , of the particular data point. This elevation is increased by one mil and the point is then reduced again, for a new ballistic coeffi-

cient, C'. A
thus:

AC C' C ed

34

The foregoing procedure is used for obtaining AX/lC for all the daLa polutb ald AC/AO for each data point whose elevatiou was equal to or less than 45*.
Because final computations for firing table entries make use of the ballistic coefficient for a projectile of standard weight, all C's must now be corrected to standard weight.

corrected

red Wobserved

By comparing the ballistic coefficient used for determining muzzle

velocity (Ccvee)lý with the corrected ballistic coefficient determined from the reduction (Crad) we can judge the significance of any error in the

CVal'

V*d (AV) dC

AO -Cvel -Corrl
If this AV, the velocity error due to using an incorrect Cvel Is greater than 0.5 meters per second, muzzle velocity must be recomputed using the ballistic coefficient obtainsei from the reduction. In actual practice, it is seldom, if ever, necessary to recompute muzzle velocity.
p, up to this point in the computations, has been defined as the angle of elevaticn of the gun. The angles listed in a firing table, however, are angles of departure of the projectile. Although the difference between the angle of elevation of rhe gun and the angle of departure of the projectile is small, it does exist and is defined as veLticsl jump. The shock of firing causes a momentary vertical and rotational movement of the tube prior to the ejection of the projectile. This

35

notion changes the angle of departure of the projectile from the angle of elevation of the static gun. Because jump depends mainly UH Lim eccentricity of the center of gravity of the recoiling parts of the gun with respect to the axis of the bore, it varies from weapon to weapon and from occasion to ozcaion. In modern weapons, vertical jump is usually small. For this reason, being only a minor contributing factor to range dispersion, jump is not considered in the field gunnery problem.
It is considered desirable, however, when computing data for a firing table, to coampute jump for the particular weapon, fired on the specific occasion for obtaining firing table data. Thus the firing table data will ba published for true angle of departure, and the jump of a weapon in the field will not be added to the jump of the weapon used for computing the tab).e.
As mentioned earlier, the ballistic coefficient, considered as a function of angle of departure, is a constant up to an angle of 45*; a variable, due to large suenital yaws, for angles greater than 45*.
Having determined the corrected ballistic coefficients for all points, we now determine the best value to use for the constant C for ( 1 45* (C).* The desired C is a function of angle of departure, not of elevation. Hence, it is necessary to take into account the effect of jump (J) on C. The C and J obtained will be used to compute or will influence, the range listed in the firing table. In the computation for C and J, the objective being to match observes data, range error (AX) must be minimized.

AZZ rounds fired with nonstandard propeZ"Imt temperature are excluded

from the computations for the fits of ballistic

coefficient and Jump.

36

A least squares method is used for the function, f - L(AX) 2 , to

minimize the residuals. The error in C will be AC - C- Ccorr. for J

where

c* + (AClAp) J.
Ccorr. for J - C corr

The product of AX/AC, obtained above, and AC gives the amount of

error in range due to selecting a given value for C aad J. Combining

this information: where

n

C.jL ] X 12

f

-

(C

aq(j

A

n u number of data points.

To minimize the residuals, the function is differentiated first

with respect to • and then with respect to J. Equating these partial

derivatives to zero, we have two equations with two unknowns which can

be solved simultaneously for C and J.

(1) ~

] - Ccorr ('X/'c)2

The value of C, thus obtained, will be uaed in all computations wherep S 45', Therefore, a check mumt be made for any significant difference between this value and the value used for computing muzzle velocity, Cvel, Just as was done for Cred and CvelI

It is assumed that the value for jump is constant for all eleva-

tions. Using this value plus the observed angle of elevation as 0, the

angle of departure, the high angle points are now reduced for ballistic

coefficient, C

The process for obtainina Cred' and other factors,

red'rd

Ccorr =Cred (Wt ata3rd/Wtobserved) as deeco'ibed on page 35.

37

for each high angle point, is the same as that for low angle points (of course eliminating the C and J computations). Ccorr is then computed for each point:

corr red standard/ observed

The next step is to fit these values of Ccorr as a function of 0,

where • _ 45o, satisfying the following three conditions.

(1) The equation must be a quadratic of the form:

},I•

. ao + a, + a2 '

0

a2

(2) The value of C * f (0 must equal C at the point of

juncture (Ok).

0i a + a, 0*+ a2 p*2.

(3) The slope of C t f (c mpust be zero at the point of

juncture.

a, + 2 a 2 *.

From (3), a1 -2 a 2 0*. Substituting this in (2),

=- + a 2

.

Substituting both of these in (1), C - C + a 2 (Ok2 -2 €* ( + The error (AC) between the observed value (Ccorr) and the computed

value (C) must now be minimized. A least squares technique is again

used, with the function F- {C

[ +a (0*2 -2(P*0p + p

The partial derivative of F with respect to a2 is equated to zero. Thus a2 can be obtained, hence ao and aI from the previous equations. In this manner, the equation for ballistic coefficient for high angle fire

is obtained.

C - f (o = ao + a, P + a2 02

38

I

I&
t. •

A computation is now made to determine the m gniLude uL LL1 LSAL

error due to using angle of elevation plus jump, and the appropriate

ballistic coefficient. For each low angle point, the range is computed

using o + J) and •. Then,

-

E Rn r

SXobevd -X[•

,•

PER Range Error

i•

X[observed]

[0 + J, E]

R

For each high angle point, the range is computed using ((o + J) and

C f W. Then,

X [observed) x[10))*+ J . C - f

PER * Range Error

A tabular sumary, of the foregoing explanation of the detemination of ballistic coefficient, may be helpful in understanding this
procedure.
Steps in the Computation of Final Values for Ballistic Coefficient
1. First approximation: C * W/d2 By an interative process, one obtains:
2. Cred (for all points)
In the same portion of the program, one obtains:
AX/AC (for all points)
AC/60 (for points: (p 5 45*)

3. %corr- reCd (Wstandard/Wobserved) 4. C and J (for points: 0 1 450)

Using: AX/SC, AC/IO and C

obtained above.

corr

In the same portion of the program, one obtains:

comparison of Cve1 and C (using C, 0+ J)

39

A•

5. New Cred (for points: ( > 450)

Using: 0 - (observed angle of elevation) + J 6. Ccorr (for points: p > 450)

7. Fit of Ccorr f (0) C

I

By minimizing AC (- Ccorr -C) 8.C - f (0) (for points: p >45°)

9. Determination of range error due to using • and C - f (p);

(Po + J b. Change in Range for Change in Elevation, Velocity and Ballistic Coefficient. For use in later computations, three other

quantities are computed in the reduction program: a change in range for a one mil change in elevation, a change in range for a one meter

per second change in muzzle velocity and a change in range for a one

percent change in ballistic coefficient. For each of these quantities,

a plus and a minus change is made to the standard value for each point

(•' -• • Imil , V' Vo *10 f/a, C' - Co h 2-8 C) and trajectories

are computed. The difference in range (e.g. x + 1

-) divided by

the change in standard (e.g. 2 mile) yields AX/40, AX/AV and AX/AC.

c. Drift. In addition to ballistic coefficient, deflection

is obtained from the reduction program. Total deflection of the projectile, or lateral displacement from the line of fire, is caused by

cross wind, rotation of the earth and drift. Drift, defined as deflection due to the spin of the projectile, is to the right of the line of fire because of the right hand twist of the rifling of the gun tube. Observed deflection is made up cf all three components of total deflection; computed deflection, of only cross wind and rotation of the earth,
40

Theretore,

Drift (meter) = Deflectionobserved - Deflectioncomputed Drift (1)- sln-' (Drift/X ) 6400/2w Drift, in mils, is fitted, by a least squares technique as a function of angle of departure. The values for drift and angle are those of the points for the given charge, fired with standard propellant temperature
and standard projectile weight. Several functions are fitted, and that function yielding a small root-mean-square error and a physically logical curve through the data points is the function accepted for use in the

computation of the table. The functions used in the various fits where D - drift, and • - angle of departure.

follow,

D a tan

f

D -a tan (P+ a2 tan2 0 D - a /(p + b)

d. Time. Still another output of the reduction program is the

time of flight of the projectile to the terminal point: time to impact

on the target with a point detonating fuze, time to burst with a time
fuze. Due to the fallibility of the mathamatical model used (particle

theory), the computed time of flight (t) is less than the observed time of flight (T). Hence, for later computations, this difference in tine

is determined.

At = T - t At is then fitted, by least squares, as a function of t. As with drift, several functions are fitted; and the best one accepted for usi in the computation of the table.(Figure 3). The functions used in the various fits are:

41

A"
T t
ii

I.I

(1) At a t Linear fits

are computed to five different terminal

points: the time for the elevations of 250, 350, 450, 55° and 650. With the data remaining beyond the ter-

minal points for 250,350 and 45'. At - ao + aI t + a2 t2

with the value of At and its first derivative, equal at the point of juncture. (2) At - a (t - to) 3 where to is set equal to the time corresponding to elevation of 25', 35' and 45'; and At is zero below this value of to.

At
MAX. • TRA I L

see

Beli6

31 5)s450

Figure 3. Differ'ence between obaeered and oonrputed timea of flight aa a funotion of oomputed time
42

3. Probable Errors, per Charge

a. Probable Error in Range to Impact. The expression used

for the determination of the probable error in range to impact is:

(FER)2 -(PE V)2 (AX/AV) 2 + (PE~d 2 (AX/A&)2 + (PE )2 (AX/AC) 210'
C

where

PEP M probable error in range, in meters

PE - probable error in velocity, in meters per second
AX/AV - change in range in meters for a change in velocity on one meter per second

PEO a probable error in angle of departure, in mile
AX/I w change in range in meters for change in angle of departure of one mil
P*C - probable error in ballistic coefficient, in percent
AX/AC = change in range in meters for change in ballistic coefficient of one percent
For the determination of PER, all points are used (except maximum trail
points) that have been fired with standard-temperature propellant. PER

and PE * were determined in the means and probable error computations.

AX/AV, AX/AO and AX/AC are computed by the following equations.
(1) AX = K1 " K2
AV 6.096

where

x - range for a velocity - V + 3.048 m/s

x2 - range for a velocity w V 3.048 m/s

(3.048 /s - 10 f/s)

(2) where

XC -X2 AX/60 - I
2
x, - range for elevation - 0 + 1 mil

S- range for elevation - - 1 mil

*The value of PE that is used in the cor•putations is a pooZed value
for all the points in a given oharge (see page 2?,). 43

ri

(3) fAX/tAC-

X. -
2 C. 7i

where

- range for ball~istic coefficient C + 2- C

I

x

range for ballistic coefficient * C - 2-8 C

Therefore, in the expression for PER, all of the quantities are known

except PE and PE These quantities are determined by a least squares
C*
technique.
Unfortunately, the values for PE R are sometimes such that the
] quantity (PER)2 - (PEV) 2 (AX/AV) 2 is negative. Whenever this situa-
tion arises, the above quantity is set equal to zero and the least squares
I C solution is computed. Occasionally, even this expedient results in a negative value for (pE )2 or (PC )2. When this occurs, the Powell method(17) is used for obtaining the uoefficients for a minimum of the

[
•

function:
[(PER)2 - (pSl) (&X/AV)2]= (PEO)2 (&X/lO)2 + (PEC)2 (AX/lC),
forcing (PE )2 and (PE )2 to be positive.
'C
b. Probable Error in Deflection. Probable error in deflection

is a function of both range and angle of departure. The least squares
solution of the following function is accepted for use in the computa-

tion of the table.

PE - a x/cos

where

PED = probable error in deflection, in meters

a - a constant, different for each charge

x a range, in meters

(a - angle of departure, in mils

44

l

|

I

|

Ii.

For each charge, all points are used that have been fired with standard-

weight projectiles and standard-temperature propellant. 4. Fuze Data.

a. Fuze Setting. When the firing mission requires a time fuze, a large proportion of modern artillery weapons use the M520 fuze. Some years ago, an exhaustive study was made of all available data on this

fuze. It was found that fuze setting for a graze burst* was a function

of time of flight and spin. The following relationship holds for this fuze, regardless of the shell on which it is flown.

PS - T + (0.00129442 + 0.00021137T) S

where

PS - fuze setting

T a time of flight, in seconds S - spin, revolutions per second - Vo/n d

Vo = muzzle velocity, in meters per second 2/n w twist, in revolutions per caliber d - diameter, in meters The fuze setting for time fuzes other than the M520 is assumed to be a function of the time of flight of the particular projectile under consideration. A least squares solution of the data is computed. FS - T a AT"a + a T+ a2 T 2

where FS - fuze setting T a time of flight, in seconds

a0 , a1, a22 constants, different for'each charge.

Grame burst is defined as burst on impact.

45

I

b. Probable Error in Time to Burst. Each time an angle is

computed to hit a given target, not only are Mne angie, range and heig•ii

of the target computed, but nlRot x - the horizontal component of velocity

-My the vertical component of velocity

t - the computed time of flight.

From theae data we can compute true, or observed, time of flight, T

(page 41); probable error in time to burst, PETBi probable error in

range to burst, PE.; and probable error in height of burst, PEHB.

Because the ballistic coefficient has been determined from

impact data, not time data, the time of flight of the projectile has

an associated probable error. When a time fuze is to be employed for

a graze burst, there is an associated probable error in fuze running

time. Thus the probable error in time to burst is a function of the

probable errors of both time uf flight and fuze running time.

From the same study discussed in connection with the fuze

setting for the M520 fuze, an expression for probable error in time to

burst was derived.
•PE

TB ".(PET 2 + (PE F)2ji

where

PETB a probable error in time to burst

PET - probable error in time to impact

PEF - probable error in fuze running time 100.
- 0.065 + 0.00220 (1 + )FS S

S

spin, am on page 45

FS * fuze setting

46

For each charge, probable error in time to impact (PE T) is fitted, by least squares, ao both a lineac and a quadratic function of time of

flight.

The better fit

PET - a T
E wea T+a T 1

T2 . 2

is used later in the computation of the table.

The probable error in time to burst for time fuzes other than

the M520 is computed by means of the same basic equation:

FE

[(PE )2 + (pEF) 1

TB

L T

FJ

For these fuzes, howevur, both PE and PE are fitted as functions of

T

F

time to impact.

PE, M a T

PE w a T . a T2 .

i 1

2

Again, the better fit for each parameter is used in the computation of

the table.

c. Probable Error in Height of Burst and Probable Error in

Range to Burst. By using the same parameters that were used for deter-

mining PETB, probable error in height of burst (PE ),

TB'

HB

error in range to burst (PE ) can be determined. RB

FE M [PE)2 +(PE )21

and probable

PE -

(PET2 + (PE )2i

5. Illuimnatin_ Pro4art{il.

The main porticn of the average firing table is in-two parts. Data on the primary, or high explosive, projectU.e are in the first

part; data on the illuminating projectile are in the second. Because

47

I'

iI

the mission oi Line laLL%:.

tc

uia

--

vl

a-

I

area, precision firing is not as essential as for the primary projectile.

A less sophisticated technique provides adequate solution of the fire

problem. No computations are made for means and probable errors,

N-factor, change in velocity for a change in propellant temperature, compensation for the rotation of the earth, jump, drift nor change in

range for a change in elevation, velocity or ballistic coefficient.

Unlike the primary (RE) rounds, which are grouped into points

of ten rounds each, the illuminating projectiles are handled round by

round. Although each projectile of the ten round group of illuminating

I

projectiles is fired with the same charge, elevation and fume setting,

the heights of burst differ significantly. eence, round by round,

rather than point, reduction of the data is necessary.

I

For the range firing program, standard-weight projectiles and standard-temperature propellant are used for firing all angles of

elevation. Meteorological data are processed in the manner previously

described, All muzzle velocities for a given charge, with the

exception o0 any obvious mavericks, are averaged. This average value is established as the standard muzzle velocity for the given charge.

Ballistic coefficients are computed as previously described,

with two exceptions% the data are processed round by round, and the

jump computation is omitted. Whereas the terminal point of the basic

trajectories for the primary shell is on the target, the terminal point

48
]V

I
(burst point) of the trajectories for the illuminating shell is at some optimum height above the target: usually 750 meters. Trajectories are, however, computed to impact as well as to burst height.
Because illuminating projectiles are not fired at elevations greater than 450, and because, for a given charge, the ballistic coefficient is constant up to 45', all individual values of the ballistic coefficient for a given charge are averaged to establish the ballistic coefficient for that charge.
Time corrections, for the difference between observed and computed time, are determined in the same manner as for the primary shell.
49

rr
I.

F
!re

VI. COMPUTATIONS FOR THE TABULAR FIRING TABLE The tabular portion of an artillery firing table contains data based on standard and nonstandard trajectories for a given weapon and combination of projectile, fuze and propelling charge. This informa-
tion is essential to the successful firing of the projectile on the target. The table also presents certain other information computed from uncorrected firing data. The whole table is divided into smaller tables, some of which are used in the preparation of fire, some of which present information useful to the artilleryman in other phases of his work. The basic parameter in the solution of the fire problem is the range. As the artilleryman uses a firing table, he makes all
corrections (due to meteorological conditions, projectile weight and propellant temperature) to range, not to quadrant elevation. Having determined a hypothetical range, which under standard conditions would correspond to the true range and height of the target under nonstandard conditions, he then finds in the table the quadrant elevation necessary
to hit the target at that range.. Thus all computations for entries in
the firing table are made to enable the artilleryman to determine the requisite hypothetical range.
Following is a detailed discussion of each of the individual tables. In order to clarify the content of each table, some explanation must occasionally be made of the method by which the artilleryman solves a fire problem. A. Table A: Line Number (page 93)
This table lists the line number of a meteorological message as a function of the quadrant elivation of the weapon system. A line number,
50

which represents a preselected standard height (Table V), is related to the maximum ordinate of the trajectory of the projectile in flight.

An understanding of the content and use of a meteorological message will aid in an understanding of the necessity for most of the information contained in a firing table. A NATO meteorological message is divided into two parts: the introduction containing, primarily, identification information; and the body of the message, containing meteorological information. The introduction consists of two lines broken into four groups of letters and numbers; the body of the message consists of a sequence of up to sixteen lines, each broken into two groups of six digit numbers. The various parts of a message are explained below.

METS 12141v 002109

SAMPLE METEOROLOGICAL MESSAGE
344983 4 Introduction
037013J
945071

012215

937079

022318

933082

032419

926084

Body of Message

042620

941075

052822

949065

063123

960051

MET indicates that the transmission is a meteorological message. The

S indicates that the message is applicable to surface fire; an A would

indicate that it was applicable to antiaircraft fire. The 3 indicates

by numerical code the weapon system to which the message is applicable.

51

"table V.

I

Number(meters)

Standard Height

000 01 02
03 04 05 06
07 08
09 10 111 12 13
14
15

200 500 1000 1500 2000 3000 4000 5000 6000 8000 10000 12000 14000 16000
18000

52

• I
The 1 indicates by numerical code the octant of the globe in which the message is applicable. The second group indicates the latitude and longitude of the center of the area of applicability. In this sample message: latitude 34" 4 0t, longitude 980 30'. The third group indicates the period of validity of the message. In this sample: the 12th day of the month from 1400 to 1600 hours Greenwich mean time. The fourth group indicates the altitude, in tens of meters, of the meteorological datum plane (MDP) and the atmospheric pressure at the MDP. In this sample: the MDP is 370 meters above mean sea level, the atmospheric pressure is 101.3 percent of standard atmospheric pressure at sea level.
All sixteen lines of the body of the message have the same form. The initial line is identified by the first pair of digits (00) and deals with surface meteorological conditions. Each subsequent line furnishes information applicable to firings for which the maximum ordinate of the trajectory is equal to the standard height associated with the first pair of digits of the line (Table V). Because all of the lines in the body of the message have the same form, an explanation of any one line will serve. Assume that the appropriate line number is 04. The full line of the sample is: 042620 941075. The first group of numbers tells that this is line 4 applicable to a trajectory whose maximum ordinate is 1500 meters, that the ballistic wind is blowing from 2600 mils (measured clockwise from geographic North) at a speed of 20 knots. The second group tells that the ballistic air temperature is 94.1 percent of standard, and that the ballistic air density is 107.5 percent of standard.
53

k_ iz.
71m|

Au InAde'rpd above, each line of the body of the meteorological message contains the ballistic wind, ballistic air temperature and ballistic air density at the indicated height. When this height is zero,
"these quantities are the actual wind, air temperature and air density at
the MDP. For other heights, there are certain effective mean values of the actual atmospheric structure which are used in conjunction with the data given in the firing table to determine the effects of the actual atmospheric structure. These mean values are computed, at the meteorological station, to apply to a trajectory having a maximum ordinate exactly equal to a particular standard height. For firings where the maximum ordinate is not equal to one of the standard heights, it has been found to be sufficiently accurate to use the ballistic wind, temperature and density computed for that standard height which is nearest to the maximum ordinate of the firing. A projectile following a trajectory whose maximum ordinate is equal to some particular standard height passes through layers of the atmosphere where winds are blowing in various directions and at various speeds. The ballistic wind for this standard height is that wind which is constant in speed and direction and which produces the same effect on the range, height and deflection of the projectile as the actual wind(15). Definitions of ballistic
air density and ballistic air temperature are essentially the same as that of ballistic wind, but differ in that there are, in these cases, no deflection effects.
Thus, if for a given firing, the quadrant elevation is known or can be reasonably inferred, Table A is used to obtain the line number, hence the ballistic atmosphere through which the projectilu will fly. An

J
,54

m

m

exception should be noted, however. When a projectile impacts the target on the ascending branch of its trajectory, height ot target rathcr than maximum ordinate must be used in obtaining line number. (If neither quadrant elevation, nor height of target on an ascending trajectory is known, line number can be obtained from Table B, as a function of range and height of target.)
The entries for Table A are obtained from computing standard trajectories at discreet intervals of quadrant elevation to obtain maximum ordinates. In order to obtain the most accurate maximum ordinates,
these trajectories are computed with the appropriate constant ballistic coefficient, not the fitted ballistic coefficient. Use of the fitted C gives the most accurate results for the terminal values; use of the constant C gives the most accurate results for the maximum ordinate. By means of interpolation, quadrant elevation is then listed against exact line number. For example, if the quadrant elevation for charge 7 for the 105mm projectile M1 fired from the M108 howitzer is 4674, the line number is 4(1) B. Table B: ;omplementary Range and Line Number (pages 94-95)
As mentioned above, line number is given in Table B as a function of range and height of the target. Primarily, however, this table lists range corrections corresponding to the complementary angle of site, tabulated as a function of range and height of the target above the gun.
In Figure 4, the angle to hit a range, x, on the ground is designated po. The angle of site to the target above the ground, T, is indicated by the dotted line. The angle resulting from adding the
55

r

angle of site to

is insufticient to bring about impact ur Lht pLu-

jectile on the target. T. The relatively small angular correction

required to place the projectile on the target is called complementary angle of site, CS.

f/

OCS

SIt

Figure 4. Corrpemntary site.e.

-p 0 + of Site + CS

The computations for complementary angle of site are based on twodimensional trajectories, computed using the equations of motion (without the rotation terms) and the ballistic data corresponding to the weapon system and charge. The basic equations are:
SPVKD_ C
-pVKD-

56

The iieLCt~ddLy

t~dir-.±

C - ()

K - f(M); T - f(t) D

and the standard ICAO atmosphere (U.S.

Standard Atmosphere, 1962) The computation of complementary angle of site is an iterative

process. Trajectories are computed with various angles until an angle

is found that will result in a trajectory whose terminal point is at a

given range and height. Trajectories are run to fifteen heights (from

-400 meters to +1000 meters, at 100-meter intervals) for each range

(at 100-meter intervals) up to maximum and back to the range at the maximum elevation of the system. Thus for any given point in space,

T, OT has been computed; 10 (for T at xW, 0) has been computed; and
angle of site is known
(tan.1 Y
xW

As explained earlier, the fire problem is solved on the basis of a hypothetical range. For this reason, complementary range, not complementary angle of site, is listed in the firinB table. In order to compute complementary range, complementary angle of site is added to o and a trajectory is run to y - 0.
The difference in range between the trajectory with an elevation of Po + CS and that with an elevation of o0 is the complementary range (Figure 5). Thus, in Table B, the change in range to correct for the complementary angle of site is tabulated as a function of range and height of target above or below the gun.

57

*

&

Yi

Ir

COMPLEMENTARY -S RANGE

Figure 5.* Comrplementary ra~nge

I
i~i•

C. Table C: Wind Components (page 96) This table resolves a wind of one knot, blowing from any chart
direction, into its cross wind and range wind components. Chart direction is defined as the azimuth of the wind direction minus the azimuth of the direction of fire. Chart direction is listed from 0 mile to 6400 mile by 100-mul intervals. The cross wind component is designated right or left; the range wind, head or tail. The determination of the wind components is a simple trigonometric computation; it was done once and does not need to be repeated. Table C is the same in all firing tables. D. Table D: Air Temperature and Density Corrections (page 97)
In this table are listed corrections which are to be added to the

K!!

baltimsptecaatrue ad te blliticairdensity, obtained from

the meteorological message, in order to compensate for the difference

II

58

I
in altitude between the firing battery and the meteorological station.
"The computations for this table are based on the standard ICAO atmos-
phere; these computations were performed once and do not need to be repeated. Table D is the same in all firing tables. E. Table E: Propellant Temperature (page 97)
This table lists corrections to muzzle velocity as a function of propellant temperature in degrees Fahrenheit and Centigrade. The function AV - f(T - 70*F), determined as described on page 31 is evaluated for temperatures from -50OF to 1300F, at 100 intervals. Also listed in this table are the Centigrade equivalents, to the nearest 0.10, of the Fahrenheit temperatures. F. Table F; Ground Data and Correction Factors (pages 98-99)
1. Ground Data (page 93). This portion of Table F is divided into nine columns: range, elevation, change in elevation for 100 meters change in range, fuze setting for graze burst (for a specific time fuze), change in range for 1 mil change in elevation, fork (the change in the angle of elevation necessary to produce a change in range, at the level point, equivalent to four probable errors in range), time of flight, and two columns for azimuth corrections: drift and a cross wind of 1 knot..
The first column lists range, by 100-meter intervals, from zero to maximum range and back to the range for the maximum angle of elevation of the weapon system. In order to obtain the entries for the remaining columns, a series of trajectories is computed using the equations of motion with the appropriate values determined according to the computa-
59

tions described in section V, above. These trajectories are com pute to find the angle of elevation to hit each range (100, 200, 300 ... ) under standard conditions. From these trajectories we obtain range, elevation and time of flight (colutm,ns 2 and 7). Elevation is printed in the table to the nearest 0.1 mil; time of flight, to the nearest 0.1 second. In order to compute the change in elevation for 100 meters change in range, for a given range (xi - 100) is subtracted ftom that of the succeeding range (xi + 100) and the result is divided by two:
(A•4x)i " (xi + 100) "O(xi - 1 0 ))/2 " A
The change in range for a one-mil change in elevation is derived directly from the above:
1X000/A/A - B These two entries (columns 3 and 5) are computed before the elevation is rounded to the nearest tenth of a mil. The change in elevation for a 100-meter change in range is rounded to the nearest tenth of a mil; the change in range for a 1-mil change in elevation is rounded to the nearest whole meter.
Fork (column 6) is computed from the above value and from the probable error in range, determined according to the method of section V.
Fork - PE /B (above) The fuze setting for a graze burst (column 4) is computed for the time of flight listed in column 7, by ujing the equations determiuted according to the method of section V, above. Drift entries (column 8) are obtained by evaluating the function determined according to the method of section V at the angles of eleva-
60
L/

tion listed in column 2. Computations are made before the pertinent parameters are rounded off.

Azimuth corrections due to, crass wind (column 9) are computed on the basis of the following equations:

1017.87Wz (T - x,/:ko)

Z

x

where

zw - deflection due to cross wind (mils) W - cross wind
z T - time of flight x - range x0 -range component of muzzle velocity

Cross wind is converted from meters to mils by the constant: 1017.87* 2. Correction Factors (page 99). This portion of Table F lists,
as a function of range, the corrections to range which must be made to account for nonstandard conditions of muzzle velocity, range wind, air temperature and density, and projectile weight. Muzzle velocity corrections are tabulated for a decrease (column 10) and an increase (column 11) of one meter per second; range wind, for a decrease (column 12) and an increase (column 13) of one knot; air temperature for a decrease (column 14) and an increase (column 15) of one percent; air density for a decrease (column 16) and an increase (column 17) of one

6400

Radians x

-mi e

4- x (factor to oonvert tangent to angle - 0•7.O?,

61

percent; and projectiie weight. LUr a UecL-Cdwz (Cuuiuzuu is) akid al LnLtiCLbae
(column 19) of one square.*
A series of trajectories is computed to find the elevation needed to hit each range (100, 200, 300 ... ) under each of the ten nonstandard
coniditions. For these computations, the values of the nonstandard
conditioas are: * 15 meters/second, L 50 knots, * 10% air temperature,
! 10% air density and : one square (or some other appropriate weight
change).
Using the angles of elevation determined above, standard trajec-
tories are next computed, and the unit range correction then determined. IA•X = x(standard) - x(nonstandard)
1 unit No. of units (nonstandard) (nonstandard)
This unit range correction is listed against nonstandard range.
G. Table G: Supplementary Data (page 100)
This table lists probable error information and certain trajectory
elements as functions of range. These additional data are not necessary
to the solution of a given fire problem, but are useful to the artillery-
man in other aspects of his work. Range is in column 1, usually listed
at 1000-meter intervals.
Me weight of most artillery projectites is indioated by the number of squares (m) stamped on the body of the projectile. Standard weight is usuaZly represented by two, three or four squares. This does not mean, however, one square of a standard three-square weight represents onethird of the weight. For 105nm projectiles, one square representa 0.6 pounds. Thues, two squares being standard (33.0 pounds), three squares "denotes 33.6 pounds. For l75imn projectiles, one square represents 1.1 "pounds. Thus, three squares being standard (147.8 pounds), two squares denote 146.7 pounds. OcoaaionalyZ, the actual weight in pounds is stamped on the projectiZe. For projectiles of this type, firing tables are oomputed for pound, rather than equare, inoreases and decreases.

• 4..

62

Column 2 lists the elevation necessary to achieve the range listed in column 1. Columns 3 and 4 list, as functions of range, probable error in range to impact and probable error in deflection at impact. The method of computing these values was described on pages 43 through 45. Columns 5 through 7 list as functions of range, probable errors for a mechanical time fuze: probable error in height of burst, probable error in time to burst and probable error in range to burst. The method of computing these values was described on pages 46 and 47.
The angle of fall, w (column 8), the cotangent of the angle of fall, Cot w (column 9), and terminal velocity, VW (column 10) are computed from the information obtained in standard trajectories.
W a tan-, Cot w-

Maximum ordinate, MO (column 11), is a function of ballistic co-

efficient, angle of departure and velocity. To determine this value,

I

a trajectory is computed with C, the given p and Vo maximum ordinate is that height where the vertical component of the velocity ()is zero.

HO0 f (0,, Vo, $= 0)

Angle of fall, terminal velocity and maximum ordinate are standard out-

I4

puts of all trajectory computations.

The last two columns in Table G (11 and 12) list the complementary angle of site for an increase and a decrease of one mil angle of site. The computations for these values are made for an angle of site of 50

63

!rla An anale • . is computed to hit a target (x , 0). 0

Another angle

I

t ,is computed to hit a target [x, y - (tan 500) xl].

Since,

T (P + CS +,) of site,
TT00. - 00- 50

then,

+CS

50

To compute -CS, OT is determined for a target [x,, y - - (tan 500) x ].

Then,

P-T

+ 50

-CS

T 50

Although the fire problem, in the field, is solved by determining

a hypothetical range, the complementary angles of site listed~in Table

"

G make it possible to make corrections to angles. Assume the target

is at a distance of 8,000 meters and a height of 500 meters. The angle

of site is, therefore, 63.616. If FT 105-AS-2 is the firing table being used, 00 is 336.3t; CS - (.096)(63.6) * 6.11. Then:

O T "o + CS + • of site 4061&

H. Table H: Rotation (Corrections to Range) (page 101)
Corrections to range, in meters, to compensate for the rotation

4

of the earth, are tabulated as functions of azimuth (in mile) and range

(in meters) to the target. The main body of the table is for latitude

0'. Below the main table are tabulated constants by which the correc-

tions are to be multiplied for latitudes from 10* to 70%, by 10* intervals. These constants, cosine functions, were computed once, and do not need to be recomputed; they are the same in all tables, for all charges.

64

izhe equations used to compute the corrections to compensatre or rotation are:

M -E x 2

x 3

9--E -g+A i

where X , X and A - values defined on page (32),

1 .2

3

EPVKD

C

Thus for each charge, the appropriate muzzle velocity and ballistic co-

efficient must be used in the computations. X1 , A2 and A3 are computed for each of the following conditions:
1. Assume L a 0*, - 16000

then A1 a 2 fl, X2

0,

-0

2. Assume L * 90*N, a 64001

then A1, 0, x2 2 SI,X3 .0

3. Assume L 0%, a v0

then A, 0, A2 - 0, A3 -2 C Trajectories are then computed for each of the above three conditionsA for all of the following angles:

0,0 2, 4, 6, 8, 10, 15 ... 30, 40, 50, 75, 100, 125 ... 1275, 1300 mile. Under condition 1, above, the range for a given angle, 01, is desig-
nated xli. (zW1 - 0, since X2 - 0, X3 * 0 and AX does not affect z.) Under condition 2, above, the range for a given angle, 01, is desig-
nated x 2j; z is designated z2i. [Since X - 0, x3i I xi (standard x).]

uTsheedrefaour ZTteabZoef It,hencootmTpaubtaZteioHn.e under the third set of oonditione are 65

* ,meter
4

Under condition 3, above, the range for a given angle, ,i' is desig-

nated x3 z is designated z3

[Since A 1 - u, x3 "

(bL .. rd X)"

Then Ax Is set equal to x2 - xl

Interpolations are then per-

formed in xl to determine the Ax for even intervals in range. This

i

±

interval is 1000 meters for 155mm weapons and larger, 500 meters for

weapons smaller than 15ýmm. This Axi, Axli relationship gives the values for the 16001h column in Table H, for latitude 0'. The value for any given

azimuth is computed as follows:

Ax - Ax1 (sin a).

The corrections are rounded to the nearest whole meter. I. Table I: Rotation (Corrections to AzLmuth) (page 102)

Corrections to azimuth, in mils, to compensate for the rotation of the earth, are tabulated as functions of azimuth (in mils) and range (in meters) to the target. A separate table is given for each latitude from 0* to 70%, by 10' intervals. The computations described in the explanation of Table R are used for the entries in Table I.

Interpolations are performed in x2 and x3 (for 500- or 1000intervals) to determine the corresponding values of z2 i and z3 i

For a given x2i (standard range) the angular deflection is computed as follows:

z - z2 (sin L) + z3 (cos L) (sin a)

i

i

S.a - tan-1 (Z/x)

If Am .s greater than zero, the angular deflection is from left to right; if less than zero, from right to left.

L

66

J. Table J: Fuze Setting Factors (page 103)

In this table are listed fuze setting changes, ao a cio ,

fuze setting, Lo compensate for the effects of the same nonstandard

conditions as are given in Table F, correction factors. Fuze setting is listed, in whole numbers, from zero to the maximum setting of the

given fuze.

A series of trajectories is computed to find the elevation needed

to hit a given range (100, 200, 300 ... ) under standard conditions. These trajectories are computed with true, or observed, time of flight (T).

T - t + At [At - f(t), see pages 41 and 42] The time of flight corresponding to a given fuze setting, in whole numbers, is computed by means of the equations given on page 45. Interpolations are then performed in the •vs T data obtained from the standard trajectories to find the angle that corresponds to the time of flight. Then, by iteration, the exact angle is determined. With this exact angle, trajectories are computed with each of the nonstandard conditions. By means of the fuze equation, the fuze setting corresponding to the time of flight of these nonstandard trajectories is computed.

Thus the unit fuze setting change can be computed:

AF w FS(nonstandard) - FS(standard)

2. unit

No. of units (nonstandard)

This AFS is tabulated against FS.

K. Table K: AR. AH (Elevation) (page 104) In this table are listed the change in range (AR) and height (AH),
in meters, for an increase of 10 mils in elevation (Figure 6). A given

67

SI
value, tabulated as a function of range and of height of the target above the gun, is the difference in the terminal coordinates of two standard trajectories having initial elevations 10 mile apart and terminating at
"the same time of flight.
The angle, 0T' to hit a given target, was determined in the computation of Table B. 0T is increased by ten mils and a second trajectory is computed which terminates with the same time of flight as the first. Thus AR and AH are differences in the terminal values of the two trajectories.
AR and AR are tabulated for every 500 or 1000 meters in ravge, from zero to maximum range and back to the range for the maximum angle of elevation of the weapon system, and for every 200 meters in height, from -400 to +1000 motors.
Y
C I
Figure 6. Chane in range and height for a 10-miZ increase in eLevation
68

L. Table L: AR. AH (Time) (page 105) In this table are listed the change in range (AR) and height (AH),
in meters, for an increase of one second in time of flight. A given value, tabulated as a function of range and of the height of the target above the gun, is the difference in the terminal coordinates between two points along a single standard trajectory at times of flight differing by one second (Figure 7).
The actual computation of. this table is no more than an additional print from the iteration trajectories.
AR •k and AHR-$
-i~
Pigure ?. Change in range and height for a I-eeoond inorease in time of flight
k and S are the horizontal and vertical components, respectively,
of the velocity.
69

I

I •tions,

M. Table M: Fuze Setting (page 106) As previously described on pages 59 and 60, data on fuze setting
are included in Table F. The data given there are for the time fuze most often used with the systems for which the firing table has been produced. Most systems, however, are capable of functioning equally well with an alternative fuze. Data on this alternate fuze are given in Table M, which lists the amount to be added to or subtracted from the time of flight (column 7, Table F) to obtain the correct fuze setting. Corrections are listed, to the nearest 0.1 of a fuze setting opposite the time span to which they are applicable. The fuze settingtime relationship is computed as explained on page 45. N. Illuminating Proisctile (page 107)
Only one table per charge is printed for an illuminating projectile. Elevation (column 2), in mils to the nearest 0.1, and fuze setting (column 3), to the nearest 0.1 are tabulated as functions of range to buret (column 1), These relationships, which are for standard condi-
are computed in the same manner as similar computations for the primary shall.
Ranges are listed for 100-meter intervals, The shortest is that range achieved by firing at an elevation of 45' to the optimum burst height on the ascending branch of the trajectory. The longest range is that achieved by firing at an elevation of 450 to the optimum burst height on the descending branch of the trajectory (Figure 8).

70

Y

OPTIMUM BURIT MIN

XMIN

X MX

Figure 8. Trajeoto2iee of ilIuminating projeotiles: range-elZeation relationship

Trajectories are computed to determine the atinimum angle

to

hit the optimum height. By an iteration process, angles are then com-
puted to hit the optimum height at even intervals of range up to an

angle of 800. The first and last entries in the table are for those angles nearest, but not greater than, 80001 which will hit an even hun-

dred meters in range. Similarly, the minimum elevation listed will be the one nearest, but not less than, min which will hit an even hundred meters in range. Times of flight, for the listed entry ranges, are obtained from the same trajectory computations. Corrected time is determined as for the primary shell (page 41):
T t + At

71

..-.-.---.-1---.---------

I

Fuze setting, as a functiou of time of flight, is computed from observed data. This function is then evaluated for the appropriate

entries in the table.

.

If for some reason an illuminating projectile fails to burst, it

is of concern to the artilleryman to know the point of impact of the

projectile. Hence, in column 6 of this table, the range to impact is

listed as a function of the range to burst. These data are computed

by running the above trajectories beyond optimum burst height to zero

height.

Column 4 in the table lists change in elevation for a 50-meter

increase in height of burst; column 5, change in fuse setting for a 50-

moter increase in height of burst. Computations for these data are made

in exactly the same way as those for columns 2 and 3 except that the

burst height is increased by 50 meters. The tabular entries are merely

differences:

"ASp FS

-8,

H+50 H

Where H - optimum burst height

0. Trajectory Charts (page 108)

Following the main body of a firing table are appendices contain-

ing trajectory charts for the primary projectile for which the table

has been produced. In each of these appendices, trajectories are shown

for a given propelling charge. Altitude, in meters, is plotted against

range, in meters, for every 100 mils of elevation, up to maximum

72

*

. .. .

eievation. Time of flight, by 5-second intervals, is marked on each trajectory. For these charts, standard trajectories are computed with the requisite angle of elevation, with a print-out for every second.

73

73

I

i i

.. . .. . ... . .. . .... . . . . .... ...... .. . . ................ . . ..

* . . . .. .. . . .. ..... ... .... . . ...

___

___

II
VII. PUBLICATION OF THE TABULAR FIRING TABLE
A program has been written for BRLESC to interpret the coding on
the output cards of the firing table computations., Thus, after the computations have been spot checked, the cards are fed back into the BRLESC. The computer spaces the numbers, pages, puts headings in the proper columns et cetera. The output goes on the IBM 1401 which tabulates the final manuscript. Transparent overlays are made for the ruling on standard pages. Pages of nonstandard length are ruled by hand. The trajectory charts described above are drawn by a Magnetic Tape Dataplotter into which are fed the output cards of the BRLESC
computations.
In addition, the final manuscript contains an introduction giving an explanation of the various tables, and sample fire problems and their
solutions. This introduction is punched on IBM cards, the BRLESC auto-
matically composes the material(19) and it is then printed in final manuscript form on the IBM 1401.
The completed manuscript is sent to the Government Printing Office for publication and distribution.
74

I
VIII. YODITIONAL AIMING DATA A. Graphical Equipment
The tabular firing table, described in the preceding sections, is the basic source of firing data for a given weapon system. In the field, however, the determination of aiming data is greatly simplified by the use of "graphical" equipment: a graphical firing table (GFT), a graphical site table (GST), and wind cards (Figure 9). The so-called graphical tables are sticks similar in appearance and operation to a slide rule. Wind cards, on the other hand, consist of tabular information printed on plastic cards.
Essentially, the same information in in these tables (in simplified form) as is in the tabular tables. The information is, however, in a somewhat different relaticnship. Hence, some additional computations are necessary. Although the Ballistic Research Laboratories are responsible for the preparation of the actual manuscript for the tabular firing table and the wind cards, they are not responsible for the design of the graphical sticks, only for the computations. The necessary numbers are sent to Frankford Arsenal (the responsible agency) and to the Artillery School, Fort Sill, for the design and manufacture of the equipment.
1. Graphical Firing Table. The graphical firing table is used principally for determining the elevation corresponding to the range to a target. Each table consists of one or more rules and a cursor, with a hairline, which slides on the rule. The range scale is the basic scale on the rule, all others being printed with reference to it. Above
75

HOW P55im OWA~ 6

i T 3 ~

~~....

U.......

Figure 9. Graphical firing table, graphical site table and wind cards
Best Available Copy
76

the range scale are a drift/deflection scale and a scale marked 1O0/R.
This scale (lO/range), representing the Langent of the angle of site
for a target 100 meters above the gun, is associated with the angle-ofelevation scale.
Beneath the range scale are three additional scales: elevation, fork and fuze setting. These six scales are repeated, with the appro-
priate relationship, for each charge. One rule can have as many as four charges printed on it: two on each side. In addition to these six scales, other information is shown on a graphical firing table. A segment of a line between the elevation and fork scales indicates the
normal range limits for the given charge. On this same line segment,
two marks indicate the optimum range limits for computing meteorological
corrections. On a heavy line below the fork scale, the dividing line between the data for two different charges, are two fuze setting gage points. The one to the right indicates the fuze setting at which the probable error in height of burst is 15 meters. The gage point to the left indicates the range at which the probable error in height of burst for the next lower charge is 15 meters.
The rules described above are affixed to the stick on a slant, so that the hairline of the cursor does not intersect the scales at a right angle. The slope of the rules is determined at BRL.
The foregoing description applies to a graphical firing table for low angle fire. The table for high angle fire differs somewhat. The top scale is 1O0/R, with below this the range scale. A heavy dividing
line separates these two scales from the remainder of the rule. Below
7ý

=hi4 •_re Io for two or three different charges: elevation, 10 mil site, drift and time of flight. (The Fork scale is dropped, a 10 mil site scale is added, and time of flight substituted for fuze setting.) The scales on this stick are parallel to the edge of the stick.
Computations for the graphical firing table are five-point, reverse interpolations of the data computed for the tabular firing table. For low angle fire, drift is determined for each mil, at the half mil, and the corresponding range printed; for high angle fire, each mil at the
whole mil. Similarly, interpolations are made for each 10 mils in elevation, for each mil at the half mil for Fork, each whole number for fuse ttin, each whole second for time of flight and the nearest whole number for fuze setting &age point. 100/R was computed once, for each mil at the half mil, and does not need to be recomputed; it is the
same, for a given range, on all graphical firing tables. The 10 mil site computation is similar to that for complementary
angle of site described on pages 63 and 64. A trajectory with a given angle, 0o, will hit a target with coordinates (x2u o). A trajectory
with an angle •0, will hit a target Ex * xW, y tan 50 (x%)]. Thus:
10 mil sits - +50 5 0
where site - CS + • of site 2. Graphical Site Table. The graphical site table is used to facilitate the computation of angle of site or of site*. It can also
be used to determine the vertical interval between the gun and the tar-
By definition, site - 0ge of eite + comptamentary angLe of aite (sea pagee 55 and 56).
78

I

L(Coi: Lui.rat p..;int) hnct, r''ric1fn1

irn~nd are known.

The graphical site table consists of the base, on which is printed the

D scale (site and vertical interval); the slide, on which is printed yard and meter gage (index) points, the C scale (range, which can be read in yards or meters), and site-range scales, for various charges, in meters; and the cursor, with a vertical hairline. The C and D scales are identical to those on any slide rule, and are used to determine angles of site, or of site, of 100 mile or less, or to determine the vertical interval when angle of site is known. (For angles of site greater than 100 mile, the vertical angle must be determined by means of the tangent functions.)

For each charge there are two site-range scales on the slide: one in black for a target above the gun (TAG) and one in red for a target below the gun (TBG). The scales are so printed with respect to the C scale (range) that when the vertical interval (D scale) is divided by the range on the site-range scale, complementary angle of site is included in the result (site). The meter gage point (when the vertical interval is in meters), or the yard gage point (when the vertical interval is in yards), rather than the normal index point, is used for multiplication or division of the result by 1.0186 and, in effect expresses the formula p (mile) a 1.0186 y/x which is more precise than the formula p (mile) - y/x. This factor is 1.0186 rather than 1018.6 (6400/2r) because the range is expressed in thousands of meters to the nearest hundred meters; e.g., 4060 meters is expressed as 4.1.

79

the output data of the double entry program used to compute Table B in the tabular firing table. These output data consist of the angles to hit targets at given ranges and at given heights (vertical intervals) below or above the gun.
Graphical site table computations are made for low-angle fire for each 100-meter interval of range up to maximum range. Computations begin with that range, at the level point, that can be reached by an angle equal to, or greater than, 200 mile. Computations are made for angles equal to, or less than, 800 mile.
The outputs of the computations are plot points: those values on the C -scale of the stick that align with the appropriate range on the TBG (target below gun) or TAG (target above gun) scale. The computational procedure is shown in the flow chart on page 81. Computations are identical, but made independently, for targets below and above the gun.
3. Wind Cards. Wind cards enable the artilleryman to transfer
fi-e, without lateral limitations, from one target to another. The
accuracy of lateral transfers is dependent on the rotation of the earth,
wind direction and wind speed. A correction for the rotation of the earth is omitted from the graphical solution of the flire problem. Wind cards, however, provide a rapid means of determining corrections to deflection, fuze setting aud range when the chart directiov of the wind,
and the range and direction of the new target are known. For a given firing table, there is one wind card for each charge:
one side of the card is designated Wind Card A; the other, Wind Card B.
80
|-

[ Enter range and examine o

Examine T for eacTh VI I(T S 800 mils
S~until
Determine site ( - • ) f or each VI Compute individual plot points for each VI -,
pp 1.018601Z site

Continue to next range a range
is found such
(0 .k 200 mile then continue
as on loft

Using PP for lowest VI Compute site (GST) for each VI

Site (GST)

_I.0186(Vi) PP

Compute site, site COST) and AS for each VI AS - site - site (GST)

Sum AS's from VImIi

to VI max

I

Use only those
PTts for V118 that satisfy
the test and continue am
on left

Using PP for succeeding VWes by 100's to VI max, compute site (GST) for each VI, thus repeating preceding 3 steps

Select the plot point that results in a minimu sum AS

_ __

_ _

_

_

_I

-1

SThis

is the plot point for this rang

Add 100 meters to this range and repeat the above procedure from step 3 to the end

81
Ii

The cards contain corrections for a one-knot wind, blowing from the
chart direction, divided into two components - the unit deflection
correction (Wind Card A) perpendicular to the line of fire, and the unit range correction (Wind Card B) parallel to the line of fire. Corrections to fuze setting are also included on Wind Card B. Corrections to deflection and range are tabulated as functions of range and wind direction; corrections to fuze setting are tabulated as functions of fuze setting and wind direction. Line number is also listed on both Wind Card A and Wind Card B, as a function of range, so that the artilleryman can select the appropriate line of the meteorological message containing wind direction and speed.
Wind card data are computed by using the range, azimuth and fuze setting corrections for wind from the tabular firing table data and applying appropriate trigonometric functions for the chart~direction of the wind. Given a wind speed, W, with some azimuth,1 1 , and an azimuth of fire, a, (Figure 10) range, azimuth and fuze setting corrections for the wind car be computed from the tabular firing table data. For a given range, the correction to range for a one-knot head wind (AX/Wh), the correction to range for a one-knot tail wind (Ax/Wt) and the change in azimuth per one-knot cross wind (Act/Wz) are obtained. For a given fuze setting, the correction to fuze setting for a one-knot head wind (AFS/Wh) and the correction to fuze setting for a one-knot tail wind
(AFS/Wt) are obtained.
82

N

• W

LINE OF FIRE

•

Figure 10. Relation between azimuth of fire and auimuth of wind The necessary computations are made in the following sequence:

2) WX- W .coso

3) A\WLEhwXWt/ -
4) RCA3.W

5) RC. (W * coouP

6) RC W4Y.iI cos)

7)AlS WX

-4F APS~ Wh Wit

8) PsIC - AFSw

83

W W in
K 'w
AC xw *WZ AC -(W sui (q) AC UA sin A)
Ut I- N
U!

F
I

.........................................................--..-.............. .[

II
9) FSC =A w(W cos
w•

•,11)
I

12

sin

Wx~ ' o

13)

. cos

X

o

where S * 0, 200, 400...6400.

[

For the definition of terms, see Table of Symbols and Abbreviation.,

pagae. 7-9.

S

:, i.4.

Graphical Equipment for Illuminating Projectile.. The graph-

•

ica2. firing table for the illuminating shell is a stick with a cursor

•
-

and hairline, one rule per charge,(Figure 11). As on the GT'T for HE projectiles, the basic scale is the range. Above this 1s the 100/R

scale. Below the range scale, and on the same base line, arm angles of elevation for impact at any given range on the rang. scale. This
combination scale serves the same purpose as column 6 (Range to Impact) in the tabular firing table. It is essentially zero height
I.pae 7G9 ahcrljEcui of buret on the descending branch of the trajectory. The major portion of the rule consists of nine horizontal scales, representing heights of burst from 600 meters to 1000 meters at 50

meter intervals. On each horiuiontal scale, angles of elevation are

r

marked off up to 800 mils. At the bottom of the rule is fuze setting,

in whole numbers. From each fuze setting, a curved line is pr6n0ed to

intersect the nine horizontal scales at the appropriate elevation,

84

Figure 11. Graphical firing tabl~e for illu~minating projectile
For each of the heights of burst (600, 650, 700...1000 moters), trajectories are computed for quadrant elevations, at 10-mil intervals, from 800 mile downi to the lowest elevation that will hit the desired height of burst (800, 790, 780 ... ). For each angle of elevation, a range and fuze setting are printed, for the given height, on both the ascending and descending branch of the trajectory (Figure 12).

AND~~H

'aESETN

DESCENDING Figure2.AS raeNDoiNG of ilumnjating pr'ojeo$les:

I
From these data, a fuze setting is interpolated for each whole number and printed with its corresponding range to burst. When an illuminating projectile is to be fired in the field, the lowemL possible charge is used in order to reduce the possibility of ripping the para-
chute when the flare is ejected from the shell. Consequently, when
the scales are printed for the illuminating projectile, the values for the ascending branch of the trajectory, for the high charges, are
omitted. This is because the same range and height can be reached by a lower charge on the descending branch of the trajectory.
For zero height of burst data (range to impact), trajectories are
computed to y- 0 for quadrant elevations up to 800 mils by 10-mil intervals.
B. Reticles and Aimine Data Charts
A ballistic reticle is a direct-fire aiming device, incorporated
into a telescope which is mounted as an integral unit with the Sun (Figure 13).
A line, approximately vertical, on the reticle represents the atimuth of fire. The slight deviation from the vertical is a correction for drift. Horizontal lines on the reticle represent distances to the target in meters or yards. In use, the weapon is traversed, and elevated or depressed so that the vertical line and the appropriate range line are on the target.
As in the case of the graphical firing table and tht. graphical
site table, BRL is responsible only for the computation of the data for reticles, not for their design. Thus the data computed for the tabular firing table is all that is required. Range (at 50-meter
86

I

90 AP M318AI

24 16----

--

--

24--

--

32--

40-
"--
48-

--

I

-'-

--

24 --

16

---

24

-32

I - 40

U

--

-48 4

vigurs' 13. Retiole intervals), elevation and drift values (up to a range designated by Frankford Arsenal) are sent to Frankford Arsenal (the agency responsible for the design and manufacture of reticles).
87

Reticles are graduated for use with a particular weapon and ammuni-

tion. Compensation must be made for differences in other projectiles

J

fired from the same weapon. Hence, an aiming data chart is provided

A

for making the necessary corrections. On an aiming data chart may be

listed two or more projectiles which can be fired from the given weapon. Listed under each projectile are a series of ranges. Also listed are
the ranges etched on the reticle. In use, the gunner finds the type of
,amunition to be fired, reads down the column to the range at which he

will fire, moves across to the reticle column to find the corresponding

standard setting. This point in the telescope is used to aim the weapon on the target.

Aiming data charts (Figure 14) are provided by BRL in final manuscript form. For each range and mid-range (half-way between

range marks) on the reticle there is a corresponding elevation.

Trajectories are computed at these elevations for all of the projectiles to be Included in the aiming data chart. The resulting ranges are rounded to the nearest 100 meters and listed opposite a range or

mid-range point of the reticle.

88

TANK, 90MM GUN, M48 SERIES
t.?/rAmm1fm Uhl ATrrh
TELESCOPE, M105

AP-T, M318A1 and

M~At1 tCA

TM WVTVVfC

ON RETICLE

ADC 90-Y-1

HE, M71
WP, M313

M318A1 RETICLE PATTERN

HE-T, M7IAl
WP, M313C

2

1

3 -------------- --- 3

57 - - - - 8 - - - - 45

8

7

10 --------------- 8

12

9

13 -.-.-.16---- 11

15

12

17 ---------------

13

19

15

20 ---- 24 ---- 16

22

18

24 ---------- ----- 19

26

21

27 ---- 32 - --- 22

29

24

31 ---------------

25

33

27

35 -.

40 - --- 29

37

30

39 ---------------

32

CAL.0.30 MACHINE
GUN

M318AI RETICLE PATTERN

ELEV. MILS

1

1.2

3 -.-.------------

2.5

4 -8--

--- 35.7.1

5 6 --------------

7 -6

- 1- -

6.4
7.8
9.3
10.8

12.3

8 --------------

13.9

9 ----

15.6 24 --- 17.3
19.1

10o --------------

20.9

22.8 11 ---- 32 --- 24.8

26.8

28.9

12

31.1

- - 40 --- 33.4

13

35.8

38.4

The reticle pattern for Cartridge, AP-T, M318A1 may also be used to fire Cartridge, TP-T, M353.

Numbers and lines under the reticle column are those which appear on the reticle for Cartridge, AP-T, M318AI

To use chart:

(1) Find the type of ammunition to be fired. (2) Read down to the range at which you will fire. (3) Move left (or right) and find the corresponding
sight setting under the reticle column. (4) Use this point in the telescope to lay and fire;

Figur'e 14. Aiming data chart
89

REFERENCES

1. S. Gorn and M. L. Juncosa. On the Comoutational Procedures

for Firina and- fobina Tables. Ballistic Research Laboratories,

Aberdeen Proving Ground, Maryland BRL R889, 1954.

S2.

Robert F. Lieske and Robert L. McCoy. Equations of Motion of

SRigid Proiectile. Ballistic Research Laboratories, Aberdeen

Proving Ground, Maryland. BRL R1244, 1964. 3. Robert F. Lieske and Rary L. ReMier. Equations of Motion for

a Modified Point..ase Trajectory. Ballistic Research Laboratories, Aberdeen Proving Ground, Maryland. BRL R1314, 1966. 4. Walter F. Braun. The Free Flight Aerod)namics Ran-a. Ballistic Research Laboratories, Aberdeen Proving Ground, Maryland. BRL R1048, 1958. 5. Walter K. Rogers. The Transonic Free Fl ight Range. Ballistic Research Laboratories, Aberdeen Proving Ground, Maryland.
BRL R1044, 1958. 6. Elizabeth R. Dickinson and Donald H. McCoy. The Zero-Yaw Dran
Coefficient for Proiectile, 175mm, HE, M437. Ballistic Research Laboratories, Aberdeen Proving Ground, Maryland. BRL MR1568, 1964. 7. L. E. Schmidt and C. H. Murphy. Effect of Spin on Aerodynamic Properties of Bodies of Revolution. Ballistic Research Laboratories, Aberdeen Proving Ground, Maryland. BRL MR715, 1953.

90

8. C. H. Murphy and L. E. Schmidt. The Effect of Length on the Aerodynamic Characteristics of Bodies of Revolution in Supersonic Flight. Ballistic Research Laboratories, Aberdeen Prov-

ing Ground, Maryland. BRL R876, 1953. 9. L. E. Schmidt and C. H. Murphy. The Aerodynamic Properties
of the 7-Caliber Army-Navy Spinner Rocket in Transonic Flight. Ballistic Research Laboratories, Aberdeen Proving Ground,

Maryland. BRL MR775, 1954. 10. Elizabeth R. Dickinson. Some Aerodynamic Effects of Head
Shape Variation at Mach Number 2.44. Ballistic Research Laboratories, Aberdeen Proving Ground, Maryland. BRL MR838, -954. 11. Elizabeth R. Dickinson. The Effect )f Boattailina on theDrag Coefficient of Cone-Cylinder Projectiles at Supersonic Velocities. Ballistic Research Laboratories, Aberdeen Proving Ground,

Maryland. BRL MR842, 1954. 12. Elizabeth R. Dickinson. The Effects of Annular Rings and
Grooves, and of Body Undercuts on the Aerodynamic Properties of a Cone-Cylinder Projectile at Ma1.72. Ballistic Research Laboratories, Aberdeen Proving Ground, Maryland. BRL MR1284,

1960. 13. Elizabeth R. Dickinson. Some Aerodynamic Effects of Bluntina
a Proiectile Nose. Ballistic Research Laboratories, Aberdeen Proving Ground, Maryland. BRL MR1596, 1964. 14. Elizabeth R. Dickinson. Some Aerodynamic Effects of Varving the Body Lenath and Head Lenyth of a Spinning Projectile. Ballistic Reswarch Laboratories, Aberdeen Proving Ground,

Maryland.

BRL MR1664, 1965. 91

I

FJ

15. Artillery Meteorolo.

Department of the Army FM6-15, 1962.

16. Charles T. Odom. The Derivation of Range Disoersion Parameters

trom Rania Firina Data. Ballistic Research Laboratories, Aberdeen Proving Ground, Maryland. BRL MR1169, 1958. 17. M. J. D. Powell. "An Efficient Method for Finding the Minimum of a Function of Several Variables without Calcolating Derivetives." The Computei Journal, Vol. 7 No. 2, Jul•y.1964.

18. fT 105-AS-2. Department of the Army, 1967. 19. Robert F. Lieske and Muriel Ewing. BRLESC Program for Compu-

terized ComDosition of Firing Table Texts. Ballistic Research Laboratories, Aberdeen Proving Ground, Maryland. BRL TN1646, 1967.

Nil

92

APPENDIX

ThA fnllnwina samnle i&5ai are from FT 105-AS-A. charce 7.

FT 105-AS-2

TABLE A

CTG, HE, MI FUZE, PD, M557

LINE NUMBER

CHARGE 7

LINE NUMBERS OF METEOROLOGICAL MESSAGE

QUADRANT
ELEVATION MILS

LINE NUMBER

0.0- 100.1

0

100l2- 201.1

1

201.2- 313.0

2

313.1- 623.5

3

423.6- 5815

4

518.6- 64b.O

5

646.1- 803,4

6

803.5- 959.7

?

959,8-l131.2

8

1131.3-1333ýO

9

NOTE - WHEN THE GROJECTILE MUST HIT THE TARGET ON THE ASCENDING BRANCH OF ITS TRAJECTORY, USE HEIGHT OF TARGEI IN 11TERS TO ENTER THE TABLE ON PAGE XXVI TO DETERMINE LINE NUMBER.

93

I :

CHA7RGE

TABLE B COMPLEMENTARY RANGE

FT 105-AS-2 CTGt HE, Ml

CHANGE IN RANGE, IN MEtERSt TO CORRECT FOR COPLEMENTARY ANGLE OF SITE

LINE NUMBERS OF METEOROLOGICAL MESSAGE

LINE RANGE

HEIGHT OF TARGET ABOVE GUN - METERS

NO. METERS -400 -300 -200 -100

0

100

200

300

10500 -128

-99

-67

-34

0

4 10600

-133 -102

-70

-36

0

10700

-106

-73

-37

0

&10uo9u0u0

--1a4. 9

--11115o

--7796

--3491

0 0

36

75

116

38

78

121

39

82

127

4431

8905

11000 -155 -120

-82

-43

5 LLOO 11200

-162 -125 :17o -131

-86 -90

-45 -

11400

-1T6

-148

-

-5

1.1..0 - ?

-

--$

11500

-196 -155 -108

-57

0

45

.94 147

46 1oo

157

51

107

169

0 0

54 -

116

A- L

0

71

•i; ':•10500

:ls'5X
7 11400
11300
11000
10000 '10600 10200

-442 -464 -484
.za -539

-All
-ý36 -352
-3 -391

-202
-215 -226 -237 -247
-256

-96
-103 -109 -114 -120
-124

-5 ?3 -5 9
-606 --566262

-420 - 373 -433 6107-0202
-- 5 -291 --449537 --3229395

-134 -138
-142 --114566

0

75

0

91

163

0

99

186

255

0

106 201

264

0

111

214

305

0

it? 225

324

0 0

1i5660

331

4441

0

135

26

385

0 0

114502

22973

334938

10400

-638 -469 -307 -170

0

164

281

473

10300

-653 -491

-305

-174

0

L18

289

428

10200

-669 -193

-323 -158

0

157

298

436

13900 -684 -563 -331 -162

0

16

306

149

90000 -700 -516 -339 -166

0

160

314

561

9400 9800 99760000

-792 -586 -346

-730 -540 -359

--7764L6

--555613 --336720

-170 -174 --118728

0

164

322

473

0

168

330

485

0 0

117762

333486

4s1907

9500

-77 -575 -_378 -186

0

ISO

354

522

9400
9300 9200

-792 -806 -824

-586
-598 -61

-383 -393 -40t
-- 409

-190 -194 -198
-202

0

184

362

533

0

Los

370

654

u

192

378

557

0

196

386

569

9000

-856 -636 -417 -206

0

200. 394

582

94

I

tI

FT 1O5-AS-2 -T~v •:EC ,.ll FUZE, PD, M557

TABLE B COMPLEMENTARY OANIVE
LINE NUMBER

CHARGE

CHANGE IN RANGE, IN METERS,

F

TO CORRECT FOR COMPLEMENTARY ANGLE OF SITE

LINE NUMBERS OF METEOROLOGICAL MESSAGE

HEIGHT OF TARGET ABOVE GUN - METERS

RANGE LINE

400

500

600

700

800

900

1O00

METERS NO.

159

206

255

309

366

429

167

21

268

324

387

456

174

282

343

411

489

238

298

365

442

55

193

253

319

395

488

499

10500

534

10600 6lF

KR2

Io7nn

6

10800

10900

206

270

346

441

11000

221

295

3

11100 11200
11S0IL300 11400

11500

349

366

385

447

476

412

487

546

576

436

521

592

647

675

550

630

698

749

775

742

805

852

497

781

854

913

516

625

726

817

998

967

534

648

754

ast

939

Lois

551

670

782

884

977

1061

568

692

8o8

916

1014

1104

585

713

834

946

1050

1145

601

734

859

977 1085 1185

618

755

884

1006

1120

1225

634

775

909

1035

1153

1263

650

795

934

1064

1187

1301

666

816

958

1093

1220

1338

682

836

982

1121

1252

1375

698

856

1007

1150

1285

1412

714

876

1031

1178

1317

1449

730

896

1055

1206

1349

1485

746

916

1079

1234

1382

1521

762

937

1103

1263

1414

1558

9_

728 875 956
1022
|LO
RN 1183 1230
1,76
1321 1364 1407 1448
1490
1531 1572 1612 1653
163

11500
11400
11300 11200 11100
11000
10900 10800 10700 10600
10500 0400o
10200 10100
10000
9900
5 900
9700 9600
9500
9400 9300 9200 9100
90001

I
•,2000

CHARGE

TABLE C WIND COMPONENTS

FT 105-AS-2
CTG, HE, MI FUZE* PDt M557

____
CHART DIRECTION
OF WIND
NIL S0

CORRECTION COMPONENTS OF A ONE KNOT WIND

CROSS WIND

RANGE WIND

CHART DIRECTION
OF WIND

CROSS WIND

KNOT 0

KNOT H1.O0

NIL 3200

KNOT 0

RANGE WIND
KNOT 71.00

100 200 300
400
o0 600 700
G00
900 1000 1100
1200
1300 1400 1500
1600
11780000 E900•
2100 2200 2300
2400
2500 2600 2700
2800
2900 3000 3100
3200

R.1O Ro*O R.29
R.38
R#.4? R,56 R.63
R,7l
Re77 R.83 RO8
R.92
R,96 R198 R199
AlO.0
R.99 R698 R696
Ro92
Ross R.83 RT77
R.71
R163 R.56 R,47
R.38
R#29 R.20 R*lO
0

H.99 He98 H496
H992
H.S8 H.83 He??
H.71
Hw63 H056 H.47
H.38
H.29 H,20 Ho10
0
TT.o12O0 T,29
T,38
T.47 T.56 T.63
T,71
T,77 Y.03 T.88
T.92
T*96 T*98 T.99
T1.00

3300 3400 3500
3600
3700 3800 3900
4000
4100 4200 4300
4400
4500 4600 4700
4800
4900 $000 5100
5200
5300 5400 5500
5600
5700 5800 5900
6000
6100 6200 6300
6400

L.10 L.20 L.29
L.38
La47 156 L.63
L,71
L.77 L.83 L9 ft
L.92
L,96 L.9A L.99
LI.00
L.99 La98 L,96
L.92
L.88 L.83 1.T?
L.71
L963 L.56 L.47
L.38
L.29 L.20 LvIO
0

T.99 T*98 T.96
T,92
T.88 T,83 T.77
T.71
T,63 T.56 T.47
T.38
T,29 T,20 T.LO
0
HH,,12O0 H,29
H.38
HT47 H,56 H.63
H,71
H,77 H.83 H.88
H°92
H,96 H,98 H,99
H100

NOTE - FOR A COMPLETE EXPLANATION OF THE USE OF THIS TABLE, SEE PAGE LVII.

96

FT 105-AS-2
CTG, HE# MI FuZel PD, A;7

TABLE D TEMPERATURE AND DENSITY CORRECTIONS

CHARGE 7

CORRECTIONS TO TEMPERATURE (DT) AND DENSITY (DO), IN PERCENT,

TO COMPENSATE FOR THE DIFFERENCE IN ALTITUDEt

___

IN METERS, BETWEEN THE BATTERY AND THE MOP

DH

0

+10- +20- +30- +40- +SO- +60- +70- +SO- +90-

0 OT 0.0 0.0 0.0 -0.1+ -0.1+ -0.1+ -0.1+ -0.2+ -o02+ -0.2+ OD 0.0 -0.1+ -02+ -0.3+ -0.4+ -0.5+ -0.6+ -0.7+ -0.8+ -0.9+

+100- OT -0.2+ -0.2+ -0.2+ -0.3+ -0.3+ -0.3+ -0.3+ -0.4+ -0.44 -0.4+ DO -1.0+ -1.1+ -1.2+ -1.3+ -1.4+ -1.5+ -1.6+ -1.7+ -1.8+ -1.9+

+200- OT -0.5+ -0.5+ -0.5+ -0.6+ -0.6+ -0.6+ -0.6+ -0.7+ -0.7+ -0.7+ DO -2.0+ -2.1+ -2.2+ -2.3+ -2.4+ -2.5+ -2.6+ -2.7+ -2.8+ -2.9+

+300- DT -OT+ -0.?+ -0.+? -0.8+ -0.8+ -0.8+ -008+ -0.9+ -0.9+ -009+ DD -3.0+ -3.1+ -3.2+ -3.3+ -3.4+ -*5.5 -3.6+ -3.7+ -3.8+ -3.9+

NOTES " 1. OH IS BATTERY HEIGHT ABOVE OR BELOW THE MOP.
2. IF ABOVE THE MOP, U$E THE SIGN BEFORE THE NUMBER. 3@ IF BELOW THE MOP, USE THE SIGN AFTER THE NUMBER.

TABLE E PROPELLANT TEMPERATURE

VARIATIONS IN MUZZLE VELOCITY DUE TO PROPELLANT TEMPERATURE

TEMPERATURE OF
PROPELLANT

VARIATION IN
VELOCITY

TEMPERATURE OF
PROPELLANT

DEGREES F

M/S

DEGREES C

-40

-13.L

-40.0

-"3-200

-1106 -10.2

-34o4 -28o9

-10

-8.9

-2393

0

-7.7

-17.8

10

-6.6

-12.2

20

-5.5

-6.7

30

-4.4

-1.1

40

-3.4

4.4

50

-2.3

10.0

60

-1.2

15.6

70

0.0

21.1

60

1.2

26.7

90

2.6

32.2

100

4.1

37.8

110

5.7

43.3

120

7.4

48.9

130

9.4

54.4

97

I

CHA7RGE

TABLE F @A&Ic flATA

FT 105-AS-2
CTG, HE, Nl FUZEv PD. MWD(

-

2

3

4

5

6

7

a

9

R

E

D ELEV FS FOR DR

F TINE

AZIMUTH

A

L

PER

GRAZE PER

0

OF

CORRECTIONS

N

E

1O0 N

BURST I NIL

R FLIGHT

G

V

OR

0 ELEV K

DRIFT

CW

E

FUZE

(CORR

OF

M564

TO L) I KNOT

m

NIL

MIL

FS

m

MIL

SEC

MIL

NIL

10500
10600 10700 10800 10900

54862
560.L 572.6 585.8 599.9

11.7
12.2 12.8 13.6 14.6

40.0
40.8 41.5 42.3 43,L

9

8

38.8

14.0

0.70

8

9

39.5

L4.5

0.71

6

9 40.2

15.0

0.72

7

10 41.0

15.5

0.72

7

10 41.8

16.L

0.73

11000

615.0 15.7 44.0

6

11 42.6

16.8, 0.74

11100 11200
11300 11400

631.3 649.5
670:1 694*9

l7.3 19.4 22:7 29,1

45.0 46*0.
47:2 48.6

6

13 43.6

5

14

44*6

4

17 45.7

3

22

47.1

17.5 18.3 19.3 20.6

0.75 0.77
0.78 0.80

11500

728s4

50.5

48,9

22.4

0.82

,

~~****$***

~**********s ***t*sts* *e*I** m,*******

,**s.*as **$***** .******

11500
IL400 11300 11200 11100
11000
10900 10800 10700 10600
10500
10400 10300 10200 10100
10000
9900 9800 9700 9600
9500

850.9
881el. 903.3 921.7 937.8
952.3
965.5 977.9 989.4 1000.4
1010.8
1020.7 1030.3 1039.5 1048.4
1057.0
1065.3 1O73.4 1081o4 1089.1
1096.6

26o2 20.3 17.2 15.3
13.9
12.8 Ll.g 1103 107?
10.2
9.8 9e4 9.0 8.7
8.5
8.2 B.0 7.6 T76
7.5

57.1
58.7 59.6 60.7 61.4
62.1
62.7 6303 6308 64o3
64.7
65.2 65.6 65.9 66.3
66.6
67.0 67.3 67o6 67.9
68.2

4 22 5 17

6

14

?

13

7 11

8 10

a 10

9

9

9

8

55.3
56.8 57.9 58.7 59.5
60.1
60.7 61.3 61.8 62.2

30.2
32o6 34.4 36.0 3?.5
38o9
40.2 41.5 42.8 44.0

1O

8

62.7 45.2

10

8

63.1

46s4

11

7

63.5

47.6

11

7

63.8

48.8

11

7

64.2

49.9

12

6

64.5

51.1

12

6

64.6

52.3

12

6

65.1

53.4

13

6

65.4

54.6

13

6

65.7

55.8

13

5

66.0

57.0

0g94
0.98 1.00 1.03 1.06
1.08
1410 1.12 1.15 1.17
1.19
1.21 1.23 1.25 1.27
1.29
1.32 1.34 1.36 1.38
1.40

98