July-August - Air Defense Artillery School

Solving Trial Shot Problems
By Major John Parmakian, Coast Artillery Corps
The necessity for firing trial shot problems is discussed
in detail in gunnery manuals. BrieRy the problem consists
of assuming a muzzle velocity for the particular combination
of ammunition and gun, of correcting for the effects of
meteorological conditions and of conducting fire with the
necessary ballistic corrections set into the director. The deviations
of the burst from the Rank and batterv are then used
to determine the actual developed muzzle "velocity of the
ammunition and gun from which the necessary ballistic
corrections for fire for effect can be determined.
The method of solving trial shot problems indicated below
is one in which the developed muzzle velocity is dctermined
very accurately and rapidly without the use of a
trial shot chart or special slide rule. It is believed that this
method approaches the ultimate in simplicity inasmuch as
the differcnce between the developed and assumed muzzle
velocities is obtained by multiplying the observed deviations
by suitable factors which arc easy to obtain. Inasmuch as the
solution is based on the small triangles that exist in space
between the trial shot point and the bursts, the muzzle velocity
can be readily determined to the nearest foot per
second provided that the spotted deviations can be considered
to be dependable for such accuracy.
A recapitulation of the necessary formulas for solving
trial shot problems is as follows:
let CT 1 = average vertical dcviation of bursts from
01 in mils.
b 1 = average lateral deviation of bursts in the
slant plane from 01 in mils.
b2 = average Rank deviation of bursts in the
slant plane from O2 in mils.
6MV = difference between the developed and assumed
muzzle velocity in feet per second.
def>= vertical correction in mils required to movc
bursts to the muzzle ,-elocity line.
dA = lateral correction in mils required to movc
bursts into the plane of the target.
d % H factor and def>factor are taken from the
graphical firing tables for factors for ballistic corrections.
(a) M1IZzle Velocity Correction
The required formula for determining the muzzle
vclocity correction is: 61\'i\' = :!:: C,CT, :!:: C2bl
:!:: C)l2'
where
C, is a factor given in the accompanying tables:
Table I is for 90 mm AA guns and Tablc II for 3
inch AA guns.
C1
C"=--sin
c1 tan T
C1
C3=---sin
£2 sin T
In the above expression for 61\lV
(1) The sign to be used with the term C1 CT1 is plus if
the obserwd deviations are aboves and mmus forl
belows.
(2) The sign to be used with the term C2&1 is given by
the following table: .
\ "hen facing field of fire
and O 2 is on the left
and O2 is on the right
TL less than
1600 mils observed
deviations.
+
(3) The sign to be used with the term Cab2 is plus for
overs and minus for shorts.
(b) Vertical correction
The formula required for the vertical correction is:
def>= - CT, + (6MV) (def>factor)
In the expression for de/>it is necessary to use the
proper algebraic sign for 6MV as obtained above
and the def>factor is always taken as positive.
(c) Lateral correction
Figure 2
TL greater than
1600 mils ob.•
served deviatiom.
left Right Left Right
+ +