User Guide
QUESTION: What angular offset, a, from the line-of-sight, AB, should an observer
on a ship, or a torpedo, take to collide with the target?
SOLUTION: A moving object at Point A will collide with the target if it proceeds
on a course such that the time it takes to travel from A to C, (the point of impact)
is equal to the time it takes the target to travel from B to C. That is, a collision
will result if:
In accordance with the trigonometric sine law :
EXAMPLE
SILENT
HUNTER
74 APPENDIX C — THE FIRE CONTROL PROBLEM
APPENDIX C:
THE FIRE CONTROL PROBLEM
by William P. Gruner
A major problem faced by the C.O.’s is to determine when and from what
position to launch the first torpedo to achieve a hit (or hits). The C.O. has a
number of objectives after determining the nature of the primary target.
These primarily include getting into a favorable launch position within a
torpedo run of something between 500 and 2,000 yards; preferably between
500 and 1,500 yards — the shorter the distance the run to the target, the
higher the probability that it will hit. The solution of the torpedo fire con-
trol problem requires that a gyro angle be entered into a torpedo such that
after it completes its turn (if any) toward the target it will be on a collision
course with the target. The following will clarify the collision course
aspects of the problem.
A primary objective of the TDC is to generate the torpedo gyro angle which will
cause a torpedo of given speed to settle on a straight course such that it collides
with a target running on a straight course at a fixed speed. A collision (hit) will
occur when the target and the torpedo arrive at the same point at the same time.
Step 1 - The General Case (See Figure 1) An observer at point A sees a target at
point B moving at constant speed, Vt, on a steady course. The angle between the
line-of-sight, AB, and the target’s heading (angle-on-the-bow) is observed to be
“b”. The observer at A is moving at constant speed, Vs,
SILENT
HUNTER
73 APPENDIX C — THE FIRE CONTROL PROBLEM
POINT A
POINT B
POINT C:
Impact Point
Collision Course
Target Bearing
a
(offset angle
for collision)
D
s
= V
s
.
t
D
t
= V
t
.
t
b
cd
(angle-on-the-bow)
(track angle)
Fig. 1.
Collision
Course
Geometry
#
t =
D
t
=
D
s
or
D
t
=
V
t
V
t
V
s
D
s
V
s
sin a
=
sin b
or sin a = sin b
*
D
t
, or sin a = sin b
*
V
t
D
t
D
s
D
s
V
s
V
t
= 15Kts, V
s
= 45Kts, observed angle on the bow, b = 70°
sin a
= sin 70°
*
15
= Ø.93969
*
1
= Ø.31323
a
= sin
-1
= Ø.31323 = 18.254°
45
3