User Guide

Step 3 - In addition, I have assumed that because of the torpedo’s need to clear
the launch tube and its inertia, the torpedo course geometry advances 10 yards
straight ahead upon being launched before it begins to turn on a circular arc of
20 yard radius in response to the gyro angle input. (See Figure 3) Thus, step 3 is
to determine the geometry at the time the torpedo starts to turn toward the tar-
get. To do this I have assumed an average torpedo speed of 40 knots (22.522
yards/sec) during the 10 yards it travels before commencing its turn. It covers
this distance in approximately 0.45 seconds (10 yards ÷ 22.522 yards/sec). In that
time a target making 15 knots will advance about 4 yards along its course. A
slower target will advance a shorter distance, and a faster target more, during this
time interval. In any case, the distance advanced by the target is relatively small
compared to inaccuracies in estimating target speed and course, plus small bear-
ing inaccuracies input to the TDC caused by the ship’s master gyro “hunting” for
true north. This can amount to as much as +1/2º. This difference becomes more
significant the farther the torpedo has to travel.
SILENT
HUNTER
76 APPENDIX C — THE FIRE CONTROL PROBLEM
Step 2 - Step 1 produces an approximation of the correct torpedo gyro angle, but
it is just the first step in the solution because the course geometry of the torpedo
at firing time is not located at the periscope, it is some 40 yards forward of it. The
TDC must correct for this linear displacement of the torpedo. That geometry is
illustrated in Figure 2 (which is not to scale).
In Figure 2 the distance BD is calculated by means of the equation where
R = the observed range to the target, and the angle f is bearing of the target rela-
tive to the heading of the ship.
The angle g may then be determined by the equation
SILENT
HUNTER
75 APPENDIX C — THE FIRE CONTROL PROBLEM
BD = R
1
+ 40
2
- (2R
*
40
*
cos f) 

g = sin
-1
(
r
*
sin f
)
and the angle h = 180° - g
BD
A
B
D
E Start of Turn
R = range to target
Torpedo track
Distance off the track
4 yds. for 15Kt. target
Target course
S/M Course
m
(track angle)
k
(gyro angle)
20 yd. 
radius
40 yds.
10 yds.
Fig. 3. Step 3,
Accounting For
Target Motion
Before the
Torpedo Turns
Periscope A
Target B
D Torpedo c.g.
R = range to target
f
g
h
40 yds.
Target course
S/M Course
Fig 2. Step 2,
Accounting for
Parallax Due to
Torpedo Location