determining target speed when abeam

[greyrider]

Now the general who wins a battle makes many calculations in his temple ere the battle is fought. The general who loses a battle makes but few calculations beforehand. Thus do many calculations lead to victory,
and few calculations to defeat: how much more no calculation at all! It is by attention to this point that I can foresee who is likely to win or lose.
O divine art of subtlety and secrecy! Through you we learn to be invisible, through you inaudible; and hence we can hold the enemy's fate in our hands.

Sun Tzu


in this post im going to introduce to you an invisible yardstick to measure target speed from the torpedo fire control manual. i will describe the method, with a description, with pictures, and a mission to test the method.









In the torpedo fire control manual, chapter 7 and 8, there lists
a number of ways to target, and obtain target speed.

CONFIDENTIAL

(c) The following basic standard firing methods are described for submerged attacks but are equally applicable to surface attacks, they are:



(1) Check bearing method
(2) Continuous bearing method
(3) Constant bearing method



the CHECK BEARING METHOD, chapter 7-2, IS the point and shoot method that i have called it, in my posts of point and shoot, going all the way back to the SH3 forums, in december of 2005, the firing bearing
is predetermined from formula, with a zero gyro angle on the torpedo, when the target crosses the firing bearing, (check bearing), the torpeos are shot, the target continues
on its course until the torpedo impacts the target at zero degrees.


701. CHECK BEARING METHOD:

(a) The Approach Officer having previously announced that SHOOTING WILL BE BY THE CHECK BEARING METHOD, BEARING EVERY ____ TORPEDOES. He then, when in all respects is ready to shoot, announces FINAL BEARING AND SHOOT - UP SCOPE.

(b) A designated member of the Fire Control Party orders STANDBY FORWARD (AFT).

(c) The periscope is placed on the desired point of aim as soon as the top of the periscope breaks water. The Approach Officer orders BEARING MARK.

(d) The TDC Operator matches the observed bearing and radar range (if taken) in the center, section of the TDC and announces SET when it has been matched.

(e) The Assistant TDC Operator announces SHOOT if the following conditions are met:

(1) Spread set
(2) Correct solution light on



i covered the constant true bearing method in the 80/10 method thread, and since then, it has become my primary method of determining long range target speeds that are closing, out to the limits of the hydrophone listening range,
while the submarine is moving at speed, whether convoys or taskforce: (many ships) or single ship encounters.


805. RELATIVE MOVEMENT

(a) Constant True Bearing

(1) When the range is decreasing, (closing), and the true bearing of the target remains constant the submarine and the target are on a collision course. In Plate XVI of the TFCM, the true bearing is remaining constant at 015 degrees T.





CONFIDENTIAL SLM 1

if both ships maintain course and speed they will collide at point A. (Plate XVI)

(2) If during the period between two observations of the target the true bearing remains constant and the target has not changed course, the angle on the bow will remain the same.

(3) If the target and the submarine have not changed course, the target has not changed speed, and the true bearing has remained constant over a period of 2 to 3 minutes, the target speed may be determined by the formula under plate XVI.

St = sm x sin LA / sin Ab

St = target speed
sm = submarine speed
LA = lead angle
Ab = angle on bow


the amazing thing about the constant bearing method is that its fast, just takes a few minutes, and it eliminates the need for plotting.



i have found that 3 minutes in best in confirming constant bearing to obtain target speed, tho i have held constant bearing with targets, single ship, convoys and taskforces well over a hour in some instances, with hydrophones only.
if the target moves off bearing in under three minutes , and keeps moving off bearing after a few attempts to keep constant bearing, most likely it is closing, but its course is almost perpenticular to the submarines course accept that it has a
slight AOB pointing in the direction of the submarine. whenever the targets aob is pointing toward the submarine, even a 1 degree aob, the sonar operator will always announce....Closing! even if the target is really moving away.
in most cases, if the bearing remains constant for 3 minutes, its going to remain constant for a lot longer period of time.

i could not cover every bearing in the constant bearing method, so i picked one, just like the torpedo fire control manual picked one, that being 015 T.




so now, after reviewing the constant bearing method with you here, its time to discuss the next method from the fire control manual and the subject of this post, that is called the Speed when Abeam, which is another method of determining target speed,
while the submarine is at speed.

basically, its like having an invisible yardstick to measure distance traveled by an unseen target or one that is in periscope view over time. it is also the method used for calling in and adjusting field artillery, mortar, or naval gunfire to put
rounds on target for destruction.


SPEED WHEN ABEAM


Definition of ABEAM


"Off to the side of a ship or plane especially at a right angle to the middle of the ship or plane's length"


by the definition of abeam we know that we have to be at a right angle to the target, the best way to do that is when a closing contact is made, whether by radar, hydrophones, visual, is to turn the submarine so that the target bears on 80 degree mark
relative to the submarines bow or stern, if a bow shot is what should take place, then turning the submarine to place closing target on 80 degrees or 280 degrees is where you want the target to bear, if stern torpedoes are going to be used in the attack it would be 100 or 260 degrees.
this sets up a 90 or near 90 degree target track, a right angle or near right angle. this is the setup to determine speed when abeam, its also the optimal for torpedo attack.


lets make an example, using the 80/10 setup, lets see where the target is, then lets see where the target is going.

obviously we know where the target is, its on bearing 80, so to find where its going we need to know its bearing, whether its bearing is less than 180 degrees or more than 180 degrees, and we need to know its AOB.

so we know the target bears on 80 degrees, since that bearing is less than 180 degrees, we have to add 180 degrees to its bearing, that adds up to 260 degrees, 80 + 180 = 260. now we have to consider the targets AOB, to determine target course,
at the moment of measurment the AOB appears to be 10 degrees port. since the AOB is port, we have to add the AOB to our sum, 260 + 10.
adding those together adds to 270 degrees, so our targets course is 270 degrees relative to submarine in the 80/10 setup i described. we know where it is, and we know where its going. 80 + 180 + 10 = 270.
thats a ninety degree target track. it is a geometric fact that all acute angles in a right angle must add up to 180 degrees, 80 + 10 + 90 = 180.










Sun Tzu said: In respect of military method, we have, firstly, Measurement; secondly, Estimation of quantity; thirdly, Calculation; fourthly, Balancing of chances; fifthly, Victory.




from the TFCM:

(c) Speed When Abeam chapter 8-7

When abeam of a vessel, the rate of change of bearing in degrees per minute is equal to 1 degrees per knot of enemy speed at 2000 yards. The above statement disregards any change of bearing due to the submarine movement.
It is reasonably accurate between angles on the bow of 50 to 130. It is based on the fact that 1 degrees subtends 35 yards at a range of 2000 yards and one knot equals 33 yards per minute.


the meaning of the above paragraph is simple, we are measuring the distance between the boundaries of one degree. think of one degree starting at the front of the submarine , it looks like a V, with the vertex of the V
in the front of the submarine, it has a left boundary, and a right boundary, the father it goes out from the submarine, the wider the boundaries get, or the bigger the V gets, in the case of the hydrophones, the maxiumn its goes out is 18.3 nm.
between those boundaries is a measurable distance, the TFCM uses 2000 yds as its sample becus 1 knot in speed will cover 35 yds in 1 minute, and at 2000 yards, the distance between the boundaries of 1 degree is 35 yards.
this is an invisible yardstick we can use to determine target speed.
at 1000 yds, distance between boundaries of one degree is 17.5 yds, at 10000 yds the distance is 175 yds, and so on until at 37000 yds, (18.3nm) the distance is 647.5 yds. this is what is called the OT FACTOR, observer to target factor in field artillery,
for every 1000 yds the OT factor increases by 1, Horizontal and Vertical measurement.

note: speed when abeam, or the method itself, probably works in the perpendicular as well.





below is a list of the distance between the boundaries on a one degree arc at known ranges, from .5nm to 18.3nm.

17.5 yds 1000 yds
35.0 yds 2000 yds
52.5 yds 3000 yds
70.0 yds 4000 yds
87.5 yds 5000 yds
105.0 yds 6000 yds
122.5 yds 7000 yds
140.0 yds 8000 yds
157.5 yds 9000 yds
175.0 yds 10000 yds
192.5 yds 11000 yds
210.0 yds 12000 yds
227.5 yds 13000 yds
245.0 yds 14000 yds
262.5 yds 15000 yds
280.0 yds 16000 yds
297.5 yds 17000 yds
315.0 yds 18000 yds
332.5 yds 19000 yds
350.0 yds 20000 yds
367.5 yds 21000 yds
385.0 yds 22000 yds
402.5 yds 23000 yds
420.0 yds 24000 yds
437.5 yds 25000 yds
455.0 yds 26000 yds
472.5 yds 27000 yds
490.0 yds 28000 yds
507.5 yds 29000 yds
525.0 yds 30000 yds
542.5 yds 31000 yds
560.0 yds 32000 yds
577.5 yds 33000 yds
595.0 yds 34000 yds
612.5 yds 35000 yds
630.0 yds 36000 yds
647.5 yds 37000 yds

in the picture below, i have drawn three ships within a one degree arc, at 8000 yds, 18000 yds, and 36000 yds, starting at the left boundary of the 1 degree arc. at 8000 yds the distance between boundaries is 140 yds, at 18000 yds, the distance is 315 yds,
at 36000 yds, the distance is 630 yds. you can see now that there is a measurable distance determined by range in a 1 degree arc, the invisible yardstick!





so lets say that at 18000 yds, listening with hydrophones, you had a sound bearing at 300 degrees, submarine is making one knot, and it takes 1 minute for the target bearing at 300 degrees to go to bearing 301 degrees, that
would translate into a target speed of 9.3 knots.

the invisible yardstick is there, the question is....how good are you with the hydrophones, how good of a sonar operator are you?
with my next post to add here, i will try to help you become good at sonar operation. with respect to Sun Tzu's military method, first Measurement, third Calculation, plays prominently in hydrophone operations.