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.

[Rockin Robbins]

Much of this is based on already knowing the enemy course and speed, which, of course, is what you are trying to find out. Circular reasoning finds nothing.

What good is linear distance per degree when we don't know the range? We take a great numbers table and reduce it to speculation. How to we obtain an AoB of 10º? Is it just because the bearing is 80º? Now 80º to the left of zero is 360-80=280º not 260º. It's entirely unclear what your arithmetic gymnastics are all about there. Maybe you're talking about taking a stern shot (180º plus or minus relative bearing from astern) or maybe not. You don't say.

And because you don't say, your method isn't clear at all and your instructions can't be followed. What is the purpose of targeting instruction? Please try again.

Especially you must get over the hurdle of proving that if a target bears 80º its AoB must be 10º. That's a real groaner.

Finally, if you have a sub with radar, what's the purpose of all these calculations? Wouldn't a graphical method be more appropriate and self-checking for error mitigation purposes? See my flash card for the Vector Analysis Targeting Method in the Bag of Tricks thread for an example of how you might proceed.

The purpose of instructions is to make crystal clear the simplest method to accomplish a task, so that the vast majority of those with the instructions can successfully follow them to the goal. Your post is far short of that standard, even for expert players.

Oh, the game only works in full degrees. Therefore a ship at bearing 15.4 is called at 15º, a ship bearing 15.6 is called at 16º giving your bearing method an error envelope of plus or minus 50 or 60% of a degree--certainly not accurate enough to do ANY targeting with no matter how good you are with the sonar. And the kicker is that we really don't know what their rounding system is so the error is actually entirely unquantifiable but very significant.

Basic error mitigation techniques mean that you must estimate expected error and they tailor your method so that errors of that magnitude still result in a BOOM at the end of the procedure. There's no evidence of ANY error mitigation analysis in your method anywhere, and no, it is NOT the method taught in the Submarine Torpedo Fire Control manual.

And forcing Sun Tsu in there is just irrelevantly irritating. He's not applicable.

I say the game changer in WWII fleet boats was radar. Use the thing all the time. Get radar ranges: the gold standard. Get radar bearings: the gold standard. Get course by radar before you ever sight the target: more accurate at 20,000 yards than a stadimeter at 1500 yards. Calculate speed by number of yards traveled in three minutes divided by 100, easily done in your head and accurate to much less than a knot. The game rounds all speeds to the nearest knot too, so everything goes to the nearest knot, nearest degree, nearest yard (or maybe nearest meter, converted to yards, rounded by unknown method to nearest yard), rounding methods throughout, unknown. So in all cases the most accurate measurement you have by far is radar. The stealthiest method you have is radar, even if the signal is detected they know you're out there, you know everything about them. Radar is also the easiest method to implement, least error prone, simplest calculations (most calculations are totally unnecessary, being solved in graphical form on the nav map.)

Looked you up, greyrider. That's who I thought you were. Folks, the 80-10 method is a fallacy. It can't be even put into understandable words because it is based on a simple fallacy that if the bearing to target is 80º its AoB MUST be 10º. That is patently false so the method fails completely. Graphs to prove upon request and I'll make a follow-up post in the Bag of Tricks thread so no one is tempted to waste their time trying to figure out this method, which is no method at all.

As a matter of fact, Aktungbby has a graph below where the bearing to target is just about 80º port by German reckoning, 280º by American reckoning. However, the AoB, shown as theta bow on the graph is in the neighborhood of 110º starboard. 80-10 dies horribly, failing on its very first claim. In fact, angle on the bow has no relationship at all to the target's bearing from the submarine.

[Aktungbby]

greyrider! All that said: I generally just aim the boat within 1000 meters; dredge up some ol' pheasant-hunting wing it techniques and use steam eels on high speed generally from within the convoy with a good overlap so if I miss one it often hits another. Down-the-throat and directly-aft shots are useful too; no calculations needed...other than recollecting the eel's arming-travel distance...300 meters. In SHV I did get 'put to it' though against a speedy Battle-cruiser at 4,000+ meters off the Spanish Coast and put a 4-eel salvo to it at 30 knots; one eel was electric so I downed the steamers' speed to 30 accordingly. BEHOLD! two out of four hits crippled the beast sufficiently to allow follow-on shots to finish her. By put to it; I was out of time for the mission requirement and so took a shot I would not otherwise consider. &gets it done when put to it (key to enlarge diagrams)

[Aktungbby]

Originally Posted by Raptor

However, the AoB, shown as theta bow on the graph is in the neighborhood of 110º starboard. 80-10 dies horribly, failing on its very first claim. In fact, angle on the bow has no relationship at all to the target's bearing from the submarine.

Well of course that's why I keep it simple: 10 AoB degrees either way...until I get a Zaunkönig into the 80-10 equation; in which case, the steamer is for coupe d' grâce; unless I'm able to rise and use the deck gun. and save the Reich 10,000 Marks per eel!

[Rockin Robbins]

Usually, for error mitigation and shortest possible warning for the enemy to avoid I'm looking for an AoB of 80-90 and looking for a torpedo track angle of 110º, the most difficult shot to maneuver to avoid from, AND the most error tolerant possible solution. I'm looking for a gyro angle under 20º to cancel out range error and I'm looking to close range to about 500 yards. Torpedo arming distance varies with mod but is 300 yd stock. I believe TMO it 400yd. In any event, a 500 yard shot at TTA 110º and a gyro angle of less than 20º with a fast torpedo is unavoidable and ends with a BOOM.

Another elementary error in greywolf''s "method" is that he says that any two acute angles contained within a right angle must total 180º. No that is not true. If you pick a 10º angle within a right angle and a 30º angle and total them 40º does not equal 180º. If you take a single angle and its compliment within the right angle their total is 90º, not 180º. After all a right angle IS a 90º angle. Divide it up any way you want and the sum of the angles contained within the right angle MUST be 90º. That's Geometry 101. Euclid would be proud!

[ColonelSandersLite]

Originally Posted by Rockin Robbins

The game rounds all speeds to the nearest knot too, so everything goes to the nearest knot, nearest degree, nearest yard (or maybe nearest meter, converted to yards, rounded by unknown method to nearest yard)

This is clearly not true. I don't know where you got that idea from.

[Rockin Robbins]

Originally Posted by ColonelSandersLite

This has largely been my finding with these methods. I found the most useful of the methods there to be determining course from collision course, specifically where you don't have radar. In SH3 I did a lot of work with passive sonar plots and this was a good way of further refining target data.


This is clearly not true. I don't know where you got that idea from.

Direct communication with the game developers. You can interpolate until the cows come home on the speed dial and the game rounds off to the nearest knot by unknown rounding method. You can interpolate on the bearing dial and for internal calculations the game rounds to nearest degree. All target speeds are whole numbers of knots. If your calculation shows 9.5 knots it is in error.

[ColonelSandersLite]

I'm going to rig a series of tests to be 100% sure, but this sounds like a miscommunication to me, or perhaps a developer that worked on another part of the game and shouldn't have been commenting on that part.

[ColonelSandersLite]

First test:
Merchant set in mission editor to move at a speed of 8 knots.
Distance traversed in one hour, exactly 8 nm.

Second test:
Same mission, only changes where to merchant speed and waypoint speed. Set to 8.5 knots.
Distance traversed in one hour, exactly 8.5 nm.


Third, Fourth, Fifth test:
Set the tdc to target a hypothetical merchant at bearing 0, speed 8 knots, aob 90 distance 1560 yards. Observed the path on attack map and Fired 1 torpedo. Torpedo malfuctions off. Test 4 the same except speed of 8.5. Test 5 the same except speed 8.75.

In all three tests, I observed that the torpedo run line on the attack map moved with expected results and torpedo tracked exactly where it was supposed to.


Test 6:
In test mission, set target heading to 144.29 degrees.
Target crossed my 0 bearing at a range of 2518 yards

Test 7:
Same as test 6, with heading changed to 143.609 degrees (closer to sub).
Target crossed my 0 bearing at a range of 1784 yards



I think that's enough. I didn't go to the effort to debunk every single item, but the picture painted is quite clear. It's more likely that the game uses the same or greater precision level used in the mission editor, which is 6 decimal places. I have some experience with these sorts of things and can tell you with certainty that 1 degree, 1 knot, and 1 meter precision would make the game very, very jumpy.