Determining Angle on Bow - reliable mathematical approach found

[B_K]

Hello to all Kaleuns! :Kaleun_Salute:
I was wondering about how to mathematically determine (in)famous Angle on Bow. That is what i found out.

First, major assumptions, very simple:
- we know exactly what target we are facing, we know its length (L) and mast height (H) - easy with our Recognition Book
- we know how to use our periscope reticle - field of view and angular scale based on magnification, both in vertical and in horizontal direction
- we can figure out if the target is closing to us or goes away

So lets start with situational drawing which is here:

http://s000.tinyupload.com/index.php?file_id=02436886106294144239

right part is just magnified left part of the drawing. All is drawn to scale.

We observe a ship of which length L is known from recognition book. Since it travels with unknown AoB, observable length is shorter and equals Lx (perpendicular projection of L in our scope view).

L-length of a target ship
D-distance (determined by stadimeter)
greek alpha - observable horizontal angular width of a target ship

The rest of the drawing is self explanatory.

Next we move into some maths - very basic trigonometry, based on again a few assumptions - self explanatory.

http://s000.tinyupload.com/index.php?file_id=99653561349984728719

For those who are not interested in math method, the final answer as we see is:

AoB=arc sin [(D tan alpha)/L]

remember that sine function is symmetrical to 90 degrees, so you must check if target is closing or gets away. sin alpha = sin (180-alpha) so you get the same results for acute and obtuse angle and must choose the right one.


As drawing is to scale, you can easy check equations.

Please, give me some feedback and tell me what do you think about it.

[Kendras]

I think we should create a sub-forum with all the threads explaining the manual targetting ....

[JuanLiquid]

While that formula may be accurate, I highly doubt a capitan or weapon officer would have an Hewlett Packard in his pocket to do it.

You have an attack disk (using some GUI mods, like Manos or Ahnenerbe) that solves that formula for you.

However I do not find any method that relies on mast height really good, because:
- Mast height is hard to measure with bad weather
- Any ship that has some damage will have different mast height
- Usually when a ship is close enough to take an estimation about its height, then its aob, is too late.

So, I think the best solution is using an eye-calculator which have even less error than the distance calculated with the mast height, is takes about 2-3 seconds and it returns you the AOB!

The only parameter you need to calculate is the Speed, which you can do with the attack disk, or with previous distance estimations, or comparing distances. While the speed is being calculated you can calculate the AOB and the distance. Eye calculator is perfect for counter attacking destroyers if that's your only way to escape. How do you do it? You must look for the clues in the target and some practise.

1. If I have a lot of time, I do distance estimations with stadimeter, map drawing, etc, I do not limit to eye-estimations, but I always do eye estimation to confirm. Also I do 2, and 3. And I do 1, 2, 3, 4 as many times as I can to get good data.

2. If I have limited time, at least 1 min, I calculate the speed of the ship with the attack disk. While the timer is running I start to look for the clues (4) to estimate its AoB.

3. If I have a very limited time (<15 seconds):

Speed: I estimate a speed of 6-9 for unware, undamaged merchants (some times they can go to less than 6 knots, take a look to their prow and how its breaks the water). Or 7-12 for aware, undamaged merchants. For destroyers, since they usually are pretty close to you, I estimate 3/4 of their maximum speed, if I do not have time to identify them, then 20-25 knots. Again, looks its prow. (3 seconds.) Step 2 calculation is the best value, step 1 is a good reference, step 3 is the machete at your ankle.

AoB: Is it going towards your sub? or is it going far from you? Its prow and its stern talks! If you cannot see too much foam in its prow, that means it's going away from you. Now, you estimate any angle, if you where in that boat, which angle would you use to see your sub. Once you have the first estimation look to the front wall (or rear wall) from the bridge, and look, in case of merchants, those duals mast that should be aligned. Now think, with your first AoB, and taking a look to those visual clues, would you think it is correct? or do you need to some correction? Dont overthink, follow your guts here. (10 seconds). Step 1 AoB, Step 2 and Step 3, all of them have the same impact on the AoB. Another clues: smoke, other ships in lanes (convoy), cargo aligment.

Distance: Almost useless unless you are using FaT torpedoes, just place whatever you feel (or you calculated in 1 or 2 if you had the time). Step 1 and Step 2 are the key here, again step 3 is your machete, but since it's almost useless, it doesn't matter.


Conclusion: you only have to calculate two values, the speed and the AoB. You have a very exact tool to calculate the speed (or you can use the formula 2*ship lenght / seconds), and your eye is very reliable to calculate the AoB. Once you do it 20-30 times, it will be almost automatic. Try it! And feel like a WWII captain!

[B_K]

Hi. Thanks for your opinion.

No HP calculator needed ;-) just precise tangens and sinus table or disk/slide rule. Good for checking eye solution if you have time.

(Edit reason: I wrote complete nonsense and I had to fix entire post leaving only the last sentence ;-) )

[Kendras]

Indeed. There is the theorical aspect, and the practical one. Both are important for a good understanding. But in the end, it's the practical method which will allow you to conduct successful attacks !

:salute:

[Nordholz]

Hey, your approach sounds very promising. Unfortunately the pictures are gone so its quite difficult, to follow. Could you reupload those pls? Would be awesome :)

[Aktungbby]

Nordholz!:Kaleun_Salute:

[Nordholz]

Ahoi Aktungbby :Kaleun_Cheers:

[blackswan40]

https://www.subsim.com/radioroom/picture.php?albumid=1246&pictureid=10895


https://www.subsim.com/radioroom/picture.php?albumid=1246&pictureid=10896

[John Pancoast]

Well, you can't get much more practical than just using a simple 90 aob for any attack. :03:

[Davidorado]

I reaaaally tried to wrap my head around this topic, but without these images it´s almost impossible.
Is anybody out there, who has these images stored or could draw something which could help me understand what is going on?


In the german book "Agru-Front Lehrmaterialien" from DonL1978 there was the same approach of calculating the AoB. But I wasn´t able to catch it either, due to the lack of explaining pictures.
At the end there was a table with AoB´s in the distance of 500-1000m with common ship lengths from 60-240m.

This might help in battle, but it´s not helpful for understanding.


Thank you in advance Kaleus :)

[Aktungbby]

Davidorado!:Kaleun_Salute: finally on the surface after a 12 year 'silent run'! Do what fellow Minnysodian, John Pancoast, said: 1: get 500-1000 yards perpendicular to the target's course; 2: set the scope or conning-tower binocs on zero; 3: set the TDC 1⁰‐2⁰s in direction target is 'crossing' your scope, and 4: as the vessel's bow crosses your zeroed scope crosshairs, 5: launch one, then a second eel in rapid succession. The quote from Iron Hearts, Steel Boats :timeout:(or some-such tedious book I actually read decades ago) holds true here: "TDC! what TDC? just aim the damn boat!"...gut hunting Kaleun! Remember von Clausewitz On War "In war eveything is simple; but sometimes the simple thing is difficult."...ie: occasionally U will miss!:O::arrgh!::yep:

[3catcircus]

I reaaaally tried to wrap my head around this topic, but without these images it´s almost impossible.
Is anybody out there, who has these images stored or could draw something which could help me understand what is going on?


In the german book "Agru-Front Lehrmaterialien" from DonL1978 there was the same approach of calculating the AoB. But I wasn´t able to catch it either, due to the lack of explaining pictures.
At the end there was a table with AoB´s in the distance of 500-1000m with common ship lengths from 60-240m.

This might help in battle, but it´s not helpful for understanding.


Thank you in advance Kaleus :)

I wouldn't put much stock in this method. No one is going to thumb through a book of trig tables.

Easiest method beside eyeballing it is to plot. Range, bearing mark. Wait 3:15. Then range, bearing mark. You now have speed and course. With course, you can draw AoB.

U don't have to be all that accurate on range and bearing. The key is to get the speed. The two plotted points get you course. If you do it early enough, you can get at least 3 points. The more points you plot, the more your error goes down. As long as you aren't trying for a shot from over 5 km away, AoB within a few degrees is fine. The key is accurate speed.

[Davidorado]

I wouldn't put much stock in this method. No one is going to thumb through a book of trig tables.



Yeah, you are right. To me it´s more about the theory and "how it COULD be done". I was just curious because I read about it and wanted to test it.


Anyway, I found the solution to my problems:
1. In the "Agru-Front Lehrmaterialien" the formula contained a "tan^-1". The photo math app I used interpreted it as 1/x, which would be normally correct, but in this case it´s just a sign for arctan. But even with Excel I couldn´t solve this. Which leads me to number
2. Excel uses Radian. I wasn´t aware of this and never came it across in school. So I had to convert it.


I built a simple Excel calculator around these formulas and I now have 2 approaches of solving this.

1. The approach with Length, Distance and the apparent length
2. Own Course, own speed and two measurements of the enemy bearing+distance. Usually you would wait 5-15min between these.
Benefit of this approach is, you get target speed and and course too!



You just enter the data and Excel calculates the AoB magically. Of course you would still use your brain.

So if anybody needs this Excel sheet, I probably could upload it somewhere. :)

[Mister_M]

So if anybody needs this Excel sheet, I probably could upload it somewhere. :)


Yes, please! :yep:

[Davidorado]

Okay, I managed to translate it as good as I could.
The coloumns A-AG are just general conversion tables I use on my patrols. I group these together with the little "-" sign above the coloumns.
AH-AU is where the AoB part lives in. Lines 1-30 is a conversion table of the calculator you find in AI42-AJ46 (origin is from DonL1978´s AgruFront-Lehrmaterialien) in case you don´t like calculating.
Generally: Every cell, where you have to enter data, is coloured gold. All of the others aren´t intended to get touched.

AI33-AS40 is the first AoB calc approach using the mast height, ship length and apparent ship length/height. The screenshots should guide you what is actually needed. The worksheet is protected, but you can click "unprotect sheet" (no password).

The second calc AI42-AJ46 is using the distance and the ship length in meter and now you need the difference of the bearing from bow to aft of the ship. DonL1978´s screenshots should assist you.
You measure the bearing to the bow of the enemy ship, the bearing to the aft, subtract it from the first bearing, divide it by to and enter it in the bearingdifference field.

The third uses a different method where you have to enter your speed, your course, the bearing and distance to target once, take the stopwatch, wait 5-15 min and take bearing and target distance a second time. You get the enemy course, speed and the AoB.

I used all three of these a few times but got mixed results. Please test it and say if I made any mistakes or you have something to criticize.


https://www.mediafire.com/file/w3oxe525qttific/UBOAT-calc-eng.xlsx/file