Angle On Bow from start to finish

[GLotsapot]

Most common question I ever get playing sub games is "How do I get the Angle on Bow?" always followed by "ok.... but how do you actually calculate it?"
Both of these I will do my best to answer here (yes, including a formula you can drop into Google Sheets)

What is the Angle on Bow
So, I've seen people try to describe this is SO many ways, but I'm gonna make it REAL simple for ya.
If you're Jack on the Titanic, and you're holding Rose over the bow (pssst... that's the front), and you look 60 degrees to you left and see a periscope sticking out of the water..... then that submarine is putting 60 degrees left into his TDC.
Time to drop her into the ocean and run for a life boat buddy, cause she won't share that rubble with you.

How to visually get the AoB
You as the submarine captain, for the most part, will pretty much just guess this most of the time. With a bit of practice it just becomes second nature. You can also use the TDC Tutorial to hone your skills by looking at a ship, making your guess, and then looking at the map to see what it actually is - If you're wrong... at least you know how far you were off, and try try again.

The actual formula
Yeah... guessing is fun, but sometimes at night it's not as easy to guess when you can barely see. Or maybe you're looking for a little less simulator, and a littler more Kaboom (cause lets be honest... in the long run it is a game)

So... if you really want to calculate it, this formula is what you need, and you can get all the ingredients right from the periscope too.

Google Sheets Formula
a = horizontal centigrade tics
b = verticle centigrade tics
c = length (m)
d = mast heigh (m)

=DEGREES(ASIN(a/b/(c/d)))

That is the formula you use if you are in front of their ship to get you AoB. If you are behind their ship (they already drove past you), then simply subtract the above number you got from 180

=180-AboveNumber

I feel like that formula was unneeded, but whatever

There you go everyone! Now get out there and math the F outta the enemy

[GLotsapot]

Almost forgot my pen and paper brethren! For SHAME right...
For you good people, I'm sure the math in the middle of the formula is easy enough to do, but you will need to look up and print out a Trigonometry Table to look up the sine values - and don't worry, these were commonly kept on subs and ships for navigational purposes back in the day, so you don't have to feel dirty for using one

Here's a link to one that will deal with the angles in degrees and radians too
https://www.analyzemath.com/trigonometry/trigonometric_table.html

[Igoooor]

Well, the asin formula has the flaw that it neglects the width of the ship - if you are in the low degree areas you will get a high error due to this.
If you like I could make you a calculation disc for the asin part so you don't have to look up in tables...
(See https://steamcommunity.com/app/490920/discussions/0/1742264309470637269/ )

[GLotsapot]

Originally posted by Igoooor:

Well, the asin formula has the flaw that it neglects the width of the ship - if you are in the low degree areas you will get a high error due to this.
If you like I could make you a calculation disc for the asin part so you don't have to look up in tables...
(See https://steamcommunity.com/app/490920/discussions/0/1742264309470637269/ )

It's true it doesn't take into account the width of the ship, but that only really affects you when you're shooting at close to 0 or 180, in which you honestly should reposition yourself to a better firing solution. That's a pretty thin slice to be shooting at.

Besides - there's nothing in the recognition manual (in wolfpack) anyways that lists the width of the ships, so I don't know where you would get that data anyways to plug it into your calculations

[Valen]

Because dividing by a ratio is the same as multiplying by it's reciprocal the following formula would also work:

=DEGREES(ASIN(a*d/b/c))

[GLotsapot]

Originally posted by Valen:

Because dividing by a ratio is the same as multiplying by it's reciprocal the following formula would also work:

=DEGREES(ASIN(a*d/b/c))

Not seeing where you added in the missing width that you were complaining about though.
If the formula I proposed can be improved, I'm all for it - but please, propose an improvement and explain why its the better solution.
Without anything in the recognition manual about the width of the ship, I can't think of a better way than treating it as a flat plane

[Valen]

Originally posted by GLotsapot:

Originally posted by Valen:

Because dividing by a ratio is the same as multiplying by it's reciprocal the following formula would also work:

=DEGREES(ASIN(a*d/b/c))

Not seeing where you added in the missing width that you were complaining about though.

I wasn't. Just re-arranging the factors to be easier input in a calculator. You are mistaking me with Igoooor.

[Igoooor]

Originally posted by GLotsapot:

Originally posted by Igoooor:

Well, the asin formula has the flaw that it neglects the width of the ship - if you are in the low degree areas you will get a high error due to this.
If you like I could make you a calculation disc for the asin part so you don't have to look up in tables...
(See https://steamcommunity.com/app/490920/discussions/0/1742264309470637269/ )

It's true it doesn't take into account the width of the ship, but that only really affects you when you're shooting at close to 0 or 180, in which you honestly should reposition yourself to a better firing solution. That's a pretty thin slice to be shooting at.

Besides - there's nothing in the recognition manual (in wolfpack) anyways that lists the width of the ships, so I don't know where you would get that data anyways to plug it into your calculations

It's the "beam" value?
I tested the asin calculation for 124 length 22 beam and got at least 10 degree error at every angle below 80 (calc range 0-90, step 5)

Edit: My calculations are also off as the shape isn't a square and for most angles only half the beam length is "visible".

[GLotsapot]

Originally posted by Igoooor:

Originally posted by GLotsapot:

It's true it doesn't take into account the width of the ship, but that only really affects you when you're shooting at close to 0 or 180, in which you honestly should reposition yourself to a better firing solution. That's a pretty thin slice to be shooting at.

Besides - there's nothing in the recognition manual (in wolfpack) anyways that lists the width of the ships, so I don't know where you would get that data anyways to plug it into your calculations

It's the "beam" value?
I tested the asin calculation for 124 length 22 beam and got at least 10 degree error at every angle below 80 (calc range 0-90, step 5)

Edit: My calculations are also off as the shape isn't a square and for most angles only half the beam length is "visible".

Math should be sound, and it matches up fine whenever I use those variables in the TDC Tutorial (That way I can verify the answers I get)

[Pikey^BOB^]

I found the single most valuable piece of information that improved my AoB estimates was the presence of a Kingpin and using it's alignment close to 90 degrees either way. I know this isn't the direct point of the post, but shooting at suboptimal AoB should be at least mentioned.
Using the Kingpin is like a magic alignment tool since the closure or widening of those two top parts give the eye everything it needs without some of the optical illusions you can some times get.
I pick out the one with the Kingpin, know immediately how close I am to 90, can reposition to be ahead of the 90 and it literally gives me a countdown to fire. A good 90 has allowed me to shoot at the highest range of torpedos.

[GLotsapot]

Originally posted by Pikey:

I found the single most valuable piece of information that improved my AoB estimates was the presence of a Kingpin and using it's alignment close to 90 degrees either way. I know this isn't the direct point of the post, but shooting at suboptimal AoB should be at least mentioned.
Using the Kingpin is like a magic alignment tool since the closure or widening of those two top parts give the eye everything it needs without some of the optical illusions you can some times get.
I pick out the one with the Kingpin, know immediately how close I am to 90, can reposition to be ahead of the 90 and it literally gives me a countdown to fire. A good 90 has allowed me to shoot at the highest range of torpedos.

I use the exact same procedure (if possible) when doing it by eye as well. Optionally, I will use the front or rear sides of the superstructure

[Sir Cornflakes]

I noticed a maximum allowed relation in centiradians of 1 (vertical) to 5 (horizontal) for a viable result.
E.g. vertical = 4 and horizontal = 26 gives an error. Is there a way to compensate for that?
Otherwise the formula is working just fine :)

[Igoooor]

The formula only works if you get the numbers right... If a/b > c/d it won't work as you would be searching for a value bigger than one on the unit circle ;)
On the other hand, that's actually a plausible measurement for angles between 90 and 80 degrees as in this angle area the effect of the ships width increasing the visible length is higher than the shortening length.

[GLotsapot]

Hmmm.... I ran this though 5 different "TDC tutorial" missions, and inputed the values from that into my excel sheet I have with the formula in, and it came out correct on all 3 ships in each test with the exception of shooting at angles close to 0 or 180, which I assumed was just my eye measurments being off as it was even pretty close on those

[boris.glevrk]

Sincerely speaking, for beginners I would simply say "you DON'T calculate it, you estimate it".
Even with so many games played and so much tonnage sank, I still mostly rely on estimation, because it's far quicker than actual calculation, and by the time you calculated it, the AOB has changed.

[Sir Cornflakes]

Well could it be, that the enemy ship was too close for zoomed in values, thus giving back a false result? Maybe I shouldnt have used the zoom.. Im pretty sure the numbers were right and the formula usually works fine.