What is your TDC up to? the Law of Cos, the perfect torpedo shot

[starvingartist507]

Originally Posted by Puster Bill

I was going to use the procedure outlined in the instructions for the SACF/IS-WAS at the HNSA site as a basis. I just never seem to get the time to sit down and do it uninterrupted.

I'll have a look at an the Is-Was I downloaded (from subsim forums), and see it involves a relation, or quick-compute way to lay out the data. I dont know if they used a vector system, but it worked for me. I finished that file I mentioned above, it seems to work pretty well, calculating the heading and speed of a target, even when the sub is moving. The math that is going on "in the clockwork" is kind of convoluted, and I'm still trying to trim it down into a simple equation. If someone can do that, they'd have the key to designing the Is-Was, and from there, infinite understanding of its function....So thats what I'm working on!

Also, I had a quick question, can you use an Is-Was when the sub is moving? If so, there most definitely is an underlying relation, and that's pretty much been my holy grail since I bought SH4. Thanks!

Originally Posted by Hitman

Seriously now, I have followed your thread with great interest

Thanks

Originally Posted by Hitman

Anyway, I have been recently coming by research to the method used by the real U-Boot kaleuns in WW2, ...

My question is: What would be the exact mathematical formula for this? I mean, there must be a mathematical formula to allow calculating the AOB like that without any table and a finger going right-down on it

I'll look at this chart you linked, its very interesting. My german is passable, but I think I get the idea. I assume the U-boat is free to manuever to maintain the 90deg bearing?
Hmm, I'll plug away at it. Thanks for the insight. Thants going to be a few more hours of fun! It doesnt get much more geeky than "fun" math!

Here's a pic of the (extremely junky but funcitonal) program I wrote today to do this math for you. It'll take the place of the stopwatch, basically. If anyone wants to try it, I guess they'll have to PM me with an email address, and I can email it to them. at least until I get my file server back up. I didnt take the time to make an installer for it either, so its just a .rar

edit: pic link was broken

[Puster Bill]

Originally Posted by Hitman

LOL it's good to see you joined the joke

Seriously now, I have followed your thread with great interest, because -believe it or not- I am a nut in maths (Though I wasn't bad in geometry) and despite having done many slide rulers for SH3-4, it was not easy for me to get the real mathematical formula behind their use. I have been dusting off some of my most buried memories from high school, but I seem to need a good amount of catch-up lessons to be able to get the whole thing again

Probably that's the main downside of having studied laws at university, where the few maths I knew got fogotten

Anyway, I have been recently coming by research to the method used by the real U-Boot kaleuns in WW2, which involved keeping constant 90º bearing on a target to get both AOB and spee.

What I have been using so far (And was posted by Don1 reed here long ago) is:

By constant 90º/270 bearing:

Sin target AOB : Own Speed = Sin target Speed : Enemy bearing

I have been using a printed table like this





to get the AOB & Speed by following method:

1- Make two range observations, and measure the time between them

2.- Starting from the top-left (For right AOB) go right as much as your U-Boat advanced. Then go down as much as the target closed in.

The resulting point in the table where it intersects the AOB tells you the result and you can later apply the above mentioned rule to get speed once you have determined the AOB.

My question is: What would be the exact mathematical formula for this? I mean, there must be a mathematical formula to allow calculating the AOB like that without any table and a finger going right-down on it

Hey, Hitman, have you considered doing a 'Super Targeting Toys/Tutorial' pack?

You've built enough, and done enough research, that putting it all together in a single, large package seems the logical thing to do. Certainly, I'd be interested in it.

I know it's a lot of work, and you have done more than your share of work for this community to get that stuff out there, but I know that I and many like me would be interested in it presented as a single coherent set of tools and instructions, perhaps with a couple of examples and the theory behind them, instead of chasing them down here and there all over Subsim.

Like I said, you've done more than enough, so I feel guilty even mentioning it, but it certainly would be helpful for us mere mortals...

[Xelif]

Starvingartist, could you elaborate a little bit about the trig method you used to solve a solution where your sub is moving? You said you solve two triangles... I've got a very rough idea and if you felt like going into the formulas briefly, I'd appreciate it.

[Hitman]

Also, I had a quick question, can you use an Is-Was when the sub is moving? If so, there most definitely is an underlying relation, and that's pretty much been my holy grail since I bought SH4. Thanks!

Yes it has a "Speed correction" feature where you substract your own ship's speed, recalculated to make sense to the observed enemy ship speed.

Thants going to be a few more hours of fun! It doesnt get much more geeky than "fun" math!

LOL we are real "Frikkies" ain't we? When I just think that I hated maths back in school If the maths and physics teachers (BTW I studied at the german school in Valencia-Spain) had used nice examples like U-Boots, Guns, Automobiles and such instead of the idiotic ones they used, I bet many more would have got hooked by maths

I'll look at this chart you linked, its very interesting. My german is passable, but I think I get the idea. I assume the U-boat is free to manuever to maintain the 90deg bearing?
Hmm, I'll plug away at it. Thanks for the insight. Thants going to be a few more hours of fun! It doesnt get much more geeky than "fun" math!

Here's a pic of the (extremely junky but funcitonal) program I wrote today to do this math for you. It'll take the place of the stopwatch, basically. If anyone wants to try it, I guess they'll have to PM me with an email address, and I can email it to them. at least until I get my file server back up. I didnt take the time to make an installer for it either, so its just a .rar

Yes the U-Boot is free to move, and what it does is change course/speed in a way that keeps the enemy at constant bearing.

The idea is to build a constant triangle with a 90º angle on it (At the corner of your U-Boot), that allows you to apply the law of Sines for getting speed, as the constant bearing neutralizes the dynamic aspect of speed (Time/Distance) and makes of it an absolute value.

What the tables do is basically build abother triangle A,B,C with a 90º degree on it like this:

A\
I \
I \
I \
I \
B___ \C

Where B-C represents the target distance covered forward (Obtained from your U-Boots own forward movement during the time measured), and A-B the distance the enemy has closed in (Obtained from the two range measurements). While the table gives you a quick visual solution, there is of course a mathematical formula behind all that, which takes into account the triangle. Since we know the lentgh of two of the sides of that triangle (And we could also get the length of the third by the Phytagoranian a2+b2=c2, but we don't need it) and one angle (90º) we should be able to calculate mathematically the other two by a formula using the Sine and Cosine....only that I don't remember any more how it was done, despite having done that back in school long ago

Here's a pic of the (extremely junky but funcitonal) program I wrote today to do this math for you. It'll take the place of the stopwatch, basically. If anyone wants to try it, I guess they'll have to PM me with an email address, and I can email it to them. at least until I get my file server back up. I didnt take the time to make an installer for it either, so its just a .rar

Sure! I'll PM you in a moment with some interesting stuff and a e-mail address

Hey, Hitman, have you considered doing a 'Super Targeting Toys/Tutorial' pack?

You've built enough, and done enough research, that putting it all together in a single, large package seems the logical thing to do. Certainly, I'd be interested in it.

I know it's a lot of work, and you have done more than your share of work for this community to get that stuff out there, but I know that I and many like me would be interested in it presented as a single coherent set of tools and instructions, perhaps with a couple of examples and the theory behind them, instead of chasing them down here and there all over Subsim.

Like I said, you've done more than enough, so I feel guilty even mentioning it, but it certainly would be helpful for us mere mortals...

Yes, more or less...

I have been collecting data and historical research in order to make somewhen a manual of the historical procedures used in german U-Boots. There is in fact no need to do something like that for US subs, as it is well documented, but german U-Boot information seems to have got lost after the war :hmm: It's a fascinating job to actually research and investigate this mistery, collecting here and there pieces of the puzzle, and I think the job is also worth it, because the methods used were very simple and with no plotting involved (Everything was done with wiz-wheels and printed tables), something that would suit perfectly a SH3 player, who is alone while playing (Not assisted by a fire control party).

What I'm currently doing is still collecting stuff (Have already tons of it, but not many form authentic sources) and doing concept sketches in paper, then testing them in SH3 to check the efectiveness.

I started following this thread with great interest because of course I wanted to explain in the manual the real maths behind all that, not just the use of wiz-wheels and tables

Anyway, I'm not in a hurry with this, it's becomed a long term project and I want it also to be a contribution for the opensource sim "Danger of the Deep"

[starvingartist507]

Ok, here's how the math works with the Tabelle:

The first thing I noticed is they set the U-boat speed to very slow rate (no respectable merchant is going to go 2-3 knots), this is so they don’t go faster than the target, effectively circling around them as they try to keep a constant bearing.

With the U-boat at a slower speed, and keeping a constant bearing, I get the following graph.


Basically, this chart doesn’t use Sin curves at all. I just says that, if a=b, then AOB has to be 45deg, because we have a standard right triangle with two equal legs.

This chart asks you to figure out the values for (a) and (b), then simply shows you their ratio. If the ratio is 1:1, then the angle is 45deg. If the ratio is a little bit less, then the angle decreases by an equivalent amount. If the ratio is more, well it increases by the same amount. This is a very neat way to figure AOB, in my opinion. Interestingly, if you want to find their speed, just use the Pythagorean Theorem to find the distance traveled (c), divide by seconds, and multiply by 1.777. No messy business with Sin curves or anything like that.



Resourceful krauts!

[starvingartist507]

Originally Posted by Weaverjd

Looking for the guide can someone pm it to me?

Originally Posted by Xelif

Starvingartist, could you elaborate a little bit about the trig method you used to solve a solution where your sub is moving? You said you solve two triangles... I've got a very rough idea and if you felt like going into the formulas briefly, I'd appreciate it.

Sorry to you and others that have asked for the guide. It is now available at
www.hoofinasia.net

I have updated my original post to reflect this.

I'm off to work on the is-was.

EDIT: just figured out the is-was, I'll post the math in a second.

[starvingartist507]

So here's the simplified relation to find merchie speed, even when the sub is moving.

DM=distance merchant traveled (unknown)
DS=distance sub traveled --> (sub speed in knots / 1.777) x seconds
B1=bearing 1
R1= range 1
B2= bearing 2
R2= range 2


[ ((Sin B1) x R1) - ((Sin B2) x R2) ]squared
+
[(DS)- ((Cos B1) x R1) - ((Cos B2) x R2) ]squared
=
[DM] squared
solve for DM, (remember to take the square root of everything...) divide by seconds, mulitply by 1.777, there's your speed. Thats actually a pretty simple equation, and works if the sub is moving or not. So there it is, in case you have a morbid fascination with math.

I'm going outside.

[Xelif]

You are my hero, starvingartist

Thank you for taking the time to painstakingly illustrate and explain these ideas!

[Hitman]

Basically, this chart doesn’t use Sin curves at all. I just says that, if a=b, then AOB has to be 45deg, because we have a standard right triangle with two equal legs.

This chart asks you to figure out the values for (a) and (b), then simply shows you their ratio. If the ratio is 1:1, then the angle is 45deg. If the ratio is a little bit less, then the angle decreases by an equivalent amount. If the ratio is more, well it increases by the same amount. This is a very neat way to figure AOB, in my opinion.

Thanks for your explanation However, I *think* you do have to use the Sine at one point for doing it with an equation: The proportion 1:1 is only correct for the 45º angle, but if my thoughts are right, the rest of the angles will not follow a linear or aritmetical proportion (F.e. a proportion of 70% height vs. length is NOT 70º AOB but rather 45º) but instead a sine curve one:hmm: Am I right?

Interestingly, if you want to find their speed, just use the Pythagorean Theorem to find the distance traveled (c), divide by seconds, and multiply by 1.777. No messy business with Sin curves or anything like that.

Yup good catch Though it can be also determined with Sines, of course. Interestingly, the quickest method is very different when using a slide ruler or pure algebra. With a Slide Ruler using Sine is way faster, while you are completely right in that using just algebra solving the problem with Sines would be an unnecessary waste of time.

But that's the lovely part of maths: Many times you can do the same thing by different ways and you can then choose which ones fits better your real purpose

[starvingartist507]

Originally Posted by Hitman

Thanks for your explanation However, I *think* you do have to use the Sine at one point for doing it with an equation: The proportion 1:1 is only correct for the 45º angle, but if my thoughts are right, the rest of the angles will not follow a linear or aritmetical proportion (F.e. a proportion of 70% height vs. length is NOT 70º AOB but rather 45º) but instead a sine curve one:hmm: Am I right?

Yes, thats true. The equation involves a trig function, so obviously the relationship would be a curve, silly me.

Here's the equation that the card used. The Trebelle basically estimated the answers for this:

inverse Tangent of (distance sub traveled / range difference). There are extenuating circumstances, but thats the basic idea.

[jmr]

Originally Posted by Hitman

Is there a larger version of this chart available?

[MudMarine]

Originally Posted by starvingartist507

Yes, thats true. The equation involves a trig function, so obviously the relationship would be a curve, silly me.

Here's the equation that the card used. The Trebelle basically estimated the answers for this:

inverse Tangent of (distance sub traveled / range difference). There are extenuating circumstances, but thats the basic idea.

This is one good ole boy who sqeaked by with Algebra 1. I am gona have ta take a trig course for dummies. This here might just get me edjamacaded. Harder ta shot a torpedo than shooten a dang rifle. I guess the same principles apply windage, elevation and lead on a moving target. A whole new world this Boat sim.
My hats of ta Annapolis graduates. That dang shinny ring means somethin. It got me lookin at a circular slide rule and I built one from;

Build your own slide rule
http://www.sphere.bc.ca/test/build.html

Just takes time ta sink into this thick Jarheads head. That brain housing a bit rusty.
It's no longer just bein a hat rack. I feel a head aches a comin on just thinkin about trig.

[Hitman]

Is there a larger version of this chart available?

Not yet. That one I made as a Beta for personal use, and the numbers below the graphics come from work done by an artist whose permission I have not yet asked for. I posted this reduced quality image to show the example to Starvingartist and make the idea understandable, but I didn't want anyone to start doing screen captures of it and using/making it public until I do the job correcty and see if I will incorporate graphics from others and thus ask permission for it :hmm:

So...when its done...I will release it

Here's the equation that the card used. The Trebelle basically estimated the answers for this:

inverse Tangent of (distance sub traveled / range difference). There are extenuating circumstances, but thats the basic idea.

Yes, exactly that's what I was looking for. That's the mathematical formulation I intuitively knew should be there but couldn't figure out Thanks

[Puster Bill]

Originally Posted by MudMarine

This is one good ole boy who sqeaked by with Algebra 1. I am gona have ta take a trig course for dummies. This here might just get me edjamacaded. Harder ta shot a torpedo than shooten a dang rifle. I guess the same principles apply windage, elevation and lead on a moving target. A whole new world this Boat sim.
My hats of ta Annapolis graduates. That dang shinny ring means somethin. It got me lookin at a circular slide rule and I built one from;

Build your own slide rule
http://www.sphere.bc.ca/test/build.html

Just takes time ta sink into this thick Jarheads head. That brain housing a bit rusty.
It's no longer just bein a hat rack. I feel a head aches a comin on just thinkin about trig.

That was close. I thought you were going to link to the thread-that-shall-not-be-linked-to.

If you are serious, though, go ahead and get Hitmans backside to the Submarine Attack Course Finder/IS-WAS-WILLBEAGAIN. Then read either the instructions in the TTSNBLT, or to the document at HNSA that describes how to use it. You will find it more intuitive and less 'mathy' than a plain slide rule, although I use a small pocket slide rule for occasions when playing might be seen as non-productive, if you get my drift.

[starvingartist507]

Originally Posted by Puster Bill

That was close. I thought you were going to link to the thread-that-shall-not-be-linked-to.

Thank God!