Mathematical Question concerning Firing Solutions - what am I doing wrong?

[HMS Vanguard]

Hey,

Okay, so I'm sitting in the training mission for torpedo runs, and I'm attempting to develop the skills in trigonometry to manually work out firing solutions on the Cruiser that sails across my bow. I'm using the process put forward in the excellent thread "http://www.subsim.com/radioroom/showthread.php?t=116064&highlight=manual" by starvingartist507, but I'm running into a snag with my calculations, and being aware of my general poor maths skills I was wondering if someone could show me where I'm going wrong?

The problem I am having is when I get to Step 4:
"4. Subtract the first total (step 1) from the second total (step 3) 339,860
(8,840,000-8,500,140)"

This is subtracting the total of A Squared + B Squared from the total of "2 x (Cos of Bearing Change) x Range 1 (R1) x Range 2 (R2)". The problem I am having when calcuating the solution is that the total of the former is larger than the total of the latter. As an example:

On the latest time I've attempted the firing solution, my two readings were Bearing 325 at 1,357 feet, and Bearing 342 at 1,242 feet, timed at 45 seconds with a bearing change of 17. The total of R1 Squared + R2 Squared was 3,384,013.

The Cos of 17 turned out to be 0.257, and 2 x 0.257 x 1357 x 1242 = 926,966.7. Subtracting 3,384,013 from 926,966.7 results in -2,457,046, which as a negative number cannot be turned into a square root according to my calculator.

What am I doing wrong here? Any help would be appreciated in this, so I can get to sinking. :)

Good hunting!

[vindex]

What the ... holy ... ???

You don't actually need to calculate this stuff. The mechanical computer on your boat does. You just need three inputs:

1) Range (the system is a bit off, but you can get it by trial and error or installing one of the fix mods)

2) AOB (either estimate it visually, which is often flawed, or by protractor -- it's the angle between the target's course and a straight line to your boat)

3) Speed (the stopwatch method is broken, hopefully will be fixed, so better to do it by marking location, waiting a specific period of time, and then marking a second location, then multiplying up to get the distance in nm you WOULD have gotten if the interval had been one hour).

Right now I don't use 100% -- it's really unfair with all the broken range-finding and speed-measurement tools -- I still allow the contacts to appear on the map. If you do this, it's relatively easy to enter a solution then look at your battle map to see how accurate it is (in all three inputs) and make adjustments accordingly.

Unless you LIKE doing math ...

[HMS Vanguard]

What the ... holy ... ???

You don't actually need to calculate this stuff. The mechanical computer on your boat does. You just need three inputs:

1) Range (the system is a bit off, but you can get it by trial and error or installing one of the fix mods)

2) AOB (either estimate it visually, which is often flawed, or by protractor -- it's the angle between the target's course and a straight line to your boat)

3) Speed (the stopwatch method is broken, hopefully will be fixed, so better to do it by marking location, waiting a specific period of time, and then marking a second location, then multiplying up to get the distance in nm you WOULD have gotten if the interval had been one hour).

Right now I don't use 100% -- it's really unfair with all the broken range-finding and speed-measurement tools -- I still allow the contacts to appear on the map. If you do this, it's relatively easy to enter a solution then look at your battle map to see how accurate it is (in all three inputs) and make adjustments accordingly.

Unless you LIKE doing math ...

Well, I'm playing on 100% realism myself, and given that the stopwatch system is not working, I was trying to work out the calculations according to the guide I was using in that link I posted. Also, to a degree, I enjoy the idea of realistically trying to input firing solutions in the way that they had to do on the submarines at the time to make it as realistic as possible. It's also quite satisfying to see a fish slam home as a result of your calculations (managed to do it once - JUST caught the rear end of the cruiser, dunno what I did differently that time), but the problem I'm having is that I'm doing something wrong with the calculations. If anyone can help with this, I'd appreciate it.

[wetwarev7]

Hey,


On the latest time I've attempted the firing solution, my two readings were Bearing 325 at 1,357 feet, and Bearing 342 at 1,242 feet, timed at 45 seconds with a bearing change of 17. The total of R1 Squared + R2 Squared was 3,384,013.

The Cos of 17 turned out to be 0.257, and 2 x 0.257 x 1357 x 1242 = 926,966.7. Subtracting 3,384,013 from 926,966.7 results in -2,457,046, which as a negative number cannot be turned into a square root according to my calculator.

What am I doing wrong here? Any help would be appreciated in this, so I can get to sinking. :)

Good hunting!


Multiply by -1, then do your little square root thingie.....

negatives are so easily taken care of with a well placed inverse.....:up:

[HMS Vanguard]

Hey,


On the latest time I've attempted the firing solution, my two readings were Bearing 325 at 1,357 feet, and Bearing 342 at 1,242 feet, timed at 45 seconds with a bearing change of 17. The total of R1 Squared + R2 Squared was 3,384,013.

The Cos of 17 turned out to be 0.257, and 2 x 0.257 x 1357 x 1242 = 926,966.7. Subtracting 3,384,013 from 926,966.7 results in -2,457,046, which as a negative number cannot be turned into a square root according to my calculator.

What am I doing wrong here? Any help would be appreciated in this, so I can get to sinking. :)

Good hunting!


Multiply by -1, then do your little square root thingie.....

negatives are so easily taken care of with a well placed inverse.....:up:

Thankyou. :) I will try that out now and post my result.

Good Hunting!

[Puster Bill]

If you really want the realism, just build a SACF/IS-WAS. That will let you calculate the AOB and speed you need to enter into the TDC (you'll alread have range and bearing).

It isn't that hard, it's basically just two circular slide rules back to back, and there are the original instructions on how to use it at the HNSA website.

[SteamWake]

You may find this thread http://www.subsim.com/radioroom/showthread.php?t=116612 usefull as well.

[Powerthighs]

The problem I am having is when I get to Step 4:
"4. Subtract the first total (step 1) from the second total (step 3) 339,860
(8,840,000-8,500,140)"

There is actually a typo in this step. If you look at the equation, this step should say:

4. Subtract the second total (step 3) from the first total (step 1)

Because of the restrictions on the values of a, b, and C in a triangle, this will always yield a positive number.

[Puster Bill]

You may find this thread http://www.subsim.com/radioroom/showthread.php?t=116612 usefull as well.

Just whatever you do, don't link to this thread:
http://www.subsim.com/radioroom/showthread.php?t=112765

[vindex]

Okay, I admire your devotion.

(shaking his head in wonder)

[HMS Vanguard]

Fellow Virtual Skippers, I got her:

http://img515.imageshack.us/img515/9924/sunkhp3.jpg

First confirmed kill in Silent Hunter 4, and this one is dedicated to those who have helped me work out my calculations in this thread. Needless to say, I'm pretty happy at putting this tin can on the bottom through a fully manual firing solution. I'm going to practice this a few more times and then go into the main campaign.

One minor thing I did have an issue with though - I was trying to work out the precise AOB using the details put forward in the guide I originally linked to, and came back with a completely wrong number. My precise figures were:

Sin of Bearing Change = 0.54
0.54 x 804 (Range 2) = 434.16
434.16 divided by 804 = 0.778
0.778 Sin-1 = 51.1 degrees

So the calculations were telling me that my AOB to the Cruiser was 51.1 degrees. However, that was clearly wrong from visual observation, as I was sitting at roughly 90 degrees to her starboard at the time. Using this 90 degree estimate I was successful, and I realise from reading elsewhere that estimating was done quite a bit on the RL boats, but I would be interested if anyone could tell me how I got this particular bit of calculating wrong?

Good hunting!

[joea]

Good work Vanguard, but you do realise the real boats had slide rules and a TDC don't you? It's not unrealistic to use the TDC (unless you are in an S-boat). ;)

[Powerthighs]

Can you provide both your range\bearing measurements?

[HMS Vanguard]

Good work Vanguard, but you do realise the real boats had slide rules and a TDC don't you? It's not unrealistic to use the TDC (unless you are in an S-boat). ;)

Fair point - however, with the lack of a working stopwatch until 1.3, I figure knowing this info is a good idea. And seeing as I seem to be getting better at it, I may just try rattling around in an S Class at the start of the war for the sake of it. :) And thankyou for the praise - I've taped the precise calculations I did to my wall to remind me of my first kill. :P

Powerthighs, I'll dig up the calculations later today - gonna go try shooting at the training convoy first with my estimated AOBs.

[Xelif]

Vanguard, the AOB calculated is from your initial observation. Add the number of degrees he's moved across your field of view to arrive at a final AOB (ie, add the bearing change to the AOB). At least, I believe that's your trouble...

Final AOB = calculated AOB + bearing change

Also, yes, it looks like the explanation was flipped like Powerthighs stated. The equation should have you subtracting (2 * cos bearing change * range 1 * range 2) from (range1 squared + range2 squared)... or the whole equation:

c^2 = a^2 + b^2 - 2 * a * b * cos C