Algebraic Firing Solution

[Dorjun Driver]

TorpX,
It’s not clear to me why your application doesn’t generate at least a partial firing solution for Case 3, i.e. the lead angle, which is all one really needs. Ceteris paribus. Given the target speed (VShip) , the torpedo speed (VTorpedo), and the interception angle (θIntercept) (180°-track angle (θTrack)), the desired lead angle (θDeflection) drops into your lap. See my Zero gyro shooting.

I admire the work you’re putting in on this topic. Please keep it up.

Dorj

[Beardmoresam]

Doesn't the TDC do this for you?

Edit:
To clarify what I mean is: I do this with the TDC all the time? I just turn off the PK and enter the predicted variables for the target and it does all this anyway? I find you just have to feed it the right info and it can give you a very accurate static solution just as much as it can give you a dynamic one.

[Dignan]

Any way you can make this an iphone app?

[c13Garrison]

After reading this thread, I am reminded of what I enjoy when reading about WWII hardware. Not just a rote repetition of facts, but rather the stories behind the engineering decisions that were being made. To wit, I would LOVE to read the original notes on the first hash-out round-table session over the design of the TDC. Real mechanical engineering.

But BTW- Awesome programming work. You clearly have a zeal for this sort of thing.

[TorpX]

Thanks.

I have gotten better at this. (This isn't really saying much, though.) I'm sure someone who was really good at this sort of thing could have finished it in a quarter of the time it has taken me.

I'm getting anxious to finish it, and go on patrol and give it a "field test".

I just put together a small program that tabulates values of Gyro angle Vs. Bearing angle, so I could more easily check combinations of torpedo reach, turning radius, and such. I am hopeful of getting more accurate results now. I'll do some more testing tomarrow.

[TorpX]

I did a little testing with the Mk. 14 torpedoes. As far as I can tell, they have the same reach and turning radius as the Mk. 10's. That makes things a little easier for me. They do have a greater lag; that is they take longer to exit the tube.

I also did some testing of torpedoes launched from deep submergence, up to 200 ft., and the results agree pretty well with the stated "max dive angle" listed the the game files. This isn't a major deal, but I wanted to put this into the solution model, so if anyone wants to try sonar only attacks, they can. I know the RL Mk. VIII Angle Solver had different plates for different depths.

[TorpX]

Since the new firing solution program is nearly ready for release, I thought I'd show the math for some of the auxiliary functions/tasks.

This is the Gyro Angle Setting calculator. Since there is currently no way to set the torpedo gyro angles directly (at least in the USN side), it is necessary to calculate a bearing, whereby the TDC mechanism, will be forced to set the gyro angle you want. This is the most important of the Auxiliary functions in the program since it will be required for most launches.

In the above diagram,

b is the distance from the periscope/TBT and the end of the torpedo tubes
q is the torpedo's reach, (distance traveled before turning)
r is the turning radius
n is the difference between b+q and the location of where the torpedo track, extended backwards, intersects the sub track
R is the range input
g is the gyro angle
theta is the bearing angle
B is the difference between g and theta

g0, in the last equation, is the gyro angle, order; the gyro angle indexed from 0 to 360 deg.



Note that the red 'X' is not a target ship, but an arbitrary point the the TDC is pointed to, to achieve the desired gyro angle.

Next up is the Torpedo Spread calculator:

This enables the user to compute a divergent spread after the firing solution has been computed.

The linear displacement is the sum of three things:

1. the torpedo track displacement
2. target displacement
3. spread displacement

The 1st is due to the movement of the sub and the angles of the torpedo track intersecting the target track. In other words, the projection of the torpedo track along the target track, as the sub moves. If the sub was not moving or the gyro angle was zero, this quantity would be zero.

The 2nd is due to the movement of the target. It is the distance the target moves in the interval between the launch of the next torpedo.

The 3rd is simply the displacement along the length of the target. It depends on the length of the target and how much "coverage" is desired.

In the above diagram:

Dp is the torpedo track displacement
Dt is the target displacement
Ds is the spread displacement

Vu is sub speed
Vt is target speed
k is constant to convert knots to ft./sec.
ti is time interval
f is fractional coverage, expressed as a percent
ln is target length

D is the total displacement

g is the gyro angle
TTa is the torpedo track angle
Z is the adjusted track range (distance of straight run)

d is offset angle, or spread angle

Using this type of spread in a set-up like that shown above, the first torpedo would be aimed near the stern, and each successive launch would be given a larger offset angle going left.

This is worthy of a big bump! A sticky even imo.

[TorpX]

Thank-you!

[TorpX]

Originally Posted by Dorjun Driver

TorpX,
It’s not clear to me why your application doesn’t generate at least a partial firing solution for Case 3, i.e. the lead angle, which is all one really needs.

Well, it won't provide a solution by itself. If you extrapolate the plot and feed in the data corresponding to a point in time when the sub has crossed the Target Track, it will provide a solution.

Maybe I should have put this capability into the program, but I didn't think the situation would occur often enough to justify the effort. To get the numbers to work right, some account has to be made for the sub speed sign, because the sub is initially closing the Target Track , then moving away. Also, the angles change. The program rejects these cases. If I hadn't put code in to do it that way, you would get incorrect numbers which would be very confusing. If there is a big demand for this, I might revise it, but judging by the limited number of responses, not many people are going to use this.

...the lead angle, which is all one really needs.

I disagree that the Lead angle is all you need. I consider the other elements, Track Range, Run Time, and Time to Position to be of almost equal importance.

I did see your posting on zero-gyro shooting. Did you see the formulas in the OP? The first one in particular will give you equivalent results.

[I restored the images in the OP. I had reorganized them at Photobucket and broke the links. Sorry!]

Doesn't the TDC do this for you?

In terms of the "lead angle", yes. It doesn't give the track range, run time, or others. In any case, S-class boats didn't have them.

If you really mean to ask "Why bother with all this?", I'm not sure I can give you a easy answer. If you never depart from using the game TDC, you may very well sink a goodly number of ships, but it is unlikely you will ever develop a real understanding of the finer points of Fire Control. I guess someone who always plays in auto-targeting mode could ask why anyone bothers with manual targeting. To me, the game would not be half as enjoyable without these detailed elements.

[Dorjun Driver]

I disagree that the Lead angle is all you need. I consider the other elements, Track Range, Run Time, and Time to Position to be of almost equal importance.

I did see your posting on zero-gyro shooting. Did you see the formulas in the OP? The first one in particular will give you equivalent results.

[I restored the images in the OP. I had reorganized them at Photobucket and broke the links. Sorry!]

I didn’t make myself clear. What I meant is that when the target takes an unexpected zig or zag at the last moment, given she maintains her speed, all that’s required is to plug in the new intercept angle given her new course. From that—and maybe a little stick and rudder work—the deflection/lead angle then drops into your lap. With seconds to spare, too!

As you may have gathered, human factors aren't my strong suit.

Dorj

[TorpX]

Originally Posted by Dorjun Driver

I didn't make myself clear. What I meant is that when the target takes an unexpected zig or zag at the last moment, given she maintains her speed, all that’s required is to plug in the new intercept angle given her new course. From that—and maybe a little stick and rudder work—the deflection/lead angle then drops into your lap. With seconds to spare, too!

Yes, if all you want at the last minute is the lead angle, you can simply change the track angle and recalculate (either in the program or manually). But, there are practical and RL considerations. If in case 1, the target ship takes a last minute zig, you will quite possibly be faced with a situation of either, "the target got by" (it has already gone past the new firing bearing), or the new track angle will be much less favorable (as well as the range being longer). In RL, it took an appreciable amount of time to calculate a firing solution without the TDC. It also takes some time to change course in a submerged submarine. The difficulty of quickly computing firing solutions, while making an approach on a zigging target lead the Navy to develop the the TDC.

From Dignan:

Any way you can make this an iphone app?

I don't own an iphone or any such device. I would think someone who knows how to make apps for these could do it without too much trouble.

Heretofore, I used my TI-85 for this sort of thing, but the display is very small and it's hard to see well in a dark room. Otherwise, it works very well, so I don't see why an i-phone couldn't handle it.

I was wondering whether anyone could run this on a tablet computer.