Ballistics

[P3D]

I don't like P3D's formula, but I have to admit that it works - somehow.

Assuming constant chamber pressure within the gun, the energy should be proportional to the volume of the gun bore - in this case D^3*L. So I tabulated most of the 6"+ guns on Navweaps and found the proportionality constant to be the same (within 5%) for most of those guns - save early breech loaders and a handful of hot-loaded ones.
The similar metric constant is 100 MJ/m3 (muzzle energy per gun bore volume).

I used imperial units as I find them more thematic in the context of warships.

The calculation sheet is attached. There might be some inconsistencies/errors in it.

[Logi]

Any ideas on how to simulate the gyroscopic drift with Magnus effect, Coriolis drift, and Eotvos effect?

Thus far, I've attacked it via the route of thinking that the rate of deflection from the ideal path occurs per rotation of the projectile. However, calculating the rotational speed of the projectile has proven troublesome as well.

[Logi]

I've got Coriolis drift working but does anyone know how to calculate gyroscopic spin drift?

I've got a feeling Eotvos effect is very minor compared to either so I'm leaving it for last.

[Sachmle]

I've got Coriolis drift working but does anyone know how to calculate gyroscopic spin drift?

I've got a feeling Eotvos effect is very minor compared to either so I'm leaving it for last.

http://www.ehow.com/how_7660060_calculate-spin-drift.html

[Logi]

How much do you all think propellant power (and thus muzzle velocity) would change between shells? This includes differences in grain structures and thus longer/slower burn times and thus higher/lower muzzle velocities.

I'm thinking of using + 5 % variation from the MV as derived from P3D's formula, but what do you all think?

[Logi]

I've also finished adding in the gyroscopic drift. I'm moving on to see if I can add variable temperature.

Then other effects and wind effect.

As an example, this is what it gives me if I put in the RRC 14"/45 SuperHeavy shell firing from east to west at 15 degrees above the equator at 30 degrees on a 8 meter high platform above sea level.

28631.75 yds, 60 sec of flight

Lands 167.74 yds to the left facing west with the shell angled -38.95 degrees (Up being positive).

Shooting east to west makes the Coriolis Effect and Gyroscopic drift ( I assume a right-twist barrel) work against each other.

[P3D]

How much do you all think propellant power (and thus muzzle velocity) would change between shells? This includes differences in grain structures and thus longer/slower burn times and thus higher/lower muzzle velocities.

I'm thinking of using + 5 % variation from the MV as derived from P3D's formula, but what do you all think?

5% is too much. If you want variation, keep it around 1%. Even that would change the range by 2% (that is 400m pattern size at 20km),

[Logi]

I've been testing the dispersion (based on changing MV) at 0.1% and it gives ~400 yds of dispersion for the 14.96"/52 on the Bismarck. I have conflicting figures on the dispersion of the Bismarck gun ranging from 170 m to 700 m.

Should I leave the dispersion then as is or lower/raise it?

[Logi]

If anyone wants to help me directly on the code, feel free to tell me. I'll set up a way to have us exchange code, etc.

[P3D]

You should just make error propagation estimate for dispersion, that would save you couple of runs.

[math]In sciencespeak. Assume you have an explicit expression for the range figure as a function of the variables f=f(x1, x2,...xn). Get the full differential of the range, df=df/dx1*deltax1+df/dx2/deltax2+...df/dxn/deltaxn. Replace the "deltax" with your actual errors/variances in the variables and you get an estimate on the final error. If your variables are independent, the sum can be replaced by sqrt(deltax1^2+..deltaxn^2).[/math]

As you don't have an explicit range function, use the ballistic range equation without air friction (good first approximation),  range=v0^2*sin(2alpha)/g. If your only variable (error source) is initial velocity v0, Delta(range)= 2*sin(2alpha)/g*v0*Delta(v0)=2*range*[Delta(velocity)/v0].

In other words, 1% error in initial velocity would give you around 2% range error.

Also, be careful about the terminology. In modern science, "error" usually refers to the standard deviation (square root of variance), or "1 sigma". Make sure there's no confusion for the terms involved.

Consider comment no. 67 in R. Lundgren's article (page 2) on navweaps:
http://www.navweaps.com/index_inro/INRO_BB-Gunnery_p2.htm

67 Plotting mean dispersion vs. range instead of pattern size vs. range yields figures more susceptible to advanced analysis.  Fortunately, converting the true mean dispersion, D, to other (possibly more familiar) measures of accuracy is relatively easy:

   D x 0.846 = Probable Error
   D x 1.692 = 50% Zone
   D x 1.2545 = Standard Deviation

[Guinness]

I wonder how hard it is to write an SMF module so [math][/math] tags actually do something....

[Logi]

Stuff

I'm not quite following, but using those functions to calculate the range? As of now, my model does calculations via step-by-step model. It runs through the equations every second until the shell impacts the water. So how would those functions work for such a model?



On another note, I'm trying to writing the hydrodynamic portion, but that'll take me a bit as I have some books to read on that subject.

[P3D]

No, those are just to estimate deviations from a nominal range (at a give initial velocity and gun elevation). That range itself would have to be calculated by your program.
So you wouldn't have to run your program "statistically significant" times at every given range to get the dispersion.

Also, the actual pattern distribution depends on how you determine the variation in the initial velocity.

Stuff

I'm not quite following, but using those functions to calculate the range? As of now, my model does calculations via step-by-step model. It runs through the equations every second until the shell impacts the water. So how would those functions work for such a model?



On another note, I'm trying to writing the hydrodynamic portion, but that'll take me a bit as I have some books to read on that subject.

[Logi]

How do you calculate the penetration of a belt?

I understand it was to use some part of the formulas given by Nathan Okun, but exactly which ones and how is it used?

For that matter, how did you calculate yours Nobody?

[Nobody]

Which one I used I don't remember, but you should find the answer in the thread to my program. Without knowing any of the necessary constants however, it's quite useless. It doesn't even scale correctly.

My dream is to reconstruct FaceHard, but it's quite a complicated program. E. g. I don't understand how he managed to split the tool over 2 BAS files.