Math formulas

[Pyros]

Hi,

I pressume that you wish to modify the existing scientific penetration formulas into a WinSPMBT game suited formula?

The simplest penetration model (from the three that I am aware of) is the Anderson equation (or for a more complicated model you may seek the Lanz-Odermatt equation).

Here is the very basic formula of the Anderson equation:

P =(1.044*V -0.194*Ln (L/d) -0.212 ) * L

V: velocity (Km/sec)
L: length of the penetrating rod (mm)
d: diameter (mm)
P: depth of armour penetrated (mm)

cheers,
Pyros

[Cameronius]

Holy @#$%, Am I in the right forum? This looks like a Mensa club meeting or rocket science forum. This is too much for my Infantry Grunt brain to handle! [img]/threads/images/Graemlins/icon07.gif[/img]

[Zocktan]

P =(1.044*V -Ln (0.194*L/d) -0.212 ) * L

i've got some questions tp this formula!
1. what does the constants discribe?
2- "-ln" because the projectile becomes slower, but why L/d?

[MarkSheppard]

Holy @#$%, Am I in the right forum?

Yes you are.

This looks like a Mensa club meeting or rocket science forum. This is too much for my Infantry Grunt brain to handle!

It's actually a quite easy formula to understand, it's basic algebra; unlike a lot of other formulaes out there

[MarkSheppard]

Actually, you got the formula wrong.

It's really

Anderson:
P = 1.044 x V - 0.194 x Ln(L/D) - 0.212 * L

V: velocity (Km/sec)
L: length of the penetrating rod (mm)
D: diameter (mm)
P: Penetration

HOW TO DO IT:

Now to provide the numbers:

V = 0.81 (810 m/s) = Velocity
L = 370.05 = Length of Penetrator (mm)
D = 88 = Diameter of Penetrator (mm)

Roughly that of a German 88mm L56 shell.

So we've got the following equation now:

1.044 x 0.81 - 0.194 x Ln(370.05/88) - 0.212

First thing first, we need to solve the Logarithimic problem; excel is great for those of us who did not pay attention in Math; it has a Logarithm function.

370/88 in Logarithimic is: 1.4363

So now the Formula is:

1.044 x 0.81 - 0.194 x 1.4363 - 0.212 * 370.05

Something that you can solve with basic infantryman math.

That formula results in

131.36mm penetration.

That's actually quite close to the actual performance of the 88mm L56 Panzergranate 39 round; which was 120mm of armor at 30 degrees (139mm total) at 100m.

[Pyros]

MarkSheppard,

Thanks, I already corrected the typo error of the formula.
(btw, you should make a small correction in the formula that you posted because I think that the L is a divider of the penetration, not just a multiplier of the 0.212)


Just to give some depth to the discussion I will add some more parameters to the basic model of Anderson's equation:

Anderson Equation:

P/L = 1.044 x V - 0.194 x Ln(L/d) - 0.212

V: velocity (Km/sec)
L: length of the penetrating rod (mm)
d: diameter (mm)
P: Penetration(mm)


1. The first condition of this formulae is that the velocity should be around 900 m/s and 1800 m/s.

2. Next we should add a modifier (multiplier) for the material of the penetrator (for instance STEEL 0.5, TUNGSTEN 1.0 and DU 1.13)

3. Finally there is also a modifier for the equation related with the scaling factor of the penetrator diameter [Scaling factor = 1+(d/6.5 x 0.05)]

So, the full equation after adding all the above parameters will be as following:

P/L = [1.044 x V(km/sec) - 0.194 x Ln(L/d) - 0.212] x [1+(d/6.5 x 0.05)] x (multiplier for material of penetrator)

Be careful to adjust your Muzzle velocity with the correct V drop (per trajectory flying distance).

You should also add in the above formula the parameter of the "Angle of Obliquity".

At an impact of 60 degree the penetration capability is halved in comparison with an impact at 0 degrees.



cheers,
Pyros

[pdoktar]

Tanknet scientific forum revisited.

[Marek_Tucan]

Where's the mass of the projectile or density or whatever?

[Pyros]

pdoktar said:
Tanknet scientific forum revisited.

This is indeed a good place full of info concerning ballistics

cheers,