Nitpicking: The .600 Nitro versus the .700

[Tallor]

Originally Posted by Fred Brackin

It wouldn't duplicate the stats for the .600 and .700 when I tried it. Those rounds are in a sort of medium velocity band that isn't very common comparatively and that doesn't work well with its' simplifying assumptions.

The Ve2 system isn't very fine-grained about velocity at all. It handles many common rifles, pistols and even artillery pieces quite well for such a simple system but it has its' limits.

This is more likely a job for Douglas Cole's ballistics spreadsheet.

Psst, Doug, if you see this, write up the LE, HE, AP and HEAT versions. >_>

[HANS]

Using the unpublished formula that yielded all the Damage stats from High-Tech downwards, the unrounded figures for the .600 NE are 9.52d and the .700 NE are 9.32d -- ie, actually lower. The reason is that Damage in GURPS is largely based on penetration, and the .700 NE has a considerably larger calibre while developing less muzzle velocity and only very little more muzzle energy. That means slightly less penetration. In other words, the Damage for .600 NE and .700 NE is correct as published. Note that Damage figures of 10d and more are expressed as multiples by preference, hence the (very minor) difference is levelled out.

Cheers

HANS

[acrosome]

Originally Posted by Purple Haze

Real world killing power is ~ k * mv * mv^2

There absolutely is no such thing as a "real world formula for killing power." At least, not in the way we're talking about here. What that is is some bizarre metric based upon momentum and kinetic energy. Where did you find it?

That said, kinetic energy obvious has something to do with it.

EDIT--

Originally Posted by Purple Haze

Yes k is determined experimentally for each type of bullet. There are tables standard things like "FMJ boat-tailed spitzer".

The units are "game weight". How massive a creature you can expect to kill with one shot to the chest.

Ah, so, yes- it's yet another one of somebody's pet formulas that has gotten propagated. Essentially, you can lose everything but k, there. It's empirics.

All sorts of weird formulae have been proposed for this, with various strange names. Producing them is one of the things that gun nuts do. None are useful. The dynamic of injury is too complex.

[Tallor]

So what is the formula GURPS actually uses..? I'm not following...

[Fred Brackin]

Originally Posted by Tallor

So what is the formula GURPS actually uses..? I'm not following...

It's not a simple formula. Google Douglas Cole spreadsheet and you'll get something close to the official system.

[Tallor]

Originally Posted by Fred Brackin

It's not a simple formula. Google Douglas Cole spreadsheet and you'll get something close to the official system.

Well... how about a Joules and/or Bore system? o.O

[AlexanderHowl]

I would think that it would be proportional to the velocity of the object and the size (as measured in HP) of the object, just like a collision. A bullet with an average velocity of 600 yards per second that did 12d of damage would have to have an effective HP of 2 (of course, bullets do damage based on design and size, but it is an approximation). Of course, it is more energy efficient to increase damage by increasing velocity (a doubling of velocity required a fourfold increase in energy) rather than by increasing size (a doubling of HP requires an eightfold increase in energy).

[lwcamp]

Originally Posted by Tallor

Well... how about a Joules and/or Bore system? o.O

I fiddled around with physics once to find a system that modeled penetration and convert it to GURPS. I posted my notes here
http://panoptesv.com/RPGs/Equipment/...le_physics.php
with a calculator here
http://panoptesv.com/RPGs/Equipment/...mCartridge.php
(The piercing damage type extends beyond pi++ and below pi-, with pi+0 the same as normal pi, pi+1 the same as pi+, and pi+2 the same as pi++. Ignore as desired.).

Luke

[AlexanderHowl]

I disagree with results of the webpage. It doubles the damage with a simple doubling of the mass of the bullet, but it only doubles the damage with an tenfold increase of the velocity of the bullet. So, in the former case, a doubling of energy doubles the damage while, in the latter case, a hundredfold increase in energy double the damage. I do not think that either result is realistic.

[lwcamp]

Originally Posted by AlexanderHowl

I disagree with results of the webpage. It doubles the damage with a simple doubling of the mass of the bullet, but it only doubles the damage with an tenfold increase of the velocity of the bullet. So, in the former case, a doubling of energy doubles the damage while, in the latter case, a hundredfold increase in energy double the damage. I do not think that either result is realistic.

Not quite. The penetration is linear in sectional density. So doubling the mass of the bullet without changing its diameter does double the penetration. This is generally accepted, and has been well validated for non-deforming projectiles.

The increase in penetration with speed initially starts out as the square of the speed (that is, proportional to the kinetic energy), but then slows down until it is increasing only logarithmically. At high speeds, it is not as simple as x100 speed corresponds to x2 penetration ... as speed gets higher and higher, it takes proportionally more and more speed to get the same proportional increase in penetration. This, also, has been observed in tests in soft media such as ballistics gelatin.

The general form used is
Penetration = X ln(1 + v0^2 / vt^2)
where v0 is the speed on impact, ln is the natural logarithm function (log to the base e), X is a projectile-dependent parameter (proportional to sectional density, but modified by shape), and vt is a target material dependent parameter. For GURPS values, use vt = 100 m/s for impacts on meat, and X = sectional density (in kg/m^2) times 0.0075 to get dice of damage. By adjusting the multiplier in X to fit your units, you can get good agreement for penetration in ballistics gelatin for a wide range of projectile speeds, from sling bullets and arrows through pistol bullets up to rifle bullets. The formula breaks down when the speed gets so high that the bullet continuously deforms - when this happens, you eventually get to a well-known plateau where penetration is independent of the projectile speed - no matter how fast you go, you don't manage to ram your projectile any farther into your target (although the subsequent blast may excavate a crater deeper than the penetration of your projectile. Note that this high speed behavior has been well validated and is used to design anti-tank and other high speed anti-armor munitions). Initial deformation followed by subsequent rigid penetration of the projectile can be handled by simply adjusting the sectional density for the new shape. Yawing can be crudely estimated by taking an average sectional density, although a more correct model would integrate the energy loss over the path with a varying frontal area.

Most everything I posted has been well known in the field of penetration modeling for decades at least. References are given in the previous links. Some of the material on penetration of hard, thin plates is original, and I have made every attempt to validate my models against known data (given in the web page).

Note that I have been careful to specify my model gives penetration, not damage. Damage in the physical sense (not as a game term) is a nebulous concept, which depends as much or more on shot placement and luck as it does on terminal ballistics, and for which you will never find a single unifying model. Given that GURPS models damage on penetration of armor, and the FBI bases its selection of firearms almost solely on penetration, using penetration as a proxy for game damage is probably not too wrong (although at speeds in excess of orbital velocity collisions, you are likely to need to transfer over to a cube root of energy model to estimate the depth of the blast crater).

Luke