The physics of shooting on other planets

[whswhs]

In thinking about my GURPS Mars campaign, I started wondering about how firearms and other missile weapons worked on Mars. This version of Mars has 0.375g, same as the real one, but surface pressure 0.34 atm. How do these facts affect missile fire? It seems that the lower gravity ought to allow a longer range. And the lower atmospheric density will make for lower drag, which will increase both the maximum range (but perhaps too marginally to matter) and the half damage range (which may be significant).

What's a gameable approximation to the physics of this? Is it going to be sufficiently accurate to treat either range as a linear function of one or both variables?

[ericthered]

according to this site (nasa putting out stuff for elementary school?) drag is proportional with air density. Yes, I know, that still leaves us with a differential equation, but its the short answer.

I don't know exactly how gravity is supposed to factor into how gurps does range -- I think the main issue is air resistance.

[Phantasm]

*thinks*

Divide range by gravity and multiply by atmo pressure? ... No, that doesn't seem quite right. I think I'm on the right track, but my numerical dyslexia is getting in the way.

[Anthony]

Originally Posted by whswhs

In thinking about my GURPS Mars campaign, I started wondering about how firearms and other missile weapons worked on Mars. This version of Mars has 0.375g, same as the real one, but surface pressure 0.34 atm. How do these facts affect missile fire?

Depends on the missile, though since those numbers are close together, not by very much. It will multiply maximum range by somewhere between 1/0.375 and 1/0.34, depending on whether the limiting factor is gravity or drag (for bullets, it will almost always be drag; in a vacuum the max range of a pistol would range from 5-15 miles, rifles might fire as far as 60 miles. Some particularly large and slow projectiles are more limited by gravity).

Half damage range in GURPS is poorly defined, and doesn't seem to have much of a relation to reality, so I'm not sure what it would do.

[Fred Brackin]

Originally Posted by whswhs

What's a gameable approximation to the physics of this? Is it going to be sufficiently accurate to treat either range as a linear function of one or both variables?

Seldom have I actually seen either 1/2D or Max come into play in a game but both will be technically affected.

I/2D should be increased by the thinner air. It will end up being almost 3x as far. that half of the bullet's KE will be transferred into approximately the same quantity of air molecules. It just takes longer to interact with that many air molecules.

Max isn't so simple to deal with. Fortunately it's even less likely to come up. The time the bullet will spend in the air is relatively simple. That time will increase by the difference in the time it takes for a bullet to fall from the height of the gun firing it in 1G and how long it takes to fall in Mars gravity. This number is not influenced by whether or not the bullet is shot out of a gun or just dropped. Bullets generate no lifting forces in flight. The Mythbisters even demonstrated this on their show.

Unfortunately, the speed the bullet travels at during that time is rather complicated. I don't really know of any mathematical short cuts and simple approximating might be the norm.

If you wanted round numbers you could call it 3x 1/2D and 6x Max. That's mostly a guess though.

[thrash]

Originally Posted by whswhs

What's a gameable approximation to the physics of this?

In all seriousness: ignore it. Neither factor is going to matter enough at typical encounter ranges to make it worth the math.

[whswhs]

Originally Posted by Fred Brackin

Max isn't so simple to deal with. Fortunately it's even less likely to come up. The time the bullet will spend in the air is relatively simple. That time will increase by the difference in the time it takes for a bullet to fall from the height of the gun firing it in 1G and how long it takes to fall in Mars gravity. This number is not influenced by whether or not the bullet is shot out of a gun or just dropped. Bullets generate no lifting forces in flight. The Mythbisters even demonstrated this on their show.

That's a valid point, and yes, I see that the physics makes sense. So with .375g you will have approximately a 66% increase in time of flight before it falls to the ground. That just leaves the problem of estimating distance from time of flight.

[Anthony]

Originally Posted by Fred Brackin

Max isn't so simple to deal with. Fortunately it's even less likely to come up. The time the bullet will spend in the air is relatively simple. That time will increase by the difference in the time it takes for a bullet to fall from the height of the gun firing it in 1G and how long it takes to fall in Mars gravity. This number is not influenced by whether or not the bullet is shot out of a gun or just dropped.

This statement is only true when the gun is aimed exactly perpendicular to the ground, which is extremely likely to be untrue in any situation where you actually care about maximum range.

If the bullet is fired with upwards velocity, which is the more common case, it will take 1/(upward velocity/acceleration of gravity) seconds to reach a perpendicular path, and an additional sqrt( ( 2 * initial altitude + (upwards velocity)^2 ) / acceleration of gravity ) to drop back to the ground. In practice this will be close enough to 2/(upward velocity/acceleration of gravity) as no difference when shooting for max range.

[Humabout]

The rough "I don't have paper to work this out right now" answer is:

1/2D_planet = [1/2D_Earth]/[Air Density_planet]
Max Range_planet = [Max Range_Earth] / [Gravity_planet]

I'm genrally confident in the latter. The former is probably a ballpark.

Also note that chemical composition of the atmosphere plays a role in density, as well as air pressure - especially on Mars where so much of the atmosphere is CO2.

[ericthered]

Originally Posted by Anthony

This statement is only true when the gun is aimed exactly perpendicular to the ground, which is extremely likely to be untrue in any situation where you actually care about maximum range.

If the bullet is fired with upwards velocity, which is the more common case, it will take 1/(upward velocity/acceleration of gravity) seconds to reach a perpendicular path, and an additional sqrt( ( 2 * initial altitude + (upwards velocity)^2 ) / acceleration of gravity ) to drop back to the ground. In practice this will be close enough to 2/(upward velocity/acceleration of gravity) as no difference when shooting for max range.

You've got enough variables in there that it doesn't prove anything. As a matter of fact, without air resistance (and with the distances involved vertically and the fact we're working with a bullet meaning that vertical air resistance is negligible), two other wise identical throws do simply divide the time of one by gravity. Its one of the bizarre things about physics: level throws are not privileged.