Advanced Marksmanship Theoritical Ballistics: effect of gravity?

[CaliShooter]

How would I figure out the theoritical trajectory of one of my loads, if it was being shot in an environment with a different gravitational pull?

For example what would the trajectory of a 175gr SMK going 2600fps with a density altitude of 15,000 ft and a gravitational pull of 30% of Earth's gravity?

 

[Killer Spade 13]

Re: Theoritical Ballistics: effect of gravity?

Oh, my God . . . .

California.

Quoed, erat, demonstratum . . .

 

[AMOK!]

Re: Theoritical Ballistics: effect of gravity?

Set aside the 15k DA for a moment. Based on projectile motion and Newtonian (non-Eulerian) mechanics, your maximum horizontal range (R) and maximum elevation (Y, ordinate) would be:

R = [v(o)^2*sin(2*theta)] / g

Y = [v(o)y^2] / 2g

where:

v(o) = initial velocity (ie. MV);
theta = launch angle (ie. LOS above horizontal);
g = accelaration due to gravity (ie. 0.3 * 32.2 ft/s^2);
v(o)y = vertical component of initial velocity.

Notice as "g" decreases, both R and Y increase linearly. A "g" of 0.3 yields a 10x increases in R and Y. Note: wind resistance is not taken into account in these equations, as a theta of 45degrees yields maximum R.....when in fact the theta would be closer to 52 degrees if wind is included.

Now, IRT determining the bullet path you would need to iteratively solve for the x, y positions via differential equations. If you accessed the JBM ballistics engine and replaced the "g" of 32.2 with a "9.6" ft/s^2, believe you would be close to a solution.

 

[CaliShooter]

Re: Theoritical Ballistics: effect of gravity?

Thanks. Very interesting equations. Will play around with them.

 

[Ledzep]

Re: Theoritical Ballistics: effect of gravity?

Ignoring that 15000 DA would be different with 30% gravity, simply divide your current drop by 3.333.

X=.5* at^2 assuming an initial velocity of 0.

a is acceleration (gravity), t is time.

Because we assume the air offers the same resistance as 100% gravity, the velocity vs time of flight will be the same. So again all you have to do is divide by 3.333 with your 100% gravity dope to get 30% gravity dope.

Now if you wanted to get more in depth, you could figure out what the air pressure would be at 30% gravity at whatever DA.

 

[CoryT]

Re: Theoritical Ballistics: effect of gravity?

Air density unrelated to gravity. If there are X number gas molecules in a box, it matters not if the box is in space and zero gravity or here on Earth at 1g, drag is drag. The mass of the gas molecules does not change.

 

[tobias]

Re: Theoritical Ballistics: effect of gravity?

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: CoryT</div><div class="ubbcode-body">Air density unrelated to gravity. </div></div>
That's wrong.
Air density will be 30% of 1 bar, if g is 30% of Earth's gravity.

 

[Ledzep]

Re: Theoritical Ballistics: effect of gravity?

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: CoryT</div><div class="ubbcode-body">Air density unrelated to gravity. If there are X number gas molecules in a box, it matters not if the box is in space and zero gravity or here on Earth at 1g, drag is drag. The mass of the gas molecules does not change. </div></div>

Air density is almost directly related to gravity. If there were 0% gravity, the air molecules would push away from each other to the point that there was no pressure.

Get a bottle of water the next time you fly. Drink it at cruising altitude, and seal the lid. Look at the bottle again once you've landed (Balloons on a road trip to/from the rockies will also work). The air at the earth's surface is more dense because it has the weight of all of the air above it pushing down, and as a gas, it compresses. Soo, there are more gas molecules per given volume at sea level than at higher altitudes, and this is the result of gravity pulling the air to earth. If that force of gravity were reduced by 70%, the air density and pressure would change considerably.

Conversely, water does not compress to any appreciable degree, so if you fill a bottle completely with water at the surface, then take that bottle to the bottom of the ocean, it will not cave in like the bottle of air will (Though the walls of the bottle may squish some if the plastic is compressable).

So if we were shooting harpoons at long range under water, one could expect that the effect of altitude is minimal in contrast to on land because water density hardly changes.

 

[CoryT]

Re: Theoritical Ballistics: effect of gravity?

I was apparently in a hurry and my post was less than precise.

The air PRESSURE would be less with less gravity, given an equal column of air, but at any given pressure/temperature, DENSITY is the same. That's why we use DA, because DA refers to a state where drag is the same, 1500' DA is the same drag on a hot humid day at a low physical altitude as on a cold dry day at a higher altitude.

Gravity affects pressure, and pressure and temperature affect density. So yes, gravity affects density in an open system, but 1500' DA is not changed by gravity.

If we created a domed city on the Moon, with 1/6 Earth gravity, we'd need to pressurize the dome so we could breathe, plus heat the air so it's livable.

At a given pressure and temperature, the DENSITY of that dome atmosphere would be the same as a matching temp/pressure here on Earth (given of course the same gas). Drag would be the same, the the pull of gravity would not.

Having an open system would be a problem at .3G, you would not be likely to hold much of an atmosphere at all, and if you did, I can't find a gas that would even be able to approach a 1500' DA.

This I suppose also presumes that 1500' DA is Earth DA and the ATM is the Earth-type gas we refer to as air, not the DA for the gas / elevations on planet in question for this exercise.

 

[AMOK!]

Re: Theoritical Ballistics: effect of gravity?

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: CaliShooter</div><div class="ubbcode-body">Thanks. Very interesting equations. Will play around with them. </div></div>

Solid primer on Projectile Motion: www.youtube.com/watch?v=rMVBc8cE5GU&feature=youtube_gdata_player

 

[Boomholzer]

Re: Theoritical Ballistics: effect of gravity?

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: CaliShooter</div><div class="ubbcode-body">How would I figure out the theoritical trajectory of one of my loads, if it was being shot in an environment with a different gravitational pull?

For example what would the trajectory of a 175gr SMK going 2600fps with a density altitude of 15,000 ft and a gravitational pull of 30% of Earth's gravity?

I know this is just fantasy stuff, but is there a way to figure this out with a ballistic app on my cellphone?

Is Bryan Litz in the house? LOL </div></div>

Never caring about shooting on moons or in bubbles... but I like math so will I throw out a quick initial thought to consider:
Atmosphere aside but included as a fixed environment of inputs; comparing angled trajectories relative to ground have "shorter" distance paths but same flight & time-of-flight paths. Time & atmosphere to projectile remain constant but the gravitational vector component is no longer perpendicular to the bullet flight as associated in velocity/time. Hense the cosine function to correct for angled trajectory.

A LOS of 72.5 degrees may provide a crude estimation. I'd have to run the trajectory and think it through to see if this makes any sense.