We are having a heated discussion in our office today about bullet trajectory, one person believes that when a bullet is fired on a completeley flat surface with no wind conditions and normal earth atmospheric conditions that the bullet will rise slightly before falling, does anyone know if this is true, if not true please provide the argument or maybe some facts to back it, he believes that there is a small rise right after leaving the barrell of the gun.

If by flat surface you mean a level surface, can see how it might. A level surface being a sphere with a constant radius and center congruent with the center of the earth. The drop of a level surface is, as I recall, about .6 ft per mile (have to find my surveying book to be sure). If the velocity of your bullet was such that it would drop less than .6 ft in its first mile of flight, then it would actually rise in reference to level. Does your friend care if the bullet is fired at the north pole or the equator? Would the balance of gravity and centrifugal force (yes, I know it is a myth) at the equator be such that the bullet would rise above its initial level? Anyway, I'd be interested in hearing your friend's argument, as it contradicts elementary physics texts of the 1950's

Jim

Ground effects and spin effects on those will alter the trajectory.

The bullet will begin to fall, under the influence of gravity, immediately upon leaving the barrel, in relation to the axis of the bore, unless some assymetrical gas dynamics at the muzzle of the gun produce a momentary net upward force on the bullet. The bullet will follow an elliptical path, not the parabolic one usually used in most elementary calculations, although the parabola is a good approximation over a relatively short distance.

For the bullet to rise with respect to the Earth's surface, after being fired parallel to the surface, its speed would have to exceed the orbital speed of a satellite in low Earth orbit - something like 17,000 MPH, or 25,000 feet/second.

Rotaryphile is correct that the bullet will begin to fall as soon as it leaves the barrel of the gun. However, if there is a crosswind, depending on the spin of the bullet and the direction of the crosswind, then the amount of drop due to gravity will be slight modified due to the spin and wind.

For the curve of the earth to enter into it, the speed would have to exceed 17,000 mph.

I don't shoot competitively, but the guys I know who do say they have to adjust for rise, for short range. I'll ask them for numbers, but here's their explanation.

The bullet's tail heavy, so as soon as it's out of the barrel, it's like a tail heavy plane. It noses up. When the aerodynamic forces balance the spinning round and keep the tail from falling further, it's nosed up a little and rising. Then it's a ballistic object, and it travels through that ellipse. It's just that initial balancing act that starts it rising.

Or so they tell me.
Dave Olson

Rotaryphile is absolutely correct. The original question specified “no wind� and “normal (standard?) Atmospheric conditions�.

The rise that the shooter observes is due to the sight being adjusted to zero at some distance from the barrel, depending on the range to the target. If the arm was bore sighted only so that the line of sight was parallel to the barrel, there would be no rise observed. However in order for the impact point to coincide with the sight picture at some distance from the barrel, the barrel is pointed slightly upward relative to the line of sight. To the shooter, the bullet does indeed appear to rise above the line of sight, but for the reason stated above.

LouW and Rotaryphile are dead nuts on, regarding trajectory and sight picture. The thing about bullets being tail heavy...etc, May apply to a low velocity round (generally considered around 1500 fps or less), but in a rifle I would seriously doubt it. The spin imparted by the rifling would stabilize the projectile enough that the precise balance shouldn't matter, although rifling can have other undesireable effects; the bullet weight and number of turns of the rifling in the barrel can cause a "dutch roll" effect where the bullet travels in a sort of corkscrew path. This is usually with a lighter slug and a barrel with a lot of twist. It's amazing to me that just the little bit of twist (say 1 turn in 12 inches or even 1-in-14) can impart a spin on the bullet in the neighborhood of 100,000 rpm or better. I used to know the formula to calculate bullet spin, has to do with bullet weight, muzzle velocity and number of turns of the rifling, but I had to dump it from my mental harddrive in order to make room for airplane stuff. This spin is what can cause a bullet to ricochet so easily, and in some cases even explode due to the centrifugal forces tearing the bullet apart.

LouW is absolutely correct, in that if the rifle's sights are set, for example, for 100 yards, the bullet, if its average velocity is 2,000 feet/second, will fall 4.35 inches below the axis of the bore in the .15 seconds required to hit the target - this is just high school physics. The bullet exiting a rifle that has its sights set for 100 yards will rise above the sight line by one quarter of 4.35 inches, about 1.09 inches, according to Newton, intersect the sight line at 100 yards, before falling increasingly rapidly below the sight line as distance increases beyond 100 yards.

Great physics aspects to everyone. There is another theory as well. I have a graduate degree in engineering and love questions like this to pose to my friends and colleagues. The guys in my office also believe that the expansion of HOT gasses as they leave the barrel behind, around and in front of the bullet will rise immediately and cause an 'updraft' if you will. This in turn causes a minimal rise in the initial trajectory of the round.

Just a theory and food for thought.

Thanks for a great fact and theory question.

[8D]

Hmmm...on most automatics the bullet would hit the ground before the cartridge...assuming barrel parallel to surface.

Your friend may be confused because of the fact that the muzzle, on most human held guns, will be elevated/inclined during firing giving the impression of the bullet rising some. I guess

Brent:
The bullet wouldn't be in the vicinity of the barrel and under the influence of the hot gases long enough for there to be any effect. Besides, I seriously doubt that the forces from bouyancy of the gas are anywhere near the order of magnitude of the forces from the gases' rapid expansion. That theory is silly and just 'junk' science.