# Projectiles, spin, momentum, and range

#### MattK

[SOLVED] Projectiles, spin, momentum, and range

Greetings. I am simply seeking information regarding the matters of the subject line.

Here is the situation:

A spherical projectile (6mm pellet) is fired out of a device at say 400 feet per second. It is fired out level to the ground (as if you are aiming a gun at a target - no real trajectory above horizontal).

To complicate things, a backspin is placed on the projectile inside of the barrel... the backspin causing a change in pressure above the pellet as it spins, thus to some degree counteracting gravity.

So if I were to speculate on the different ranges (distances the pellet would travel before hitting the ground) of a pellet fired at 250 feet per second vs. one fired at 500 fps, what all would come into play?

Thanks for any input.

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#### chroot

Staff Emeritus
Gold Member
Originally posted by MattK
the backspin causing a change in pressure above the pellet as it spins, thus to some degree counteracting gravity.
The spinning causes no pressure effects -- if it were to, it would affect the top and bottom equally. Bullets are spun by a rifle barrel not to "counteract gravity," but to make them aerodynamically stable. The spinning bullet takes advantage of gyroscopic rigidity in space, and resists its direction being changed by moving air.
So if I were to speculate on the different ranges (distances the pellet would travel before hitting the ground) of a pellet fired at 250 feet per second vs. one fired at 500 fps, what all would come into play?
If you neglect air resistance (which is non-linear -- it's quadratic in the velocity), the problem is simple. The bullet falls vertically at the same acceleration (9.8 m/s2) as anything else. You can calculate how long the bullet's in the air just as a function of how high above the ground it is fired. You can calculate the distance covered by multiplying its muzzle velocity by that time.

- Warren

#### MattK

Re: Re: Projectiles, spin, momentum, and range

Originally posted by chroot
The spinning causes no pressure effects -- if it were to, it would affect the top and bottom equally. Bullets are spun by a rifle barrel not to "counteract gravity," but to make them aerodynamically stable. The spinning bullet takes advantage of gyroscopic rigidity in space, and resists its direction being changed by moving air.
Its not rifling I am talking about. The pellets are sperical, and they have actual backspin on them. The backspin allows the air to move faster over the top surface of the BB, and slower over the bottom surface.. thus producing lift as seen in an airplane wing.
If you neglect air resistance (which is non-linear -- it's quadratic in the velocity), the problem is simple. The bullet falls vertically at the same acceleration (9.8 m/s2) as anything else. You can calculate how long the bullet's in the air just as a function of how high above the ground it is fired. You can calculate the distance covered by multiplying its muzzle velocity by that time.
But air resistance is in fact what I am interested in. :) Thanks.

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#### damgo

The lift effect of spinning has a lot to do with the exact shape of the ball and turbulent flows around it -- this is part of the reason baseballs have seams IIRC. I think it's one of those really complicated fluid mechanics problems... I certainly don't know of any simple formulae or approximation for the effect.

Air resistance can be roughly given by the drag force

F = C*rho*v^2*A/2

where A is the area of the projectile (pi*r^2 here), rho is the density of the fluid (air), and C is the drag coefficient -- probably about 0.5.

#### chroot

Staff Emeritus
Gold Member
Yeah, the amount of life generated by the backspin will depend upon the specifics of the surface of the projectile. It seems that technically, if the projectile were a perfect sphere, it would not move the air around it at all, and would not generate any lift. In general, I wouldn't try to calculate the effect from first principles -- I would just measure it.

- Warren

#### LURCH

As has been stated, the specific aerodynamics of the pellet is one factor that must be considered. Atmospheric conditions are also important. For example; on Mars, the pellet would actually fall faster than it would without backspin, and forward spin would cause it to climb.

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