Projectiles, spin, momentum, and range

In summary, the conversation discusses the effects of projectiles with backspin, including the change in pressure and lift generated. It also mentions the factors that affect range, such as air resistance, atmospheric conditions, and the aerodynamics of the projectile itself. Calculations and measurements are necessary to accurately determine the range of a projectile.
  • #1
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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  • #2
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
 
  • #3


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.
 
  • #5
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.
 
  • #6
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
 
  • #7
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.
 

1. What is a projectile?

A projectile is any object that is thrown, shot, or launched through the air and moves under the influence of gravity.

2. How does spin affect the trajectory of a projectile?

Spin refers to the rotational motion of a projectile. When a projectile has spin, it experiences the Magnus effect, which causes it to curve in flight. This can affect its trajectory and make it more accurate or unpredictable.

3. What is momentum and how does it relate to projectiles?

Momentum is a measure of an object's motion, taking into account its mass and velocity. In terms of projectiles, momentum is important because it determines how far the projectile can travel and how much force it can exert upon impact.

4. How do you calculate the range of a projectile?

The range of a projectile is the horizontal distance it travels before hitting the ground. It can be calculated using the formula: Range = (Velocity² x sin(2θ)) / g, where g is the acceleration due to gravity and θ is the launch angle.

5. How does air resistance affect the motion of projectiles?

Air resistance, or drag, can slow down the motion of a projectile and change its trajectory. This is because air resistance creates a force that opposes the direction of motion, reducing the projectile's velocity and increasing the time it takes to reach its target.

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