Newton's 2nd Law: Calculating Side Wind Effects on a Projectile

[mark-ashleigh]

Hi,
I just have one quick question ..
How can i use Newton's 2nd law to account for side wind (cross wind) against a projectile?
I want to find this equation or the diff equation to solve it as i want to be able to find the effects the cross wind will have on the drift of the projectile.
I know that i will have to model my simulation in 3-D on exclel (x,y,z) , but i am in great need of this equation to be able to solve z.
thank you

 

[maverick280857]

Basically, a crosswind will exert a force on the projectile (in the direction of the crosswind of course). You are right that the deviation may be in a direction perpendicular to the plane of motion of the projectile (if the motion without the crosswind were perfect and not disturbed by dissipative or deflecting forces that is).

In real life though, no projectile can be thin enough nor can the motion be really planar as modeled (inaccurately) by our equations. Besides, precission of the projectile may also occur and the projectile may even spin like Earth as would a bottle at an angle with the horizontal (as though the bottle were toppling in air). As far as simulating the actual thing is concerned, you might not be able to do it very accurately as crosswind is not consistent and may change with time.

Finally, Newton's Second Law simply states that the force and the accleration produced by it are related as

$$F= ma$$

So if you can get an expression for the crosswind force, you can divide it by the mass of the projectile to get the acceleration. This would give you a differential equation which you can (a) either solve to get a or (b) incorporate the acceleration function in your computations to get the equation for trajectory...

Now you can either

(a) look for a crosswind model on the internet
(b) think of some function yourself that could do your job (as you are doing a simulation and practically any physically possible function should work)...and change it as you test the simulation

Cheers
Vivek

 

[mark-ashleigh]

Thank you for the help. Was much needed