Model Railgun Project - Don't have a grasp of the physics

[CuriousCynic]

My hypothesis is that increasing rail length will increase the distance a projectile travels, ( which is true) unfortunately I can't quite make sense of physics behind railguns to understand how to prove the hypothesis mathematically. Thank you for your time.

 

[rock.freak667]

Consider how the work done affects the kinetic energy and hence the velocity the projectile will leave the rail gun at.

 

[Fr1ki]

I don't know if this still works for railguns...but F= ma, get a. then vf^2 = vi^2 + 2ax
vf = final velocity
vi = initial velocity
x = rail length
And to answer your question, a higher vf will surely increase the distance the projectile travels.

 

[Fr1ki]

Please disregard what I stated previously.

A railgun can achieve very high muzzle velocities because of the constant acceleration that is achieved. Meaning, that, the longer the barrel, the higher the muzzle velocity will be.

If you were looking for a few formulas :
F = ma ; F -> force generated by magnetic field.
.; m -> mass of projectile
. ; a -> acceleration of said projectile due to F

then v = sqrt(2*a*x) ; v -> muzzle velocity
. ; a -> as above
. ; length of barrel

This is all assumed that you will only use 1 pair of rails. I don't know the mathematics behind more than 1 pair. To me it seems though as if it scales linearly, which can't be right.