- #1
MaximumTaco
- 45
- 0
Hi all.
I've been trying to nut out an expression for the force on the projectile
( i hope you have an understanding of the basic structure of a railgun, i don't want to draw it)
Anyway, i is known, w is the rail seperation, and R is the circular rail's radius.
F(x) = i B(x) dx
(the scalar magnitudes of F and B, we know what the directions are of course)
So we need to integrate across the whole length of the projectile, w
[tex]
|\vec{B}(x)| = \frac{i \mu_0}{2 \pi}(\frac{1}{x} + \frac{1}{-x+R+w})
[/tex]
at any point distance x along the gap
Thus,
[tex]
|\vec{F}| = \frac{i^2 \mu_0}{2 \pi} \int_{w}^{0} \frac{1}{x} + \frac{1}{-x+R+w} dx
[/tex]
And ultimately get...
[tex]
\frac{i^2 \mu_0}{\pi} log(\frac{r}{r+w})
[/tex]
Does this look right?
I've been trying to nut out an expression for the force on the projectile
( i hope you have an understanding of the basic structure of a railgun, i don't want to draw it)
Anyway, i is known, w is the rail seperation, and R is the circular rail's radius.
F(x) = i B(x) dx
(the scalar magnitudes of F and B, we know what the directions are of course)
So we need to integrate across the whole length of the projectile, w
[tex]
|\vec{B}(x)| = \frac{i \mu_0}{2 \pi}(\frac{1}{x} + \frac{1}{-x+R+w})
[/tex]
at any point distance x along the gap
Thus,
[tex]
|\vec{F}| = \frac{i^2 \mu_0}{2 \pi} \int_{w}^{0} \frac{1}{x} + \frac{1}{-x+R+w} dx
[/tex]
And ultimately get...
[tex]
\frac{i^2 \mu_0}{\pi} log(\frac{r}{r+w})
[/tex]
Does this look right?
Last edited: