How can I optimize the velocity and power of a Gauss Cannon with magnets?

[John_Rainbow]

I am currently working on constructing a Gauss Cannon using the simple method of some chrome balls with a neodymium magnet on a track arranged thus:
0_____||0000____ so when the ball (0) on the left is released it is attracted by the two magnets (|) and smashed into them, and with the same principle as the Newton’s cradle the final ball is fired off the end with a much greater force than the initial ball that hit the magnets. What i would like to know is how to calculate the velocity and therefore the force at which the 22m Chrome bullet is fired from the end of the 4 ball line up.
Also what effect does the starter balls' velocity have on the final balls velocity and how can i make the system as fast and as powerful as possible. I am currantly in use of 2:
22mm dia x 10mmA N42 - NiCuNi plated (13.8kg Pull) (roughly 4500 gauss) magnets and i am using 5 chrome balls the the arrangement above.
Any infomation would be helpful.
Thanks.

 

[pallidin]

Are you sure the chrome balls are not chrome-plated iron balls?

In any event the Gauss cannon does work. One of your questions was exactly mine, that is "how can I make the system as fast and powerful as possible"

So, let's look at that. For myself, I immediately determined a flaw in the standard Gauss Cannon which limits accelerative staging: NEO magnets are brittle(even when coated), so using NEO magnets to attract a ball is one thing, but to use NEO magnets as a momentum transfer medium is another.

My improved design(only on paper) is either to go around or go through the NEO, such that impact with the NEO is eliminated. In other words, I use the NEO as the magnetic attractive force, but NOT as the momentum transfer medium.

Make sense?

So, instead of using solid block or rectangular NEO magnets, consider using a disk NEO with a hole through it's center, and the NEO's firmly affixed to the "channel".

Now, place a fracture resistance solid plastic plug in the hole of the disk NEO's, of such a diameter that is fairly loose and can move easily(you don't want impact expansion causing the plug to "sieze-up").
Also, the length of the plug is such that it protrudes, say, 1/8th inch on the impact side and is flush on the other side.
The flush side of the plug will be in direct contact with the next "chrome" ball.

As the first ball is attracted and accelerated towards the NEO, it eventually hits the protruding plug, which transfers momentum to the second ball and thus stopping the first ball from directly impacting the NEO magnet.

This method can be continued, varying the length of the plug as necessary to accommodate more or less stacked NEO's.

 

[pallidin]

With all that, it is prudent to know that there is a practical limit on acelleration using any form of a Gauss Cannon. Even one that is non self-distructive, or distructive-limited.

When I did research on this years ago, I came across a web-site which indicated, through math, that it would take 7,000 - 20,000 NEO magnets in a linear Gauss Cannon to propel the final ball at speeds necessary to achieve low-earth orbit. I'm sorry that I don't recall that specific link.
Sure, it wasn't optimized like my configuration, but nonetheless gave the math regarding acellerative potential using static NEO magnets.

Not that you want to do LEO with a Gauss Cannon, but thought I might add it here.

 

[John_Rainbow]

Ok, yes I did mean chrome plated balls, my bad.
Your method does seem interesting, But how to make it practical? I am assuming it’s the same as my idea but instead of the disk magnets I am using, using a ring magnet with a hole in the middle that is filled by a plastic bung. (non tight fitting)
http://www.unitednuclear.com/supermagnet310th.jpg
This is indeed good as there are some stronger magnets I can get my hands on that are ring shaped...
0____:-0000____ (0 = Balls, - = Bung, : = Magnet, ___ = Track)
However my resources with a track are limited and so is my knowledge of materials, what sort of material would the bung need to be made out of to withstand a force from a 12,500 Gauss magnet.
Also any information on calculating the forces, or velocity of ball before contact or even an acceleration curve. Would be greatly appreciated, currently I have some equations and ideas on how to work it out, although I am proberly wrong. One of then is using the equation for force between 2 bar magnets and then halving the result to calculate the force on the ball ad a distance x from the magnet. Although the problem is this equation has $$\frac{1}{x^2}$$ where x is the distance, as x decreaces towards 0 the fraction gets ridiculous and so does the force.

The equation I am currently trying to use is:
$$F=\left[\frac {B_0^2 A^2 \left( L^2+R^2 \right)} {\pi\mu_0L^2}\right] \left[{\frac 1 {x^2}} + {\frac 1 {(x+2L)^2}} - {\frac 2 {(x+L)^2}} \right]$$
B0 is the magnetic flux density very close to each pole, in T,
A is the area of each pole, in m2,
L is the length of each magnet, in m,
R is the radius of each magnet, in m, and
x is the separation between the two magnets, in m

 

[pallidin]

I have to go to work, but will be back.

 

[John_Rainbow]

Can anyone else help me with my problem?