[ExI] Physical limits of electromagnetic launchers

[BillK]

On Sun, Jun 3, 2012 at 3:15 PM, Anders Sandberg wrote:
> OK, let's say I want to send off my payload using a circular launcher. Then
> it needs to hold against a centripetal force of mv^2/r (what is the
> relativistic version of this formula, BTW?)
>
> For v on the order of 0.1c and m=0.03 kg, the force will be 2.7e13/r. So
> assuming materials can handle a few hundred gigapascals (what we get in
> diamond anvils) and that the payload is nice and flat with an area of 0.01
> m^2 (it is not actually pressed against the accelerator, but the EM fields
> will transfer the force) I get a max acceptable force of 10^9 N, which
> corresponds to r > 27 km. Thats actually not bad at all.
>
> I suspect the real problem is coupling the accelerating fields with the
> payload without losing too much in Bremsstrahlung.  It scales with the
> square of the acceleration for both circular paths and linear ones, but in
> the linear case there is also a sixth power dependency on gamma, while the
> circular one is just to the fourth power.
>
> [ OK, think I found a derivation of the relativistic formula:
> http://www.physicsforums.com/showthread.php?t=187041
>
> So the force would be mv^2/R(1-v^2/c^2) - for a 90% c payload the
> relativistic correction makes the force about 5 times larger, and in this
> case the radius need to be about 11,000 km. Still small. I think this
> approach has merit. ]
>


Maybe it is just me, but I find all these different units confusing.  :)
You've got pascals in there (pressure) and newtons (force). The
conversion depends on your payload design. You started with velocity
0.1 c, then talked about a 90% c payload. Do you really think you can
get up to 90% c velocity? It must be a solid state payload you are
thinking about with such high forces? How about rephrasing it in g
forces that people are familiar with?

30 gm is a very tiny payload. A can of beans is 464 gm. (in UK)

So how about some examples using real numbers?

gm, velocity 0.1 c, km radius,  resulting force in no. of g.
(force of Earth's gravity on a human being with a mass of 70 kg is
approx 686 N).

You probably need to add time in there as well, as you can accelerate
at a reduced force for longer.

BillK