The railgun equation

One megastructure idea which need not be polar is Erk Inger, "Mass Driver Design Traveling Earth to the Moon" (2019). That is, the railgun. If it "only" gets to 1 km/s this blog has been pondering this as an assist into the Ice Gun.

What we need is an equation as relates current to force. Unfortunately Inger's paper is chaotic. I do see a factor he names "inductance". Doesn't help that the diagram includes stuff in German (or Turkish) and includes variables like h which don't appear in the text. AT LEAST STEAL STUFF WE CAN UNDERSTAND

Further afield Ehresmann, Herdrich, and Laufer delivered "Low-Cost Prototype Development of a Lunar Massdriver" at a conference the prior October. Their equation (4) much resembles Inger's (3). Problem here? Ehresmann, Herdrich, and Laufer weren't building a coilgun! They're building something on horizontal rails. So they don't care.

It's also not the first space-enthusiast prototype. The O'Neillies at NSS have been at this since the late 1970s. I take it that the military has the best stuff and they just care about firing bullets.

For what it is worth, EHL's main equation is F=L' I²/2. They call L' "reluctance" and run with that. Best efficiency means raising L'I, that they get the most force for the least current(squared).

L' would (if EHL cared) equal μ₀/π ln[w/r - 1]. EHL point out that w cannot equal r or else they'll get singularity. I'll add w > r or else we're all getting Euler'd up (πi = ln[-1]). Also if w = 2r wouldn't L'I be, um, zero? Raising w to infinity might get the best results but then... is that one single "coil" extending the entire route? Then there's w between r and 2r which runs backward (negative F).

I'm thinking we need better papers. Barry's site seems good.