3 ms·
Hmm, relativistic velocity under constant acceleration is v(t) = a t / sqrt(1 + a^2 t^2) and relativistic kinetic energy is Ek = m c^2 / sqrt(1 - v^2
by sampo 10y ago
Hmm, relativistic velocity under constant acceleration is
v(t) = a t / sqrt(1 + a^2 t^2)
and relativistic kinetic energy is
Ek = m c^2 / sqrt(1 - v^2/c^2) - m c^2
Leave out the constant -mc^ and for simplicity put m=1, v=1, c=1, and
we get
Ek = (1 - t^2/(1+t^2))^(-1/2)
which is linear in larger values of t, not square.
Proof:
d/dt Ek = t sqrt(1 / (1 + t^2))
= sqrt(t^2 / (1 + t^2))
which is always < 1.
- DennisP 10y agoSo at the extreme efficiencies Shawyer claimed, overunity was at decidedly nonrelativistic velocity. It'd be interesting to calculate a maximum drive efficiency before you get overunity. I've seen claims that the max is the efficiency of a photon rocket, but I haven't seen it backed up with math.