
Post by yehang79 on Oct 25, 2023 12:25:16 GMT
As widely known, Tsiolkovsky rocket equation only works with speed under 14%c
How do we fix it?
The relationship between the final mass M and velocity V of a rocket is derived as follows:
Let the initial mass of the rocket be M0 and the velocity of the ejected material be U, initially at rest. We can use the classical conservation of momentum equation:
d(Mv)  dM(vu) = 0
Therefore, Mdv + udM = 0
Hence, dv = u*(dM)/M
Integrating both sides, we get:
v = u*ln(M0/M)
In an upgraded derivation, let's assume the "dynamic mass" of the material ejected by the rocket in the inertial frame to be dm. By energy conservation, dm = dM. Therefore, we have:
Mdv' = udM
Using the Lorentz transformation, we have dv' = (dv)/(1v^2/c^2), where c is the speed of light. Thus,
dm/M = (c^2/u)*(dv/(c^2u^2))
Taking the natural logarithm, we get:
ln(M0/M) = (c/2u)*ln((c+v)/(cv))
Simplifying further, we have:
M0/M = ((c+v)/(cv))^(c2u)
Continuing to simplify, we obtain:
v (or ΔV) = c*(1(M/M0)^(2u/c))/(1+(M/M0)^(2u/c)) (or Ackley Equation? idk its official translation)
quite simple, isn't it?



Post by sage on Nov 12, 2023 2:29:33 GMT
As widely known, Tsiolkovsky rocket equation only works with speed under 14%c Just a question, but do our ships reach speeds over 14%c, and when?



Post by yehang79 on Nov 12, 2023 2:41:26 GMT
As widely known, Tsiolkovsky rocket equation only works with speed under 14%c Just a question, but do our ships reach speeds over 14%c, and when? well i mean exhaust speed



Post by sage on Nov 21, 2023 3:17:15 GMT
Just a question, but do our ships reach speeds over 14%c, and when? well i mean exhaust speed So, when during the sim should these equations be used then?



Post by yehang79 on Dec 12, 2023 14:15:31 GMT
well i mean exhaust speed So, when during the sim should these equations be used then? When exhaust speed or ship speed reaches 14%c or more, that causes relativistic thingy effecting newtonian physics



Post by sage on Jan 7, 2024 0:43:23 GMT
So, when during the sim should these equations be used then? When exhaust speed or ship speed reaches 14%c or more, that causes relativistic thingy effecting newtonian physics If you know how to mode the game so we could use your equation, I would not mind downloading it. But the only problem that I see is that the game has a black box system that does not allow for us to see or edit equations, only material properties. As well as to share parts and ship with each other. I think it would be best if you could list out the entire equation, complete with what units you are using. as well as listing each variable next to the equation.

