On the burn time to half Δv under constant thrust and specific impulse
eggrobin opened this issue · 1 comments
As mentioned in #544 and over IRC, the current calculation for the burn time to half-Δv (which is the lead time from a node used by MechJeb to start a burn) is inaccurate.
#544 only gives a calculation for the total burn length of a circularization burn.
Here is the general formula from readily-available data, and a formula for other fractions of total Δv to account for multiple stages, e.g., if the first stage contributes a third of the total Δv and the second contributes the rest, the time of half-Δv is one sixth of the way through the second stage burn.
The formula for the burn time to half-Δv for a constant-thrust, constant-specific impulse burn is
, where
is the effective exhaust velocity (the specific impulse by mass),
is the initial mass,
is the final mass, and
is the thrust.
For a fraction λ of the total Δv (so that the above corresponds to λ = 1/2), the time to λ Δv is
.