MechJeb2

MechJeb2

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On the burn time to half Δv under constant thrust and specific impulse

eggrobin opened this issue · 1 comments

commented

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
codecogseqn, where
codecogseqn is the effective exhaust velocity (the specific impulse by mass),
codecogseqn is the initial mass,
codecogseqn is the final mass, and
codecogseqn 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
codecogseqn.

commented

the centroid of the burn though is closer to ∆t / 2, not ∆v / 2.

PVG upgrades to the node executor will just figure this out correctly for the given burn, existing code doesn't really need tweaking.