[Answered] Rocket Equation Gravity Acceleration Term

[BlkBltChemie]

Just a sanity check so hopefully pretty straightforward:

When using the rocket equation to calculate deltaV, the KSP wiki gives deltaV = ln(mass full/mass empty) * Isp * 9.81 m/s^2.  The 9.81 m/s^2 corresponds to the surface gravity on Kerbin.  For calculations in other SOI's do we need to substitute the local gravity acceleration constant instead?

(This is my assumption and it sort of makes sense, but this means the available deltaV changes per celestial body which I am having a hard time wrapping my head around - for example, the same ship would have less deltaV at the Mun than at Kerbin.)

Edited December 9, 2015 by BlkBltChemie

[blowfish]

2 minutes ago, BlkBltChemie said:

Just a sanity check so hopefully pretty straightforward:

When using the rocket equation to calculate deltaV, the KSP wiki gives deltaV = ln(mass full/mass empty) * Isp * 9.81 m/s^2.  The 9.81 m/s^2 corresponds to the surface gravity on Kerbin.  For calculations in other SOI's do we need to substitute the local gravity acceleration constant instead?

(This is my assumption and it sort of makes sense, but this means the available deltaV changes per celestial body which I am having a hard time wrapping my head around - for example, the same ship would have less deltaV at the Mun than at Kerbin.)

9.81 m/s² is fixed - it's built into the way I_sp is calculated.  The more fundamental units are m/s (which tells you effective exhaust velocity - equal to real exhaust velocity in a vacuum), but we use Isp in seconds by convention ( I_sp = V_e / g₀).

[Red Iron Crown]

Always use 9.806665m/s² for g in the rocket equation (or round to 9.81). It's not gravity, just a convenient constant.

The reason for this is historical. After WW2, metric-using Germans and Imperial-using Americans were working together closely on rocketry, neither could easily understand exhaust velocity expressed in speed units of the other groups, so it was decided to use specific impulse in seconds instead, a unit familiar to both. To convert from a speed to a time requires an acceleration, so they used one that was already memorized by every engineer and rocket scientist, standard gravity.

[BlkBltChemie]

Thank you both very much.  This certainly explains why many of my landers have been over-specification for the mission at hand.  Kind of interesting, picking a value everyone already knows in order to use as an arbitrary constant - makes sense when you think about it; thanks for the background.