# Understanding the rocket equation - calculating Starship delta v

I am trying to calculate delta v of Starship - both as separate stages (Starship [SS], Super Heavy [SH]) and as a fully stacked rocket including 100t payload.

I know that I have to calculate 2 separate delta v values:

1. for tha phase of flight when only SH fires and SS is a dead weight
2. for when SS separates and fires its own engines

However I must be doing something wrong as I come up with very low total delta v for the full stack.

Here is s screen of my calculations:

Here it is with formulas:

Your formulas are using a base-10 logarithm, not the natural logarithm. This causes all your delta-v values to be off by a factor of 2.3

In google sheets, you can supply the base of the logarithm as a second argument to the LOG function. For other systems, the identity $$log_a(x) = \frac{log_b(x)}{log_b(a)}$$ may be useful if you need to obtain a logarithm in some base $$a$$, but only have a function for some other base $$b$$.

Additionally, it appears that you have swapped the the sea level and vacuum exhaust velocities for the two stages.

Using sea level exhaust velocity for the entire burn of the first stage may also give you a slightly pessimistic estimate compared to an actual flight profile, where it will increase as the atmosphere gets thinner.

• Ah yes you're absolutely right. Fixed the formulas now. I would expect that the "excess" delta v is used fighting drag on the way up. – PunchyRascal Feb 21 at 20:56
• Regarding increasing ISP for sea level nozzle as it climbs higher - I thought it would get less and less efficient overall due to the over-expansion in higher levels of the atmosphere. – PunchyRascal Feb 21 at 21:03
• @PunchyRascal Would be interesting to know exactly how that nozzle design performs by altitude. I certainly don't know. – SE - stop firing the good guys Feb 21 at 21:08
• The expansion after leaving the nozzle doesn't decrease efficiency, it just means there's efficiency to gain by making the nozzle larger. Sea level engines still become more efficient at higher altitude, they just become less optimal. – Christopher James Huff Feb 21 at 22:27