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deltavmap / deltavmap.github.io

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Delta-v calculation method is incorrect #5

Open Paul451 opened 3 years ago

Paul451 commented 3 years ago

I noticed that the calculator seems to simply add the intervening delta-v's to calculate the overall delta-v of a trip. That is not the correct method if the trip is assumed to be a single burn (or two, transfer burn and end-burn circularisation.)

Instead, you have to convert the velocities to energies, sum the energies, then convert back. Thankfully, this is simply squaring the intervening delta-v figures and then taking the square-root of the sum.

For example: LEO to LLO includes the steps: 2.44, 0.68, 0.14, 0.68km/s, and the calculator produces 3.94km/s.

The sum-squares result (using those same figures) would be 2.53km/s to get to LTI, then 0.69km/s to capture into a circular LLO. The wrong method increases the calculated delta-v by over 20%. And it gets worse the more intervening steps there are; you can end up more than doubling the calculated delta-v. Given the exponential nature of the rocket equation, that can make a huge difference in the viability of a proposed flight.

deltavmap commented 3 years ago

Thanks for the feedback. I agree that the calculation is wrong. I added a warning about this to the about page. I've made a hohmann transfer orbit calculator https://deltavmap.github.io/calculators.html and I've just begun incorporating this into the main map.

I could try and incorporate what you suggest in the mean time. Can you give me any more information on this sum-squares method? Why does this produce the correct result? Cheers.

Paul451 commented 3 years ago

It relates to... https://en.wikipedia.org/wiki/Specific_orbital_energy... which relates to the vis-viva equation, which you are presumably using for your hohmann transfer calculations.