What would be the maximum velocity of SpaceX Starship if...

[Dave_S]

...If you suspend limits of thrust/weight ratios, escape velocity, exorbitant costs, and perhaps..a few laws of physics, here is my scenario:

- SpaceX has a Super Heavy Lift stage in LEO, configured as giant gas tank w/ new rocket motor tech. It will hook up w/ a SpaceX Starship, one-way, into deep space. I know. But it's for science!
- Starship reaches LEO & joins w/ the fueled 'Special' SHL vehicle (re-named "S-SHL vehicle"). They proceed to escape velocity from Earth's gravity well, into deep space.
- The new 'special tech' allows constant rocket motor burn 24 hrs per day, until fuel depletes, which will be exactly (10) non-stop days. I'm trying to keep the math easy.

(Q): What would be the maximum velocity (relative to departure) from Earth's orbit, at the end of 240 hrs of continuous burn?

 

[COLGeek]

While I am certainly not a rocket scientist, I don't think there is enough info here to answer this question. Then there is the whole "few laws of physics" and "special tech" thing.

There are definitely some folks here with 40 pound brains. Lets see what they come up with.

 

[Dave_S]

While I am certainly not a rocket scientist, I don't think there is enough info here to answer this question. Then there is the whole "few laws of physics" and "special tech" thing.

There are definitely some folks here with 40 pound brains. Lets see what they come up with.

Thanks for the response. I tried to keep the post as brief as possible for a quick read.
I implied certain assumptions. For example:
- No one can reasonably, feasibly launch the SHL into LEO, and be fully fueled B4 Starship went up. It uses its own fuel to get up there. And,
- No rocket motors can burn 24/7 for 10 days without stopping. Also,
- There's a point of diminishing returns regarding thrust/weight ratios and the cycle of needing more fuel for more mass. Also,
- current fuels (LOX, kerosene, etc.) can't produce the energy required to burn 24/7 for 10 days and still 'fit' in the SHL tanks.
I was inspired by things like the series, The Expanse, where their 'Epstein Drives' can burn continuously, almost indefinitely, allowing constant exceleration to maintain 1G for the crew.
Lastly, what if Saturn V carried more fuel? What velocity could the Apollo missions achieve?

 

[Slarty1080]

Thanks for the response. I tried to keep the post as brief as possible for a quick read.
I implied certain assumptions. For example:
- No one can reasonably, feasibly launch the SHL into LEO, and be fully fueled B4 Starship went up. It uses its own fuel to get up there. And,
- No rocket motors can burn 24/7 for 10 days without stopping. Also,
- There's a point of diminishing returns regarding thrust/weight ratios and the cycle of needing more fuel for more mass. Also,
- current fuels (LOX, kerosene, etc.) can't produce the energy required to burn 24/7 for 10 days and still 'fit' in the SHL tanks.
I was inspired by things like the series, The Expanse, where their 'Epstein Drives' can burn continuously, almost indefinitely, allowing constant exceleration to maintain 1G for the crew.
Lastly, what if Saturn V carried more fuel? What velocity could the Apollo missions achieve?

The key factors in calculating the maximum velocity of a simple rocket are the exhaust velocity of the gases ejected from the combustion chamber and the mass fraction of the rocket (the percentage of the rocket that is propellant v the rest)

Tsiolkovsky rocket equation - Wikipedia

en.wikipedia.org

If Saturn V carried much more fuel (or more correctly propellants) it would not perform as well. The reason being that any benefit from running the engines longer would be counter balanced by the rocket accelerating more slowly in the first place due to the extra mass it was carrying.

Unfortunately Saturn V was not a simple rocket. The total thrust of the engines and the total amount of propellant in the rocket were optimised for a particular mass of payload and the calculation was not at all straight forward (Multiple stages with different fuels, different engines and different numbers of engines, air resistance, engine throttling at Qmax to reduce stress on the vehicle, engine throttling in later flight to reduce stress on the crew, propellant margins, and the rest.