Calculating spacecraft fuel consumption

Junghalli · Post by **Junghalli** » 2006-10-09 02:16pm

A question that occurred to me during the discussion on the amount of fuel Voyager carries that sprung up in the OVEG thread on PST. How would one go about calculating the amount of reaction mass a ship would need for a given trip? I mean, calculating the fuel used by the reactor is easy: multiply the power output by the length of the trip, divide by the energy density of the reaction in question, and then factor in inefficiency. But what about the stuff you actually throw out the back to make the ship go?

For instance, say you want to get up to a velocity of 800 km/s and then back down to close to relative zero at the end of your trip, your acceleration is 10 m/s^2, and you're using some kind of fusion drive. How would you go about figuring out how much fuel you need to bring along?

kheegster · Post by **kheegster** » 2006-10-09 02:42pm

In 1903 Tsiolkovsky published the rocket equation v = u ln s, where v is the velocity of the spacecraft, u is the propellant velocity and s is the mass fraction between before and after the rocket fires. This basically answers your question in terms of fundamentals, although actual mission design is a bit more complicated than that!

Get the answer from the horse's mouth...

NASA Education web site

Howedar · Post by **Howedar** » 2006-10-09 06:29pm

Take a control volume, apply conservation of momentum. Integrate as appropriate to find anything you could possibly care about.

Rocket science, strictly speaking, isn't all that hard.

Xenophobe3691 · Post by **Xenophobe3691** » 2006-10-09 08:00pm

Howedar wrote:Take a control volume, apply conservation of momentum. Integrate as appropriate to find anything you could possibly care about.

Rocket science, strictly speaking, isn't all that hard.

F = (dm/dt)v + m(dv/dt), if you're using a rocket, to elaborate on what Howedar said.

Then again, integration isn't exactly known for it's ease of use.

kheegster · Post by **kheegster** » 2006-10-09 09:00pm

Staging makes things slightly more complicated, but still it's straightforward to calculate (although it's been 4 years since I've looked at this stuff).

For interplanetary missions most of the fuel consumption is on boosting the spacecraft into transfer orbits, and then braking into the correct orbit around a planet. There also be attitude control rockets, usually hydrazine, required for any scientific mission, but that's usually considered as part of the payload for simple calculations.

Ender · Post by **Ender** » 2006-10-09 10:07pm

www.projectrho.com

select atomic rocket. Covers most of what you need to know.

Coalition · Post by **Coalition** » 2006-10-09 11:26pm

Assuming you are using H-B Fusion engines (specific impulse roughly 100,000 seconds), and you need a total of 1600 km/s delta V (accelerate to 800 km/s, then decelerate to 0), then you are looking at ~81% fuel fraction. If you only have a fusion engine providing 50,000 seconds, then you will need roughly 96% the mass of the ship as fuel.

www.projectrho.com, using the Delta-V nomogram. Took me about five seconds to look up (I had already printed it out from boredom).

Winston Blake · Post by **Winston Blake** » 2006-10-10 04:56am

The simple answer is that the ratio between your rocket's mass and your total fuel mass depends on how much you change your velocity added up over the whole trip time. Change in velocity depends on the mission you're flying, so once you know that, you just use how heavy your rocket is to calculate the necessary amount of fuel.

The Projectrho thing probably explains the specifics.