# Mass Fraction

The velocity that a rocket can get to depends on the type of fuels and what fraction of the total lift-off mass is fuel. Every pound used for rocket engines, tanks, and structure means a pound less for payload (holding fuel and needed velocity constant).

A formula called the rocket equation calculates how fast a single stage rocket can go. The critical term in the formula is the isp, which is a measure of how powerful the rocket fuel is per pound, and the percentage of the takeoff weight that is fuel. The formula for change in velocity is: DeltaV = isp * g * ln(Mo/Mf) . Mo is mass at liftoff and Mf is mass after burn (the final mass). The ratio Mo/Mf is called the mass ratio. This is the lift off mass divided by the final mass. The term 'g' is the acceleration of gravity. So the DeltaV scales linearly with the isp and with the natural log of the mass ratio. The inverse of the mass ratio is the fuel fraction, which seems easier to think about. We plot the DeltaV as a function of fuel fraction for several different isp values in the following graph.

An X-prize vehicle with an ISP of 250 needs to have about 45% fuel percentage. This is not that far from the SSTT 75% fuel percentage. If you removed wings, landing gear, and presurization from an X-prize class vehicle you might get to 0.75 fuel.

For comparison a SSTO vehicle needs to be about 0.96 fuel. It should be possible to evolve one of the X-prize vehicles into something like the SSTT rocket that SpaceTether's proposal requires. If so, the development costs might not be very high.

http://www.shuttlepresskit.com/expedition1/03-soyuz_launch.htm

## Tank Mass

For a pressure fed rocket (no pump) the tank needs to be strong. This can make it heavy. Our rocketequation applet is able to calculate how thick tank walls need to be for a given pressure and how heavy that would make the tanks. ( see this site for info on how to calculate tank mass). Other online tools are available at EngineerOnline.ws and also etank.com.

The materials for composite tanks have improved. It is now possible to make pressure tanks for rockets out of composites. Two examples are the tanks for the Space Ship One at Scaled Composites and the Scorpius tanks at Microcosm Inc..

## Rocket Engine Mass

Most engines use "regenerative cooling" a process where the fuel or oxidizer is used to cool the outside of the rocket engine just before the fuel is fed into the engine. For a regeneratively cooled engine, the mass of the engine is around 1% of the thrust. Thrust is typically around 1.5 times the Gross Lift Off Weight (GLOW). So the engine mass should be around 1.5% of the GLOW.

There are engines that are cooled by internal ablation which are lighter than a regeneratively cooled engine. But these engines are for a single use. It may be possible to design one that can be refurbished.

Regenerative cooled engines have proven that they can be reused many times, so they are the established technology for reusable rockets.

## Examples from Rockets that have flown

The values in the table are derived from data on the SpaceAndTech.com web site.

Rocket Stage Fuel Type Fuel Kg Dry Kg Dry/Fuel
Delta-IV 1 LOX/LH2 200,000 18,030 9.02%
Delta-IV 2 - 4mf LOX/LH2 20,412 2,718 13.32%
Titan-IVB1 N2O4/Aerozine155,0008,0005.16%
Titan-IVB2 N2O4/Aerozine35,0004,50012.86%
Titan-IVBCentaurLOX/LH220,9502,93013.99%
Ariane 51LOX/LH2155,00015,0009.68%
Ariane 52N2O4/MMH9,7001,20012.37%
Zenit 21LOX/RP320,90732,89310.25%
Zenit 22LOX/RP80,9009,60011.87%
Zenit 23LOX/Syn-Thin14,6502,55017.41%
Long March 31N2O4/UDMH144,0007,0004.86%
Long March 32N2O4/UDMH35,0004,00011.43%
Long March 33LOX/LH28,5002,00023.53%
Soyuzstrap-onLOX/RP39,2003,5509.06%
Soyuz1/coreLOX/RP94,5006,5006.88%
Soyuz2LOX/RP23,0002,40010.43%
Soyuz3LOX/RP3,4501,05030.43%

## Examples from paper Rocket Designs

 Rocket GLOW Dry Mass Dry Mass Fraction
The thing that caught my eye on Rascal was that the second stage has 1800 kg of fuel, but only 323 kg of rocket and tanks. (It does not have an outer skin). Frame and tanks are 12% of gross mass. But this does not have any aerodymanic shielding.

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