Ribbon Propellant Engine Injector Power

A ribbon propellant rocket plane has different pump/injector power requirements compared to a typical liquid engine. A 100% efficient liquid engine's pumping power requirement comes from the equation:

Power=volume per second * pressure

So for example, the Space Shuttle pumps 1.1 cubic meters of oxygen per second to 30 MPa (about 300 atmospheres). This requires 33 MW of power. It also pumps 3 cubic meters of hydrogen per second to 45 MPa (about 450 atmospheres). This requires an additional 135 MW of power. The overall power delivered by a rocket engine is given by the equation:

Power=force * velocity

The Space Shuttle's engine produces 2 MN of thrust at 4.5 km/s. This makes a total engine power of 9 GW - so the pump takes about 2% of the total engine power.

Note that the liquid engine has to pump the propellants to a much higher pressure than the chamber pressure (about 200 atmospheres, 20 MPa). This is because of injector and line losses in the feed system. So about half the power requirements of the pump system are due to these losses.

On the other hand the ribbon propellant feed system uses a rack and pinion like feed mechanism, where the ribbon is fed into the engine between drive gears. This is an extremely efficient feed mechanism, with very low power requirements. In addition, solid propellant rockets neatly bypass the injection problem - there is no need to have a large injector pressure drop for chamber stability. A further advantage solids have is higher density. Typical solid propellants are many times denser than liquid propellants.

Assembling all this, injecting a ribbon propellant into an equivalent thrust engine at 200 atmospheres chamber pressure takes 10 MW. (This assumes a 1.5 g/cc propellant density, 270s Isp, and 2 MN of thrust. This leads to a volume flow rate of 0.5 cubic meters per second.) This can be compared to the engine power of 5 GW (This is lower than the SSME because solid propellants have a lower Isp). So the pumping power requirement is only 0.2% of the engine's power.

All is not perfect with ribbon propellant, however. The engine does need to lift the propellant before it is injected. The power required for this can be calculated using the formula:

P=force * velocity

The force required is easy to estimate - assuming that most of the mass is in the ribbon (which is valid during peak power requirements), the force on the ribbon is equal to the engine thrust (2 MN for this example). The velocity is similarly easy to calculate: It is the length of the ribbon divided by the Isp, times the current acceleration in Gs. So for a 1 G acceleration (as planned for the time of max power requirements), a 1 km ribbon feeds in at 4 meters per second or so. This yields a power requirement of 8 MW, bringing the total pumping/injector power required to about 0.4% of the total engine power.

The power required to lift the ribbon approximately doubles the power requirements of our notional "similar to SSME" engine - but note that the total pumping power required is still only 1/8 the power of the liquid propellant rocket engine. This is primarily due to the more efficient injection and higher density.

All this said, this is nowhere near the engine we are designing. But the overall message remains - pumping requirements for ribbon propellant rocket vehicles are much lower than more typical liquid propellant rocket vehicles.