Rockets and the Altitude Conundrum

A rocket powered vehicle, like any aircraft, needs maximum thrust at takeoff. No matter if you have wings or just a pillar of fire, that's where you need the most bang for your engine kilogram. With turbojets and propellers that happily coincides with maximum engine thrust - because those engine types use the air to their advantage. Unfortunately, rocket engines lose some of their thrust in the normal atmosphere.

A rocket engine's efficiency is related to the ratio of chamber pressure inside the engine to the air pressure outside the engine. This means that on takeoff (deep within the atmosphere) a rocket engine is less efficient. Some of the engine's power is used up just getting the air out of the way, as it were. This can be compensated for somewhat by increasing the engine's internal pressure, but that makes the engine much heavier (not to mention more difficult to actually build).

As the rocket vehicle climbs out of the atmosphere, the engine produces more thrust. A simple equation gives you a rocket's thrust:

Thrust = ThroatArea * (ChamberPressure*ThrustCoefficient + ExpansionRatio*[NozzleExitPressure-AtmosphericPressure])

Notice that the thrust is decreased by the term "ThroatArea * ExpansionRatio * AtmosphericPressure". This can result in on the order of 10% less thrust at ground level than at high altitude in low pressure engines. So when you need the highest thrust, a rocket engine provides 10% less thrust than normal!

Under these conditions, a rocket aircraft using ribbon propellant has an advantage. Because the propellant ribbon is supported by ground equipment during liftoff, maximum thrust is not required at lift off, but rather when the ribbon is fully deployed. By the time the ribbon is fully deployed, the aircraft is already at 5,000 feet or so. At this altitude, air pressure is about 15% less than at ground level.

It is not a huge effect (your engine can be made 1-2% lighter), but it is another advantage of using ribbon propellants.