Friday, April 24, 2009

Figures of merit

Do you sometimes lay awake at night, wondering how a solid ribbon rocket vehicle stacks up against typical rockets using various figures of merit? Me too! Let's look at a few of the common ones:


A common figure of merit among rocket vehicles is the ratio of payload to gros lift off weight. While the utility of the figure of merit is debateable (GLOW has little relation to actual costs), it is common enough to merit investigation. Current vehicles with a 9,000 m/s delta-v capability are about 1% payload. For example, the space shuttle is 1.2% payload at takeoff. The Ariane 5 is 2.06%. Both of these vehicles have multiple stages, and use liquid hydrogen as a fuel.

The solid ribbon rocket design, if used as a powerplant for a disposable vehicle like the Ariane, would consist of just the engine, propellant, and payload. The engine masses less than 1% of the gross lift off mass. Since the rocket equation specifies that 97% of the mass is used applying 9,000 m/s delta-v, more than 2% of GLOW is payload. This is equivalent to the Ariane 5, though relatively uninteresting to me. I'm not really that excited about disposable rockets...

The Space Shuttle is much closer to a rocket airplane - it has wings, landing gear, etc. A rocket aircraft built around the solid ribbon rocket engine like we are building is expected to be one third engine, one third airplane, and one third payload. This gives a Payload:GLOW of 1% - very respectable for a small rocket plane!

Payload:Dry Mass

The dry mass is the amount of vehicle left over after you have gotten where you were going. It is perhaps the most important figure of merit in my opinion, because dry mass is expensive. When you build a rocket aircraft, you are building the dry mass.

The Space Shuttle has a payload to dry mass ratio of 23.2%. A solid ribbon rocket vehicle would have a 33% ratio. So for a given payload, it would be 40% lighter dry!


An ideal rocket should be payload, engine, and propellant - and ideally, the engine should weigh nothing! The ribbon rocket comes very close to this ideal - the ribbon is 97% of the mass at takeoff. Although the engine weighs quite a bit, it is slightly smaller than the payload. This is fairly unusual as most rocket vehicles have engines much heavier than the payload, not to mention the proppelant tanks! When you add in the fact that the solid ribbon rocket plane has a much lower dry mass, it is the clear winner in a minimality contest.


Well, Isp as normally formulated is mainly a function of the propellants used. It is the amount of time the propellant can provide enough force to lift itself. For example, solid propellants typically have an Isp of about 300 seconds. That means 1 lb of solid propellant can provide 1 lb of thrust for 300 seconds. Liquids in general have higher Isp (350-450 seconds). Since solid propellants have marginal Isp (and this is our blog, so we have to win!) we will cheat :)

Thinking about the Space Shuttle vehicle as a system the "propellant" includes not just the oxidizer and fuel - most of the rocket is also useless mass (from a payload perspective). Looking at it this way, the system as a whole has an "effective Isp" that can be calculated by using the rocket equation. Just plug in the delta-v provided (about 9,000 m/s), the starting mass (the GLOW), and the end mass (payload). A simple calculation later you have the "effective Isp" of about 200 seconds.

Performing the same calculation on the solid ribbon rocket aircraft, and you also get 200 seconds. So our "effective Isp" is just as high as the Space Shuttle!

Do you have a favorite figure of merit that I have left out? Let me know in the comments.

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