## Thursday, February 4, 2010

### The Rocket Equation

Although this is essentially a business blog, some basic engineering knowledge will be required to evaluate potential space business concepts. The rocket equation is one such concept which must be understood. This interactive spreadsheet should give you better idea about how the rocket equation works. The spreadsheet should also give you the formulas which you can use in your own calculations. I have included multiple versions of the rocket equation, solving for: specific impulse, dry mass, propellant, and delta-v. In layman's terms, here is a brief definition of each rocket equation components:
• Specific Impulse (Isp): The efficiency of the engine. The higher the value, the greater the efficiency. Measured in seconds.
• Dry Mass: The mass of the spacecraft. Measured in kilograms.
• Propellant: The mass of the propellant. Measured in kilograms.
• Delta-V: The standard unit of measure for the cost of movement in space. The higher the maximum delta-v for a spacecraft, the more movement that spacecraft can perform. You are out of gas if you run out of delta-v.
• Gravity: Constant for LEO/GEO.

1. Colin,
Here's a few thoughts that might help:

1-Isp: One way of visualizing Isp (and why its units are "seconds") is that Isp is how many pounds of thrust you could get out of an engine with that efficiency if you fed it one pound of fuel per second. Another way to look at it is that one pound of fuel will give you an impulse (thrust x time) equal to the Isp number.

2-Gravity actually isn't constant in LEO and GEO. It varies with the distance from the center of the earth (in a 1/R^2 type relationship, where R is the distance). The g in this case is gravity on the surface of the earth--it's just a constant you have to use if you use Isp units of "seconds". If you take the metric route and use the effective exhaust velocity (which is exactly Isp * g), the g term is buried way inside. I still like using Isp and living with the "g" term, because it makes more intuitive sense, and makes some calculations a lot easier to do in ones head. Plus effective exhaust velocity is only the velocity at the exact pressure that the engine is optimally expanded. So it's always seemed like a sort of bogus unit to me.

Anyhow, I think I've crossed the line now between clarifying and confusing.

~Jon

2. Jon:

Great clarification. I agree "g" works as a simplification for gravity. I would love a new spreadsheet for dealing with the gravity of lunar activity or even GEO if you think using a gravity assumptions of 9.80665 for lunar and GEO is inappropriate. If you send me any updates, I will post it here.