Lecture P5: Rocket Performance

I began with finishing maneuverability. Key concept: Power available minus power required = time rate of change of potential plus kinetic energy. Requirements for T/W are set by maneuverability requirements. These can be found knowing aircraft weight and aerodynamic information. Note that there are typically three kinds of calculations requested for manueverability: a) steady climbing flight (so no acceleration term), b) constant altitude acceleration (no term for change in potential energy), and c) steady, constant altitude turning flight (no terms for acceleration or change in potential energy, but drag increases in response to increased lift required to overcome centrifugal acceleration). I gave a PRS question to give you practice on applying these concepts.

Then I talked about principal figures of merit for aircraft engines (thrust, efficiency, weight, installed drag, cost--acquisition and operations).

Then I started rockets with a PRS question. This was intended to stress the idea that WEIGHT IS EVERYTHING for rockets. Payload may be only 1-2% of the take-off mass of a rocket -- with most of the remainder being fuel. The principal figures of merit for the propulsion system are thrust, efficiency (Isp), weight and cost. We then derived an expression for the static thrust of a rocket and discussed the specific impulse (Isp) asa measure of efficiency. The specific impulse measures the amount of thrust produced per unit weight flow rate of propellant (where the weight flow rate is evaluated using the gravitational constant on earth). This information is covered in Chapter V of the notes and Chapter VI.

Next lecture we will cover the last part of rockets: given the principal figures of merit, how to calculate overall vehicle performance. Please review Chapter V of the notes.

Responses to 'Muddiest Part of the Lecture Cards'

(14 respondents, 60 in class)

1) What exactly is Isp? (1 students) Isp is a measure of the efficiency. It is the thrust one would get for a unit weight flow rate of propellant where the weight is as measured here on earth.

2) Why is Isp small for more thrust? (1 student) It isn't.

3) If rockets are mostly fuel, doesn't that mean that a lot of fuel gets burned to lift more fuel? Isn't that ironic? (1 student) I don't know if it is ironic, but it is the way it works (for airplanes too, but to a lesser extent).

4) If Isp always uses earth's gravitational constant, then isn't it just scaling the exit velocity? (1 student) Yes.

5) You mentioned that the only way to get into space is with a rocket that is pressurized and filled with fuel. Why is it that you think we will never be able to design a rocket that can hold more than 2% payload? (1 student) I hope I didn't imply that this is the only way to get into space (there are certainly other concepts besides a chemical rocket system). However, it is the case that all of the systems have very small ratios of payload mass to lift-off mass. At the heart of the matter are the physical properties of the materials and chemicals (structures and fuels) that are available to us. Also, one typically brings the oxidizer along for the ride (however there are hybrid concepts that breath air up to a certain height and then cross-over to space-capable propulsion systems). While I can foresee opportunities for significant improvements (several percent increase in payload mass ratio), it is hard to foresee it ever reaching the level of commercial aircraft (25% roughly) because of the limited chemical and material properties. But never say never...

6) Can we actually lift off the earth with ion thrusters currently. (1 student) No. They are too heavy relative to the amount of thrust produced (even though they are very high efficiency). You can learn much more about these in "Rocket Propulsion Elements" by Sutton and Biblarz, 7th edition, John Wiley & Sons, 2001. And one of the world's leading experts is our own Professor Manuel Martinez Sanchez.

7) Can Elton John's "Rocket Man" be the musical accompaniment for the propulsion test? (1 student) Sure.

8) Why two different V terms in the maneuvering equation? (1 student)

9) Can you again explain the sign on the pressure terms in the static rocket thrust equation? (1 student)

10) No mud (6 students). Good.