Lecture P6: Rocket Performance

I covered the derivation of the Rocket equation, which relates principal figures of merit for rockets (structural efficiency and Isp) to rocket performance (velocity, height, etc.). This is described in Chapter V of the notes. Please note however, that the equation is derived in a different (but equally valid) manner in the notes. We did two PRS questions (PRS #1, PRS#2)

Next lecture we will go back to aircraft engines and develop relations that connect principal design paramenters (like compressure pressure ratio, turbine inlet temperature, and flight Mach number) to the principal figures of merit for air-breathing engine performance(thrust and efficiency). Please review Chapter VIII of the notes.

Good call on the Wednesday donuts. (1 student)

Donuts are great, except over Passover!!! (1 student) Donuts are great, but it's Lent! (1 student) My apologies, it was a snap decision when I walked in on Tuesday afternoon and saw how hard everyone was working on the homework. I didn't think about Passover/Lent.

Thanks for the heads-up on the homework, it kind of makes me want to start early. (1 student)

Just curious, are you from the NY or NJ area?. (1 student) Yes, I grew up in Warren, NJ, about 15 miles outside of NYC.

Responses to 'Muddiest Part of the Lecture Cards'

(36 respondents, 53 students in class)

1) The integrals seem a little shady to me, but I guess the results look nice. (1 student)Would we drop the term in the integral momentum equation if it were a liquid propellant? (1 student) Yes. The time rate of change in momentum (relative to the coordinate frame) is small relative to the magnitude of the other terms in the equation. Dropping the unsteady momentum term in the integral momentum equation seems counterintuitive given how much mass is thrown out the back? (1 student) Yes it is counterintuitive. What we did was say that the change was small enough over a certain period of time that we could consider it to be a constant mass system and evaluate the equation at that point. We then later related the mass flow to the change in vehicle mass which allowed us to track the relatively slower change in these quantitites over time. This is analogous to the derivation in the notes, which evaluates the impulse differentially for a small element of mass, dm, ejected over a small period of time, dt.

2) Why did you drop out the drag term in the duo equation? (1 student) Only in order to simplify the analysis. Typically, drag would be included and would be expressed as a function of altitude and flight velocity (e.g. Cd*1/2ru^2). This complicates the integral.

3) Are rockets continually accelerating throughout or is there a point perhaps due to increased drag that it stops accelerating? (1 student) I think they keep accelerating, but there may be special cases where this is not the case.

4) Can you make a brief argument about what "forces" mean in the integral momentum equation, I am not sure whether they are forces on the flow or forces on the body? (1 student). The forces (usually the left hand side of the integral momentum equation) are all external forces that act on the mass within the control volume. These can be pressure forces, body forces, shear forces, and external forces. The exact nature of the forces can change depending on where the control volume lines are drawn. For example, consider a situation where pressure is acting on a body and these are opposed by a reaction force, say within a strut, that holds the body in place. If the control volume is drawn around the surface of the body, the forces are pressure forces. If the control volume is drawn through the strut, the external force is the reaction force in the strut.

5) I was just curious about rockets, what is the difference between boosters and stages? At burn out, doesn't that mean the fuel/oxidizer is all used up? Why isn't the stage released right away? (1 student) In a two-stage rocket, does the 2nd stage coast before the second motor kicks or does the second stage light once the 1st is clear? (1 student) I don't know the anwers to these questions.

6) Will the spreadsheet you mentioned in class (for the homework problem) be useful for other problems? (1 student) No. You will get only one homework problem like this, but it is almost as easy to put it into a spreadsheet (easier in my opinion) and it then allows you to play with it to better understand the sensitivity of rocket performance to the various design parameters. This is strictly however, and "exercise for the reader" as they say. It is not required that you do this. I just thought you might be interested in doing it if you are into rockets.

7) So where is the equation for the final height? Also, instead of hcoast, maybe you should call it hballistic since this was the terminology used in 8.01 and the water rocket? (1 student). The equation is in the notes. I agree, "ballistic" is better.

8) Which way does the fuel burn? (1 student). Solid propellant rockets use a variety of propellant geometries to tailor the propelllant burn rate to meet mission needs. For more discussion see Hill and Peterson, Mechanics and Thermodynamics of Propulsion, 2nd edition (available in the library).

9) What does Isp= ? (1 student). Please explain Isp again, what is it? (1 student). See notes.

10) In the rocket equation, isn't g a function of t?. (1 student) Yes it is, however, for many applications (low earth orbits for example) it does not vary a great deal between the surface of the earth and the orbit and thus can be considered constant. I set it equal to a constant to simlify the analysis. In a more advanced treatment, this would be written as a function of height.

11) What are typical rocket accelerations? (1 student). It depends on the application (e.g. manned launches typically have lower g-loadings that instrumentation and warhead payloads which can be designed to withstand greater acceleration), but I think typical values are 5-10g's.

12) No mud (21 students).