nozzle shape

Translation: 15 degree taper.

If you are going to put words in my mouth, let me be more specific.

At atmospheric pressure the optimum LINEAR expansion is 15 degrees and the optimum expansion ratio is very near 6.5:1.

The performance disadvantage for a solid to run choked rather than expanded is 15% of (thrust or ISP).

Please pardon the tech post.

Mega-tech Jerry

This should be in the FAQ

From a general standpoint, a well designed nozzle can give you an increase of around 30% over the thrust generated by the motor pressure (pressure thrust = chamber pressure * nozzle throat area).

In other words, if you have a motor with no divergent nozzle section, just a 'hole' for the exhaust, you'll get n lbs of force. If you add a 'perfect' nozzle to that motor you can get 1.3n lbs of force.

In theory.

In practice between the actual inefficiency of rocket motors and the "virtual nozzle" formed in the exhaust and rocket base drag itself, only a 15% loss. Also most "consumer" motors do not operate at 2500 psi, but at a mere 300-750psi.

Reality bites.

You can quote me.

Mega-Tech Jerry

"Thanks for the kind words Mark. And sincere thanks for being a good customer. We definitely need every customer we can get these days. Jerry is right (cough). The market is too small and getting smaller by the day.

"Even Jerry tried to steer you in the right direction! (Er... sorry about the 'even' part, Jerry... but your single post showed that perhaps you, alone, are the only person here that understands the complexities of acceleration as it relates to the REAL world!)"

- "Mark"

:)

Good call. But I believe 15 deg isn't "optimum", but rather the max half angle before thrust starts to drop some.

Also, I think the 15 deg doesn't change for a vacuum (does it?), although the expansion ratio would.

Anyone ever seen the nozzle expansion units on some of the 'big dogs' that kick in at a certain altitude? Cool stuff.

Dave

I've actually done altitude testing based on this, and the difference in altitude was closer to 20%.

Mike Fisher

Not much, but a bell shape is something like 7% (of the difference) better at that point.

Jerry

Perhaps it's worth mentioning what a BAD nozzle will do, as compared to a generic or perfect nozzle. I'm certainly no motor designer, but at the extreme case, the result will be a cato.

Bob Kaplow NAR # 18L TRA # "Impeach the TRA BoD" >>> To reply, remove the TRABoD!

Well, sure, if you don't have a hole through it, or it's mechanically inadequate such that it comes apart, or something... :)

I think the preceding discussion more or less assumed that the motor was firing normally through the appropriate throat area, as a basis for comparing various exit configurations.

-dave w

It's not a stupid question.

Theoretically, a motor with an unexpanded nozzle, i.e. simply a hole, works at a "thrust coefficient" (Cf, a figure of merit indicating the gain in thrust caused by the function and efficiency of the divergent nozzle.) of one. If for example the motor has a chamber pressure of 500 psi, and a nozzle throat/exit area (the same in this case) of 0.5 square inches, the thrust would equal 500 psi x 0.5 in^2 x 1 = 250 pounds.

If however the nozzle has a properly designed divergent section, which allows the gases to expand and cool thereby exchanging thermal energy for kinetic energy, you can achieve values of Cf of up to about 1.4 or so with typical hobby AP composite propellant working at typical pressures. The optimum expansion ratio is the ratio that allows the gases to expand to ambient pressure at the exit plane. Further expansion results in reduction in thrust coefficient. Thus the motor mentioned above may generate up to about 350 pounds of thrust with no change other than a properly designed nozzle.

The Cf increases with increasing chamber pressure, because the ratio between the chamber pressure and ambient pressure is greater, thereby allowing more expansion and thus extraction of more heat energy.

Low pressure motors (like Estes BP motors) use very low expansion ratios for the same reasons, thus the nozzle exit is not much larger than the throat.

The shape of the divergent section can be optimized as well, in order to reduce losses associated with radial gas flow - you see, when the gases leave the nozzle exit they are not all travelling exactly parallel with the body of the rocket. The shallower the angle at the nozzle exit, the less radial flow there is, so the losses are less. Other issues with fluid dynamics come into play as well.

A very typical expansion section is a 15 degree half-angle cone. Reasons: it is easy to make, results in a nozzle that is not overly long (thus heavy), and the losses are pretty small, 1.7% in fact fcrom radial flow.

Nozzle design is an exercise in trade-offs. You start with the optimum, then you assess what you are willing to do in terms of effort and expense to stay as close to that as possible. For hobby motors, the simplest nozzle uses a molded or machined exit cone of about 15 degrees half angle. Also note that unless the motor works at constant chamber pressure, the optimum expansion ratio is always changing. Also true as the rocket climbs, and atmospheric pressure drops.

Hope that made some sense. If you're really interested, find a copy of Rocket Propulsion Elements by Sutton, ISBN 0-471-52938-9, and read the section on nozzle theory.

Mike D.

Interesting stuff, Mike. One thing I'm unclear on: How does the cooling of exhaust after it leaves the motor translate into more thrust?

Conservation of energy. The heat energy has to go *somewhere*, and some of it goes into doing work on the nozzle, giving an extra "push" to the rocket.

- Rick "Physics man" Dickinson

Ok, but how does it do that? If the gas is cooling after it's expelled, that would make it contract, right? Seems to me if that had any effect on thrust it would be to reduce it, not increase it.

If you cool a gas by removing heat from it, it contracts (at a given pressure)... but if you allow a gas to suddenly expand from an initially-pressurized state, it becomes colder. (If you take the valve core out of an inflated tire and let the air out, or vent compressed gas - such as nitrogen - rapidly from a cylinder, the escaping gas will be colder than the initial temperature. This will happen whenever gas is released from a pressurized source.

-davew

The expanding gasses add to the thrust, and the cooling is a result of that expansion.

Right, but I don't understand how the change in temperature causes increased thrust. The thrust is the result of expanding gas being expelled from one end of the motor while pushing against the other end. Once the gas is outside of the motor, how can a change in temp affect the thrust?

Yes, I understand that. But if I'm reading Mike's post correctly, he's saying that the cooling itself increases thrust by converting thermal energy to kinetic energy:

"If however the nozzle has a properly designed divergent section, which allows the gases to expand and cool thereby exchanging thermal energy for kinetic energy, you can achieve values of Cf of up to about 1.4 or so with typical hobby AP composite propellant working at typical pressures."

The gas expands and drops in temperature when it is released in any case. If this happens in the exit cone, the expanding gas pushes against the inside of the cone, pressurizing it and pushing it forward, which also pushes the gas backward at a faster rate than its flow through the throat.

-dave w