The second part of my latest tech article in High Power Rocketry (HPR)

Magazine, "Departures from Ideal Performance for Conical Nozzles and Bell

Nozzles, Straight-Cut Throats and Rounded Throats" has now been out for a

while. You can order both parts of the tech article as back issues from HPR.

The tech article is in the October 2004 (Vol. 35, No. 7) and the November 2004

(Vol. 35, No. 8) issues.

The tech article covers departures from ideal performance, nozzle thrust

coefficients, and losses from theoretical specific impulse to delivered

specific impulse. The big news is the development of simple design

modifications for straight-cut throats which have the potential to increase the

thrust, total impulse and specific impulse of most high power solid rocket

motors, and almost all experimental/amateur solid rocket motors by 3.5% to 8%,

a significant across-the-board increase in performance for two entire classes

of rocket motors. As noted in the HPR Editorial this is going to have a big

impact, first for EX motors, somewhat later for high power motor manufacturers

due to the cost of replacing existing nozzle molds and retooling for new nozzle

"blanks" used on production motors. The article contains extensive

experimental test data, both for professional motors and from recent

instrumented tests of high power and experimental/amateur rocket motors. The

experimental data, and the models based on experimental data for performance

losses from straight-cut throats are unique, and to my knowledge, the first

published anywhere.

Please note that there was an error in Equation 7 on Page 27 of the article.

Put a "divide" ( " / " ) in front of g0 in Equation 7. There is a formal

Errata note at the end of the second half of the tech article with the

corrected Equation 7.

I've posted here a quick summary of the tech article with the key technical

results. Newsgroup posts can't support Greek symbols so I've written out the

key equations as best I can. See the tech article for the full equations.

I'm already deep into writing my next HPR tech article, but can answer a

limited number of good technical questions on this post and the article.

A quick summary of the tech article:

1) I derive and propose what I call the "Standard Method" for correcting the

ideal thrust coefficient and the theoretical specific impulse to the actual

thrust coefficient and the delivered specific impulse. The key summary

equations are the following equations:

Actual Thrust Coefficient = (Divergence Correction Factor)

*** (CF Efficiency**

Factor) *(Ideal Thrust Coefficient)

Factor) *

For reference the Ideal Thrust Coefficient is Equation 3-30, and for conical

nozzles the Divergence Correction Factor is Equation 3-34, from the 7th Edition

of Sutton, "Rocket Propulsion Elements".

Delivered Specific Impulse = (Divergence Correction Factor)

*** (CF Efficiency**

Factor) *(c

Factor) *

*** Efficiency Factor) ***(Theoretical Specific Impulse)

Where c* is the characteristic velocity.

2) To my knowledge at the time of the writing of the article, with the

exception of some of my internal-use computer programs, every solid rocket

motor, hybrid rocket motor, and liquid rocket engine computer program,

software, spreadsheet, performance charts, etc., for predicting performance and

calculating thrust from chamber pressure used by model, high power, and

experimental/amateur rocketeers is based on simply multiplying the ideal thrust

coefficient by the nozzle divergence correction factor to obtain the actual

thrust coefficient.

Actual Thrust Coefficient = (Divergence Correction Factor)

*** (Ideal Thrust**

Coefficient)

Which is equivalent to assuming that the CF Efficiency Factor is equal to 1.0.

All of these computer programs, software packages, spreadsheets, performance

charts, etc., can be easily updated to the Standard Method by simply

multiplying the Ideal Thrust Coefficient and the Divergence Correction Factor

with the CF Efficiency Factor

Actual Thrust Coefficient = (Divergence Correction Factor) *(CF Efficiency

Coefficient)

Which is equivalent to assuming that the CF Efficiency Factor is equal to 1.0.

All of these computer programs, software packages, spreadsheets, performance

charts, etc., can be easily updated to the Standard Method by simply

multiplying the Ideal Thrust Coefficient and the Divergence Correction Factor

with the CF Efficiency Factor

Actual Thrust Coefficient = (Divergence Correction Factor) *

Factor) * (Ideal Thrust Coefficient)

The tech article presents models for the CF Efficiency Factor for straight-cut

throats (both high performance and low performance) and for rounded throats.

These CF Efficiency Factor models can be retrofitted into existing computer

programs, software packages, spreadsheets, etc., using the equation above.

3) Many high power and experimental/amateur rocketeers run programs such as

PROPEP, or the USAF ISP code, and assume that the Theoretical Specific Impulse

predicted by the program for their propellant will be the Specific Impulse for

their rocket motors using the propellant. Based on the Standard Method

Delivered Specific Impulse equation

Delivered Specific Impulse = (Divergence Correction Factor)

*** (CF Efficiency**

Factor) *(c

Factor) *

*** Efficiency Factor) ***(Theoretical Specific Impulse)

this is equivalent to assuming that the Divergence Correction Factor = 1.0, the

CF Efficiency Factor = 1.0, and the c

*** Efficiency Factor = 1.0. Even if**

correct values for the Divergence Correction Factor and the CF Efficiency

Factor are used, representative values for the c*Efficiency Factor are still

correct values for the Divergence Correction Factor and the CF Efficiency

Factor are used, representative values for the c*

required.

Simply put the Theoretical Specific Impulse is what comes out of programs such

as PROPEP and the USAF ISP code. The Delivered Specific Impulse is what your

motor will actually deliver. In the tech article I detail how to make the

corrections to the Theoretical Specific Impulse to get the Delivered Specific

Impulse.

Continued in Next Post???