[Tech] HPR Tech Article - Thrust Coefficient Losses from Straight-Cut Throats

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)
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* 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
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
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* 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
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
Continued in Next Post???
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.....Continued from Previous Post.
3) Continued....
Smaller, shorter motors using aluminized or metallized propellants will have lower residence times in the motor, thus reduced combustion efficiency, and hence producing a lower c* Efficiency Factor. Larger motors are more efficient than smaller motors, due to increased residence times, proportionally less heat transfer into the motor case and nozzle, and proportionally smaller boundary layers for lower boundary layer losses. Thus for any given propellant it is important to track the variation of the c* Efficiency Factor with motor size.
Based on representative data presented in the tech article, as the motor size is increased from 1 lb propellant weight the delivered specific impulse can be increased by 5% for 50 lb propellant weight motors, and 7.5% for 350 lb propellant weight motors.
4) For the first time to my knowledge, thrust coefficient losses from using straight-cut throats for high power and experimental/amateur solid rocket motors have been quantified. The thrust coefficient losses were much higher than most high power and experimental/amateur rocketeers probably would have expected. While most high power and experimental/amateur rocketeers have performed thrust coefficient calculations assuming no losses beyond divergence losses (equivalent to CF Efficiency Factor = 1.0), the actual thrust coefficient loss from using a straight-cut throat was found to be approximately 10% (CF Efficiency Factor = 0.90) for the straight-cut throat lengths used on most high power and experimental/amateur rocket motors. While the results were primarily based on historical Thiokol solid rocket motor nozzle thrust coefficient data, static firings with chamber pressure measurements for determining experimental values for thrust coefficient were also performed for two large high power rocket motors, the test results from which confirm the trends from the historical Thiokol data.
5) Most high power and experimental/amateur rocketeers, beyond expecting thrust coefficient losses from straight-cut throats to be small, probably expected a somewhat linear variation of thrust coefficient loss with straight-cut throat length. A surprise finding from the CF Efficiency Factor results was a definite jump in the CF Efficiency Factor, and hence the nozzle thrust coefficient as the straight-cut throat L/D was reduced to less than 0.45. Figure 28 (CF Efficiency Factor plotted versus straight-cut throat L/D) is the key figure, and graphically shows the jump in CF Efficiency Factor when the straight-cut throat L/D is less than 0.45.
The CF Efficiency Factor models I've developed from the historical Thiokol data and the recent experimental data from static firings, both of which are plotted in Figure 28, are as follows:
For Conical Nozzles with Straight-Cut Throats:
For Throat L/D < 0.45
High Performance:
CF Efficiency Factor = 0.99 - ( 0.0333 * L/D )
Low Performance:
CF Efficiency Factor = 0.95 - ( 0.0333 * L/D )
For Throat L/D >= 0.45
CF Efficiency Factor = 0.905
For Conical Nozzles with Rounded Throats:
CF Efficiency Factor = 0.99 (high performance) to 0.95 (low performance)
6) From the above models it's clear that if the nozzle designer can get the throat L/D of the straight-cut throat under 0.45, there will be a large (3.5% to 8%) jump in performance. Based on this result, I recommend the following throat design criteria for conical nozzles with straight-cut throats:
Throat Design Criteria for Conical Nozzles with Straight-Cut Throats:
Throat L/D
Reply to
Post a drawing to a website (email it to me for posting if you do not have that capability) of a typical (say 75mm) HPR nozzle mold blank with the proposed shape change installed.
Tech Post Jerry
Reply to
Jerry Irvine
I checked out jpegs of your nozzles for your motors on your web site. Up through the 98mm motors there are frankly a lot of clones of Aerotech and Kosdon nozzles, nozzles designs I'm quite familiar with which do not have straight-cut throat L/D's less than 0.50. From the outside nozzle envelopes and knowing the convergent/divergent angles you favor it looks like a lot of your nozzles have straight-cut throat L/D's between 0.50 and 1.0. I'd be surprised if the straight-cut throat L/D's were under 0.50, although some nozzles might be just above 0.50.
Jerry, you just had to make the straight-cut throats just a LITTLE shorter, (to a throat L/D of 0.45, 0.40 for margin) and you would have improved the performance of your motors 3.5%-8%!
Most of the very large motors, where there are actual photos of the motors, have good looking short throats, although there are a few motors where the straight-cut throat L/D looks a little marginal on being below 0.50 or 0.40.
The above is similar to the nozzle survey results I included in the tech article, where 76% of E-N motors surveyed and 67% of H-N motors surveyed had straight-cut throat L/D's > 0.40, and which would get a 3.5%-8% increase in performance by reducing the straight-cut throat L/D's to less than 0.40.
Frankly Jerry, I'd be willing to bet you haven't even been tracking throat L/D on your nozzle designs. You've probably been figuring "keep the throat L/D somewhere between 0.50 and 1.0, 0.50 is probably better than 1.0". I'd be willing to bet you've never backed-out the thrust coefficient and compared it to the ideal/predicted thrust coefficient for any of your nozzles. The tech article points out techniques on how to optimize nozzle design and thrust coefficient performance using only load cell thrust-time curve data with no chamber pressure instrumentation required, but I'm guessing you didn't do a systematic study using those or any other techniques and basically have been guessing at what throat L/D to use.
It took some very detailed data to find the "magic" throat L/D of 0.45 (with margin 0.40) for the big jump in thrust coefficient performance. 0.45 or 0.40 are pretty specific numbers, not something you'd guess for a throat L/D (like 0.25, 0.30, 0.50, etc.) In fact another conclusion you can reach from the CF Efficiency Factor versus Throat L/D data plotted in Figure 28 in the tech article is that once you get the throat L/D down to 0.40, there is little additional benefit from further throat L/D reductions or even from replacing the straight-cut throat with a rounded throat. A straight-cut throat L/D of 0.40 has a performance close enough to a rounded throat, that there is no need to use a rounded throat.
Jerry Irv>
Well, if your nozzle designs are already so great, why do you need a copy of the Optimal and Universal Nozzle designs? :)
The Optimal Nozzle design is presented in the HPR tech article as Figure 29, the Universal Nozzle design is presented as Figure 30. Those interested can order the two back issues of HPR. The geometry for each nozzle is defined in the nozzle drawings based on being scaled from the throat radius/diameter. Larger or smaller throat radius/diameter, scale the nozzle geometry up or down. Included with the Optimal and Universal nozzle designs are the predicted CF Efficiency Factor based on the CF Efficiency Factor models presented in a previous post, and the calculated Divergence Correction Factor.
A nozzle pretty close to the Optimal Nozzle design was tested and the test data is presented in the tech article (Figures 22-27). It delivered a CF Efficiency Factor of 0.99. I'm claiming a CF Efficiency Factor of 0.98 taking into consideration the other data included in the CF Efficiency Factor models.
Chuck Rogers snipped-for-privacy@aol.com
Reply to
You would not know this because the motors that are at issue were "lost" under your tootleidge at TRA, but all those SU motors had 0.3:1 or so. The divergent depth and exit area ratio varied a bit, but the throat was in this long known, but now characterized for HPR spec.
Too bad HPR has been killed (largely by your efforts) "just in time", eh?
I have both of course.
0.3. How close was I?
Now I am not saying I did that 100% of the time, but as a product moved into mass-production it became reasonable to emphasize details. Like targeting exit ratios of 6.5:1 if possible, but 4:1 at miniumum.
Unfortunately any foray into Tripoli as a motor sales increaser failed, and any emphasis on either unaffiliated launches (Fest) or lone rangers, was a grand success.
Hence why all the stuff you have been doing for a decade is a royal buttfuck supreme to everyone.
Consumer cerets made mandatory
Bad cert policies making larger motors be "born regulated" and inviting ATF to the party unnecessarily.
Banning every motor supplier who was bold enough to live the ATF exempt lifestyle. Several.
YOU personally started it.
I agree. Congrats.
Reply to
Jerry Irvine
Jerry -
Do you always have to be such an asshole? Hijacking every tech thread into a thread against TRA or those that don't share your opinions.
Has that guy from the ATF contacted you yet?
Reply to
Phil Stein
A thread is only "hijacked" if everybody is more interested in the tangent than the original discourse...
Note that Jerry also made positive comments, but you focus on the negative...
-dave w
Reply to
David Weinshenker
He started with accusatory remarks. I just cited fact in reply.
I assume you do not agree, as you WANT more regulation AND you have no frst hand information on anything related to this.
Reply to
Jerry Irvine
Chuck started with a tech thread. you, jerry irvine attempted to hijack and subvert the thread into yet another jerry "wackathon".
Reply to
Dave Grayvis
Well, based on my nozzle survey in the tech article, and a random survey of EX nozzles referred to in the tech article, apparently not.
Looks like new info to me, published for the first time with extensive professional data and recent high power/EX test data to back it up.
Because I posted 0.30 as one of the numbers that would have been a good guess in the post right before?
And all the above has what to do with nozzle thrust coefficients?
Chuck Rogers snipped-for-privacy@aol.com
Reply to
How do you know what Jerry's primary interest is? I think that due to the consistency of his regurgitating the same old shit, his only objective here is as I stated. The rest is a diversion.
Did you notice how Jerry first came out with how he has always done things as Chuck's artile suggests. Then he asks for pictures of the nozzels. Based on this my only conclusion is that Jerry is running his mouth and has no clue of what the entire article says.
Reply to
Phil Stein
If I wanted ATF to go after you, I'd do more than bust your chops about it. I think what you say on public forums makes you worthy of a closer look by ATF. I doubt if my opionon on this matters much since your friends at DOT have put in a few good words for you.
Reply to
Phil Stein
David, this was clearly a tech thread. It was labeled as a tech thread. On the 6th post Jerry was already working on derailing the tech thread, which he apparently has succeeded at.
Jerry's strategy; If the thread is not about him, or his Wackathon issues, derail it.
It seems that it's something like 4 or 5 to 1 that the majority of the participants in this thread would like to see it stay a tech thread, not a Jerry Wackathon thread.
Jerry Irv>>Hence why all the stuff you [Chuck Rogers] have been doing for a decade is a royal buttf*&k supreme to everyone.
Dave; That was a real positive comment. Were there any others I missed?
Chuck Rogers snipped-for-privacy@aol.com
Reply to
As I have repetitiously stated, you have been the leader of banning ATF exempt willing motor suppliers since at least 1992.
That is your legacy.
As I said I agree with that and to repeat myself, kudos.
Reply to
Jerry Irvine

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