Most efficient vertical flight speed?

I'm writing a simulation to determine the most efficient thrust profile for a rocket to achieve the highest altitude with the least amount of
fuel. Given the following:
mass (as a function of time) diameter Cd air density
The results were surprising. But before I state the results I got (in order to have a "blind" confirmation), has anyone else attempted this kind of calculation before? And if so, what results did you get?
Thanks in advance! Dave
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Yes.
The results are in books called "Flight sheet guides" and "Malewicki Charts."
Jerry
www.v-serv.com/crp
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I'm not asking to find a ideal weight for a given engine... What I'm talking about is doing it in reverse. Say you're given a rocket with parameters Cd and D. Now you're given "x" amount of fuel (with an isp of 'you pick')... if you could control the thrust curve, what's the highest you can make it go?
For example, say if I use a K1100 with a rocket with a diameter of 5.5", a Cd of .75, and an initial mass of 5.8kg (which is about optimum for that engine). That'll get you an altitude of about 3872 ft. But using an optimized thrust curve for the same rocket with same fuel (and isp), I'm predicting an altitude of 5013 ft.
It's not as applicable to solids as it is to hybrids (or liquids). It's not a really big difference until you start looking at optimizing curves for spaceshots, where fuel is the majority of your weight and atmospheric density changes significantly.
Dave
Jerry Irvine wrote:

profile
of
(in
this
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For typical model/HPR conditions, optimum thrust/time for altitude seems to be a bit on the long duration side, compared to what you really want for a clean hard liftoff - but a "kicker" motor generates high velocity at low altitude, which coasts off rapidly... some motors seem to hit a "sweet spot" (in "typical" consumer rocketry airframes) - Cesaroni Pro38's, Econojet G38FJ, and Apogee 18mm D10 mini composites come to mind: they come off the pad clean and hard, and then keep going and going like the energizer bunny...
-dave w
"dave.harper" wrote:

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The results are in books called "Flight sheet guides"

What is your test case?
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Jerry Irvine wrote:

I'm
with
isp
My test case? You mean this?

optimum
(and
Dave
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5.5 x 80" rocket CDr 0.55 8-20lbs 80 degrees 29 inhg at ground level. Neutral Thrust Motor CDA (IN^2).066677 ORBIT98.BAS COPYRIGHT JERRY IRVINE WEIGHT ALTITUDE BURNOUT BURNOUT MACH ALTITUDE COAST (LBS) (FT) ALT (FT) VEL(FPS) MAX (MILES) TIME (S) --------- --------- --------- --------- ----- --------- --------- 8.0 4641.3 1665.6 1319.9 1.2 0.9 10.3 9.0 4896.3 1559.3 1287.5 1.1 0.9 11.1 10.0 5130.8 1460.8 1256.0 1.1 1.0 11.8 11.0 5326.7 1368.3 1223.2 1.1 1.0 12.4 12.0 5495.7 1279.8 1191.4 1.1 1.0 13.0 13.0 5644.4 1196.4 1154.4 1.0 1.1 13.5 14.0 5735.9 1119.0 1108.6 1.0 1.1 13.9 15.0 5764.0 1048.3 1057.6 0.9 1.1 14.2 16.0 5697.3 984.3 1000.1 0.9 1.1 14.4 17.0 5603.7 926.8 947.2 0.8 1.1 14.5 18.0 5490.8 874.9 898.5 0.8 1.0 14.6 19.0 5362.0 828.0 853.8 0.8 1.0 14.7 20.0 5221.0 785.3 812.6 0.7 1.0 14.6 TOTAL IMPULSE POUND-SECONDS = 575 TOTAL IMPULSE NEWTON-SECONDS = 2557.6 AVERAGE THRUST NEWTONS = 1278.8 AVERAGE THRUST POUNDS = 287.5 SPECIFIC IMPULSE (LB-SEC/LB) = 203.496094 TIME (SEC)= 0 THRUST (LBS)(7.5 TIME (SEC)= 2 THRUST (LBS)(7.5
5.5 x 80" rocket CDr 0.55 8-20lbs 80 degrees 29 inhg at ground level. Progressive Thrust Motor CDA (IN^2).066677 ORBIT98.BAS COPYRIGHT JERRY IRVINE WEIGHT ALTITUDE BURNOUT BURNOUT MACH ALTITUDE COAST (LBS) (FT) ALT (FT) VEL(FPS) MAX (MILES) TIME (S) --------- --------- --------- --------- ----- --------- --------- 8.0 4637.5 1561.1 1450.7 1.3 0.9 10.4 9.0 4888.6 1449.6 1399.2 1.2 0.9 11.2 10.0 5110.0 1348.9 1349.2 1.2 1.0 11.9 11.0 5292.5 1253.7 1297.4 1.1 1.0 12.5 12.0 5465.6 1166.6 1246.6 1.1 1.0 13.1 13.0 5595.8 1086.7 1197.5 1.1 1.1 13.6 14.0 5714.5 1013.6 1147.1 1.0 1.1 14.0 15.0 5743.8 947.0 1087.8 1.0 1.1 14.3 16.0 5714.8 887.5 1029.2 0.9 1.1 14.5 17.0 5617.5 834.0 972.3 0.9 1.1 14.7 18.0 5503.5 786.0 920.3 0.8 1.0 14.7 19.0 5373.3 742.7 872.8 0.8 1.0 14.8 20.0 5230.5 703.4 829.3 0.7 1.0 14.8 TOTAL IMPULSE POUND-SECONDS = 574.8 TOTAL IMPULSE NEWTON-SECONDS = 2556.7104 AVERAGE THRUST NEWTONS = 1278.3552 AVERAGE THRUST POUNDS = 287.4 SPECIFIC IMPULSE (LB-SEC/LB) = 203.425312 TIME (SEC)= 0 THRUST (LBS)9.8 TIME (SEC)= 2 THRUST (LBS)85
5.5 x 80" rocket CDr 0.55 8-20lbs 80 degrees 29 inhg at ground level. Stepped Thrust Motor (realistic) CDA (IN^2).066677 ORBIT98.BAS COPYRIGHT JERRY IRVINE WEIGHT ALTITUDE BURNOUT BURNOUT MACH ALTITUDE COAST (LBS) (FT) ALT (FT) VEL(FPS) MAX (MILES) TIME (S) --------- --------- --------- --------- ----- --------- --------- 8.0 8760.2 6614.4 676.9 0.6 1.7 9.8 9.0 8603.4 6294.1 660.9 0.6 1.6 10.3 10.0 8409.1 5977.9 644.1 0.6 1.6 10.7 11.0 8183.0 5667.5 626.4 0.6 1.5 11.0 12.0 7929.3 5364.6 607.5 0.5 1.5 11.3 13.0 7652.5 5070.5 587.5 0.5 1.4 11.4 14.0 7355.6 4786.5 566.5 0.5 1.4 11.5 15.0 7042.6 4513.4 544.6 0.5 1.3 11.5 16.0 6716.8 4251.8 522.1 0.5 1.3 11.4 17.0 6381.8 4001.8 499.2 0.4 1.2 11.3 18.0 6040.9 3763.7 476.1 0.4 1.1 11.2 19.0 5697.5 3537.3 452.9 0.4 1.1 11.0 20.0 5354.9 3322.3 429.8 0.4 1.0 10.7 TOTAL IMPULSE POUND-SECONDS = 575.85 TOTAL IMPULSE NEWTON-SECONDS = 2561.3808 AVERAGE THRUST NEWTONS = 213.4484 AVERAGE THRUST POUNDS = 47.9875 SPECIFIC IMPULSE (LB-SEC/LB) = 203.796914 TIME (SEC)= 0 THRUST (LBS)0 TIME (SEC)= 1 THRUST (LBS)0 TIME (SEC)= 1.1 THRUST (LBS)C TIME (SEC)= 12 THRUST (LBS)C
Jerry
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Jerry Irvine wrote:

(S)
---------
10.7
First, are you accounting for reduction in mass due to propellant burn? Just checking to make sure we're using the same methods.
Anyway, using this one as an example, I get 7966 ft max altitude, 5816 ft at burnout, and a velocity of 608 ft/s at burnout, so we're relatively close (within about 5%).
Using an optimized thrust profile with the same amount of propellant, same mass, Cd, dia, isp, etc... I get a max alt of 9487 ft, burnout alt of 8565 ft, and a burnout velocity of 292 ft/s. That's almost a 20% increase in altitude using the same amount of fuel (and using mine as the reference). That's what I mean by optimizing the thrust.
Dave
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Yes using the thrust curve as a proxy.

But you do not say what that thrust profile is.
I do.
Also my run is a practical buildable motor.
Your run if ever disclosed could probably be approximated by a buttkicker booster motor cluster (0.4s) and a central endburner with a very low probabibility of vertical flight.

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Jerry Irvine wrote:

level.
COAST
TIME
burn?
5816
propellant,
Well, I'll post the full profile when I get home tonight, if that'll make it more believable.

Considering I haven't stated what my thrust profile is (as you mention above), this is a big assumption, isn't it?

a
Actually, it is pretty similar (in profile), not nessesarily in a that configuration... Much like your "Stepped Thrust Motor" profile, only with a lower, longer sustained flight (which is what the optimization simulation calculates). And it hits 200mph in under a second, so I don't know why you say it'd probably fail to go vertical...?
Dave
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We'll look forward to it.

Nope. A unlateral statement.

The low thrust combined with gravity turn and greatly accelerated by wind perturbation.
Tech Jerry
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Jerry Irvine wrote:

ground
propellant
altitude,
that'll
Try this run:
TIME THRUST 0.00 445 1.25 445 1.26 107 20.00 107 20.01 0
It's simplified from my optimized profile.

mention
It seemed to me that you implied that a motor based on my thrust profile wasn't buildable.

with
that
only
optimization
I did a run with an 80deg shot (10deg from vertical), accounting for arcing due to gravity, and it still hit 8100 ft, which is higher than the "Stepped Thrust Motor" profile used for reference.
Would you want to use the profile I presented on a windy day when you're shooting for fun? Probably not. Would you want to use it if you were trying to break records? Maybe.
Dave
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I stated, not implied.
Until now it was not even possible to judge if your profile was buildable.
Assuming 54mm solid, still probably not.
The fatter the rocket the less likely your 20 second burn is going to fly anywhere near vertical.
You have not stated you assume the use of active guidance.
I assume you at least are doing minimal mass, minimal drag minimal diameter configuration so perhaps it will only arch over after 17 seconds instead of 9.
My practical experience (I used to have a TRA CERTIFIED long duration motor BTW), is that there is a trade-off for performance and burn time and how vertical the unguided flight is.
I have found 15 seconds is stretching it.
Free advise.
We all know the impractical is optimal.

Wait till you see it in reality. :)
Reality bites.

I flew a flight with two E6's on a mildly windy day. I launched it slightly WITH the wind so it arced back to vertical. Each of the two motors were stepped thrust and 9 seconds burn. That's 18 seconds with two steps.
It was a record of 80ns 1992 M, but it was very difficult to achieve.
Good luck.
Jerry

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9*6T - which would make that an F6, unless E6 is some kind of adjusted designation to indicate higher thrust off the pad.
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Niall Oswald
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EACH E6 was an Aerotech 24mm 40ns E6 motor. E6-0 to E6-8.
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Jerry Irvine, Box 1242, Claremont, California 91711 USA
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Let's spoon feed the masses:
http://nar.org/SandT/pdf/Aerotech/E6.pdf
;-)
-Fred Shecter NAR 20117
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Good. They need it.
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Ok, but in your previous post you stated that:
"Each of the two motors were stepped thrust and 9 seconds burn. That's 18 seconds with two steps."
Am I wrong in saying that you are stating that the E6 motor in question has a burn time of 9 seconds?
A motor with a 9 second burn and 6N average thrust is a 54Ns 'F' class motor.
The file Fred just posted a link to states the burn time as 6 seconds.
40Ns/6N = 6 2/3 seconds. I see no way in which you could have an E6 which burns for 9 seconds!
Why I am bothered about this I don't know, but hey, this is RMR after all :)
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Correct. I believe they are now on the Apogee website.
It used to be a USR relabel item.

http://www.v-serv.com/usr/motors/f9.html
E6 is its "name".

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So in conclusion, said 'E6' is not actually an E6! I guess 'the average thrust is less than 6N' would have answered my question :)
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