Author Topic: F9v1.1 Stage 1 (and FH booster) recovery trajectory, burns, drag evaluation.  (Read 17658 times)

Offline cambrianera

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@aero, please check your calcs, because with a simple formula ( http://en.wikipedia.org/wiki/Terminal_velocity )
sea level terminal velocity for Falcon 9 should be 200 m/s.
(mass 20000 kg, air density 1.2 kg/m3, area 10.5 m2, Cd 0.8 ).
Oh to be young again. . .

Offline MP99

Altitude = 15 km, Vz= 88.7 m/s (using Cd = 0.8)  Vz = 124.5 m/s using spherical drag model
Altitude = 10 km, Vz= 58.6 m/s (using Cd = 0.8)  Vz =   89.3 m/s using spherical drag model
Altitude =   5 km, Vz= 43.6 m/s (using Cd = 0.8)  Vz =   70.0 m/s using spherical drag model

You need to tick the "Don't use smileys." box!

cheers, Martin

Offline MP99

I'm linking this mostly because of the fab Calvin & Hobbes strip, but it may also be of interest:-

https://sugarshotsolidworks.wordpress.com/2013/12/22/numeric-analysis-of-nose-cone-heating-first-steps/

cheers, Martin

Offline aero

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@aero, please check your calcs, because with a simple formula ( http://en.wikipedia.org/wiki/Terminal_velocity )
sea level terminal velocity for Falcon 9 should be 200 m/s.
(mass 20000 kg, air density 1.2 kg/m3, area 10.5 m2, Cd 0.8 ).

What would I check? Oh, I see one thing. Been fooling with my Raptor model so had the wrong ref. area in the recovery portion. (I thought my Launch and recovery segments were independent) With the F 9 v1.1 ref. area = 10.5209 m^2 I now have:

15 km----------236.9 m/s   Mach 0.8
10 km----------156.4 m/s   Mach 0.53
  5 km----------121.5 m/s   Mach 0.38
SL ---------------98.96 m/s Mach 0.29

My drag Coefficient  drops from ~ .62 to ~ .35 over that range of Mach numbers.

This is much better. I did have a thought although I'm not addressing it in my simulations. Aren't the propellant tanks filled with helium during recovery? That should give them about 400 kg of buoyancy if so.

As for checking my calculations, what else could be wrong? If the Mach # is correct and it is, see:

http://www.grc.nasa.gov/WWW/k-12/airplane/mach.html

Mach numbers check, so the Cd look-up is correct, checked against the graphs for Cd for a sphere up thread, dynamic pressure and drag calculations are very hard to mess up and that's it. I did verify my simulation against the advertised F 9 v1.1 payload to orbit and it does reach orbit with 13150 kg of payload, just barely but it makes it, so I'm confident of my integrator. That means to me that my latest numbers are probably as close to reality as I'll get.

I should try to add legs, which will be easy to do if we can decide at what altitude they are deployed. First thing would be to change the area at a given altitude, then if we can figure it out, change the Cd model to represent the stage with the legs extended.
« Last Edit: 12/23/2013 05:55 PM by aero »
Retired, working interesting problems

Offline guckyfan

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You could try to do the evaluation backwards, assuming Elon Musks statement is correct. He said the final burn will consume less than 5% of the empty stage weight. So calculate the burn for 1t of fuel and see what terminal speed can be killed with that burn. Then you can calculate the drag required to achieve that terminal speed. Should be interesting.


Online Pete

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 Aren't the propellant tanks filled with helium during recovery? That should give them about 400 kg of buoyancy if so.


Their content is irrelevant, as the first stage is a volume-constrained rigid object.
Its buoyancy would be exactly that of the air mass displaced, which is about 440m3. At sea level, that is about 525kg. At anything over 10km altitude, a very very good approximation of zero.

All this will affect is the weight of the stage, not its mass. So the only real difference is a reduction of final terminal velocity of about 1.3%. *way* under the error bars of our guesstimates for mass, drag, and even thrust.

Online Pete

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You could try to do the evaluation backwards, assuming Elon Musks statement is correct. He said the final burn will consume less than 5% of the empty stage weight. So calculate the burn for 1t of fuel and see what terminal speed can be killed with that burn. Then you can calculate the drag required to achieve that terminal speed. Should be interesting.

Matches our figures, as a first approximation.
5% of empty stage mass is about 1000kg.
At sea level, full throttle, the single merlin 1d impart 3.1g to empty stage + 1 ton.
It would burn through that 1 ton of fuel in 4.25 seconds, delivering total delta of about 129m/s.

We are assuming terminal velocity without legs as about 100m/s, and terminal with legs of about 70 m/s.
Stopping 70m/s under these conditions would require only 2.3 seconds of full thrust, leaving a fuel reserve of only 2 seconds.. not enough? Maybe we need to leave a bit more reserve fuel, to give us some leeway for inexact fuel sensors, fuel line burps, etc.
This is totally out of my expertise... When you have a device that pumps 235 per second, and you dare not let it run dry, how empty can you run your tankage before the inevitable airbubble, unexpected pressure due to empty plumbing, etc? Just how much juice is available to the turbopump, when the tank itself is exactly empty? Even worse, its not just one fluid you need to worry about, but two completely separate sources that *must* be in the correct ratio. A hiccup in either would shred the pump, thus RUD the engine.

How much propellant will be left when the engine starts complaining about it?
  and how much more do we need to keep in reserve, due to various inaccuracies?
(I'm sure this would have been discussed previously, I just could not locate the thread)

Offline guckyfan

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You could try to do the evaluation backwards, assuming Elon Musks statement is correct. He said the final burn will consume less than 5% of the empty stage weight. So calculate the burn for 1t of fuel and see what terminal speed can be killed with that burn. Then you can calculate the drag required to achieve that terminal speed. Should be interesting.

Matches our figures, as a first approximation.
5% of empty stage mass is about 1000kg.
At sea level, full throttle, the single merlin 1d impart 3.1g to empty stage + 1 ton.
It would burn through that 1 ton of fuel in 4.25 seconds, delivering total delta of about 129m/s.

Thanks, good comparison.

Offline MP99


 Aren't the propellant tanks filled with helium during recovery? That should give them about 400 kg of buoyancy if so.


Their content is irrelevant, as the first stage is a volume-constrained rigid object.
Its buoyancy would be exactly that of the air mass displaced, which is about 440m3. At sea level, that is about 525kg. At anything over 10km altitude, a very very good approximation of zero.

Yes, that is the buoyancy. If the stage contained air at ambient pressure, then the internal gas would weigh the same as the displaced gas, and there would be no net buoyancy.

However, if the stage's O2 tank contains O2 at 5 atmospheres, then 5x the weight of that volume of O2 at sea level would be added to the tank's dry mass (and this would be more than 5x the weight of that pressure of air, given the population of molecules involved).



Think of this another way. In vacuum, the mass/weight of the stage constitutes the hardware, any remaining prop, and any pressurisation gas.

As the stage goes lower in the atmosphere it experiences a certain amount of buoyancy, until at ground level it experiences lift equating to 1x atmosphere over the volume of the tank. But that lift may be less or greater than the mass of gas in that tank, depending on which gases are involved, and their pressure.

cheers, Martin

Offline Aerospace Dilettante

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Thanks to the OP, even though I don't understand all of it.  While read through this thread, I remembered something Elon said at the National Press Club:

Quote
“(Also worth noting,) you don’t need wings to steer aerodynamically, you just need some lift over drag numbers and lift vector.”


Does anyone think that the boost-back burn could be reduced and stage could be sort of glided part of the way back to the launch site.  Don't know what the L/D is for a ginormous cylinder is.

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