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Calculating air drag for a massive rocket 
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#1
Sep2606, 06:12 PM

P: 83

Not just a little rocket that goes a 1000 feet in the air, but one that can get into space. How does one take into account that the air density grows less with altitude, etc?
Anyone know of any good resources for a problem like this? 


#2
Sep2606, 08:47 PM

P: 51

Usual practrice in aerodynamics is to work in "indicated airspeed" by assuming sea level density (1.225 kg/m^3). If you want actual velocity you need to account for density. General formulae:
L = 1/2 . p . v^2 . S . Cl D = 1/2 . p . V^2 . S . Cd Where : L = Lift Force D = Drag Force p = density (1.225 kg/m^3 @ sea level) V = velocity S = surface area Cl = coefficient of lift Cd = coefficient of drag Depending how complicated you want to go will have changing density, acceleration, and Cd with Reynolds number due to velocity so you will have either to estimate by calculation in small incriments or use integration. Good luck. Ken 


#3
Sep2706, 04:50 AM

P: 83

So, I suppose I cant get it as an explicit function of time.



#4
Sep2706, 04:17 PM

P: 38

Calculating air drag for a massive rocket
When one of your variables changes (like air density at various altitudes), and you have a formula for how it changes (like air density at various altitudes), there's this marvelous mathematical tool that lets you do calculations. It's called "calculus." Get an adult to help.



#5
Sep2706, 04:29 PM

HW Helper
P: 7,033

An old equation I found for up to 300,000 feet (more boundaries above this):
http://www.centennialofflight.gov/es...sphere/TH1.htm Drag versus speed gets complicated once you're near or beyond supersonic. The range above .95 to 1.00 is different than below .95. The range between Mach 1.0 and Mach 1.4 is different than above Mach 1.4. Regarding sources, obviously NASA and space oriented companies deal with this stuff all the time, but I wasn't able to find any links with all the required formulas. 


#6
Sep2706, 04:39 PM

HW Helper
P: 7,033

Then there is real world testing of high speed aerodynamics. Rocket sleds can be fun: http://www.46tg.af.mil/world_record.htm 


#7
Oct106, 06:29 AM

P: 83

Thanks everyone. I am stepping through the equations at 0.1 second intervals and my results are fairly close to conditions of a Saturn V rocket at 80 seconds into flight.
For the air drag, I intend to use what Ken put forth: [itex]D_{f}\; =\; \frac{1}{2}\mbox{C}_{d}pV^{2}\mbox{S}[/itex] Now, I can presumably just have the density as a function of height. Now Cd is just the reynolds number as a function of velocity? 


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