
#1
Dec2909, 07:12 AM

P: 4

Hi, just found these forums, and they look very useful.
I'm a second year Aerospace Engineering student, and as part of a project I'm modelling the first stage of a Saturn V rocket. I'm using a linear and nonlinear model, and have all the equations sorted out. The only problem is I can't really find a value that I can use for the drag coefficient. I'm aware that in real life this would change with velocity, as the Reynolds number would be changing, and the rocket would accelerate to supersonic speeds. But for the linear model, I need to just use an average figure. I'm wondering if anyone knows where I can find a value for this, or maybe just give me an estimate? Thanks 



#2
Dec2909, 09:12 AM

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P: 2,234

This thread from 2006 might help you, it discusses how a Cd is applied for a simple model of large rocket such as the Saturn V.
http://www.physicsforums.com/showthread.php?t=133721 



#3
Dec2909, 09:17 AM

P: 4

Thanks, that looks useful. That thread doesn't seem to show any specific values for the drag coefficient though.




#4
Dec2909, 04:34 PM

P: 261

Drag of a Saturn V
I found a program called RockSim that calculates Cd as a function of Mach number for model rockets up to M = 2. It isn't intended to analyze something as complex as a Saturn V, but it may give some useful results. There is a fully functional 30day trial available.
Here is the link: http://www.apogeerockets.com/rocksim.asp EDIT: Apogee Components also offers a 1/70th Saturn V rocket kit. If I were you, I would ask them for a RockSim file for the Saturn V rocket. http://www.apogeerockets.com/Saturn5.asp 



#5
Dec2909, 05:44 PM

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#6
Dec2909, 06:00 PM

P: 4,780

[tex]C_d = f(Re,Ma,\delta_c)[/tex] Typically, we account for this by having a series of lookup tables for aerodynamic data when coding the simulator. 



#7
Dec2909, 07:53 PM

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P: 2,507

Do those lookup tables include Cd's for a Saturn V?




#8
Dec2909, 07:57 PM

P: 4,780

For instance, each lookup table has tabulated values of Cd, CL, Cy, Cl, Cm, Cn for various explanatory variables like: angles of attack, side slip, Reynolds and Mach number, controls deflection, throttle setting, etc. 



#9
Dec2909, 11:06 PM

P: 594

By definition, Cd is a coefficient, and therefore a constant, for any given body. It's usefulness is limited to the common "drag equation," Fd=Cd*1/2*p*v^2*A.
Drag rise effects occur beyond this simple equation, both at very slow velocities, as well as approaching mach. At supersonic speeds, it's useless, and is replaced by equations for friction, vortex, liftdependant wave, and volume wave. More here. 



#10
Dec2909, 11:33 PM

P: 4,780





#11
Dec3009, 02:44 AM

P: 4

Thanks for the information people, this is all useful stuff. Do you not think it's really viable then to use a constant value of Cd?
This is a rather basic model, and many assumptions are made, such as fixed control surfaces, thrust, and the rocket is travelling vertically. We haven't really covered much about the aerodynamics of supersonic flight yet, so it might be a bit beyond me to try and model that. 



#12
Dec3109, 01:01 AM

P: 594

However, I will say I've seen Cd's use (I call it a misuse) as a function. Sure, one can take that approach. However, by definition, a coefficient is a constant, not a function. Second, if you're going to incorporate other factors into Cd, call it Fd, not Cd. Third, keeping Cd as a constant and incorporating other factors in the drag equations outside the simple drag equation helps to keep them separate, a critical factor in design. When I earned my degree in the 80s, we were taught to keep Cd a constant and keep the other factors separate, and for some very good reasons. Perhaps they're teaching people differently these days. 



#13
Dec3109, 01:09 AM

P: 4,780

Clear as day, the drag varies with Mach number and is not constant! A few posts ago you said: Instead of quoting some website ad nauseum, I strongly suggest you see: [1] Aircraft System Identification by E.A. Morelli [2] Dynamics of Flight by Etkin/Reid [3] Flight Stability and Automatic Control by Nelson for more rigorous background theory, and I will help to dispel further misconceptions. To jr1104: In light of the plot above, if I were in your position I would try to find some drag data on a missile that goes from subsonic to supersonic Mach numbers and use that. This will be "somewhat"  and I use this term very loosely  accurate. The problem is that at upper atmosphere the Saturn V is no longer flying through 'air', but rarefied gas. The underlying flow physics change dramatically and the Cd values you will find will be pretty useless. All sorts of fun stuff happens in rarefied gas: like the no slip condition on the boundary layer no longer being true!! 



#14
Dec3109, 03:56 AM

P: 4

Cheers Cyrus, I'll look into that. I used the Rocksim app linked above, and found a model of a Saturn V, and that uses a Cd value of about 0.95. Once I've coded the model, I'll try running it and see if I get sensible numbers out of it. I'm only modelling the rocket up to 68km, which is the limit of the first stage.




#15
Dec3109, 04:29 PM

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P: 5,095

Are we really gonna argue about the use of the term coefficient is? Puhlease. I think there is enough professional usage since the beginning of forever to allow the usage. All drag coefficients depend on many factors, especially mach number and AOA.
Here's the plots for the V2 



#16
Jan510, 11:58 PM

P: 594

The latter school of thought won out, but someone forgot to change it's name from a drag coefficient to a drag function. In the 1980s, I worked as a Fortran programmer for NASA's computer complex in Slidell, LA. Although I worked on hull design (my degree was in AOE), my love was flying, and discussed many aerospace engineering concepts with the engineers there, including this issue of which you are apparently unaware. While the latter school is by far the most common approach, it's not the only approach, and various researchers and designers have been known to separate the terms, for clear reasons relating to more precise enumeration of the various components of drag, most notably in transonic and supersonic research and design. 



#17
Jan610, 12:16 AM

P: 4,780

Is there something wrong with Fred's graph? If so, please point it out.
I honestly don't know why you think the drag coefficient is a constant, it is not. At a freshman level, it varies with angel of attack. We both already know this, but I don't understand why you wont accept it. You seem to be caught up in nomenclature, all the drag coefficient does is represent something physically. It is a 'coefficient' and I say that in quotes, at each slice of time. At each instant we can think of it as a constant. But in general it is a multivariate surface! (It's an ndimensional function) I have never seen anyone state the drag coefficient is a constant  ever. You are going to need to have some references here. Even Anderson 4ed, chapter 1 p.84, has plots of drag coefficients as early back as the Wright brothers. There is even a chart of variation of normal and axial forces for various angles of attack by Lilienthal circ. 1897. 



#18
Jan610, 04:20 PM

P: 594

Again, in the early days of the drag equation, it was considered a constant (or approximately so) as well. Somewhere along the line, however, some aero engineers began cramming variables into it while never bothering to change it's name from "coefficient" to "function." Then, by definition, it is not a "coefficient." And it is indeed a function. 


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