# Drag of a Saturn V

by jr1104
Tags: drag, saturn
 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 non-linear 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
 Sci Advisor PF Gold 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
 P: 4 Thanks, that looks useful. That thread doesn't seem to show any specific values for the drag coefficient though.
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 30-day trial available.

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
PF Gold
P: 2,234
 Quote by jr1104 Thanks, that looks useful. That thread doesn't seem to show any specific values for the drag coefficient though.
I think the basic problem is that the drag varies with speed and altitude, so a constant Cd doesn't work... but I'm not an aero guy.
P: 4,780
 Quote by Mech_Engineer I think the basic problem is that the drag varies with speed and altitude, so a constant Cd doesn't work... but I'm not an aero guy.
The drag coefficient never varies with altitude, as altitude only affects the density; however, the Cd will change as a function of Mach and Reynolds number, controls deflections $$\delta_c$$, and other variables I have omitted here for the sake of simplicity.

$$C_d = f(Re,Ma,\delta_c)$$

Typically, we account for this by having a series of lookup tables for aerodynamic data when coding the simulator.
 Sci Advisor P: 2,507 Do those lookup tables include Cd's for a Saturn V?
P: 4,780
 Quote by LURCH Do those lookup tables include Cd's for a Saturn V?
If one were to code a simulator for a Saturn V, then it would. Each table is specific to an airplane. It's not a lookup table of different airplanes. I think this is what you are asking?

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.
 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, lift-dependant wave, and volume wave. More here.
P: 4,780
 Quote by mugaliens 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, lift-dependant wave, and volume wave. More here.
Hey mugaliens, you have some misinformation concerning the drag equation so I am going to give you a slight course correction. The form of the drag coefficient is simply a consequence of dimensional analysis of the Buckinham-Pi theorem. It does not say, any where or at any time, that Cd is a constant in its derivation of Cd. I very carefully explained how Cd changes in my previous post. Please reread it again. The drag coefficient is defined for any flight regime, be it subsonic or hypersonic and has no relation to: "friction, vortex, lift-dependant wave, and volume wave."
 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.
P: 594
I saw it.

 The drag coefficient is defined for any flight regime, be it subsonic or hypersonic and has no relation to: "friction, vortex, lift-dependant wave, and volume wave."
Yes it does.

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.
P: 4,780
 Quote by mugaliens I saw it. Yes it does.
The only time your link comes into play is if one is trying to analytically calculate the drag coefficient. This does not mean the drag coefficient is constant, or that one necessarily has to care about: "friction, vortex, lift-dependant wave, and volume wave" because you can find the drag coefficient experimentally (and should to validate any calculations). Notice the plot in your link:

Clear as day, the drag varies with Mach number and is not constant!

A few posts ago you said:

 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, lift-dependant wave, and volume wave.
You need to be careful here: the equation is fully 'useful' - at all times. I think you do not understand the application of this equation in calculating the drag vs. your link which is to calculate the drag coefficient. They are two very different things, and the implications are profound.

 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.
Then what you were taught, and have stated above, is wrong. It is not a misuse, it is standard practice to express the drag as a function of several explanatory variables and these functional dependencies are exactly what is known as the aircrafts stability derivatives, which is what I work with on a day-to-day basis as a flight dynamicist. These derivatives tell use about the stability, control authority, and performance of the aircraft and are used for finding the gains of autopilot design.

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!!
 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.
 Sci Advisor P: 5,095 Are we really gonna argue about the use of the term coefficient is? Puh-lease. 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 V-2 Attached Thumbnails
P: 594
 Quote by FredGarvin Are we really gonna argue about the use of the term coefficient is? Puh-lease. 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.
The drag equation came into existence long before mach flight was ever possible, and at the time, its coefficient was considered a constant. Two schools of thought emerged. One was to include varying terms as additional functions in the equation, and the other was to cram it all into the drag coefficient.

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.

 Here's the plots for the V-2
Sure...
 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 n-dimensional 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.
P: 594
 Quote by Cyrus I honestly don't know why you think the drag coefficient is a constant, it is not.
"In mathematics, a coefficient is a constant multiplicative factor of a specific object." (source) More sources. They all say the same thing: A coefficient is a constant.

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."

 At a freshman level...
Gee, if you weren't taught at the freshman level that a coefficient is a constant, heaven help you! That doesn't speak well of your school.

 I don't understand why you wont accept it.
I accept it's widespread use as something beyond a coefficient. I simply don't agree with it. Having done test and evaluation (research and design), I know for a fact we break out the variables into separate components, and for very good reasons: We want to know, precisely, the independant contributing factors of drag beyond simple incompressible and non-wave drag flow.

 You seem to be caught up in nomenclature...
Actually, I'm caught up in reality, while you and Fred (and admitedly, a lot of other aero engineers) are caught in an inappropriate handling of the issue which began long ago.

 But in general it is a multivariate surface! (It's an n-dimensional function)
(italics mine)

Then, by definition, it is not a "coefficient." And it is indeed a 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.
The error of using the term "coefficient" instead of the more appropriate "function" (which you mentioned yourself, above) is indeed rather deep-seated...

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