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# How to Approximate Aerodynamic Coefficients

## How to Approximate Aerodynamic Coefficients

(OP)
Hello, this is a very specific question so any help is much appreciated!

GOAL: I'm trying to get a first-pass analytical approximation for the lift and drag coefficients for hypersonic flow over a blunt-body capsule spacecraft (similar to NASA's Apollo or SpaceX's Dragon) during atmospheric reentry from LEO.

METHOD: I understand that modified Newtonian fluid theory is the best (most accurate for its simplicity) approach before considering any computationally-demanding and time-consuming CFD simulations. The basis of this theory is to integrate the pressure coefficient over the portion of the 3D body that is exposed to air flow ("non-shadowed region") using the equation Cp = Cp(max)*sin^2(theta).

ISSUE: I've done a fair amount of research, however, not having an extensive background in aerodynamics am struggling with how exactly this is applied. For a given vehicle shape, angle of attack, and mach number, how exactly is this done? Every paper I read (3 of which I've referenced below as examples) seem to skip over the actual calculations and reference some code that's been written or use an existing program like CBAERO that I don't have access to. I've also found a couple of the original documents from the 60's (NASA TM-53391) that go over this but are pretty hard to follow. Has anyone done this before and could walk me through the process or point me to an example calculation for my scenario or code? If this approach is reportedly simpler than CFD and used as a means of quick design iteration, I would think it's not super difficult but I'm lost with the complex integrations and limits.

SOURCES:
https://engineering.purdue.edu/~mjgrant/48th-aiaa-aerospace-science.pdf: "After analytic relations are developed, they are output to a Matlab-based aerodynamics module."
https://www.intechopen.com/chapters/21789: "A computer program is written to compute the aerodynamic coefficients using the Newtonian sine-squared law"
https://www.researchgate.net/publication/269802955_Application_of_Modified_Newton_Flow_Model_to_Earth_Reentry_Capsules: "A Fortran code has been written, making benefit of existing in-house library"

### RE: How to Approximate Aerodynamic Coefficients

If it is accessible to you, I highly recommend you take a look at Introduction to Flight by John D Anderson. Specifically section 10.3 and example 10.1.

An example is illustrated, showing how to apply the theory you mentioned to predict the pressure coefficient at one point of a body. First you need to predict the pressure coefficient at the stagnation point, which is also covered. What you'd need to do is break the surface of the body into many discrete points for which you calculate the angle with V_inf.

However, this is only applicable to 2D flow. In the same way that Cl and Cd can be predicted for an airfoil, but are affected by the #D geometry of the wing, the same would hold true here. You could predict the lift and drag coefficients for any cross section of the body using this technique, but coming up with a total life and drag profile for the body is a bit more complicated.

Keep em' Flying
//Fight Corrosion!

### RE: How to Approximate Aerodynamic Coefficients

Dikusa... distantly-related to Your question... for 'fun'...

Regards, Wil Taylor
o Trust - But Verify!
o For those who believe, no proof is required; for those who cannot believe, no proof is possible. [variation, Stuart Chase]
o Unfortunately, in science what You 'believe' is irrelevant. ["Orion", HBA forum]
o Only fools and charlatans know everything and understand everything." -Anton Chekhov

### RE: How to Approximate Aerodynamic Coefficients

WKTaylor - amazing reading in the NASA publication in your link! Science, and discovery, and engineering all rolled up with determination and ingenuity- amazing!

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