# How do I calculate the drag on a structure like a rocket heat shield?

The equation I have learnt in high school goes,

$$F=k \times density \times velocity$$

Although I suspect there should be some realtion to the shape of the body. So how does the factor $k$ change with the shape of the vehicle. And how universal is this formula? Is it applicable everywhere? Or do you have to resort to some finite element method for accurate analysis ?

• You should checkout the NASA pages on drag (search 'drag equation' and The Drag Equation - NASA should be in your top results). It has some really nice pictures that explain the various aspects of the question. – scrappedcola Dec 23 '16 at 15:02
• The formula you "remember" is not applicable to anything. It is quite universal, however, in that it is universally wrong. – Pirx Dec 23 '16 at 15:11
• @Pirx there is really no need to be condescending. Yea his understanding of the drag equation is wrong, but all you needed to say was that equation was incorrect or point them to a reference to help straighten them out. It's possible that the school in question is "teaching" the equation wrong. But to be sarcastic about it being wrong and then to make a disparaging comment on the answer below about how he Op won't understand it is wrong. – scrappedcola Dec 23 '16 at 17:50
• @scrappedcola: There was absolutely nothing condescending about my answer above or the one below. Given the level of understanding apparent in the original question it is entirely clear that the OP will not understand the answer s/he is given. I notice that there is nothing disparaging about the statement of this fact. Nobody is competent in every field of science, and there are plenty of people with no deep competence in any field of science. There is no shame in this. I would have no problem with someone pointing out that I know next to nothing about organic chemistry, say, either. – Pirx Dec 23 '16 at 18:05

At the conceptual stage of design, a pencil and paper (usually integrated into a simple code) is used to estimate the drag coefficient on certain components of a rocket. A very common technique is to look at the body as a two-dimensional object, and compute the inviscid flowfield around this object. Depending on the Mach number you are flying, there are many different panel method techniques for doing this. With knowledge of the inviscid flowfield, you can estimate the boundary layer flow properties using the Thwaites-Walz method. This is an empirical recast of the von Kármán integral momentum equation into a more useful empirical formulation. This method only works for incompressible flows. However, engineers typically extend this method to include compressible flows by using the Eckert (1956) reference temperature method. Basically, by evaluating all the thermophysical properties of the gas at a temperature defined as $T^*$, and using this within the Thwaites-Walz method, you will obtain surprising good agreement with compressible experimental data. Oddly enough, the reference temperature method was considered nearly top secret during the WWII era and paved the way for the success of the V2 rocket nozzle. Anyways, this will provide you enough to estimate the compressible skin-friction distribution over a two-dimensional body (representation of the heat shield) to calculate (estimate) the viscous drag. Obviously there is wave drag as well, but this can easily be obtained by classical aerodynamic methods.