I need to build a drag model for my rocket optimization program and I stumbled upon by the following formula:

$CD = CD_c(M)$, $K_n < K_{nc}$,

$CD = CD_{fm}$, $K_n > K_{nf}$,

$CD = CD_c +(CD_{fm} − CD_c) \cdot (\frac{\log_{10}(AK_n)}{3}+B)$, $K_{nc} < K_n < K_{nf}$

Where $K_{nc}$ is knudsen continuum limit and $K_{nf}$ is the knudsen free-molecular limit.

Now, the author states that "The constants, (A,B), of the logarithmic interpolation in the transition regime (called the bridging relation), as well as the limiting Knudsen numbers, (Knc,Knf ), depend exclusively upon the vehicle’s geometry, and are selected in order to have a smooth transition between the continuum and the free-molecular flow regimes."

Since I need to change my rocket design in every iteration, I would need to know the relation between design and the Knudsen limits, as well as discovering the constants A and B.

Anyone knows how to discover the constants or has a better drag model that I could apply?

Note: It's for zero - lift.

The book is Advanced Control of Aircraft, Spacecraft and Rockets (Ashish Tewari, 2011) pp. 267 - 268

  • $\begingroup$ @peterh I know LaTex, didn't even knew it was supported on the website. But thanks for the edit. $\endgroup$ – Fábio Morgado Mar 13 '18 at 16:58
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    $\begingroup$ What do you know so far about the drag coefficients for your rocket? When the aero drag is big enough to have a significant effect on your vehicle, the Knudsen number is low (that's kind of what it means) and when it's in the high Knudsen number regime the aero drag is pretty negligible unless you have a really weird configuration. For a first approximation you need to get a good handle on your drag coefficients in the sensible atmosphere and don't worry about aero drag in the exosphere. $\endgroup$ – Organic Marble Mar 13 '18 at 19:18

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