I used my Back-of-the-Envelope (BOE) Entry Analysis to model an Apollo command module capsule returning from the moon. Historically, this was a very shallow entry angle below local horizontal, and essentially at Earth escape speed. I used the very best estimates I could find for the Apollo capsule ballistic coefficient (313.5 kg/sq.m) and heat shield radius of curvature (4.59 m). Historically, we also know that Apollo returning from the moon peaked at about 11 gees deceleration during entry.
The BOE model is described in reference 1, and again in the more detailed user’s guide (reference 2). The original Earth entry workbook in the spreadsheet model was set up as a generic example. I modified this to reflect Apollo data, and tweaked the entry angle from the original 1 degree, up to 2 degrees, at which point peak gees matched the historical value. (At 1 degree, peak gees was closer to 5.5, and the heating numbers were a little smaller.)
All the other spreadsheet results are then presented here, for others to compare with actual Apollo entry results, at their leisure. I think that at least the dynamics look pretty close, especially considering just how over-simplified this model really is. As I have always said, the heating model leaves a lot to be desired.
Figures 1-4 present the trajectory profiles of relevant data, annotated to show the Mach 3 point at which model applicability ends. Figure 5 is an excerpted spreadsheet image of the inputs. Figure 6 is a set of excerpts from the entry analysis portion of the spreadsheet showing the relevant calculated values. All figures are below, at the end of this article.
1.“Back-of-the-Envelope Entry Model”, 7-14-12, posted at “http://exrocketman.blogspot.com”
2.“BOE Entry Model User’s Guide”, 1-21-13, posted at “http://exrocketman.blogspot.com”