trial and error? Math?
In: 14
Well, they knew the speed the Apollo capsule would be traveling when it hit the atmosphere. They were able to approximate what temp the heat shield would have to withstand from the experimental data they had from the Mercury and Gemini missions and some non-linear gas laws. It was pretty obvious that too steep a descent would overload any heat shield that would be light enough to make the lunar journey. (They already had a rough mass budget for various phases of the mission.)
At that point it was doing a rough approximation on different angles and paths and seeing what didn’t work at all. Someone came up with the genius idea of having the capsule use its lofting ability to climb a little and let the heat shield radiate some heat then resume the descent. Once they had the general idea they did a bunch of more detailed calculations to make sure that the heat shield could handle it, that the astronauts could handle the g forces and that the descent wouldn’t take too long so they ran out of battery power or air.
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