I saw the question Could escape velocity be achieved in the atmosphere? and thought it probably could've been asked better.
I'm sure there's an equation to calculate the average heat generated by an object traveling in the atmosphere. More specifically, I am asking for an equation simplified based on the following variables:
- Speed of Object
- Height of Atmosphere (or density of atmosphere)
Which results in:
- Heat/Energy Applied to Object
Taking this even further I would like my rocket to be made out of something which has a melting point of 1,650 °C (3,000 °F) (atmospheric re-entry for the average space shuttle mission).
Can anyone provide me a graph for how fast I am able to go at altitude $X$ without melting?
You may make any assumptions you would like, I do not mind an ideal world here. I would love to see this done with equations if possible.