Mathematically, what is the argument in favor of skipping reentries?

Question

As a tangent while looking for numbers for the L/D ratio impact on entry profile, I came upon this site which seemed to favor skipping reentries in almost all cases. Reading further, I realized that it's not dictated by fundamental physics and is intentionally designed in the trajectory planning.

The Wikipedia page gave the following reason for using skips:

to achieve greater entry range or to slow the spacecraft before final entry, which helps to dissipate the huge amount of heat that is usually generated on faster descents

This doesn't make sense to me, because by dipping further into the atmosphere (to generate more heat, in order to get upward velocity), the vehicle would generate more heat, which means that the time spent outside of the atmosphere would merely be compensating for that heat generation. It's not obviously better on-balance. In the long run, you still have to generate the same time-integrated amount of drag...

Can someone give a complete argument as to how skipping reduces the thermal load on the craft?

Answer 1

The two systems that I know of that were qualified for skip entry, Apollo and Shuttle, did so purely for cross-range capability. The skip entry would have been used for an emergency return that could not wait for a more favorable alignment with respect to the landing/splashing site. The purpose of qualifying those vehicles for skip entry was not related to heating. (As it happens, neither vehicle ever made use of the skip entry capability.)

A skip entry will reduce peak heating due to the shallower entry, at least on the first entry. The lower entry velocity of the second entry would also permit a shallower entry flight path angle than for a single entry that does not skip out. The double entry may result in increased heat load (the integral of the heat rate). On the other hand, it can also provide a short period of heat dissipation in space to cool the heatshield before the next entry, reducing the consequences of the total heat load across the two entries.

As an extreme example, aero-braking orbiters at Mars and Venus use many "skip entries" at very high altitude to reduce apoapsis with very low heat rates and complete dissipation of the heat load between skips.

I do not understand "by dipping further into the atmosphere (to generate more heat, in order to get upward velocity)". A skip entry dips less into the atmosphere, not more. You don't need "upward velocity". The curve of the trajectory still goes down. It just curves less than the curvature of the planet, so it exits the atmosphere.

The drag goes with the square of velocity, whereas the heating goes more like the cube of the velocity. (It is more complicated than just the cube, but thinking of it as the cube suffices for this discussion.) As a result the total heat load depends on the profile of the velocity, and is not directly related to the total integrated drag.

Answer 2

It seems to work for me. Let’s say you have X number of BTUs you have to generate to get a spacecraft to the surface. Let’s say a direct reentry is 6 minutes to terminal velocity. So that’s X BTUs in 6 minutes. But if you skipped several times you might be creating X BTUs in 20 or 30 total minutes. Also there is the fact that you would be skimming higher up and creating lower temperatures. Plus there is the radiating off heat between skips. By the time you couldn’t skip anymore and had to go down, your velocity would be a lot less. I see a lot of advantages there. Is there a flaw in that logic somewhere?