Jacob Samorodin said:

"since reentry from LEO involves roughly "half" the kinetic/heat energy of a lunar-return mission [assuming the LEO and lunar-return spacecraft are, roughly, the same weight].
MY QUESTION IS?... Is it a good rule-of-thumb to DOUBLE the mass of the ablative heatshield material on a LEO spacecraft [Command- Module] modified for a circumlunar mission ?"

First we'll check your first assumption. A nominal Low Earth Orbit (LEO) velocity is about 7.5 km/sec. A nominal lunar return velocity is about 11 km/sec. Kinetic energy for fixed mass scales as

1/2 * V * V

The above quantity is sometimes called "C3" or specific energy. The C3 for LEO is 28 [km/sec]^2 and for lunar return is 61 [km/sec]^2.

Your first assumption is close enough for government work.

Your second assumption was "Is it a good rule-of-thumb to DOUBLE the mass of the ablative heatshield material on a LEO spacecraft". Your intuition is good here because heat shield mass does scale with the heat DEPOSITED onto the heat shield. This deposited heat is called "total heat load". However there is an implied assumption that the vehicle's initial kinetic energy scales with the deposited heat. A properly designed thermal protection system transfers as much as possible of the original kinetic energy of entry into the atmosphere and NOT into the spacecraft's thermal protection system. Energy is transfered into the atmosphere as small scale turbulence, increased temperature of the atmospheric gas and radiation.

Energy is transferred into the vehicle's heat shield through three mechanisms:

1) Heat convected from the shock layer gas directly onto the heat shield material.
2) Chemical recombination of the decomposed shock layer gas on the heat shield surface through catalysis thus releasing chemical energy into the heat shield.
3) Radition from the shocklayer onto the surface of the heat shield.

The heat flux due to the first two mechanisms is modelled by the "Fay-Riddell equation" (deposited energy is time integrated heat flux). Fay and Riddell were two Einstein / Leonardo da Vinci class geniuses who were active in the aerospace industry back in the 1950s. The derivation of the Fay-Riddell equation was incredibly complicated but the final result is relatively easy to use (a good engineering approximation).

Calculating the heat flux due to radiation is essentially Voodoo black magic that is modelled through curve fits and table look ups. The data for the curve fits and tables comes from numerous shock tube experiments done over the last 50 years. Fortunately for entry from LEO by a modest sized spacecraft, the radiative heat flux is insignificant. It is also insignificant for small spacecraft entering the atmosphere of Mars at velocities less than 7 km/sec. However radiative heat flux dominates for lunar return entry of an Apollo CM sized spacecraft (you're screwed).

Radiative heat flux is a result of the gas being in thermodynamic nonequilibrium after passing through the bow shockwave. The atoms in the gas are kicked into a higher energy state by the shockwave and then through various quantum processes the atoms transition down to lower energy levels, spitting out photons in the process (this takes a few a microseconds to happen). The color of the photons depend upon the main excited molecule (typically a nonsymmetric diatomic molecule like NO, CO or CN). CN likes to emit in red and ultraviolet. If the Huygens atmospheric probe burns up during its entry into Titan's atmosphere, it'll probably be due to excessive CN emission. Modelling equilibrium thermodynamics is not too difficult (I've done it). Typically a Gibbs Free Energy method is used. However correctly modelling a nonequilibrium thermodynamic system is an unsolved problem (it's like modelling hypersonic turbulence). The fundamental equation is the Schroedinger equation describing a multispecies recombining gas with radiation transfer.

Getting to your punch line question:

"Is it a good rule-of-thumb to DOUBLE the mass of the ablative heatshield material on a LEO spacecraft [Command- Module] modified for a circumlunar mission ?"

No. It's much more difficult than that. The answer depends upon whether the vehicle is manned or unmanned. Whether the heat shield material is to be reusable. Whether the peak flux requires ablation. The issue of being manned or unmanned drives the peak G loading. You can't whack your astronauts with over 4 Gs if they've been in deep space for more than four months. A low decelleration means a low peak heat flux which means poor ablation and a long time in the atmosphere to soak in heat from the shock layer. A high deceleration means a sharp peak heat flux that produces nice ablation that blows the shocklayer heat back into the atmosphere and away from the vehicle. Is this comprehensible? The sort of entry required for a manned lunar return means that lots of heat will get soaked into the heat shield. The Apollo CM got hot after lunar return. An Apollo CM landing on the ground rather than in the ocean would have required the astronauts to get out of the CM quick before getting cooked by the residual heat. They probably would have burned their feet on the CM's floor when they got out of their couches. Landing in the ocean solved the heat soak problem nicely.

Gary