where Hs and Hf are the specific heat and heat of fusion of lunar regolith,respectively, Tm is the melting point of lunar basalt, TL is the mean daylight temperature of the lunar surface under direct sunlight at the LMF site, and p is the mean density of lunar basalt.
Assuming that heating time is long compared to melting time so that the latter may be neglected, the mean radiative power loss through the exposed face of the slab is given by:
- Pr~(ELax2&integral;0tT4dt')/t
where EL is the emissivity of lunar regolith, a is the Stephan-Boltzmann constant, and T is temperature at elapsed time t'. If heat is applied such that temperature rises at a linear rate, then:
- Pr~(1/5)ELax2(Tm-TL)4
- Pc~(1/2)(Tm+TL)Cx2/d
where C is thermal conductivity of lunar soil and d is the depth at which regolith temperature returns approximately to TL.
Taking the parameters listed in table 5.10 as typical, then for a team of five paving robots each capable of processing two slabs at once:
- t = 10r(x + s)2/πR2 = 30,600 sec
and
- P = 20,530 W
| R = 60 m | Tm y= 0.03 m |
| r = 1 yr = 3.14×107 sec | Tm = 1573 K |
| x = 1 m | TL = 503 K |
| s = 0.05 m | p = 2700 kg/m3 (for melt) |
| Hs= 840 J/kg | Hf=4×105 J/kg |
| EL = 0.80 (typical for silica brick and fire brick) | a = 5.67×10-8 W/m2-K4 |
| C = 1 W/m K | |
| d ~ 0.2 m |
5C.3 Paving Robot Design
For the given platform layout there are many possible different modes of operation for paving robots. For instance, each robot might scoop out a hole of the appropriate dimensions, "ingest" the soil and melt it in an internal furnace, then drain the basalt magma back into the hole, neatly filling the depression. Alternative heating techniques may be readily imagined - resistance heating, controlled oxyhydrogen combustion torch with hydrogen recovery, are furnaces (molten basalt is surprisingly electrically conductive), or induction/dielectric heating using vertical-parallel plates, finger electrodes or "stray field heating" (Cable, 1954; Curtis, 1950; Davies and Simpson, 1979). However. from a pragmatic standpoint, direct solar energy is preferred both for practical convenience and to reduce total external demand on the main LMF power grid.
