Page:Advanced Automation for Space Missions.djvu/277



5C.2 Power Requirements for Paving Robots

To obtain a baseline design for LMF paving robots a rough estimate of the power required to fuse the basalt slabs required (in a reasonable amount of time) must be made. For this crude model, basalt platform slabs were taken as square plates with horizontal dimension x and vertical dimension y, with a sintering margin of width s (2s between slabs). A platform of radius R must be constructed within a time r, so a total of πR2/(x + s)2 slabs must be produced in 7 sec, a rate of t-1 = πR2/r(x + s)2 slab/sec.

The total input power to each square meter of lunar regolith for slab production is given by:


 * P = Ph + Pm + Pr</SUB> + P<SUB>c</SUB>

where P is total power required, P<SUB>h</SUB> is the power needed to heat the basalt material to its melting point, P<SUB>m</SUB> is the power necessary to melt the slab at the melting point, P<SUB>r</SUB> is the rate at which energy is lost due to radiation from the top surface of the slab, and P<SUB>c</SUB> is the rate of energy loss by conduction into the lunar subsurface (modified from Davies and Simpson, 1979). Radiation losses through the thin slab side walls are ignored.

To a first approximation it is sufficient to simply calculate the total energy which must be supplied and divide this by the length of time spent on each slab, hence:


 * P<SUB>h</SUB> = H<SUB>s</SUB>(T<SUB>m</SUB> - T<SUB>L</SUB>)x<SUP>2</SUP>yp/t


 * P<SUB>m</SUB> = H<SUB>f</SUB>x<SUP>2</SUP>yp/t