There is tons of info out there on the ARCAS, some references to the propellant, but I haven't been able to find anything even resembling a formula.
The propellant used in ARCAS was Arcite-373D. This is about 80% solids, highly aluminized (21%) propellant. Binder system is not HTPB based, but is actually PVC plastisol. PVC plastisol is a mixture of PVC and plasticizer (dioctyl adipate or dibutyl sebacate). This is not a chemical reaction as PVC is already polimerized. When the propellant is heated to curing temperature the PVC disolves in plasticizer and when cooled solidifies in a flexible plastic material.
ARCAS motor used a steel casing 0,04 inches thick, made from 4130 alloy steel. Thermal insulation was 0,15 inches thick, made from molded asbestos/phenolic. Propellant grain had 19 longitudinal silver wires arranged like this:
- 1 wire in the center of the grain
- 6 wires evenly spaced on 1,60˝dia
- 6 wires evenly spaced on 2,77˝dia
- 6 wires evenly spaced on 3,20˝dia
Aft end of the grain also had a six slots 2,38˝deep arranged in a star patern, to increase the thrust at the beggining. Average chamber pressure was about 1000psi (depending on ambient temperature).
The purpose of the wires in the grain is that the wire (silver is very good heat conductor) preheats the propellant in front of the flame zone. Propellant that is hot burns much faster than cold propellant. Therefore you can get about 4-5 times increase in burn rate. Because the propellant next to the wire burns faster than the propellant in the surounding a conical burning pattern forms around the wire, increasing the burning surface.