Belt speed, load, incline and friction against power and slip.
-Material on the belt (kg/m)
-Effective tension T_e (kN)
-Slack tension needed (kN)
-Tight-side tension (kN)
-Motor power (kW)
-Energy per tonne (kWh/t)
-Froude number v^2/(gR)
-Discharge
-Drive pulley
The science
The motor must supply the effective tension T_e = f g L cos(a) (q + q_b + q_r) + g q L sin(a): rolling resistance of the idlers and belt flexing (factor f), plus lifting the material up the incline. Here q = Q / (3.6 v) is the material mass per metre (Q in tonnes per hour), q_b the belt and q_r the idler rotating mass per metre. The motor power is P = T_e v / eta.
The drive pulley moves the belt through friction on its wrapped arc, described by the capstan (Euler-Eytelwein) equation T1 / T2 <= e^(mu theta) with T1 = T2 + T_e. A smaller wrap angle or lagging friction forces a higher slack-side tension from the take-up; if the take-up is set below T_e / (e^(mu theta) - 1) the belt slips.
At the head pulley a lump follows the belt only if gravity can supply the centripetal force; the Froude number v^2 / (g R) above about 1 means it is thrown off along a projectile path, x = v t cos(a), y = v t sin(a) - g t^2 / 2.
Honest simplifications: the 95 percent drive efficiency and constant resistance factor are typical values; secondary resistances (skirts, ploughs, belt-bending detail), sag between idlers, belt stretch dynamics and start-up transients are ignored.