Size an open belt or chain drive from pulley diameters and center distance — belt length, wrap angle, belt speed, shaft tensions, and the number of belts needed, all checked against a service factor and drawn to scale.
From the belt maker's HP tables for your section & small-sheave diameter. Used to compute belt count.
120° typical for V-belts, 90° for chain, 165° for flat.
Drawn to scale. Belt shown in brass, pulleys in steel; wrap arc on the small pulley is highlighted.
Geometry. Belt length L = 2C + 1.57(D+d) + (D−d)²/4C (open drive). Wrap angle on the small pulley θ = 180° − 2·asin[(D−d)/2C]. Speed ratio SR = D/d.
Belt speed. v = π·d·n / 60000 (m/s, d in mm, n = driver rpm). V-belts are generally kept under 30 m/s; above that centrifugal tension erodes capacity.
Tensions. Effective pull Fe = P_design / v. Tension ratio from the capstan equation — flat: T₁/T₂ = e^(μθ); V-belt uses the effective wedge friction e^(μθ/sinβ), which is why V-belts grip far harder. Shaft (bearing) load ≈ T₁+T₂.
Belt count. N = P_design / (P_perBelt · K_θ · K_L), rounded up. Here the arc-of-contact factor K_θ is applied from the wrap angle; the length factor K_L is left at 1 (enter a length-corrected per-belt rating if you want it folded in).
Timing belts and chains don't slip, so their tension check is about tooth/roller load and allowable working tension rather than the capstan ratio — treat the T₁/T₂ figure as indicative only for those families.