Band Brake / Capstan Torque

ScopeThe tight-side tension grows exponentially from the applied slack tension with the friction mu and wrap angle theta, and the braking torque is T = (T1 - T2) r. A 50 lbf pull, 270-degree wrap, mu 0.3 on a 6 in drum gives a 4.1 tension ratio, 206 lbf tight side, and 933 in-lbf (78 ft-lbf) of braking torque - wrap another 90 degrees to a full turn and the ratio jumps to 6.6. Same physics as a rope around a bollard or a capstan (a couple of turns hold a boat). Enter the band width (and thickness) for the peak lining pressure T1/(b r) and the band stress; the lever geometry, self-energizing sign, and heat of braking are separate. A design aid; Shigley and the brake maker govern.

Formula or tabletheta in radians; T1 = T2 e^(mu theta); tension ratio = e^(mu theta); T_brake = (T1 - T2) r.

Source and editionThe Eytelwein / capstan belt-friction relation T1 = T2 e^(mu theta) and the band-brake torque T = (T1 - T2) r (Shigley, Mechanical Engineering Design, Ch. 16; capstan equation), by name.

Free accessThe capstan/Eytelwein relation and the band-brake torque are standard published mechanics results; the tensions, wrap angle, friction, and drum radius are the user's inputs.

What governsEstimate. AHJ and licensed professional govern.

API field namesslack_tension_lbf, wrap_angle_deg, friction_coefficient, drum_radius_in, tension_ratio, tight_tension_lbf, brake_torque_in_lbf

• Eytelwein T1 = T2 e^(mu theta), theta the wrap angle in radianscapstan equation
• Brake torque T = (T1 - T2) r on the drumShigley Ch. 16
• Scope tension ratio, torque, and (with the band width and thickness) peak lining pressure and band stress; lever geometry, self-energizing, and heat are separatescope of this tile