Belt Transmissions  Speed and Length of Belts
Calculate length and speed of belt and belt gearing.
Belts (or chains) are used to transfer power (or convert torque) through rotational motion from one shaft to an other. Belt driven fans are common in heating, ventilation, airconditioning and cooling (HVAC) systems. Chain are common in many transmission systems like bicycles and other.
 friction belts  transfer the power through friction between the pulley and the belt
 synchronous belts  transfer the power through a mechanical linkage between the teeth in the belt and the grooves in the pulley
Belt Length
The length of the belt can be calculated as
l_{b} = (d_{m} π / 2) + (d_{f} π / 2) + (2 l_{fm}) + ((d_{f}  d_{m})^{2}/ (4 l_{fm})) (1)
where
l_{b} = length of belt (mm, inches)
d_{f} = pulley (sheave) diameter fan (mm, inches)
d_{m} = pulley (sheave) diameter motor (mm, inches)
π = 3.14..
l_{fm} = center to center distance of fan and motor pulleys (mm, inches)
Belt Velocity
The velocity at which a belt travels may be expressed as
v = π d_{m} n_{m} / 12 (2)
where
v = velocity of belt (ft/min)
n_{m} = revolutions motor (rpm)
 or alternatively in metric units:
v_{b} = π d_{m} n_{m} / 60 (2b)
where
v_{b} = velocity of belt (m/s)
d_{mb} = diameter motor pulley (m)
Pitch Diameter of Pulley (in)  Velocity (ft/min)  

Revolutions Pulley  n (rpm)  
850  1050  1075  1140  1550  1725  3450  
1  223  275  281  298  406  452  903 
2  445  550  563  597  812  903  1806 
3  668  825  844  895  1217  1355  2710 
4  890  1100  1126  1194  1623  1806  3613 
5  1113  1374  1407  1492  2029  2258  4516 
6  1335  1649  1689  1791  2435  2710  5419 
7  1558  1924  1970  2089  2841  3161  6322 
8  1780  2199  2251  2388  3246  3613  7226 
9  2003  2474  2533  2686  3652  4064  8129 
10  2225  2749  2814  2985  4058  4516  9032 
Belt Gearing
The relationship between the rotational speed of the motor and the fan and the disc diameter can be expressed as
d_{f} n_{f} = d_{m} n_{m } (3)
or
n_{f} = n_{m }d_{m} / d_{f}
Belt Gearing Calculator
Horsepower
If belt tension and belt velocity are known  horsepower transferred can be calculated as
P_{hp} = F_{b} v_{b} / 33000 (4)
where
P_{hp} = power (hp)
F_{b} = belt tension (lb_{f})
v_{b} = velocity of belt (ft/min)
If torque and revolution per minute are known  horsepower transferred can be calculated as
P_{hp} = T n / 5252 (4)
where
P_{hp} = power (hp)
T = torque (ft lb_{f})
n = revolutions per minute (rpm)
Speed Ratio
Speed ratio can be calculated as
SR = n_{f} / n_{s} (5)
where
SR = speed ratio
n_{f} = revolutions per minute  fastest machine
n_{s} = revolutions per minute  slowest machine
Related Topics

Mechanics
The relationships between forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more. 
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Design of systems for ventilation and air handling  air change rates, ducts and pressure drops, charts and diagrams and more.
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