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T–79 SECTION 22    CENTER DISTANCE FORMULAS 22.1   Nomenclature And Basic Equations Figure 40 illustrates the notation involved. The following nomenclature is used: C = Center Distance (in) L = Belt Length (in) = p NB p = Pitch of Belt (in) NB    = Number of Teeth on belt = L/p N1 = Number of Teeth (grooves) on larger pulley N2 = Number of Teeth (grooves) on smaller pulley f = One half angle of wrap on smaller pulley (radians) q = p/2 – f = angle between straight portion of belt and line of centers (radians) R1 = Pitch Radius of larger pulley (in) = (N1) p/2p R2 = Pitch Radius of smaller pulley (in) = (N2) p/2p p = 3.14159 (ratio of circumference to diameter of circle) Figure 40    Belt Geometry The basic equation for the determination of center distance is: 2C sinf = L – (R1 + R2) – (p – 2f) (R1 – R2)     (22-1) where C cosf = R1 – R2    (22-2) These  equations  can  be  combined  in  different  ways  to  yield  various  equations  for  the determination of center distance.  We have found the formulations, which follow, useful. 22.2   Exact Center Distance Determination – Unequal Pulleys The exact equation is as follows: C = (1/2)p [(NB – N1) + k(N1 – N2)]     (22-3)      1            p       f where   k = (––) [tan(–– – ––) + ]     (22-4)     p     4       2 and f is determined from:   1      (NB – N1) (––) (tanf f) =  –––––––––– = Q (say)     (22-5)   p      (N1 – N2)