Roller Chain Length in Pitches (ANSI B29.1)
The even-link round-up and corrected center distance people skip: L = 2(C/p) + (N1+N2)/2 + ((N2-N1)/(2 pi))^2/(C/p) pitches. The count must come out EVEN -- an odd count forces a weaker offset (half) link -- so it is rounded UP, and then the center distance is recomputed so the chain fits with proper sag. A 17-to-51-tooth #40 drive (0.5 in pitch) at a 30 in center is 154.49 pitches -> 156 to order, with a corrected 30.38 in center (0.38 in of take-up the skipped step misses); pull the center to 20 in and it is 114.73 -> 116 pitches, 20.32 in corrected. Keep the center at least ~30 pitches for wrap. A design aid; the sprocket selection and take-up govern.
Formula and source
Cp = C/p; L = 2 Cp + (N1 + N2)/2 + ((N2 - N1)/(2 pi))^2 / Cp; round L up to an even L_even; A = L_even - (N1 + N2)/2; C_corr = (p/4)[A + sqrt(A^2 - 8((N2 - N1)/(2 pi))^2)].
The ANSI B29.1 roller-chain and sprocket chain-length relation, with the even-pitch round-up and corrected center distance, by name; the sprocket selection and take-up govern.
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