To find the chord pitch of a wheel take 180 (= half the degrees in a circle) and divide it by the number of teeth in the wheel. In a table of natural sines find the sine for the number so found, which multiply by 2, and then by the radius of the wheel in inches.
Example.--What is the chord pitch of a wheel having 12 teeth and a diameter (at pitch circle) of 8 inches? Here 180 ÷ 12 = 15; (sine of 15 is .25881). Then .25881 × 2 = .51762 × 4 (= radius of wheel) = 2.07048 inches = chord pitch.
+--------+--------++--------+--------++--------+--------+ |Degrees.| Sine. ||Degrees.| Sine. ||Degrees.| Sine. | +--------+--------++--------+--------++--------+--------+ | 1 | .01745 || 16 | .27563 || 31 | .51503 | | 2 | .03489 || 17 | .29237 || 32 | .52991 | | 3 | .05233 || 18 | .30901 || 33 | .54463 | | 4 | .06975 || 19 | .32556 || 34 | .55919 | | 5 | .08715 || 20 | .34202 || 35 | .57357 | | 6 | .10452 || 21 | .35836 || 36 | .58778 | | 7 | .12186 || 22 | .37460 || 37 | .60181 | | 8 | .13917 || 23 | .39073 || 38 | .61566 | | 9 | .15643 || 24 | .40673 || 39 | .62932 | | 10 | .17364 || 25 | .42261 || 40 | .64278 | | 11 | .19080 || 26 | .43837 || 41 | .65605 | | 12 | .20791 || 27 | .45399 || 42 | .66913 | | 13 | .22495 || 28 | .46947 || 43 | .68199 | | 14 | .24192 || 29 | .48480 || 44 | .69465 | | 15 | .25881 || 30 | .50000 || 45 | .70710 | +--------+--------++--------+--------++--------+--------+
The principle upon which diametral pitch is based is as follows:--
The diameter of the wheel at the pitch circle is supposed to be divided into as many equal parts or divisions as there are teeth in the wheel, and the length of one of these parts is the diametral pitch. The relationship which the diametral bears to the arc pitch is the same as the diameter to the circumference, hence a diametral pitch which measures 1 inch will accord with an arc pitch of 3.1416; and it becomes evident that, for all arc pitches of less than 3.1416 inches, the corresponding diametral pitch must be expressed in fractions of an inch, as 1/2, 1/3, 1/4, and so on, increasing the denominator until the fraction becomes so small that an arc with which it accords is too fine to be of practical service. The numerators of these fractions being 1, in each case, they are in practice discarded, the denominators only being used, so that, instead of saying diametral pitches of 1/2, 1/3, or 1/4, we say diametral pitches of 2, 3, or 4, meaning that there are 2, 3, or 4 teeth on the wheel for every inch in the diameter of the pitch circle.