This section is from the book "The Tinman's Manual And Builder's And Mechanic's Handbook", by Isaac Ridler Butt. Also available from Amazon: The Tinman's Manual And Builder's And Mechanic's Handbook.
To find size of Teeth necessary to transmit a given Horse Power.
Horse power X 240/ Diameter of wheel . ft. X Revs. per min. = Strength of tooth.
√Strength/Breadth, ins. = Pitch, ins. Strength / (Pitch, ins.)2 = Breadth, ins.
The above rule will be found very suitable for a speed of circumference of about 240 feet per minute. For speeds above, add to 240 half the difference, for speeds below, deduct half the difference, between 240 and the actual speed, the result being a suitable multiplier.
For instance; at 800 ft. per minute, 60 being the difference] 240 + 30 = 270 multiplier.
At 160 ft. per minute, 80 being the difference, 240 - 40 = 200 multiplier.
The reason being, that with higher speeds, the friction, wear, and liability to shocks is increased, at lower speeds decreased, and the teeth may advantageously be proportioned accordingly.
To find the Horse Power that any Wheel will transmit. (Pitch, ins.)2 X Breadth, ins. X Diameter ft. X Revs, per minute / Appropriate No. according to speed, as above.
= Horse Power.
To find the multiplying number for any Wheel. (Pitch, ins.)2 X Breadth, ins. X Diameter ft. X Revs, per minute / Horse Power
= Multiplying No. as above.
To find the size of Teeth to carry a given load in lbs.
Load, lbs. - 1120 = Breaking strength of teeth.
Load, lbs. ÷ 280 = Strength for very low speeds, and for steady work; being 4 times the breaking strength.
Load, lbs. ÷ 140 = Strength for ordinary purposes of machinery; being 8 times the breaking strength.
Load, lbs. ÷ 100 = Strength for high speeds, and irregular work; or when the teeth are exposed to shocks.
Strength / (Pitch, ins.)2 = Breadth, ins. √Strength /Breadth, ins. = Pitch, ins.