This section is from the book "The English And American Mechanic", by B. Frank Van Cleve. Also available from Amazon: The English And American Mechanic.
To Compute how much Lap must be given on the Steam Side of a Slide.Valve to rut off the Steam at any given Part of the Stroke of the Piston.
From the length of stroke of piston subtract the length of the stroke that is to be made before the steam is cut off; divide the remainder by the stroke of the piston, and extract the square root of the quotient. Multiply this root by half the throw of the valve, from the product subtract half the lead, and the remainder will give the lap required.
Having stroke of piston 60 inches, stroke of valve 16 inches, lap upon exhaust side ½ inch = 1/32 of valve stroke, lap upon steam side 3 ¼ inches, lend 2 inches, steam to be cut off at | the stroke ; what is the lap ?
60 - 5/6 of 60 = 10. 10-16 = .166. .166 = 408. .408 x 16/2 = 3.264,
2 and 3.264 - 2/2 = 2.264 inches or the lap - half the lead.
To Compute the Lap required on the Steam Side of a Valve, to cut the Steam off at various Portions of the Stroke of the Piston.
 
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