Using the Bilgram diagram to calculate the dimensions for the valve of the working cylinder

Fig. 1: Determining the angle C-O-D for a given length of piston travel at cutoff.O-E: Radius of Eccentric CircleE-F: Outside LapE-Z: Inside LapL: Linear Advancea-a: Angular Advance

Many of we hobbyists and buffs like to design a steam engine from the ground up, and one of the principle jobs here is to design the valve for the working cylinder.

There are two approaches to this problem: the cut-and-try method which is best accomplished by constructing a wood or tin working model to some convenient scale of measurements, and then there is the engineering method which follows after a long period of systematic scientific pursuit that usually involves much empirical data and calculation.

This article is concerned with the latter method which is considered to be much more positive and is actually based on the results of much study by the profession over the past 125 years. This leads to direct results through utilization of a limiting drawing-board mockup based upon use of the Bilgram diagram which was most widely used by design engineers during the period when Steam grew from Boyhood to King. Some few engineers worked with a somewhat similar Zeuner diagram; however since this is one of a cut-and-try method, it should likely be consigned to the simple mechanical cut-and-try method mentioned above.

After having decided upon the bore and stroke of our engine for a desired power output and engine size, the very next problem is that of determining the dimensions of the cylinder ports. While steam at, say 150 psi may have an open jet velocity in excess of 3,000 feet per second, this velocity is reduced by the friction and bending of the ports in an ordinary slide valve engine to a value accepted from empirical tables as that near 8,000 feet per minute; and this is further reduced during the opening and closing portions of valve travel to an average value of 6,000 feet per minute.

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Now, if we have selected a cylinder size and number of revolutions of crankshaft speed per minute, we can readily calculate the total amount of steam to be passed per minute and consequently the port area of the valve. We must also take into consideration the maximum point of cutoff for our engine, of course, since there will be no steam admitted after this point in each stroke.

So suppose we have selected a 4-inch bore by 5-inch stroke, with maximum cutoff at 3/4 stroke, and speed of 250 rpm. A bit of simple arithmetic reveals that the total amount of steam to and from each end of the cylinder per minute figures out to be: 4 × 4 × 0.7854 × 3/4 × 5 × 250 which, by slide rule, equals about 23,600 cubic inches.

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