An engineer, however, is rarely called upon to solve the question from this stand-point, which properly belongs to the draughtsman or engine designer.
If the amount of valve travel is given, however, all the other elements may readily be found by the following construction:
Fig. 3311.
Suppose that in [Fig. 3311] a D valve is to be designed to cut off the steam when the piston has travelled from position b′ to r′, or at three-quarters of its stroke. Then to find the position the crank pin will be in when the cut off occurs, we draw a circle, b d, representing the path of the crank on the same scale that the length of the piston stroke is represented. The straight line from b to d will, therefore, represent the piston stroke without drawing the piston or cylinder at all (this being done in the figure to make the explanation clear). When the crank is on its dead centre, b, the piston, will be at b′, and the valve in the position shown (supposing it to have no lead). As soon as the crank and valves begin to move, the steam will enter steam port a, and to find where the crank will be when the piston is at three-quarters stroke, and is, therefore, in position r′, we mark a point at r three-quarters of the distance from b to d. Then, taking no account of the length of the connecting rod, we draw a vertical line y from r to the circle, and this line gives at h the position the crank will be in when the piston is at r. We have so far, therefore, that while the piston travels from b′ to r′, the crank will travel from b to h. Now, it will be found that if we set a pair of compasses from b to f, which is half-way from b to h, and then rest the compasses at d, and mark an arc v, then a line from v to the centre of the crank will give us the proper position of the eccentric. As the centre of the crank pin and also the centre of the eccentric both travel in a circle, we may, therefore, take a circle having a diameter equal to twice the throw of the eccentric, (or, what is the same thing, equal to the full travel of the valve), and let it represent the paths of both the eccentric centre and the crank pin centre, the latter being drawn to a scale that is found by dividing the length of the piston stroke by the travel of the valve; thus, if the travel is 3 inches and the stroke 30 inches, the diameter of a 3 inch circle will represent the valve travel full size, and the piston stroke one-tenth full size, because 30 ÷ 3 = 10. It has been shown on page 376 that the length of the connecting rod affects the motion of the piston by distorting it, and it is necessary to take this into account in constructing the actual diagram, which may be done as follows:
Fig. 3312.
The valve travel and point of cut off being given, to find the required amount of lap, there being no lead, draw a circle equal in diameter to the travel of the valve, and draw the line of centres b d, [Fig. 3312]; mark on the line of centres a point r, representing the position the piston is to be in at the time the cut off is to take place.