Design and Layout of a Valve Gear

The North American Live Steamer, January 1956

H.J. Coventry

Design and Layout of a Valve Gear

From time to time there has appeared references to valve gears or parts, but no complete or logical method of deriving proper proportions. it is hoped that the following notes will be of use, particularly to anyone building free lance or without proper original drawings. As the Walschaert, invented by a Belgian engineer of that name in 1844, is popular among model locomotive men, this gear will be taken. it will be assumed that certain engine dimensions have already been decided upon, namely:


 * Cylinder bore
 * Stroke
 * Distance between cylinder center line and valve spindle center line
 * disposition of wheels

All other features will be decided by design, but first a few definitions relating to valves.

The lap of a valve is the amount by which the edge of the valve overlaps the port, covering the port entirely, when the valve is at the middle of its stroke or travel. Lead is the amount by which the valve opens the port when the piston is on either end of its stroke, or dead center'.

Now most locomotives are designed on a basis of diameter speed, that is a speed in miles per hour equal numerically to diameter of the '''driver wheel in inches'''. For example, an engine with 80 inch drivers would be calculated for 80 miles per hour. The same can easily apply to models, an engine with 3-5/16 inch drivers would run at 3-5/16 M.P.H. This also has another advantage in that any wheel whatever, running at 336 revolutions per minute will travel as many miles in an hour as its diameter in inches. Here is proof: Diameter of wheel in inches (D) multiplied by 3.1416 (PI), divided by 12 to bring to feet, multiplied by R.P.M. per hour, will equal Diameter times 5,280 feet per mile or equation:

D * PI (inch/round) * 336(rounds/minute) * 60(minutes/hour) --- = D(miles/hour) * 5280(feet/mile) 12(inch/foot)

D(miles/hour) * 5280(feet/mile) * 12(inch/foot) 336(rounds/minute) = --- D * PI (inch/round) * 60(minutes/hour)

Now for the port opening, first find the piston speed, which will be given by:

336(rounds/minute) * (2 * Stroke)(inch/round) ---           12 (inch/foot)

For example, a cylinder with 1-1/8 inch bore by 1-3/4 inch stroke, substituting these values will give 98 foot-

336(rounds/minute) * 2 * 1.75(inch/round) - = 98 (feet/minute) 12 (inch/foot)

Volume swept by the piston per minute will be 98 multiplied by the area of the piston in square feet. So for our example, it will be:

Cylinder Bore = 1-1/8(inch) = 1.125(inch)

Cylinder Bore Area = PI * r^2 = 3.1416 * (1.125(inch) / 2)^2 = 0.994(inch^2)

98 (feet/minute) * 0.994(inch^2) = .676 (cubic feet per minute) 144 (inch^2/foot^2)

Now obviously the steam must follow up the piston and pass through the port of such area as will provide a definite steam speed or velocity. Full size engines having piston speeds of between 1200 and 2000 feet per minute, may use steam velocities of 4000 to 12000 feet per minute, but as model piston speed is so low, to use these high steam velocities would produce unduly small ports. We will take 2000 feet per minute and find the area of port required:

2000(feet/minute) * area of port(feet^2) = 0.676(feet^3/minute)

0.676(feet^3/minute) area of port(feet^2) = - = 0.000337(feet^2) 2000(feet/minute)

Converting to inches:

0.000337(feet^2) * 144(inch^2/feet^2) = 0.0487(inch^2)

A port 0.100 inch wide and 0.487 inches long will satisfy the conditions. For practical purposes we will use a port 0.100 inches by 0.500 inches and the steam passage four 1/8 inch holes drilled (area of one 1/8 inch hole equals 0.0123 square inches).

Having the port width settled, the next job is to provide the lap to the valve to provide a certain "cut off" in full gear, or in other words maximum travel of the valve.



The standard "cut off" for most American locomotives ranges from 85 per cent to 87 per cent for fast passenger, 87 per cent to 89 percent, for freight, and 89 to 90 per cent for switchers. Note these are cut-offs in full gear, earlier "events" are obtained by linking up the gear, thus shortening the valve travel until "mid-gear" is reached when the valve travels by an amount equal to twice the lap plus lead, and maximum port opening to steam is equal to the lead. The minimum required valve travel must be equal to to twice port opening plus lap but as the lap is at present unknown, we will assume a travel. This may be taken as scale of the full size, which ranges from a minimum of 5-1/2 to 7-1/2 inches. Assume we are dealing with 3/4 inch scale, we may take a travel of 3/8 inch and 85 per cent cut-off in full gear. To establish the proper lap a simple diagram is drawn, to an enlarged scale, ten or twenty times the model dimensions. We will take 20, so referring to diagram Fig. 1, describe a circle A.B.C.D. of radius 3.75 inches and horizontal and vertical diameters A.C. & B.D. From point A, set off a distance A.E. equal to 85 per cent of length A.C. which in our case will be 6-3/8 inches. From point E erect a perpendicular E.F. cutting the travel circle. From A as center describe a circle of radius equal to the "lead". This may be taken as 1/100 actual or 0.20 on the diagram. From point F draw a line tangent to the "lead" circle F.G. Now from center of travel circle O, describe a circle to touch the line F.G. and draw in the line O.J. at right angles to line F.G. The distance O.H. will be the required "lap", which may be measured off the diagram and divided by 20 to establish the actual lap of valve.

If a circle is drawn on line O.J., the position of the valve in relation to the crank positions can be read off. Imagine the line O.A. representing the crank to revolve counter-clockwise, when the crank is at O.M. for example, the port will be open by the amount K.L. and the distance the piston has traveled will be the amount A.N. When position O.J. is reached, the port will be wide open and starting to close from J. to F. at which point 'cut-off' occurs, and piston reaches point E. The release or exhaust point is found by drawing in the line R.S. parallel to line G.F.

For the dimension we have taken we will have lap 0.0675, cut-off 85%, release 95.7%, in full gear.

It was stated above that minimum valve travel should be equal to twice port opening plus lap. Now that we have found the required lap (0.0675), and port was taken as 0.10, we will have 0.1675 as half-travel, but seeing that we have taken 0.1875 as actual half-travel, the valve will overrun the port by 0.020.

This can be shown on the diagram by stepping off from point H a distance H.T. equal to port and striking an arc of radius O.T. From what has already been said, it will be evident that the valve has opened the port wide at L. and it will remain wide open until point U. is reached when the valve will just begin to close. This will illustrate why long valve travels are an advantage, besides maintaining steam pressure, wire drawing is reduced.

All the above working will be suitable regardless of type of valve, whether slide, piston, inside admission or outside admission.

Now we can get back to the Walschaert valve gear, although there must be certain modifications, whether inside or outside steam admission piston valves, slide valves, or whether radius rod is to be at top or bottom of the expansion link, when engine is running forward.

So to avoid confusing the reader, we will take piston valve with inside admission, and arrange for the radius rod to be at the bottom of the link with the engine running forward. This is the more usual arrangement, for a number of reasons, which will not be gone into now, so we will start the design of the gear.



The first part to design is the Combination lever (Those not familiar with the names should refer to the layout, Fig.3) It will be seen that the end of the radius rod and the Valve Spindle Crosshead Pin are close together, and the centers are decided by the distance in which the two connecting pins can be assembled. 3/16 inch would be a suitable center, admitting the eye end of the radius rod, and the crosshead pin, for 3/4 inch scale locomotives.

Now when the gear is in mid-position the valve derives no motion whatever from the expansion link, and as the combination lever is connected to the main crosshead, the stroke of the piston must be converted to an amount on the valve spindle equal to twice lap plus lead, which we have already found to amount to twice 0.0775 inches required to find the total length of the lever. This will be in proportion, or, as 0.0775 is to the stroke of the piston, so is 3/15 inches to the length. Expressed as an equation and referring to Fig. 2:



2 * Lap * Lead  0.1875 -- = --  Stroke          ac

Stroke * 0.1875 ac = --- 2 * Lap * Lead

Assuming a stroke of 1-3/4 inch for 3/4 inch scale locomotive, the length of the lever will work out to 2.137. (No appreciable error will be made if we take this as 2-1/8 inch).

Now we are ready to layout the whole mechanism. The various steps will be taken in order, and if followed, the amateur should have little difficulty in deriving a correct gear.

(1) Draw a horizontal line representing the center line of Cylinder, Crosshead and Axle, also another above it, the center line of the valve spindle at the distance already decided upon.

(2) Draw a vertical line A.B.C. representing the Combination Lever, A.B. being equal to 3/16, and A.C. equal to 2-1/8 (dimensions as found above).

(3) From B. on valve spindle line, set off each side points equal to Lap plus Lead, and also half the valve travel, namely 0.0775 and 0.1875.

(4) At this time it is advisable to establish the vertical center line of the cylinder, sufficiently far forward to avoid any interference of the end of the Combination Lever with the cylinder head. Then from this line the position of the Cross Head may be marked when the piston is at Front or Back dead center (End of stroke).

We will take Back D.C.

(5) From A as center and with radius equal to the total length of the Combination Lever, describe an arc D.C.E. Draw a line from A. passing through Lap and Lead point, and produced to cut the arc.

(6) Draw a tangent to the arc, measure the distance between it and the intersection of the arc and the end of the lever, and carry across to the Cross Head center line.

(7) Join the end of the lever and the point found on the Cross Head. This establishes the location and the length of the Union Link, so that it swings through an equal angle during the stroke of the piston. The connection of the Union Link to the Crosshead may or may not come below the Write Pin center. This depends upon the distance between cylinder and valve chest. Any way the above working still holds good.

(8) The ideal position of the center of the Expansion Link is on a line horizontally from the top of the Combination Lever, this is not always possible so center may be somewhat below. The length of the Radius rod and Eccentric rod are approximately equal, the Eccentric rod being a little longer. With the position of the Driving wheel known distance from the combination lever, the center of the Expansion Link is fixed.

(9) With center A. and radius A.G., strike the arc R.R. and from point C. draw lines C.U. and C.V. equal to the length of the Combination Lever, passing through the points of total valve travel.

(10) From points V. and U. with radius A.G., describe the arcs W. and X. Now if the link is made short, it will have to swing through a large angle which is bad, making the gear hard to reverse especially if the link is at the end of its swing. On the other hand if a long link is used, its swing is small, but the angular movement of the radius rod becomes excessive. So it is good practice to limit the swing of the Expansion link to about 40 degrees, on no account should it be more than 45 degrees. We will use 40 degrees.

(11) Draw a tangent T.T. to arc R.R. and set off 20 degrees each side of the tangent. Draw these lines in T1 and T2 and from point G. draw a line G.O. at right angles to the tangent line T2. Line G.O. should be equal to Radius rod or A.G. With this radius and center O, describe the arc R2 cutting the arc X at H2 and the arc W. at the bottom. This establishes the length and position of the link in its backward swing. Carry out the same working for the forward swing.

(12) We now have the position of the link in full back and forward stroke (swing) and also the extreme positions of the radius rod for fore and back gear. It is quite possible that the distance G.H1 and G.H2 are not exactly equal or equal to the bottom halves of the link. The amount will not be much if the Radius rod is a reasonable length, the error is brought about my the angularity of the rod, and will cause the Die Block to slip by the amount. Select the longer of the four distances and take this for the minimum dimension of the link length.

(13) It will be noticed that the tangent line T.T. when the link is in mid-position slopes, leaning to the rear. Here is where the back set of the foot comes in, and in order that the foot connection shall swing equally in relation to the movement of the return crank. If the foot center is to be on the center line of the engine, then the back set is made equal to the difference of the angle at which T.T. leans and 90 degrees.

(14) Set off 20 degrees front and back of the position of Foot Connection, along an arc tangent to the main center line, the total length will be the diameter of the return crank circle.

(15) Set out the return crank circle as found above, and join point K. to J. The point K. in this case will be exactly at right angles to the main crank.

(16) Distance K. to J. is the length of the Eccentric Rod. This will complete the layout.

If the proportions result in a link, the foot of which is considered excessively far from the trunnion center then it may be raised above the engine center line, thus reducing the throw of the return crank. IN this case draw a line from center of the axle to the foot connection point, and use this line as the base for the back set. This will cause the return crank to be a few degrees more than 90 behind the main crank pin.

The following points should be observed if conditions are different than above. With a valve having OUTSIDE ADMISSION--- (Slide valves, and Outside admission piston valves) the valve spindle is connected to the combination lever above the connection to the radius rod.

If the Die Block is in the LOWER half of the link when in forward gear, the Eccentric crank LEADS the main pin.

If the Die Block is in the UPPER half of the link when in forward gear, the Eccentric crank FOLLOWS the main pin.

With a valve having INSIDE ADMISSION--- The Valve Rod is connected to the Combination Lever BELOW is connection to the Radius Rod.

If the Die Block is in the LOWER HALF of the link when in forward gear, the Eccentric Crank FOLLOWS the main pin.

If the block is in the UPPER HALF of the link when in forward gear the Eccentric Crank LEADS the main pin.

The LEAD is constant for all positions of Cut-off and cannot be altered without upsetting the motion. This is the distinguishing feature of any radial gear from the Stephenson. In the latter gear the Lead increases with the cut-off.

The COMBINATION LEVER should not swing through an angle more than 60 degrees, and the LINK not more than 40 degrees.

Favor long rods rather than short, and keep the angles below those given when possible.