(A bit of a disclaimer: what's found on here is basically copied from another site, which I'll link it here at some point. The reason for this page's existence is just to streamline and simplify the wording, give more straightforward equations, and explain where certain numbers come from as the original site wasn't too clear on these things.

I will be using James the Red engine's measurements as an example alongside equations for photo-context when I complete this)

(EVERYTHING WILL BE IN IMPERIAL)

Dimensions & Planning

Glossary + Abreviations

first your going to need a few things beforehand:

using james as a base, it will be using 5 foot 6 inch drivers, using 20.5 inch x 26 inch pistons. which will be

so first, we need wheel speed, which is diameter of wheel(in) times Pi times 336 times 60 divided by 12,this will equal mph/diameter times 5280 feet which will look like this if you want to put it in google

example:

for port area, we will start with this equation this will be the piston speed in FPM. which is 336 times the sum of 2 times the piston stroke(in) divided by 12

next we need volume swept by piston, which will be the piston speed times the area of the piston, which will need 1 other equations first, the area of the Cylinder bore. which is Pi times the sum of the radius of the bore squared, which is

now that we have that, we input this number into the equation for the volume swept by the piston, which will be fpm times bore area divided by 12 squared

now that we have the volume of how much cubic feet the piston moves per minute,we can finally get to port size, it will be volume per minute divided by 7874, which is the average speeed of steam in meters per second (40)/p>

convert to inches

for the shape of the port, id recomend a wider port than long, but for here, i will just go for 18 inches wide, it will still need to be the same as the area

now we move onto some of the more complicated looking stuff, now pull out a CAD program or vector program with mesurements, you will need it for the next part, unless your very skilled at mesurement drawing in real life

so you add both the lap and port length, being

now we mesure where the port is placed, we take the estemated half travel, subract port length from it, and then move it from the valve end that distance, in our case,

if it is ever negative, just make circle ABCD bigger until it isnt. now we find out the combination lever, the vertical rod that is near the crosshead of a piston, the equation being:

now we move onto the next part, which is making the actual valve gear part, this will take multiple steps, but not much more math,because if you have a CAD or vector program, it will be way simpler, it is generally advised to put the piston under the smokebox, this is so that the steam pipe and exhaust align with the piston, to make the piston do what it should do., if it is kinda fucked then just give a different number till it works

now, you have finished all the steps for planing, make all lines that arent the rods at center (with the exception of the expansion link, use the one where the bottom is leaning back, and make a copy of the line and rotate it 180 degrees around the center of the expansion link) to construction,trim them, or delete them, and model them all.

building

building the valve gear is significantly more simpler and no math is truly reqquired, unless you want to balance the weights, but that wont be nececcary, unfortunately, james's proportions makes it so that the expansion link will most likely interfere with any realistic size for material that could withstand more than 2 pounds of pressure, fortunately, we can move parts to the side since james is a dual piston engine, if it is like james, then also account for the fact that there will be another axle in the middle of the main rod, and you will need to angle it upwards so no interference will happen and lock or blow up the valve gear, you can move the length of the piston to the crosshead as much as you want unless it interferes with the combination link.