Steam locomotives have large drive wheels because they have a single gear. Each push of the piston turns the wheels once. The bigger the wheel, the farther the train will go with each push. This means you can estimate the top speed of a steam engine by measuring the diameter of the drive wheels.
Identify the tires on the outside of the wheel. Both the wheel and the tire are made of iron, but the tires are designed to wear down and be replaced. You can spot the tire because it will be the flanged hoop of iron that the train rides on.
Measure the wheel's diameter, using the measuring tape or stick. For fitting a new tire, this should be measured to the thousandth of an inch, but for general speed estimates, a quarter of an inch is accurate enough.
Measure the tyre's thickness. Ideally, you will be measuring a new, unworn tire. The minimum thickness is 1 1/2 inches, according to the U.S. Code of Federal Regulations.
Calculate the difference between the maximum and minimal wear on the tire by subtracting the minimal thickness from the thickness of a new tire, which is set by the Code of Federal Regulations and depends on the type of locomotive.
Subtract one half of the difference between the maximum and minimal tire wear from the tire thickness to calculate the thickness of the tire at average wear.
Add the diameter of the drive wheel to twice the thickness at average wear to calculate the diameter of the drive wheels and tires when the tires are halfway worn.
Estimate the maximum speed of the steam locomotive by converting your measurement to inches and adding 10. The maximum speed in miles per hour will be between the wheel diameter in inches and 10 miles per hour faster than its diameter in inches.
This calculation is most accurate for engines built before 1940. The size of the drive wheels is determined by a gear ratio, trading speed for power. Locomotive factories could make one size boiler and then attach different size wheels for freight or passenger work.