A 4-6-0, historically called a ten-wheeler, has a four-wheel leading truck and three coupled driving axles. This calculator evaluates a historical two-cylinder simple-locomotive rated starting-tractive-force convention, not actual rail pull or train performance.
Resources for separate linear-actuator projects
For a separate project using a linear actuator, calculate its mounting geometry and load throughout travel. The locomotive starting-force estimate on this page does not size a linear actuator.
Where springs or counterbalances are involved, calculate the actuator force over the full travel. The highest load may occur at a different position than the most obvious one.
The actuator stroke should also be checked against the useful motion, not just against the visible travel. End clearance, hard stops, bracket rotation, and wire routing can all reduce the usable stroke in the final build.
- Calculate actuator force at the worst bracket angle, not just at mid-stroke.
- Check stroke, retracted length, and extended length against the mechanism envelope.
- Confirm the structure can accept the higher loads created by a stronger actuator.
For a FIRGELLI actuator application, run the FIRGELLI actuator force calculator, then compare available stroke, force, and mounting envelope in the FIRGELLI linear actuator range. If the goal is to replace an existing unit, use the linear actuator replacement finder before assuming the new actuator is a direct fit.
Ten-wheel Freight Locomotive Interactive Calculator
Enter cylinder bore, stroke, boiler gauge pressure and driving-wheel diameter. Results use the historical two-cylinder simple-locomotive 0.85 convention.
Equation Used
- The convention represents an ordinary two-cylinder simple locomotive at low speed.
- Entered pressure is boiler gauge pressure and all entered lengths use inches.
- The 0.85 factor is fixed by the selected historical rating convention.
- Adhesion, weight on drivers, valve gear, crank-angle variation, speed, boiler steaming rate, losses and train resistance are omitted.
Historical 4-6-0 Arrangement
A 4-6-0 steam locomotive has four leading wheels, six coupled driving wheels and no trailing wheels. Side rods couple the three driving axles while the cylinders and connecting rods transmit reciprocating effort to the drivers.
The animation is conceptual and does not reproduce a particular locomotive, valve gear, crank geometry or wheel loading.
What This Explanatory Calculator Does
A 1915 locomotive-operation text gives rated tractive force T = 0.85Pd²s/D for a two-cylinder simple locomotive, describing it as a low-speed rating convention rather than force available at every speed.
The calculator applies that convention, converts the estimate to kilonewtons, and shows a nominal rim-torque equivalent and an equal-share comparison across three axles. It does not predict drawbar pull, adhesion, acceleration, grade capacity, speed or train tonnage.
Historical Rated Starting-force Convention
P is boiler gauge pressure in psi; d, s and D are cylinder bore, piston stroke and driver diameter in inches; T is pounds-force. The kN output uses the NIST conversion 1 lbf = 4.4482216152605 N.
Worked Convention
For d = 19 in, s = 24 in, P = 180 psi and D = 63 in, the historical convention gives about 21,041 lbf, or 93.6 kN. Multiplying by the 31.5 in wheel radius gives a nominal 55,233 lb-ft rim-torque equivalent; division by three gives 7,014 lbf as equal-share arithmetic.
Neither derivative represents measured axle loading or adhesion-limited rail force.
Model Boundary
- Calculated: one historical rated starting-force estimate, a unit conversion, a force-times-radius equivalent and division by three.
- Historical scope: an ordinary two-cylinder simple locomotive at low speed using a fixed 0.85 rating factor.
- Not calculated: actual mean effective pressure, cylinder count alternatives, valve events, crank-angle force ripple, steam chest pressure, back pressure, boiler evaporation, speed, mechanical efficiency, adhesion, driver loading, wheel slip, drawbar pull, rolling resistance, gradient, curvature, acceleration, braking, capacity or safe operation.
Frequently Asked Questions
Is this actual drawbar pull?
No. It is a historical rated starting-force estimate before train resistance and other real limitations.
Why is 0.85 used?
It is the fixed factor in the selected historical convention; other practices used other assumptions.
Does the estimate include adhesion?
No. Weight on the driving wheels and wheel-rail conditions are absent.
Is force really divided equally among three axles?
Not necessarily. T/3 is displayed only as equal-share arithmetic.
Does rim torque include crank geometry?
No. It is simply estimated force multiplied by driver radius.
Can this determine train tonnage or grade capacity?
No. Those require drawbar force, resistance, speed and operating data.
References
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
