The Bourdon horizontal centrifugal governor described by Hiscox uses a pivoted ball arm, meshing sectors and a spring inside a hollow spindle to move a throttle push rod. The calculator illustrates one part of the physics: radial force for masses rotating at an entered radius and speed. It does not solve the governor’s spring balance or throttle position.
Horizontal Centrifugal Governor Interactive Calculator
Convert engine speed through an entered ratio, then calculate mrω² for each of two prescribed point masses at an entered radius.
Equation Used
- Two equal point masses rotate symmetrically at the entered fixed radius and speed.
- Drive ratio is exact and slip-free.
- The displayed pair value is only twice one scalar magnitude.
- No arms, pivots, spring/gravity restoring force, sleeve/linkage projection, friction, throttle, engine or closed-loop dynamics model.
The sum of two radial force magnitudes is not a net external force, sleeve force or governor authority. A symmetric pair's opposing radial vectors cancel; linkage projection and equilibrium require missing geometry and spring/load data.
Rotating-mass identity only
Entered engine speed is multiplied by the entered drive ratio. Converting spindle rpm to angular speed allows the radial force magnitude mrω² to be calculated for each prescribed mass and radius.
The illustration shows two prescribed rotating masses. The Bourdon governor’s meshing sectors, helical spring and throttle push rod are not represented, so it cannot show the governor’s equilibrium position or response to a changing engine load.
Use as a force-scaling comparison
The arithmetic can show quadratic sensitivity to speed for prescribed rotation. It cannot design, adjust or diagnose a governor or control an engine.
Speed conversion and radial force
Spindle speed is neR, angular speed is 2πn/60, and each rotating point mass requires inward radial force mrω². The mechanism supplies that inward force while the mass exerts the corresponding reaction on its arm.
Worked example
At 120 engine rpm and 2:1 drive ratio, spindle speed is 240 rpm or about 25.13 rad/s. A 2 kg mass at 150 mm radius has radial force magnitude about 189.5 N.
Scope and limitations
A governor model needs arm and pivot geometry, mass centres, restoring spring or gravity terms, preload, sleeve and linkage ratios, friction and hysteresis, valve/actuator forces, engine torque-speed response, load disturbances, damping, delays, equilibrium, droop and stability analysis.
Questions
Does the pair value push the sleeve with that force?
No. It is only a scalar sum; sleeve force depends on linkage projection and equilibrium.
Does higher force mean better regulation?
Not by itself. Regulation depends on the entire mechanical and engine-control loop.
Is entered radius predicted?
No. It is prescribed by the user.
Historical source and calculation basis
Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances, entry 304, describes the Bourdon horizontal governor: a pivoted ball arm drives meshing sectors and a throttle push rod, with a helical spring inside the hollow spindle providing the restoring action.
The calculator uses angular-speed conversion and the point-mass radial-force relation F = mrω². Radius is entered, not derived from the spring and linkage balance. The two-force sum is a comparison of magnitudes, not a throttle or sleeve load.
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