Dawson’s compensating governor uses two rotating balls linked to a central moving weight. Hiscox describes it as intended to be isochronous, with the central weight directly connected to the throttle-valve stem.
Follow the outer arms and inner links as they connect the balls to the central weight and guided stem. The calculator finds ideal static balance for your dimensions and masses. Compare the required speed across arm angles to see whether the selected geometry approaches isochronous behavior.
Compensating Governor Interactive Calculator
Explore Dawson’s linked central-weight arrangement using exact rods and ideal static balance. The curve tests the selected geometry; it does not assume automatic isochronism or model engine feedback.
Equation Used
- Lower pivot radius 0.25L; weight-link pin radius 0.10L.
- Two equal ball masses and one central weight; massless rigid links.
- Central weight follows exact inner-link closure on the shaft axis.
- No friction, stem load, damping, spring or engine feedback.
Dawson’s linked-weight arrangement in Hiscox figure 295, shown with illustrative proportions. Rotation lets you inspect the geometry; damping and engine response are not simulated.
Ball motion lifts a compensating weight
The outer arms pivot on the lower rotating carrier. As the balls spread outward, their centers descend along those arm arcs. The inner links connect the balls to two pins on the central weight. In the selected geometry, outward spread raises that weight and its connected stem.
The central weight therefore opposes outward movement through gravity, while the ball weights themselves assist it. The equilibrium calculation balances both gravitational contributions against the balls’ centrifugal effect.
The animated rotation is an inspection view at the selected arm angle. It is deliberately slowed and does not model acceleration, a speed transient or actual throttle opening. The graph compares the ideal speed required at different arm angles.
Explore dimensions and equilibrium speed
Outer-arm length scales the mechanism. Inner-link ratio changes how the weight rises. Ball and central masses change the balance speed. Arm angle selects the current spread and the highlighted point on the equilibrium curve.
The model uses a lower pivot radius of 0.25L and a central-weight pin radius of 0.10L. Those dimensions, the weight silhouette and ball diameter are illustrative proportions rather than manufacturing dimensions. Rods and bearings are treated as massless and frictionless.
If the gravitational balance cannot support a positive steady speed, the geometry remains visible and the result says so. A curve with varying required speed is not isochronous: the chosen dimensions and masses require different speeds at different arm angles.
Exact linkage and virtual-work balance
Use meters for lengths. Let outer arm length be L, inner length l, lower pivot radius a=0.25L, central pin radius b=0.10L, and outer angle θ measured from upward vertical.
ρ=a+L sinθ; z=L cosθ; H=√[l²−(ρ−b)²]; zc=z−H
The central weight pins are at height zc relative to the lower arm pivots. Its center of mass has a fixed offset above those pins, so its height derivative is the same:
dzc/dθ=−L sinθ+(ρ−b)L cosθ/H
With ball mass m on each side, central mass M and standard gravity g, the potential-energy derivative is U′=g[−2mL sinθ+M(dzc/dθ)]. The centrifugal generalized force is 2mω²ρL cosθ. Equilibrium requires ω²=U′/(2mρL cosθ), and rpm=60ω/(2π).
A nonpositive result gives no positive equilibrium speed. At a positive balance, an increasing required ω² with spread gives a local restoring tendency at fixed speed; decreasing required ω² gives a diverging tendency. This is a mechanical small-displacement test, not a closed-loop engine stability result.
Compare the weight and ball contributions
The default uses 250 mm outer arms, an inner-link ratio of 1.05, 1 kg per ball, a 12 kg central weight and a 25° spread angle. Each inner link is 262.5 mm long. The ball-center radius and central-weight elevation follow exact rod closure.
Increasing both masses by the same factor leaves the ideal balance speed unchanged. Increasing only the central mass increases its restoring gravitational contribution. Increasing all lengths proportionally decreases the ideal balance speed in proportion to the inverse square root of scale.
Limits of the ideal balance
Hiscox figure 295 identifies Dawson’s compensating governor but does not specify the complete geometry and mass distribution. The dimensions and masses entered here define an illustrative static model, not a particular manufactured governor.
The calculation includes the ball and central-weight gravity, exact rigid-link geometry and ball centrifugal action. Link inertia, friction, stem load, spring forces, throttle dynamics, damping and engine feedback are excluded. Ball and weight sizes are illustrative; entered masses are not inferred from drawn density.
The static balance gives no settling time, hunting reduction or operating limit. Predicting regulation would also require the throttle, damping and engine response.
Compensating-governor questions
Why can the result say no positive balance?
For some masses and geometry, gravity already encourages outward movement strongly enough that adding centrifugal action cannot provide the required static balance at that angle.
Does restoring mean the complete engine is stable?
No. It describes only a small mechanical displacement at fixed speed. Engine feedback, damping and throttle response are not included.
Is the governor automatically isochronous?
No. Isochronism would require the same equilibrium speed over a working range. The plotted curve shows how the required equilibrium speed changes with the selected geometry.
Is there a dashpot in the model?
No. The historical figure shows a linked central weight. No dashpot or damping law is inferred.
Why does the animation rotate with an unavailable speed?
It remains a rotating geometry inspection view. Its playback rate is not a prediction of operating speed or steady balance.
Construction reference
Hiscox, Mechanical Movements, Powers, Devices and Appliances, printed page 83, figure 295, describes Dawson’s compensating governor, its central weight and direct throttle-stem connection.
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