This calculator applies a square-root interval to an entered nominal speed and an entered percentage variation in a quantity proportional to speed squared. It does not predict an inverted governor's spring tolerance or regulated-speed band.
Inverted Governor Interactive Calculator
Explore how a symmetric percentage interval in an assumed N²-proportional quantity maps to an asymmetric speed interval.
Equation Used
- An unspecified governing quantity Q is exactly proportional to speed squared near the nominal point.
- The entered percentage gives symmetric lower/upper bounds on Q, not necessarily on a spring dimension or rate.
- All geometry and other terms in the proportionality are fixed.
- The animation preserves constant arm and toggle lengths and shows qualitative spool lift against a spring around the spindle.
- No ball mass, actual geometry, spring rate/preload, gravity, friction/hysteresis, throttle/engine/load dynamics, stability, travel limits, overspeed trip, strength or safety model.
The percentage input describes a quantity assumed proportional to speed squared. It is not automatically a spring manufacturing tolerance. The animation illustrates the spring, flyball arms, toggle links and sliding spool; it does not calculate their equilibrium at the entered speed.
Inverted-governor linkage and separate square-root mapping
Hiscox describes the inverted governor with centrifugal ball force resisted by a spring around the spindle; outward ball motion lifts the lever spool through toggle joints. The animation preserves symmetric constant-length arms and toggles and shows that axial spool lift.
The calculator uses a separate mathematical relationship: if Q is proportional to N², multiplying Q by 1±t changes speed by the square root of those factors. No force equilibrium links the animation pose to the reported bounds.
Use as sensitivity arithmetic
The outputs can check a square-root propagation when an independently justified N² proportionality exists. They cannot set a governor spring, predict droop, determine stability or establish overspeed protection.
What the percentage means
The input t bounds the assumed N²-proportional quantity: Qlow=Q0(1−t/100) and Qhigh=Q0(1+t/100). Taking square roots produces the reported speeds.
A spring-rate or preload tolerance does not automatically equal this Q interval because the equilibrium includes geometry, displacement and other forces.
Worked example
At nominal 350 rpm and entered N²-quantity variation ±2%, lower bound is 346.48 rpm, upper bound is 353.48 rpm, band width is about 7.00 rpm and maximum offset is about 3.52 rpm.
What the calculation does not establish
A real governor balances centrifugal force, spring force and other loads through its linkage. Predicting the controlled speed also requires the engine, valve and load response. These speed bounds do not establish regulation accuracy, stability or overspeed protection.
Questions
Is the input a real spring tolerance?
No. It is an abstract variation in a quantity assumed proportional to N².
Does the speed band predict regulation?
No. Engine/load dynamics and the governor equilibrium curve are absent.
Can this set overspeed protection?
No. Use a validated governor/trip design and qualified engineering.
References & further reading
Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances, mechanism 299, Inverted Governor. Hiscox describes a spindle spring resisting outward ball movement and toggle joints lifting the spool.
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