This calculator converts an entered signed speed drop over an entered number of revolutions into constant-angular-acceleration point-mass inertia quantities. It does not model, tune or size an inertia governor.
Inertia Governor Interactive Calculator
Explore a signed constant-acceleration interval and the torque and tangential-force equivalents for one ideal point mass at radius r.
Equation Used
- Initial and final speeds are positive, with final rpm=rpm0−entered drop.
- Angular acceleration is constant through the entered angular travel of N revolutions.
- Flyweight is represented as a point mass m fixed at radius r from the rotation axis, giving J=mr².
- Reported force is only the signed tangential equivalent tau/r at that radius.
- No pivoted-weight kinematics, centrifugal force, spring, linkage, friction, damping, throttle/cutoff, engine torque, control loop, stability, stress, fatigue, balance, containment or safety model.
Sign convention: a positive entered speed drop means final speed is lower than initial speed and therefore angular acceleration, inertia torque and tangential-force equivalent are negative. These values describe the applied torque and tangential force needed for the stated point-mass acceleration. They do not predict throttle-linkage force or governor response.
Signed constant-acceleration scenario
The entered drop D defines final speed rpm1=rpm0−D. Positive D is deceleration; negative D is acceleration. Assuming constant angular acceleration over N revolutions, elapsed time follows from angular travel divided by average angular speed.
The diagram shows one mass fixed to a rotating carrier. Its phase motion is illustrative and does not follow the calculated constant-acceleration trajectory; a pivoted governor and its control linkage are absent.
Use as rigid-body arithmetic
The calculation can check sign, units and the relation among angular acceleration, point-mass inertia, torque and tangential force. It cannot predict governor trigger, response, setpoint, stability or engine speed regulation.
Time, acceleration and point-mass inertia
For constant alpha, average speed is (rpm0+rpm1)/2 and dt=60N/rpmavg. Signed alpha=(omega1−omega0)/dt. For an ideal point mass J=mr², tau=Jalpha and Ft=tau/r.
A real pivoted inertia governor has moving geometry plus spring, centrifugal, friction and linkage forces; none are represented.
Deceleration example
At 600 rpm initial speed, positive drop 50 rpm over 0.5 revolution, final speed is 550 rpm and interval time is about 52.17 ms. Signed alpha is about −100.36 rad/s². For m=1 kg at r=0.1 m, tau is about −1.004 N·m and tangential equivalent is −10.04 N.
What a governor model would require
A governor model needs the actual moving masses, pivots, springs and control linkage, together with engine and load behavior. Those coupled effects determine response and stability. The fixed-point-mass calculation here cannot establish a governor setting, overspeed protection or a safe operating speed.
Questions
Why is acceleration negative for a positive drop?
Because final speed is lower than initial speed under the stated convention.
Is tangential force the force on a governor linkage?
No. It is only tau/r for the ideal point mass.
Does response revolutions predict how fast a governor reacts?
No. It is an assumed interval entered by the user.
References & Further Reading
- Wikipedia contributors. Centrifugal governor. Wikipedia
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