This revision limits the familiar loaded-governor equation to its actual symmetric special case and removes unsupported universal performance and maintenance claims. Exact equal-length arm closure connects the flyballs to the weighted sliding sleeve.
Symmetric Porter Governor Equilibrium Explorer
Enter equal arm length, common arm angle, each ball mass and central sleeve mass. The worksheet derives exact ball radius, governor height and ideal frictionless equilibrium speed for this one symmetric geometry.
Equation Used
- Both upper arms and both lower links have the same declared length L.
- Upper-arm and lower-link angles to the vertical spindle are equal, so q=1.
- Each flyball has declared mass m and the central sliding load has declared total mass M.
- Arms and links are massless and pivots, sleeve and spindle are frictionless.
- The model is a static equilibrium identity; animation phase only indicates spindle rotation.
- Friction, linkage offsets, arm/link mass, spring or valve forces, backlash, damping, speed range, sensitivity, stability, hunting, power, transient response, strength, wear, tolerances, maintenance and safe engine control are excluded.
Constrains the loaded height-speed relation to the explicit equal-arm equal-angle Porter special case and enforces exact link closure.
A central load moves with the governor sleeve
Two flyballs sit at the junctions of upper arms and lower links. The upper arms pivot at a fixed point on the rotating spindle; the lower links meet a sleeve that rotates with the spindle but slides axially. The Porter modification adds a central dead load to that sleeve.
The drawing enforces equal upper and lower link lengths and equal angles. Moving the declared angle moves both balls and the sleeve while every pin remains coincident.
Use this worksheet only for the declared symmetric ideal case
The result can audit geometric closure and the frictionless equilibrium relation for one explicitly symmetric Porter arrangement. It cannot design, tune or validate an engine governor or its valve linkage.
State the geometry before using the loaded height relation
Equal upper and lower arms at equal angles close between the fixed top pivot, each ball joint and the sleeve pivot on the spindle.
This is the q=1 special case of the Porter relation, with m equal to each ball mass and M the total central sleeve mass. N=60 omega/(2 pi).
A transparent symmetric example
For L=250 mm and alpha=40°, ball radius is 160.7 mm and governor height is 191.5 mm. With each ball m=3 kg and central sleeve mass M=18 kg, the ideal equilibrium speed is 180.8 rpm and the load raises speed by sqrt(7)=2.646 relative to the same unloaded geometry.
This is a frictionless equilibrium result, not an operating-speed recommendation.
Real governor response needs more than static equilibrium
Offsets, unequal arm angles, arm/link masses, sleeve and pivot friction, valve force, linkage leverage, backlash and stops change the equilibrium. Damping, engine torque, steam flow and feedback dynamics determine sensitivity, stability and hunting.
The former universal speed and mass ranges, dimensional fits, failure diagnosis, maintenance schedule, application history and control-performance claims are removed because they were not supported for a specific documented governor.
Porter-governor questions
Why is this called a symmetric case?
Upper and lower links have equal lengths and equal angles to the spindle, so q=tan(beta)/tan(alpha)=1.
What does the central load change?
In the ideal special case it multiplies omega squared by 1+M/m at fixed height.
Does the model predict stability or hunting?
No. It is static and frictionless.
Can it set an engine speed?
No.
Porter-governor references
- NITK Virtual Labs: Porter components, q=tan(beta)/tan(alpha), and the q=1 equilibrium relation.
- Government Polytechnic Kendrapara Theory of Machines: free-body derivation for flyballs and central sleeve load.
- Hiscox, Mechanical Movements (1903): historical illustrated governor reference.
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