NASA describes a swashplate Stirling-engine drive with axially parallel pistons connected to a disk mounted concentrically but at a skew angle to the shaft; rotation makes each attached axial rod execute simple harmonic motion. The calculator compares two entered angles using ideal full-stroke geometry normalized by pitch-circle diameter.
Swashplate Engine Interactive Calculator
Vary two entered swashplate angles to compare ideal full stroke divided by pitch-circle diameter. The normalized geometry is explanatory and is not an engine performance or design calculation.
Equation Used
- Piston axes are parallel to the output shaft.
- The attachment pitch-circle diameter is unchanged between the two entered cases.
- Angles are measured from a plane perpendicular to the shaft.
- Connections follow the ideal swashplate plane without offset, compliance or clearance.
How an Axial Swashplate Drive Works
NASA's Stirling-engine review describes axially parallel pistons driven by a disk-like rotor mounted concentrically with, but at a skew angle to, the engine shaft. As the inclined plate rotates, piston rods constrained to fixed axes parallel to the shaft reciprocate sinusoidally. The two opposed pistons in this cutaway move in opposite phases; their cylinders do not orbit the shaft. The two drawings compare the entered angles at the same phase and scale.
A separate NASA report describes a variable-angle construction in which changing the swashplate angle changes piston stroke, including a zero-angle, zero-stroke position and a maximum-angle, maximum-stroke position.
Using the Animation and Calculator
The calculator compares how two entered plate angles change ideal normalized stroke while pitch-circle diameter is held constant. The comparison shows how angle affects stroke without requiring a physical engine diameter.
A real axial engine, compressor or pump requires verified joint geometry, clearances, phasing, bearing and slipper design, lubrication, loads, speed, thermal behavior, sealing and application-specific safety analysis.
Ideal Normalized Stroke
For pitch-circle radius R and swashplate angle alpha, ideal full stroke is 2R tan(alpha). With pitch-circle diameter D = 2R:
A swashplate-device patent states the equivalent full-stroke relation L = 2R tan(alpha). The ratio between two cases is tan(alpha2) divided by tan(alpha1).
Worked Example: Two Entered Angles
At 5 degrees, S/D = tan(5 degrees) = 0.087. At 20 degrees, S/D = tan(20 degrees) = 0.364. Holding pitch-circle diameter constant, the ideal stroke gain is 4.16 and the angle change is 15 degrees.
These are dimensionless geometric comparisons. They do not specify a physical engine, displacement, power or safe operating angle.
What the Calculator Includes
- Mechanism shown: axially parallel piston rods, skew swashplate, simple harmonic reciprocation and variable stroke with plate angle.
- Calculated: ideal S/D at two angles, their ratio and angle difference.
- Not calculated: bore, cylinder count, swept volume, compression ratio, combustion, torque, power, side force, bearing or slipper contact, lubrication, heat, fatigue, efficiency or durability.
Frequently Asked Questions
What does S/D mean?
It is ideal full piston stroke divided by pitch-circle diameter.
Why is the tangent used?
A plane tilted by alpha changes axial height across radius R by R tan(alpha); the opposite extremes span twice that height.
Does a larger angle always improve an engine?
The calculator only shows geometric stroke. It does not evaluate force, contact, clearance, lubrication or durability limits.
Is the motion sinusoidal?
In this rotating-plate arrangement, each piston stays on a fixed axial guide while the rotating inclined plane changes the height at its follower contact. Its axial coordinate varies sinusoidally.
Does the stroke ratio equal a power ratio?
No. Power depends on many omitted thermodynamic and mechanical variables.
Can these values design an engine?
No. They are normalized kinematics only.
References
- NASA Technical Reports Server, Stirling-engine assessment: axiparallel pistons driven by a skew swashplate and simple harmonic piston-rod motion.
- NASA Technical Reports Server, variable swashplate mechanism report: piston stroke controlled by swashplate angle.
- EP0499961A2, swash-plate plunger device: full stroke L = 2R tan(alpha).
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
