An elastic wheel places compliant members between the axle hub and its outer rim. This illustration uses the curved steel-spoke form of a historical spring wheel. The calculator retains load, whole-wheel radial stiffness and radius, and shows a loading/unloading cycle instead of a wheel rotating through the road.
Elastic Wheel Interactive Calculator
Compare ideal peak radial deflection and stored energy using the complete wheel’s stiffness. The curved spring-spoke wheel shows a stationary load test; its shape is illustrative.
Equation Used
- Linear reversible whole-wheel radial stiffness.
- No stress, damping or tire rating prediction.
- Illustrative spoke profiles and rim deformation.
Constant whole-wheel radial stiffness. Chord is a circle geometry comparison, not a predicted tire footprint.
Flexible spokes connect the hub and rim
The steel rim, curved spring spokes, bolted hub and axle are shown against a stationary ground line. The entered stiffness describes the complete wheel under radial loading; it is not the stiffness of each spoke.
The prescribed inspection cycle increases load from zero to the selected peak and then unloads. Axle displacement follows the same linear stiffness equation as the calculator. The curve shapes and local rim flattening illustrate compliance; they are not a finite-element solution or a historical wheel performance reconstruction.
The wheel does not rotate in this test. There is no invented rolling speed, slipping contact point or tire tread passing through the ground.
Compare a measured radial stiffness
Use a stiffness measured or specified for the complete wheel and applicable load range. The original three sliders remain usable. A larger load increases deflection; a larger stiffness reduces it. Radius changes the relative deflection and the separate geometric chord.
The historical reference identifies steel rims and spring spokes. Modern non-pneumatic tires can use different materials and load paths; this diagram does not represent every airless tire.
Linear spring results and a separate geometric comparison
For radial load F in newtons and whole-wheel stiffness k in N/mm, deflection is δ=F/k. Stored energy is U=Fδ/2000 joules. This assumes a reversible linear load-deflection relation without damping.
The former “Patch Length” output has been relabeled “Circle-chord comparison.” Its expression c=2√(2Rδ−δ²) is the chord of an undeformed circle cut at depth δ. It is not a calculated tire contact length: real rim, spoke and tread deformation require additional information.
The relative deflection is 100δ/R percent. All four numerical outputs describe the selected peak load. The animation labels the changing current load separately.
A 1,200 N peak load on a 150 N/mm wheel
At the retained defaults, ideal deflection is 8 mm, stored elastic energy is 4.8 J and deflection/radius is about 2.67%. The circle-chord comparison for a 300 mm radius is approximately 137.64 mm.
Doubling load doubles linear deflection and quadruples stored energy. Doubling stiffness halves deflection and energy at the same load. Those dependencies are independent of the decorative spring-spoke profile.
Large extrapolations are not operating predictions
Real spring stiffness can be nonlinear and direction dependent. This model does not determine spoke stress, allowable load, contact pressure, rolling resistance, damping or fatigue life.
The visible wheel uses an illustrative hub envelope. When requested deflection would exhaust that envelope, it remains visible as an undeformed preview with an explicit message. The numerical linear-spring extrapolation remains available and must not be interpreted as a physically fitting loaded wheel.
The unrelated sector-wheel baling-press video has been removed.
Elastic-wheel questions
Is the orange chord the road footprint?
No. It is a separate circle geometry comparison and is labeled accordingly.
Why is there no rolling animation?
The controls describe a radial load test, not rolling speed or road motion.
Is each spoke stiffness equal to the entered value?
No. The input is the aggregate radial stiffness of the complete wheel.
Why does energy grow faster than deflection?
With fixed stiffness, U=F²/(2000k), whereas δ=F/k.
Reference
Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances, printed page 220, figures 850–852: steel spring rims, jointed spokes and curved spring-spoke forms. The illustration uses the spring-spoke family, not an exact Huxley jointed-link reconstruction. The source does not supply a validated stiffness or tire-contact model.
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