A Spring Wheel is a wheel that replaces the pneumatic air chamber with mechanical spring elements — coiled, leaf, or flexible polymer spokes — that deflect under load to absorb shock. The Michelin Tweel and the Apollo Lunar Roving Vehicle wheel are two of the best-known examples. It exists because air-filled tyres puncture and lose pressure, which is unacceptable on the Moon, on a battlefield, or under a 50-ton mining loader. A well-designed Spring Wheel gives you a controlled vertical compliance of 30–80 mm with zero risk of going flat.
Spring Wheel Interactive Calculator
Vary spring-wheel load, rated deflection, speed, and wheel diameter to see stiffness, ride frequency, contact force, and rolling speed on an animated compliant-wheel diagram.
Equation Used
The calculator treats the spring wheel as a vertical spring. Wheel load gives contact force F = m*g. Dividing that force by selected deflection gives the effective vertical stiffness. The same stiffness and supported mass estimate the undamped vertical ride frequency.
- Load is the static vertical load carried by one wheel.
- Compliant spokes behave as a linear vertical spring at the selected deflection.
- Ride frequency estimate ignores damping, tire tread hysteresis, and vehicle suspension linkage effects.
- The article reference deflection band is 30-80 mm for a well-designed spring wheel.
Operating Principle of the Spring Wheel
A Spring Wheel works by separating two jobs that a pneumatic tyre normally combines into one: carrying the vehicle weight and absorbing road shock. The hub takes the load through a ring of compliant elements — coil springs in the early Martin and Cowey designs from the 1900s, woven leaf springs on the Lunar Roving Vehicle, or moulded polyurethane spokes on the modern Michelin Tweel. Those elements deflect under load, the contact patch flattens against the ground, and the rim transfers torque around the circumference. No air, no valve, no inner tube.
The geometry matters more than people think. Spoke stiffness sets the ride frequency, and you want that frequency in the 1.0–1.5 Hz band for human comfort, higher for unmanned platforms. If the spokes are too stiff the wheel rides like a solid rubber tyre and pounds the chassis — you'll see fatigue cracks at the hub flange within a few hundred hours. Too soft and the rim buckles laterally during cornering, which is the classic failure mode on cheap airless wheelbarrow tyres. Spoke pre-load tolerance on a precision build like the Tweel is held to roughly ±3% across the ring, because uneven spokes show up as a once-per-revolution vibration the driver feels in the steering wheel.
What happens if you get the tolerances wrong? On a flexible spoke wheel, asymmetric spoke stiffness causes the contact patch to walk around the rim as it rotates, generating a hop at wheel rotation frequency. On a coil-spring wheel, a single broken spring drops one sector of the rim and the wheel goes oval — you'll hear it before you see it. Heat is the other killer. A puncture-proof tire flexing 60 mm at 60 km/h dissipates real energy in the spokes, and polyurethane above about 90°C starts to creep, which is why early Tweel variants were rated for low-speed loaders rather than highway cars.
Key Components
- Hub: The central rigid mounting interface that bolts to the axle. Typically machined aluminium or steel with a bolt circle matching the host vehicle — 4×100 mm or 5×114.3 mm for automotive applications. Carries 100% of the vertical load into the spoke array.
- Compliant spokes: The deflecting elements that replace air pressure. Can be steel coil springs (5–15 mm wire diameter), woven steel leaf bands (LRV used 0.83 mm zinc-coated piano wire), or moulded polyurethane fins. Spoke stiffness sets ride frequency and load capacity, with typical deflection range 30–80 mm at rated load.
- Outer rim or shear band: The circumferential element the spokes attach to at the outside diameter. On the Tweel this is a glass-fibre-reinforced shear band that deforms locally at the contact patch but stays circular elsewhere. On historical spring wheels it was a steel rim with a rubber tread bonded on.
- Tread: The wear surface in contact with the ground. Bonded rubber on automotive Spring Wheels, woven titanium chevrons on the LRV, or hardened steel cleats on military half-track variants. Tread depth and compound determine wet grip and wear life — Tweel SSL units run roughly 2-3× the hours of comparable pneumatic skid-steer tyres.
- Lateral stiffening rings: Optional side plates or hoop rings that prevent the rim from collapsing sideways during cornering. Critical on any compliant wheel above about 25 km/h, because lateral spoke buckling is the dominant failure mode when these are absent or undersized.
Where the Spring Wheel Is Used
Spring Wheels show up wherever a flat tyre is unacceptable, where the vehicle operates somewhere a tyre shop cannot reach, or where the load profile destroys conventional pneumatic tyres. That's a narrower window than it sounds, but inside that window the airless tire wins on every metric.
- Space exploration: The Apollo 15, 16, and 17 Lunar Roving Vehicle used woven piano-wire mesh wheels designed by GM Defense and Boeing — pneumatic tyres would have frozen and burst in the lunar vacuum
- Construction equipment: Michelin X Tweel SSL fitted to Bobcat S550 and S650 skid-steer loaders working on rebar-strewn demolition sites where pneumatic tyres rarely last a week
- Military vehicles: Polaris MRZR-D tactical vehicles fitted with airless run-flat inserts, and earlier WWI-era Pavesi-Tolotti tractors that ran on coil-spring wheels for trench crossing
- Mining and quarrying: Bridgestone Air Free concept wheels trialled on underground LHD loaders at Boliden mines in Sweden, where a tyre puncture 800 m underground means a 6-hour recovery
- Agricultural and turf: John Deere ZTrak commercial mowers fitted with Tweel Turf wheels at golf course operations like Pebble Beach, eliminating the daily pressure check on a 14-mower fleet
- Powered wheelchairs and mobility: Permobil F5 power chairs offered with airless caster wheels, removing the risk of a flat stranding a user away from home
The Formula Behind the Spring Wheel
The core sizing question for a Spring Wheel is how stiff the spoke array needs to be to support the vehicle at a target deflection. Get this wrong at the low end of the operating range — say a lightweight unmanned ground vehicle on a heavy-duty wheel — and the wheel barely flexes, transmitting every pebble straight to the chassis. At the high end, an overloaded wheel bottoms out, the spokes go solid, and you destroy the bond between spoke and shear band on the next pothole. The sweet spot lives where rated load gives you 60–70% of maximum spoke deflection — that's where ride frequency, contact patch area, and fatigue life all converge.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| kwheel | Effective vertical stiffness of the spoke array at the contact patch | N/m | lbf/in |
| Fload | Static vertical load carried by the wheel | N | lbf |
| δtarget | Target vertical deflection at rated load | m | in |
| fride | Natural ride frequency at the wheel station | Hz | Hz |
| msprung | Sprung mass supported by that wheel | kg | lb |
Worked Example: Spring Wheel in an autonomous orchard inspection rover
Your robotics team at a Washington State apple orchard is specifying compliant wheels for a 4-wheel autonomous inspection rover that drives between tree rows on packed dirt and irrigation hose. Total rover mass is 80 kg, distributed evenly across 4 wheels, so each wheel carries 20 kg static. You want a target deflection of 25 mm at static load to give a comfortable ride for the onboard LiDAR, and you need to know whether the resulting ride frequency lands in the usable band.
Given
- mtotal = 80 kg
- Fload per wheel = 196 N (20 kg × 9.81)
- δtarget = 0.025 m
- msprung per wheel = 20 kg
Solution
Step 1 — at the nominal 20 kg/wheel load with 25 mm target deflection, compute the required spoke stiffness:
Step 2 — compute the resulting ride frequency at nominal load:
That's high for human comfort but absolutely fine for a LiDAR-equipped rover — you want it above the 1–2 Hz band where pitch motion gets confused with low-frequency terrain features.
Step 3 — at the low end of the operating range, an empty rover with sensors removed weighing 60 kg total (15 kg/wheel), the deflection drops:
The wheel barely flexes — ride feel goes harsh and the rover starts skipping over irrigation hose instead of rolling over it. Step 4 — at the high end, with a payload module bringing rover mass to 120 kg (30 kg/wheel):
This is approaching the deflection limit of a typical 150 mm-diameter polyurethane spoke wheel. Above ~50 mm deflection on a wheel that size, the spokes contact the hub and the ride goes solid.
Result
Each wheel needs an effective vertical stiffness of about 7,840 N/m, giving a 3. 15 Hz ride frequency at the nominal 20 kg/wheel load. That frequency feels firm but controlled — the LiDAR data stays clean over packed dirt at walking pace. Across the operating range, the wheel deflects 18.8 mm empty (slightly harsh), 25 mm nominal (the sweet spot), and 37.6 mm fully loaded (approaching but not hitting the bump-stop). If your measured deflection is significantly off the predicted value, check three things: (1) spoke pre-load asymmetry — even one sector that's 10% stiffer than the others will skew static deflection and produce a once-per-rev vibration, (2) a hub bolt that wasn't torqued to spec lets the spoke array shift on the hub flange and reads as soft, and (3) ambient temperature — polyurethane spokes lose roughly 15% stiffness between 20 °C and 50 °C, which matters in a sun-baked orchard.
Choosing the Spring Wheel: Pros and Cons
Spring Wheels are not a drop-in replacement for pneumatic tyres. Compare them on the dimensions that actually decide the buy: top speed, load rating, ride frequency, cost per wheel, and service life. Solid rubber wheels are the other obvious alternative — cheaper, simpler, but with no compliance whatsoever.
| Property | Spring Wheel (Tweel-type) | Pneumatic tire | Solid rubber wheel |
|---|---|---|---|
| Top speed rating | Typically 40–80 km/h on production units | 200+ km/h on passenger car tyres | 10–25 km/h before heat failure |
| Puncture risk | Zero — no air chamber | High — single nail ends the trip | Zero |
| Vertical compliance at rated load | 30–80 mm controlled deflection | 20–40 mm with damping | 2–5 mm — effectively rigid |
| Cost per wheel (skid-steer size) | ~3–5× pneumatic equivalent | Baseline | ~1.5× pneumatic |
| Service life on rough terrain | 2–3× pneumatic life on debris-rich sites | Baseline (often <500 hr on demolition sites) | Limited by tread wear, ~50% pneumatic life |
| Maintenance interval | Visual inspection only — no pressure checks | Daily/weekly pressure check | Visual only |
| Best application fit | Skid-steers, military, lunar/planetary rovers, mowers | Highway, passenger, high-speed haul | Forklifts, hand trucks, low-speed trolleys |
Frequently Asked Questions About Spring Wheel
That's resonance between the wheel's natural frequency and a once-per-revolution forcing function — almost always caused by spoke stiffness asymmetry around the ring. Even a 5% stiffness difference on a single sector creates a radial force imbalance that excites the suspension at wheel rotation frequency.
To diagnose, jack the vehicle up, mark one spoke, and press down on the rim at each spoke position with a luggage scale. If you see more than ±10% variation in force at the same deflection, the wheel needs replacing or the spokes need re-tensioning. On polyurethane wheels, asymmetry often comes from one sector having taken a permanent set after being parked under load for months.
No, and the reason is heat, not load. A flexing spoke dissipates energy on every rotation, and dissipation scales with rotation frequency squared. Run a 40 km/h-rated Tweel at 70 km/h with half load and the spoke core temperature climbs past the polyurethane glass transition within minutes — the spokes soften, take a permanent deflection, and the wheel becomes oval.
The speed rating exists because of thermal limits in the compliant element. Lighter load buys you maybe 5–10% more speed margin, not 50%.
It comes down to debris ingress and serviceability. Coil-spring wheels in the Pavesi or modern bicycle Loopwheel pattern shrug off mud and stones because there's nothing for debris to wedge into permanently — a stone caught between coils gets ejected on the next rotation. Polyurethane spoke wheels trap mud between the spokes and add unsprung mass that throws off the ride frequency calculation.
Polyurethane wins on weight, cost, and noise. Coil-spring wins on serviceability — you can replace one broken spring in the field with hand tools, whereas a damaged Tweel is a complete throw-away.
Lateral spoke buckling. Under hard braking, longitudinal load shifts to the front wheels and the contact patch tries to lengthen. If lateral stiffening is marginal, the spokes on the loaded side buckle sideways before they buckle vertically, and the rim walks off-centre relative to the hub.
Check for visible spoke kink near the rim. If you find one, the wheel is finished — buckled polyurethane spokes don't recover. The fix on a future build is either thicker spokes or adding a hoop ring on each sidewall to constrain lateral motion.
Yes, but you'll get less deflection than your target and a stiffer ride. With a 12,000 N/m wheel under your 196 N load, deflection drops to 16 mm instead of 25 mm, and ride frequency climbs to about 3.9 Hz. That's still inside the usable band for a sensor rover but the ride feel will be noticeably harsher.
Manufacturer stiffness ratings are also typically quoted at a specific reference deflection — Spring Wheels are often progressively stiffening, so the rated value at 50% deflection may not match your operating point at 20% deflection. Always test at the actual load before committing the design.
Temperature range and outgassing. The lunar surface swings from -170 °C to +120 °C between shadow and sunlight, and any polymer would either freeze brittle or boil off volatiles in vacuum. The LRV used 0.83 mm zinc-coated piano wire woven into a flexible mesh with titanium chevron treads — stiffness stays nearly constant across that temperature range and there's nothing to outgas.
This is the same reason modern lunar wheel concepts from Bridgestone and Michelin for the Artemis programme still use metal mesh or shape-memory alloy spokes rather than polymer. A Tweel works on Earth because it never sees -170 °C.
References & Further Reading
- Wikipedia contributors. Non-pneumatic tire. Wikipedia
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