HOW  STRANGE  ARE  WHEELS ?

I've long been intrigued by the fact that whereas cars have come to have a more or less common over-all shape there is absolutely no logic whatever as regard their wheel designs - other than being circular to accommodate tyres of course.  On one day in March of 2025 I took my camera with me on my daily constitutional walk, a route which includes some ordinary houses with parked cars and a couple of car parks on the edge of an industrial estate.  These thirty-two designs are simply a random selection of those wheels that were easiest to photograph.  Just to be clear - these are all showing wheel constructions: I ignored disc wheels with clip-on decoration.  Each hub bears the maker's name or trademark, so the individual images are set out in alphabetical order, top-left to bottom-right.

Composite image of 32 different wheels designs.

So what can we conclude from this array?
In other contexts, a high-speed pulley system perhaps, the design requirement would be likely to include minimal air drag during rotation.  So intuition suggests either a minimal number of the slimmest spokes consistent with required robustness or indeed no spokes at all - plain discs instead!

But what do we find when we look at road vehicles where efficiency is paramount?

Record breaking cars.
Racing cycles.
Clearly all the old land speed record-breaking cars chose aerodynamic disc wheels.  (More modern contenders hide their wheels under fairings.)

At the other extreme, when propulsion is limited by Olympic thigh-power the choice is disc wheels again.

Well then, just test the aerodynamics of the wheels on normal cars.

Sorry - can't be done!  Putting a wheel in an air-tunnel would simply measure the forces set up as air passes the wheel.  But a car wheel is both moving and rotating in synchrony, with much more complex patterns.  It's easiest to think about the movement of a single tyre tread block.

Imagine a moment with the wheel going along the road when that block is on the leading surface of the tyre. So the tyre doesn't disintegrate: the tread block's double speed at the top of its circuit exactly makes up for the fact that it's not moving along the road at all while it's in contact with the road.  On average, the whole tyre and the whole wheel get from A to B together!

This kind of motion is dignified with the technical name, cycloid.  It can be visualised like this, the red line following that tread block going up and down as it moves along the road.

Centroid line graph.
Incidentally, the tread block's velocity graph is almost exactly the same shape, with momentarily zero speed as it touches the road, up to double the vehicle speed at the top of the curve. Hence -
    Silly quiz question: Which parts of your car travel fastest?  Answer: the tops of the tyres.
    Ridiculous quiz question: Which parts of your car never move?  Answer: the bottoms of your tyres.
Another complication with car wheels which doesn't arise with other kinds of wheels is that they have to be dish-shaped over-all, to accommodate the brakes on the insides.  And they need a generous airflow to achieve cooling when necessary.  (That's a shame.  Why not use oil-cooled transmission brakes on powered wheels?  They're not subject to reduced effectiveness after driving through a flood.)  So, it seems that measuring the aerodynamic properties of competing wheel designs is impossible.

But it's not really necessary to measure anything.  Can the aerodynamic efficiencies of competing wheel designs be compared?  The answer is a theoretical "Yes", but with practical difficulties: differences would be small, even at high speeds.

However, in making inter-design comparisons it wouldn't really matter what fluid was involved.  Hydrodynamic comparisons would be relatively simple and equally valid.  A few hours' use of the wave tank on some maritime university's campus could see the job done.  A heavy rig with the competing wheels on opposite sides could be dragged along the bottom of the tank - quite slowly - using a central towing point.  The direction of swing of the rig would indicate relative hydrodynamic efficiencies.

It would have to be done only once.  Any positive verdict would simplify and reduce the costs of manufacturing wheels to a more nearly-standard design, as well as making some small contribution to improved fuel economy and reduced global warming.  So with four of them on almost every car it would seem to be a worthwhile undertaking.

By whom?