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!

Indeed, 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. 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.

Cycloid 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.
Of course that does refer only to tread blocks.  Aerodynamic complications are even more confused on considering the design of elements between tyre and hub - the patterns I amassed in my photos.

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.)  Be that as it may, disc wheels can be perforated of course, as used on many a light van for example.

At the other extreme, single-spoke wheels are possible, as used for some stylish steering wheels.  Two spokes would be safer but still need very bulky spokes for adequate rigidity.  Could it be relevant that three seems to be the near-universal choice for wind turbine blades?  But in any case car wheels also have to withstand twisting and torsion strains during cornering so it would seem that the best compromise is five spokes, just as five castors provide stability on almost every office chair.

OK then, if five spokes seem intuitively optimal, surely it is equally intuitive that in cross-section those spokes should be as aerodynamic as possible.  And unless anyone is going to advocate having near-side wheels different from off-side wheels the need is for the drag on each spoke to be minimal in either direction.  The only sensible option is evidently for spokes of oval cross-section - certainly not the miniature Mississippi paddle-wheel spokes that can be seen on our streets and car parks.

It's a shame that we've earlier found 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 extreme practical difficulties: differences would be small, even at high speeds.  So the whole matter has evidently been dropped, ignored - "If nothing sensible can be measured and efficiency comparisons can't be made we can simply give the artistic designers free rein to make pretty patterns."

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 an intuitively optimal wheel on one side and an equal-sized test example on the other 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?
Academia?  Government?  Industry?

There does seem to be just one cutting-edge commercial organisation that has at least taken the problem seriously - Lightyear - as featured on the BBC's The Secret Genius of Modern Life.

Lightyear car wheels.