'And the wheel,' said the Captain, 'what about this wheel thingy? It sounds a terribly interesting project.'
'Ah,' said the marketing girl, 'well, we're having a little difficulty there.'
'Difficulty?' exclaimed Ford. 'Difficulty? What do you mean difficulty? It's the single simplest machine in the entire Universe!'
The marketing girl soured him with a look.
'All right, Mr Wiseguy,' she said, 'you're so clever, you tell us what colour it should be.'

- The Restaurant at the End of the Universe, Douglas Adams

The wheel is not exactly the single simplest machine in the entire universe. It is one of a small number of basic machines of which the absolute simplest are the inclined plane (ie, the ramp) and the lever. The wheel is technically a variant of the lever, as we shall see, but it's still pretty darn simple. In its various incarnations it has transformed our daily lives, simultaneously removing the drudgery of walking for miles carrying heavy things, and indirectly causing more deaths than both World Wars put together¹. There are more wheels on the planet than human beings and, whether you realise it or not, you have probably made use of many wheels in your lifetime and perhaps even own several. You may be familiar with the existence of the wheel, but do you actually know how it works? This entry will attempt to explain some of the fascinating engineering involved and dispel some of the myths behind this truly wonderful device.

Why Fish Don't Need Bicycles

But first, some perspective. The wheel is not nearly as universal as you might think. It is, for example, of no use whatsoever for travelling through the vast majority of mediums. In fact, the only situation where the wheel becomes useful at all is at the boundary between a hard, flat solid surface (the ground, generally), and a gas or liquid one of low viscosity (the air, for example). The existence of a gravitational field is also a prerequisite, but we won't worry too much about that as in the absence of such a field you probably wouldn't need a wheel in the first place.

Given its limited range of operating environments, the only potential users of this astonishing invention are the minority that live on land. It is therefore no coincidence that human beings invented the wheel before the dolphins got round to it.

The fact that the wheel has never evolved in nature has caused much philosophising amongst biologists and naturalists. A human on a bicycle can travel faster and further, using substantially less energy and wearing much sillier attire in the process, than one on foot. Nature has evolved many other adaptations that are apparently more complex than the wheel, such as the aerofoil wing and jet propulsion, so anything that gives such a huge boost in efficiency should be of major evolutionary advantage. There are, however, reasons for this anomaly that will become apparent.

The Best Thing Since...

Like most truly great inventions, the identity of the real inventor of the wheel has been lost in the mists of time². Many theories abound as to how the idea first came about. It is possible that the spark of inspiration was the result of a potter's wheel being overturned in an early domestic argument. Perhaps the most romantic theory is that of stone-age man sat alone on a hillside, contemplating how he can get out of carrying all those heavy rocks back to his village, when a log rolls down the hill before his eyes. This seems unlikely however, given that trees are not well known for falling over, losing all their branches and then rolling down hills of their own accord.

In fact, most respectable historians believe that the real development of the wheel began with the sledge, a contraption that was used to transport heavy things such as the component parts of Stonehenge or the Great Pyramid. Workers found that the sledge would move with far less resistance if logs, with their branches hacked off, were placed underneath and it was allowed to roll over them.

After a while, the sledge runners tended to wear grooves in the logs, which not only kept them aligned correctly but actually made movement even easier, due to the gearing provided by the smaller diameter groove and the larger diameter part of the log in contact with the ground (see below). So, the theory goes, as the grooves got deeper the wheel evolved all by itself for a while, until some bright spark saw what was happening, connected two large discs to a shaft, fixed the shaft under the sledge and thus created the first proper wheeled vehicle or cart.

The earliest known evidence for a proper wheeled vehicle was found in the Sumerian city of Uruk in southern Mesopotamia, and dates from around 3200 to 3100 BC. It is also known that the Aztecs built wheeled children's toys, but this was much later on. The Incas also knew of the wheel, but as they lived in mountainous terrain with a surplus of llamas to do the heavy shifting, they clearly didn't feel the need to pursue development any further.

The first proper wheels comprised a solid wooden disc fixed to an axle. Radial spokes were probably added in around 2000 BC to reduce weight. It is thought that the first people to use iron in the construction of wheels were the Celts, circa 500 BC, who used it to reinforce their chariots' wooden rims. The first solid iron wheels were probably used on rail vehicles whose weight justified the extra strength, coinciding with the first iron rails laid in Britain in the early 1700s. Iron was quickly replaced by steel following its invention in the mid-1800s. Although steel is still very much the material of choice in wheel construction today, lighter and stronger materials such as aluminium, metal alloys and even carbon composites are used where the parent vehicle is expected to fly or win races.

Re-inventing the Wheel

The Basics

Two properties are required from a well-engineered wheel: it must be easy to move forward or 'tip over' its axis, and it must cause very little friction with the ground. This is actually rather complex from a mathematical standpoint.

To begin with a simpler example, let us examine the square wheel, a device not in common usage due to its appalling inefficiency. To get a square wheel to move forward, you either have to drag the lower face (the contact area) over the ground, in which case you might as well revert to using a sledge, or get it to pivot over the lower front corner. In the latter case, the wheel hub is actually lifted in the process by an amount proportional to the length of the wheel side, so to get it to move forward you also have to waste energy lifting the payload – and this happens no fewer than four times during one revolution of the wheel.

Now imagine an octagonal wheel. The same situation arises, but the wheel face is shorter, giving less drag over the ground, and the hub/payload has to be lifted by a lesser height. Thus, the more faces the wheel has, the smaller the contact area and the easier it is to tip over.

As we all know, a wheel of real quality is perfectly round, a shape that could be described by mathematicians as a polygon with an infinite number of faces. A straight line extended from one of these faces and perpendicular to a line from the centre of the circle to that point (the radius) is called a tangent. The contact area is where the tangent (the ground) meets the circle and is, in theory at least, vanishingly small and offers virtually no resistance to the tipping action of the wheel. The wheel hub, and therefore the payload, follows a perfectly smooth horizontal path over the ground as it moves forward.

An alternative analogy for a wheel is to visualise a dead weight, representing the centre of gravity at the wheel hub, perfectly balanced atop a pole with a very sharp point at the bottom. Given any slight push, the weight will make the pole tip over, pivoting around the point at the bottom of the pole. Now, if there is another pole of the same length protruding from the hub at a slight angle in the direction of travel, it will hit the ground next and take the weight. Arrange these poles all around the hub and the device will keep falling over itself until something stops it.

Although technically correct, the above explanations are not terribly helpful as they only explain why the wheel is round, not why it is so efficient. Fundamentally, it comes down to overcoming the friction inherent to any system incorporating parts that move relative to each other.

The wheel is actually based on an even simpler device, the lever. A lever is a stick or pole resting on a pivot somewhere along its length, though not in the middle. Any movement applied to the long end of the lever is translated into a shorter movement at the other end, but the shorter end carries proportionately more force. The lever allows people to move or lift far heavier objects than they would otherwise be capable of. It is a simple gearing mechanism, but one with no theoretical limit. Given a long enough and strong enough lever, you could lift Mount Everest³.

Back to wheels: imagine a very simple cart, with fixed axles and spoked wheels. Think of each spoke of a wheel as a lever, the rim end of the spoke as the long end of the lever, and the pivot being all the way along at the hub. Apply a small force to the wheel, for example by pushing the cart. This small force causes the wheel to roll along. The large movement of the rim-end of the spoke is translated into a smaller movement but greater force at the hub end. This larger rotational force, or torque, allows the friction between the rotating hub and the fixed axle to be more easily overcome. Put another way, the hub covers far less distance relative to the axle than the cart does relative to the ground. In the same way that a longer lever is easier to pull, a cart with larger wheels is easier to push.

It is perhaps ironic that most powered vehicles transmit their power directly to the 'weak' end of the lever, necessitating large gearboxes to increase the torque at the axle only for the wheel to reduce it again at the rim.

Traction

Problem one – a perfectly round, infinitely efficient wheel with infinitely small ground contact area isn't really of much use. It may glide over the ground effortlessly, but in most practical applications you also need it to stop and start again on occasion. To accelerate or decelerate a mass, you must apply a force to it. You could achieve this using jets or rockets, but for the sake of the development budget we'll take the easy option and apply a torque directly to the axle or to the wheel itself. To slow down, for example, we need to apply a counter-rotational torque to the wheel, which is usually done by increasing friction between rotating and non-rotating parts. But the forward momentum of the vehicle will try to keep the wheel moving forwards. Something has to give, and a perfect wheel with very small ground contact area will lock up and slide instead.

Therefore, we need some way of sticking the wheel firmly to the ground, without increasing friction. Clearly, the perfect circle is no longer an option. The trick is to make the wheel out of a flexible substance that deforms under the weight of the vehicle. We do this by making the wheel rim out of rubber or similar, and we call it a tyre.

The tyre works as follows: when under compression, the lower part of the normally-circular tyre deforms against the ground, forming a flat patch and thereby increasing the contact area. As the wheel rolls forwards, the bit of rubber on the floor is constantly replaced, and – this is the clever bit – is always stationary relative to the ground, like a caterpillar track, so there is no friction. Rubber has a further advantage in that it is quite tacky, giving even more traction.

The tyre can be made even more compressible by hollowing it out and filling the inside with air under pressure. John Boyd Dunlop⁴ is usually credited with the invention of the pneumatic tyre, which has become ubiquitous on the vast majority of large wheeled vehicles⁵.

The exception, of course, is the train. Rail vehicles always have solid metal wheels, and run on solid metal rails. The main reasons for this are:

1. Trains usually don't have to accelerate or brake particularly quickly;
2. Several hundred tonnes of ironwork sitting over the wheels gives them a modicum of traction anyway;
3. It is difficult to jack up a locomotive by the side of the track to fix a puncture.

Of course it is still possible for a wheel to lose traction, for example if the torque applied by the engine or brakes exceeds the ability of the tyre to grip. This is known as wheelspin when accelerating and lock-up when braking. The size and shape of wheels and tyres are designed to prevent this happening on most vehicles nowadays, and many cars now incorporate electronic traction control and advanced braking systems, both of which detect abnormal rates of spin between wheels and apply or release the brakes as appropriate.

As always there are exceptions, although these are largely limited to the vehicles of Hollywood, Los Angeles, California where all vehicle tyres lose traction and screech at every change of speed or direction, even in the pouring rain, indicating an appallingly poorly-balanced and potentially dangerous set-up.

Axles

Problem two – how to attach the wheel (which rotates) to the vehicle (which doesn't): part one. As most wheels come in pairs, you can connect the centres of the wheels with an axle. In its simplest form, the axle is fixed to the wheels and rotates within guides, called bearings.

Most modern vehicles don't have rotating axles at all, they have fixed axles, and these very rarely look like shafts between pairs of wheels either. If the rotating joint is at the wheel hub itself, each wheel is free to turn independently. This makes turning corners easier, as the inside wheel takes a shorter path than the outside one and must revolve more slowly.

This however presents another problem – how do you accelerate the vehicle if there is no shared axle to rotate? Braking is simple enough, as you can put a separate brake on each wheel, but giving each wheel its own engine to allow them to rotate at different rates is not so easy⁶. The solution is the differential, the operation of which only the absurdly clever can understand.

Bearings

Problem three - how to attach the wheel (which rotates) to the vehicle (which doesn't): part two. With a sledge, most friction is generated between the vehicle and the ground. It is not always possible to engineer the ground surface to minimise friction, and even when it is – for example, covering it in sheet ice - the results are not always desirable. But, as explained in monotonous detail above, the main advantage of a wheeled vehicle over a sledge is that in the former the friction is transferred from the ground to the hub. And the design of the hub is entirely within your control, and you can make it as frictionless as you like, providing you remember to put the brakes on the rotating side of it.

However, no matter what, somewhere one surface has to scrape across another, and friction will occur. The consequences of excess friction are not merely excess wear and tear; we have all seen the movie in which the Roman chariot's wheel falls off, leaving the occupants dazed on the ground and about to be brutally murdered; or the movie where a plane, minus its wheels, does a spectacular belly-flop onto the deck of an aircraft carrier⁷.

Where weight on the bearing is minimal, such as in a child's toy, the bearing may just be a little plastic cylinder with a hole through the centre, called a bush. For bigger loads, you might use more resilient or slippery substances such as PTFE (polytetrafluoroethylene - also known as Teflon), or allow the bearings to be replaced when they wear out. In either case you minimise the friction by making sure the bearing is perfectly round and as smooth or as slippery as possible. You can also lubricate it with something slippery, and preferably quite gloopy as well so it doesn't fly off everywhere.

But by this point in the entry it should be obvious what to do when you need something to move over a surface with little resistance - you use a wheel. So hidden away in the hub of larger wheels nowadays are lots more little wheels in the form of very hard metal spheres, called ball-bearings, or cylinders, called roller-bearings. These wheels merely rotate between two surfaces, an outer one fixed to the road wheel, and an inner one fixed to the axle. The whole assembly is enclosed in a sealed housing filled with grease.

Suspension

Problem four – keeping the wheels on the ground. There are many other aspects to good traction, and one of the most important is keeping the wheel planted on the ground even when the vehicle itself is bouncing around like a spacehopper filled with helium. As a vehicle accelerates, decelerates or corners, it will pitch and roll. In a completely rigid vehicle, this would cause some of the wheels to leave the ground, losing traction. The other consequences of a completely rigid vehicle would be a very sore coccyx and a very broken chassis on hitting the first speed-bump.

Some 'give' is required in order to ensure that both the wheels stay on the ground and the vehicle and contents remain intact. On the simplest of vehicles, such as bicycles and Harley-Davidsons, the tyres provide sufficient give. However, on most vehicles, the chassis is suspended from the wheels by springs and dampers of some kind, collectively known as the suspension. The more weight suspended the better – on contemporary vehicles only the absolute essentials such as the brakes, bearings and steering components are rigidly attached to the wheels. These parts are referred to as the unsprung mass, and have to be engineered to survive the higher shock and vibration they experience.

Very roughly speaking, the harder the suspension (within reason) the better the traction, and the springier it is the comfier the ride. Such discussions go beyond the remit of this entry, but may offer some explanation for the strange lack of traction exhibited by vehicles in the Western US.

Revolution and Evolution

To return to our earlier question, why has the wheel never evolved in nature? In actual fact, it has. Some prokaryotic⁸ bacteria have a rotating device called a flagellum that actually spins in a 'bearing' set into the cell's membrane and propels the cell forward. Although, strictly speaking, this is a propeller rather than a wheel, we shall give them the benefit of the doubt for overcoming most of the major engineering problems.

Rephrasing the question somewhat, why has the wheel never evolved in multicellular organisms? As stated in the beginning, such a creature would appear on the surface to have a distinct evolutionary advantage, so their eventual emergence would seem inevitable. Escher explored the idea with his Curl-Ups: creatures that could curl into a ball and roll about when desired. Philip Pullman's His Dark Materials trilogy features a sentient race called the Mulefa, who attach large seed pods to their limbs to get about. However, in reality, such creatures do not exist and nature being what it is, there must be a very good reason for this.

On a macro scale the design of the actual rotating joint may seem difficult, but evolution has solved much more challenging engineering problems before, and such a joint would not be too far removed from the ball-and-socket joints featured by many vertebrates. Wear and tear on the wheel rim may also be an issue, but some kind of circular hoof would probably suffice.

A more acceptable reason could be the difficulty in applying a rotational force to it. A muscle connected via a ligament would quickly get twisted round the axle bone. But again you could say the same thing about the con rod and crank arrangement in a piston engine.

The real reason however is far more obvious – a large wheeled organism would simply be a stupid idea. By allowing a creature to move far faster and carry far more weight than it would otherwise do, the wheel would dramatically reduce the creature's chances of survival, and any species so equipped would quickly die out. Perhaps one day we will find such an animal in the fossil record, but you only have to consider the effort we put into building bigger and stronger cages to protect us while we continue to misjudge the speed, momentum and traction of our own wheeled vehicles to see why such a species would be doomed from the start.

Wheel of Fortune

It is perhaps the very danger posed by the wheel that has encouraged its adoption into one of the principal mating displays performed by the human male. Studies have consistently shown that the females of many species tend to opt for the males that display the most confidence, aggression and disregard for their own safety. The reasoning behind this is less clear, but the results are unequivocal.

In all parts of the world the young human male, lacking any large, colourful tail feathers or chest to puff out, will get into his car and cruise around nonchalantly for the benefit of any females present. He will crank his sound system to the max to attract attention to himself, as he also lacks the impressive roar of the big cats. At the centre of this display are the wheels themselves, and the bigger, wider, shinier, chromier and more expensive looking they are, the better.

In summary, we shouldn't just look at the wheel as a device of horror and death; it also has a role in the conception of new life, and makes all the intervening bits so much less tiresome. So next time you go cruising with your wheels, just remember that they are not merely fashion accessories. If it wasn't for the wheels on your car, it wouldn't be nearly as useful.