As children we are fascinated by anything that goes round: a spinning top, a bicycle wheel, or even an old-fashioned gramophone record on its turntable. The magic fades as we grow older and become used to the wheel as a part of everyday life. But do we understand how it works? At one level, the motion is simple, but as we look more deeply into the matter, some curious features emerge. For example, in school physics, the wheel is pictured as a rigid circular disk rolling along a flat surface like a coin on a marble slab. The slab is smooth and hard and the rim is narrow, so at any given moment, the wheel is supported at a single point. This is a useful model for some purposes, but since no part of the wheel touches the slab for a finite period of time, it doesn’t explain how the wheel ‘knows’ which direction it is supposed to be rolling in (figure 1). Nor does it represent what actually happens.
A real wheel carries a load, however small. The load passes through the rim into the slab, and if the area in contact with the slab were infinitesimally small, the stress, which is equal to the force divided by the contact area, would be infinite. No material can withstand infinite stress: it must deform or break. So locally, the shape of the wheel and shape of the slab must change (figure 2). The idea of a perfectly circular wheel running on a perfectly flat surface exists only in the imagination.
For example, the wheels on a car have squashy rubber tyres. Each presses down on the road over an area about the size of your hand. This area - the contact patch - bridges across chippings in the road surface that would otherwise rattle the springs, and contrary to the classical laws of friction, a large contact patch grips the road better than a small one. Consequently, the pneumatic tyre helps to smooth out the ride and keep the car on the road. Without it, road travel at present-day speeds would be intolerable.
In fact, the rubber tyre generates two distinct kinds of friction. One is the conventional kind that stops your tea-plate skidding across the table when you pick up your toast: the molecules on the underside of your plate form temporary bonds with those on the table top. The other is less obvious because it only works when the tyre is moving relative to the road surface. On a dry road, both are present, but when it rains and a water film covers the road surface, the conventional friction all but disappears and we are left with something called hysteresis grip. As you might imagine, with two friction processes taking place simultaneously, the question of how tyres grip the road and exactly what happens within the area of the contact patch when the driver steers round a curve or applies the brakes turns out to be quite complicated. The rubber doesn’t simply ‘stick’ to the road, but creeps along the surface, draping itself over the stones that project from the asphalt. Because of the relative motion, the stones plough through the rubber, and in fact towards the rear of the contact patch, the relative motion increases sharply and there is a well-defined area of slip (figure 3).
Railway wheels grip the rail in a different way. On a typical passenger coach, there are eight wheel disks, each having a steel tread that rolls along a steel rail. Again, the coach is well insulated so it’s smooth and quiet inside; riding in a train nowadays is exquisitely comfortable compared with a century ago, or indeed compared with most other forms of transport. Each wheel carries a load of 10 tonnes, about the same as the rear axle of a double-decker bus. However, compared with a pneumatic tyre the contact patch under a railway wheel is minute, only about the size of your thumbnail. It must support the wheel and transmit all the braking forces and most of the lateral forces that steer the wheels round curves in the track. (You may find the idea of steering a railway train somewhat peculiar, and we’ll return to it in a later section.)
In fact the ‘real’ contact area is even smaller than it appears. Although the wheel and rail look smooth to the human eye, under a microscope they are not. Within the contact patch there is very little contact at all: the load is focussed on small peaks on the surface, so that the stress at the tip of each peak (force divided by area) reaches gargantuan proportions and the peaks themselves are deformed and harden under repeated impacts until they break away as tiny flakes of steel (figure 4). Moreover the tread and the rail do not grip each other firmly across the whole of the contact area. They grind, and under traction or braking there is a zone of pronounced slip towards the rear. All these processes generate high-pitched vibrations such that each wheel resonates like a church bell. This is why trains rumble and squeal: there is no compliance within the contact patch, and compared with a road vehicle, the suspension has to filter out vibrations over a wide range of frequencies. Fortunately, the irregularities in the wheel and rail are small so that from the passenger’s point of view, a modern train gives a smooth ride.
But not as smooth as the ride in a submarine, where the ‘contact patch’ extends over the entire hull, and the supporting material is not solid but liquid. The submarine is special because when cruising at depth it doesn’t make bow waves, which draw off energy and slow the craft down; nor does it encounter sea waves that would otherwise cause it to heave, pitch and roll. Both kinds of wave are formed at the boundary between the two media, air and water. This is where surface craft operate, and where most of the trouble occurs. There are two main options for a sea-going craft: plough straight through the sea waves or skip over the top. Quicker boats skate along the surface, supported on a relatively small area of contact. They do this because water has inertia. Under impact, particles of water must be accelerated out of the way, and this requires considerable force when the impact takes place at high speed. It’s the reaction from these impact forces that supports the stone that you skim along the surface of a pond. Under these circumstances, the water seems to behave like a solid rather than a liquid.
Slower vessels need buoyancy to keep them afloat. The buoyancy comes from the pressure exerted by the surrounding water: the deeper you go, the greater the pressure, and the greater the thrust on the hull. The sum of the pressures acting on each square millimetre combine to produce an upward force that exactly counterbalances the vertical load (if it didn’t, the ship would sink a little until it did). But this alone doesn’t guarantee that the ship will stay afloat. It is necessary to profile the cross-section in such a way that if the ship rolls to one side the changing pressure distribution acting in combination with the ship’s own weight restores the hull to an upright position - the ship rights itself automatically. Many early ships were lost because the interplay between the centre of mass and the centre of buoyancy was not fully appreciated, and the sequence of disasters continued up to recent times notably with the loss of two passenger car ferries because water was allowed to leak in through the bow doors and upset the balance.
Aircraft are supported by the atmosphere, which is also a kind of fluid. But unlike the ship floating in water, the aircraft must be moving. Motion relative to the surrounding air changes the pressure on the wing surface. Strangely, most of the lift is provided not by air pressing upwards from below, but by suction on the upper surface, as if the wings were hanging from invisible wires. At least, that’s how it appears on the scale at which humans normally view things. But if we look more closely, we see that the atmosphere consists of vast numbers of molecules. Unlike the molecules in a solid, they are darting about at random and often collide with one another as well as any solid object that happens to get in the way. It is the collisions that we interpret as pressure. If large numbers impinge per unit area, the pressure is high, while if small numbers impinge, the pressure is low. At the molecular level, there is no such thing as ‘suction’, only a reduced frequency of impacts. Hence the notion of suction and that of molecular impact are alternative mind pictures that work best at different scales of measurement.
None of this, though, explains why there are fewer impacts per square millimetre on the upper surface of an aircraft wing compared to the lower surface. It seems that there are six distinct explanations for the ‘lift’ that keeps an aircraft flying, and eventually as this web site approaches completion we’ll look at them in detail. Incidentally, none refer to molecular impacts at all.
When an aircraft stops, it drops. A ship can capsize, which is equally disastrous for passengers. Trains occasionally leave the rails. Cars run out of control. Engineers who work in the sphere of transport worry about safety more than anything else. The reason they worry is that there is no foolproof method for designing, for example, the perfect airliner. Any new model carries hidden risks. All one can do is try to imagine the risks in a systematic way, then configure the design so that the worst doesn’t happen, or at least, not very often.
One of the reasons that vehicles occasionally get out of control is that they are in some sense unstable. For example, a car that oversteers will amplify the driver’s actions. A small deviation to the left or right will develop into a progressively tighter curve, and the forces generated thereby within the vehicle suspension tend to accentuate the swerve and make matters worse, rather like a badly designed ship that capsizes when it rolls past a certain point. Such behaviour is difficult for ordinary drivers to correct, and in certain circumstances makes the car undriveable. Aircraft are subject to analogous forms of instability in three dimensions, some of which involve oscillations suffiently violent to shake the airframe to pieces. Trains can snake from side to side in a phenomenon called ‘hunting’ that plagued steam railways well into the 1970s.
But not all the things that engineers worry about are so dramatic. In fact most are mundane, but no less interesting for that. Many are common to different kinds of vehicle, one of the most pervasive being vibration. Vibrations are injected into your car from the road surface on which it travels, and the same applies to a passenger coach travelling on steel rails. In addition, any machine with rotating parts is liable to shake if the rotating components do not exactly balance. Whatever the source, the resulting vibrations usually shorten the life of the machinery, and they can leak into a part of the structure that resonates in sympathy, making conditions unpleasant if not unbearable for passengers. Another pervasive phenomenon is friction, which resists movement of the vehicle and steals energy directly from the rotating components. On the other hand, friction is essential for some kinds of vehicle to operate at all. A car would be impossible to control without friction between the tyre and the road, nor could a train start or stop unless there were friction between wheel and rail.
The aim of this web site is to examine the way vehicles move, and in particular, the interaction that takes place in the contact area between the vehicle and its surroundings. We go quite deeply into some topics and where necessary explain the physical processes in terms of mathematics. Engineers use mathematics because they have to quantify things in order to arrive at a practical design. But the maths needs a foundation to build on, namely an intuitive understanding of what is going on. This entails thinking in pictures – mental images that are unique to every individual. After all, physical phenomena can be understood at different levels, no one of which tells the whole story. We have seen one example already in connection with aircraft wings. Another would be the rolling resistance that slows down a railway train, an element of which arises because the track is not completely rigid. You can tackle this either (a) by writing down equations for the energy that is injected into the ground and absorbed through visco-elastic deformation, or (b) by painting a simple mind-picture: the track sags beneath each wheel and the depression is dragged along, a little behind the wheel because the ground is sticky and it takes a moment to recover. The wheel is therefore travelling uphill. Even if you can’t predict the forces involved, at least you can make sense of what happening. If the maths doesn’t work for you, the pictures might.
Eventually, the material in this web site will extend to four main areas, each area being divided into a number of topics. Each topic will be labelled with a prefix to indicate the area to which it belongs. The prefix C denotes road vehicles. R will indicate railway trains, M marine craft, and A aircraft. There are also some general topics prefixed G that are scattered among them.
The digits that follow the letter prefix reflect the position of the topic within a notional structure. Like the roots of a tree, the content divides and subdivides as it penetrates more deeply into the subject. Topics located high on the stem are concerned with the vehicle as a whole, while those lower down have to do with matters of detail. In fact there are really two kinds of root. The first kind relates to hardware: the mechanisms and materials that make up a working vehicle. The other relates to principles, specifically, those that govern how objects behave.
The web site is a work in progress. At the time of launch, it includes only the section covering road vehicles together with some general content that will eventually link together a wider range of topics as they appear. We anticipate that each additional area (rail, marine, and aerospace) will take about a year to complete, with the last area appearing in 2015. Most of the content is adapted from books and papers published by other writers, and is therefore second-hand. To the extent that many of the sources are themselves are re-workings of other people’s material, it is third-hand. We are building on the work of others. This is inevitable because transport engineering spans across a number of distinct technological disciplines and no-one can be expert in them all. Our excuse is that not all the topics are easily available in published form, and some kind of overview might be useful. And from time to time we do attempt to tie up loose ends or re-interpret an obscure topic in a way that the newcomer can more easily understand.
The structure is not particularly important because the topics are self-contained. You can dip into them at random, or if you prefer, tackle them in the order in which they are set out. We start at the bottom, not the top, that is to say, we start with the contact patch and work upwards in stages to the behaviour of the vehicle as a whole. You may find this a little odd at first.
Within limits, you are welcome to use the material for your own purposes. This includes the text and the diagrams, which are copyright under the Creative Commons framework. This means you can download them, copy them into your own documents and change them if you want. But please acknowledge where they came from and don’t use them commercially for gain of any kind. The photographic images and artwork are copyright under a different arrangement, and you will need to contact the owners separately for details.
As explained earlier, most of the material in this web site is a re-interpretation of material produced by other people. There is always a risk of mistakes, so please don’t take anything you read here for granted. There are plenty of mistakes (or misrepresentations) in what follows. It’s just that we don’t know where they are yet. If you find some, please let us know. We would greatly welcome your comments, criticisms and suggestion for improving the site. Please email firstname.lastname@example.org