Explainers

How trains work

The physics that moves a train, from coal and steam to 25,000 volts. How a train gets round a bend without steering, why rails buckle in a heatwave, and why a fast train needs most of a mile to stop.

Colours in the figures:fresh steamused steamelectric currentcurrent sent back by brakingmovement and sound

1

From steam to electric

Every train turns stored energy into turning wheels. What changed over two centuries is where the energy is kept and how well it's used. A steam engine burns its fuel on board and wastes most of it as heat. A diesel-electric also burns fuel on board, but far more efficiently, and uses electricity to get the power to the wheels. An electric train carries no fuel at all: it takes its power from the line.

  • Steam1804Trevithick's locomotive hauls a train at Penydarren, in South Wales.
  • Steam1825The Stockton and Darlington Railway opens: the first public railway to use steam locomotives.
  • Steam1863The Metropolitan Railway opens under London: the world's first underground railway, worked by steam.
  • Electric1890The City and South London Railway opens: the first deep-level tube, worked by electric trains from the start.
  • Electric1920s–30sThe Southern Railway electrifies its suburban lines with a third rail.
  • Diesel1955British Railways' Modernisation Plan sets out to replace steam with diesel and electric trains.
  • Diesel1968British Railways runs its last steam passenger trains.
  • Diesel1976The High Speed Train enters service, and diesel trains reach 125 mph (201 km/h) in everyday running.
  • Electric2007High Speed 1 opens in full, and trains from St Pancras run at up to 186 mph (299 km/h).

How much of the fuel's energy reaches the rails

Steam
≈ 6%
Diesel-electric
≈ 37%
Electric (from the wire)
≈ 88%*

Steam: about 8% of the coal's energy reaches the cylinders, and three-quarters of that the drawbar, for engines from 1930 on. Diesel: today's figure; in 1960 it was about 23%. Both from a 2024 study of the world's railways (Tostes and others, Applied Energy). *The electric train's figure is an estimate, counted from the wire: the same study takes 90% from the motors to the wheels, but no source read gives one figure for the whole train. Power stations and the grid lose some energy before it reaches the wire, but an electric train also gets some back: it can return power to the line when it brakes.

Next: Steam

2

Steam: fire, water and a piston

A steam locomotive is a boiler on wheels. A coal fire heats water until it boils, and the steam, trapped and under pressure, pushes a piston. Rods turn the piston's back-and-forth push into the turning of the wheels. The engine below is a Metropolitan Railway A Class tank engine, cut open. The Metropolitan opened in 1863 with borrowed engines; the A Class, from 1864, were its own.

Inside a Metropolitan Railway A Class
  1. Coal burns in the firebox.
  2. Hot gases run through tubes in the boiler and boil the water round them.
  3. Steam collects at the top, above the water. The driver's regulator, in the dome, lets it along a pipe to the cylinder.
  4. A slide valve above the cylinder, pushed to and fro by an eccentric on the axle, sends steam to one end and lets the used steam out of the other, then swaps. So steam pushes the piston one way, then back, and rods turn the wheels.
  5. The used steam blasts up the chimney. This draws air through the fire, making it burn hotter, and gives the "chuff".
Drawn on this site's drawing of the A Class (No. 23 as preserved), with cut-aways; the inside is schematic. Red is fresh steam pushing; grey is used steam leaving. The valve is a slide valve: its hollow underside always joins one end of the cylinder to the exhaust, while the other end opens to the fresh steam filling the chest. An eccentric, an offset disc on the driving axle a quarter-turn ahead of the crank, pushes it to and fro (drawn faintly: on the real engine the valve gear is hidden between the frames). A second eccentric and a curved link let the driver reverse the engine, and choose how early in each stroke to cut off the steam so that it works by expanding. The firebox is surrounded by water, so the fire heats it from every side. The cylinder on the far side is a quarter-turn out of step, so the engine makes four beats for every turn of its wheels. In the tunnels the driver could turn the used steam into the side tanks to condense it, rather than up the chimney. No company lettering or numbers are drawn.

Most of the heat goes up the chimney or warms the air, which is why a steam engine turns less than a tenth of its coal's energy into pulling power. It also needs hours to raise steam, regular stops for water, and a fireman shovelling tonnes of coal.

Next: Diesel-electric

3

Diesel-electric: a power station on wheels

The figure below is a Class 68, built in Valencia from 2013, first by Vossloh España and later by Stadler, which took the works over, and used on both passenger and freight trains. A diesel engine is far more efficient than steam, but it has a weakness: it can't pull from a standstill, and it gives its best power only over a narrow range of speeds. A car gets round this with a clutch and gearbox. A gearbox for a Class 68's 2,800 kilowatts (about 3,750 horsepower) would be enormous, so most diesel locomotives don't use one. Instead, the engine turns a generator, and the electricity drives motors on the axles. An electric motor pulls hardest from a standstill and needs no gear changes.

Inside a Class 68
  1. The fuel tank hangs under the frame.
  2. The diesel engine: a Caterpillar V16, with eight cylinders on each side. One side's eight are drawn.
  3. The engine turns a generator (an alternator), which makes electricity.
  4. Power electronics turn the generator's alternating current (AC) into direct current (DC), then back into AC at whatever frequency the motors need, which sets their speed and force.
  5. A traction motor turns each of the four axles.
Drawn on this site's drawing of the Class 68, with a cut-away: the machinery inside is schematic, and its positions are approximate. The amber dots stand for the flow of electric current, not individual electrons: those only drift a few millimetres a second, and in an AC wire they shuffle back and forth. No operator lettering, logos or numbers are drawn.

Most of Britain's diesel multiple units (the Sprinters and most Turbostars, for example) use a hydraulic transmission instead: a torque converter, in which oil driven by the engine turns the output, takes the place of the generator and motors. Some, like the Class 172 Turbostar, have a mechanical gearbox, as a car does. Bi-mode trains carry both a diesel engine and a pantograph, and use whichever the line allows.

Next: Electric

4

Electric: power from the line

The figure below shows two cars of a Class 387 Electrostar, a four-car electric unit built to run on both overhead wires and third rail. An electric train carries no engine and no fuel. It collects electricity from a wire overhead or a rail beside the track, and its motors turn the wheels. With no engine to carry, it's lighter for its power, so it can accelerate harder. And when it brakes, its motors can work as generators and send power back into the line for other trains to use.

A Class 387 Electrostar on overhead line
  1. The contact wire carries 25,000 volts AC, held level by a catenary wire above it.
  2. The pantograph, on one car of the four, is pressed up against the wire.
  3. A transformer under the same car steps the voltage down, and a cable carries the power along the train.
  4. Power electronics under each motor car turn the AC into DC and back into AC at the frequency the motors need, which sets their speed and force.
  5. Traction motors turn the motor cars' axles.
  6. The current returns through the wheels and rails to the substation.
Drawn on this site's drawing of the Class 387: the pantograph car (right) and a motor car (left). The drawing has the pantograph folded down in its roof well; here it is raised to the wire. The equipment under the floor is schematic. Press "Braking" to see regenerative braking: the current flows back up to the wire (green). No operator lettering, logos or numbers are drawn.

Next: Third rail or overhead

5

Third rail or overhead line?

Britain uses two main systems. South of London and on Merseyside, trains collect 750 volts DC from a third rail beside the track. Most other electrified main lines, and High Speed 1, use 25,000 volts AC from an overhead wire, and High Speed 2 will too. The Underground has a fourth rail as well, between the running rails, so that the return current doesn't stray into tunnel linings.

Third rail, 750 V DC
A Class 387 from the front. A shoe on the bogie slides along the top of the live rail, which sits on insulators just outside the running rail, under the edge of the train. The current returns through the wheels and along the running rails.
Overhead line, 25 kV AC
The same train under the wires. Its pantograph, on the third car, shows above the roof, pressing up on a contact wire about 15 ft 5 in (4.7 m) above the rails. The current returns through the wheels and along the running rails.

Why the voltage matters

Power is voltage times current. A third rail's 750 volts is about a thirtieth of 25,000, so for the same power it must carry about 33 times the current. The heat lost in a conductor grows with the square of the current. So a third rail has to be a heavy conductor, and it needs far more substations to feed it than an overhead line does.

4 MW
Third rail, 750 V
Overhead, 25,000 V
Current drawn, in amps, for the chosen power: the power divided by the voltage.
Third railOverhead line
Supply750 V DC (630 V on the Underground's four-rail system)25,000 V AC at 50 Hz
WhereSouth London, Kent, Sussex, Surrey, Hampshire, Dorset; MerseyrailThe West Coast and East Coast main lines, the south end of the Midland, Great Western to Cardiff, Anglia, Scotland's central belt, HS1, and HS2 when it opens
Top speedAbout 100 mph (161 km/h) at most: the shoe strikes the ramps at each gap125 mph (201 km/h) on the main lines; 186 mph (299 km/h) on HS1
Cost to buildCheaper: no masts, and bridges and tunnels need no rebuilding for clearanceDearer: masts, wires, and often raising bridges
SafetyLive at ground level: dangerous to anyone on the trackOut of reach, but deadly if touched or approached
WeatherIce on the rail stops current reaching the train; heaters helpWind and heat can bring wires down or make them sag
GapsBreaks at junctions and crossings; a short train can stall on a gapContinuous, with short neutral sections between supplies

Next: Going round bends

6

Going round bends

A train has no steering wheel, and its wheels are fixed to a solid axle, so both turn at the same rate. Yet on a bend the outer rail is longer than the inner one. The trick is in the shape of the wheels. Their treads aren't flat but slightly coned: larger in diameter next to the flange, smaller towards the outside.

A wheelset from the end
The path of the wheelset, from above
On straight track the cones keep the wheelset centred: it weaves gently from side to side. On a bend it settles towards the outer rail. The cones and the sideways movement are exaggerated; a real wheelset moves only a few millimetres, and its wide treads never leave the rails.

On a bend the wheelset drifts outwards. The outer wheel then rolls on a larger part of its cone, so it travels further with each turn, and the inner wheel rolls on a smaller part. The axle steers itself round the curve.

Each wheel also has a flange: a lip on its inner edge, which runs just inside the rail. If the wheelset slides too far sideways, on a very tight curve or through a set of points, the flange presses against the side of the rail and holds the train on the track. Normally the coned treads keep the flanges clear, so they're a safety net rather than the steering.

Cant: leaning into the curve

To keep passengers comfortable and the load even on both rails, the outer rail on a curve is raised. This is cant (a road engineer would call it banking). At just the right speed, the push outwards and gravity add up to a force straight down through the floor, and you feel nothing. Go faster and you feel pushed outwards: the shortfall is called cant deficiency. Tilting trains lean their bodies further in, so they can take curves faster.

A carriage on a canted curve
A Class 387 (which doesn't tilt) and, with "Tilting train" ticked, a Class 390 Pendolino, whose body tilts up to 8° on its bogies. The Pendolino's narrower, tapering body is what lets it lean without striking platforms and bridges. Both are drawn from the front, from photographs, to one scale. The strap shows which way "down" feels to a passenger. The dashed line is straight down through the floor: where the two agree, the curve is balanced. The cant is drawn to scale against the track's width.

Next: Heat and cold

7

Rails in heat and cold

Steel grows as it warms. A 60-foot rail gets about a fifth of a millimetre longer for every degree, and in summer sun a rail can be far hotter than the air. Older track was laid in short lengths bolted together with fishplates, leaving a small gap at each joint so the rails had room to grow. Wheels crossing those gaps make the clickety-clack.

Rails in the heat and cold
Two cars of the Underground's 1972 Stock (from this site's drawing) on 60 ft (18.3 m) rails, drawn to one scale; the circles under the joints magnify each gap, and the buckle is exaggerated. Each time a wheel crosses a gap it strikes the far rail end, and the sound spreads from there; when the gaps have closed, the clacks stop. "Sound on" lets you hear it, made in your browser.

Most main lines now use continuous welded rail: lengths welded into one rail that can run for miles. It has no room to grow, so it's held down hard by concrete sleepers, clips and ballast, and the heat becomes force instead. To keep that force manageable, the rail is stretched as it's laid so that it's under no stress at about 27 °C. Colder than that, it's being pulled; hotter, it's being squeezed. Too hot, and it can buckle sideways. On the hottest days, speed limits are imposed until the rails cool, and some rails are painted white to keep them cooler.

Next: Noise

8

Why wheels are sometimes noisy

A train running on smooth, welded track is quiet. Most of the noise you hear comes from something being slightly wrong at the point where the wheel meets the rail.

Four railway noises
Schematic. The trace underneath sketches the sound's shape: it isn't a recording. "Sound on" plays a rough imitation, made in your browser.
  • Clickety-clack: wheels crossing the gaps at the joints of older, jointed track. The sound comes in pairs because a bogie has two axles. Welded track has no joints, so no clacks.
  • Squeal on tight curves: on a sharp bend the coned treads can't make up the whole difference between the inner and outer rails, and a bogie's two axles, fixed parallel, can't both line up with the curve. The wheels are dragged sideways across the railhead in a fast stick-slip, and a wheel, usually the leading inner one, rings at one of its own notes, high and piercing. The leading outer wheel's flange rubs the rail and adds a hiss. You hear it most on tight curves. Treating the rail head or lubricating the flange quietens it.
  • A rhythmic thump: a wheel that has slid under braking, often on leaves, wears a flat spot. It bangs once a turn until the wheel is reprofiled on a wheel lathe.
  • A roar: corrugation, ripples worn into the top of the rail. Grinding trains smooth them away.
  • Brake squeal as the brake pads or blocks grip.

Next: Leaves on the line

9

Leaves on the line

It sounds like an excuse, but it's real physics. Wet leaves that fall on the line are crushed by passing wheels into a thin black film that bakes onto the rail. It's slippery as ice: a wheel can lose almost all its grip. Braking trains slide past platforms and signals, and starting trains spin their wheels. The film can even insulate the wheels from the rails, so the signalling briefly loses track of where a train is.

A braking wheel on leaves
Train
Wheels
The leading bogie of a Class 387, from this site's drawing, to scale. Electrostars have disc brakes, so there are no brake blocks on the wheels; the sander drops sand ahead of the leading wheel. The mark near each wheel's rim shows whether it's turning. When the wheels stop turning but the train keeps going, they're sliding, and each rubs a flat spot (drawn larger than life), which then thumps once a turn. Real trains have wheel slide protection, which eases the brake off a sliding wheel. The braking rates are illustrative, and the animation runs at 8× speed.

The railway fights back each autumn. Railhead treatment trains blast the film off with high-pressure water jets and lay a gel of sand on the rails. Trains carry sanders that drop sand in front of their wheels, and wheel slide protection eases the brakes off a sliding wheel and on again, like a car's ABS. Lineside trees are cut back, and timetables allow extra time.

Next: Stopping

10

How long trains take to stop

A car's rubber tyres grip tarmac hard. A train's steel wheels on steel rails grip far less: that's what makes trains so efficient to keep rolling, and so slow to stop. A train also can't brake harder than its wheels can grip without sliding, and sliding wheels wear flat spots and stop no sooner. Add hundreds of tonnes, and a train at 125 mph (201 km/h) needs well over a kilometre, most of a mile, even with its emergency brake. So the signals for 125 mph (201 km/h) lines are spaced for about 2 km.

Brakes on: who stops first?
Every driver takes the Highway Code's 0.67 seconds to react, and the brakes then take hold at once; real train brakes take a moment to build up, so real distances are a little longer. The car brakes as in the Highway Code's stopping distances. The LNER Azuma (a Class 800: the front car of this site's drawing) uses its emergency brake, 1.2 m/s², Hitachi's figure; its normal full brake is 1.0 m/s². The freight train brakes at 7.5% of g, the rate Britain's train protection system assumes for freight; many freight trains, with their wagons' brakes, do less well. Its top speed is 75 mph (121 km/h), a Class 66's. With "Autumn leaves" the trains can brake no harder than a leaf film's grip allows: 0.05 at best, and it can fall to 0.01. The car and the freight train are plain outlines, and all three are drawn larger than the distance scale. The race runs in real time, with a clock counting up from the moment the driver sees the danger; "4× speed" runs it four times faster.

Grip

How hard a wheel can push or brake before it slips, as a share of the weight on it, and what a train's brakes are designed to need:

A car braking hard (the Highway Code's figures)
≈ 0.66
Steel wheel on clean rail, pulling
0.2–0.4
What a train's brakes are designed to need
≈ 0.1
Crushed leaves on the rail
0.01–0.05

That is why leaves matter so much: trains are designed to brake without needing more grip than about 0.1, and a leaf film can leave far less, as little as an ice skate on ice (see Leaves on the line).

Why signals warn so far ahead. At speed, a driver can't stop within the distance they can see, so a fast line warns them early. On a four-aspect line, a double yellow comes first, then a single yellow, then the red: at 125 mph (201 km/h) the first warning comes two signals before the red, which gives the train room to stop.

Sources

Show the 41 sources from Wikipedia, Network Rail, Applied Energy and 17 more
unverified
  • The electric train's efficiency, about 88% from the wire, is an estimate: no source read gives one figure for the whole train
  • The timeline's dates, the supply voltages and third rail's 100 mph (161 km/h) limit rest on Wikipedia
  • The Pendolino's tilt of up to 8 degrees and its 11 ft 8 in (3.56 m) height rest on Wikipedia, and the height it tilts about (drawn at 5 ft 3 in (1.6 m)) is an estimate
  • The Class 387's width and height rest on Wikipedia
  • The Azuma's brake rates are Hitachi's, read on Wikipedia: the Hitachi paper has moved
  • Steel's rate of expansion rests on Wikipedia; the joint gaps and the rail temperatures at which the heat figure warns are illustrative
  • The A Class's stroke is unsettled (16 by 20 inches as built, or 17 by 26), and its valve is drawn as a slide valve, usual for its date
  • The machinery inside the Class 68 and the Class 387 is placed approximately, and the live rail's position beside the running rail is drawn from a quotation of the standard

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