Look at a map of almost any old railway and you will find it running alongside water. The builders were not sentimental about rivers. A river has already done the hardest part of the survey: over thousands of years it has cut the gentlest continuous slope through the country, and gentle slope is the one thing a railway cannot do without.
Grip is the limit, not power
A locomotive moves a train by pushing its driving wheels against the rail. The most it can push before the wheels spin is its adhesive weight — the weight resting on the driven wheels — multiplied by the coefficient of adhesion between wheel and rail. For clean, dry steel on steel that coefficient is roughly a quarter to a third. On wet rail, or rail coated in crushed autumn leaves, it can fall far lower.
That is the railway's appeal and its weakness. Steel on steel rolls with very little resistance, so on the level a modest engine keeps a huge load moving. But the same smooth contact means the engine can never pull more than a fraction of its own weight. Adding horsepower to a locomotive that is already slipping only makes it slip faster.
On a slope, a share of the train's weight acts backwards down the hill, and for railway gradients that share is very close to the gradient itself. On a 1% slope, about 1% of the train's weight pulls against the engine — near enough 98 newtons, or 10 kilograms-force, for every tonne.
How gradients are written
British practice writes a gradient as 1 in N: one unit of rise for every N units along the track. Most other countries use a percentage or per mille. The conversion is simply 100 divided by N.
| 1 in N | Percent | Rise per mile | Rise per km |
|---|---|---|---|
| 1 in 1,320 | 0.08% | 4 ft | 0.8 m |
| 1 in 200 | 0.5% | 26 ft | 5 m |
| 1 in 100 | 1% | 53 ft | 10 m |
| 1 in 75 | 1.33% | 70 ft | 13 m |
| 1 in 37.7 | 2.65% | 140 ft | 26.5 m |
The notation hides how small these numbers are. A road sign warning of a 10% hill describes something nearly four times steeper than the steepest main-line climb in Britain.
In Valley Rail: Train Tycoon you build railways between small towns and buy a train that runs its route on its own.
The arithmetic of a climb
Put the two forces together. Take a locomotive with 100 tonnes on its driving wheels and an adhesion coefficient of 0.25: it can exert about 25 tonnes-force before slipping. On a gradient of 1 in N, each tonne of train needs 1/N of a tonne-force just to hold its place against gravity. So the heaviest train it can haul up the slope, locomotive included, is 25 × N tonnes.
| Gradient | Heaviest train (tonnes) |
|---|---|
| 1 in 200 | 5,000 |
| 1 in 100 | 2,500 |
| 1 in 75 | 1,875 |
| 1 in 37.7 | 942 |
The rule to take away is that the load is inversely proportional to the gradient. Double the steepness and you halve the train. Real loads are lower, because rolling resistance, curves and wind take their share too, but the proportion holds.
A railway is only as easy as its hardest stretch. The steepest climb a train must make unaided on a route sets the load for the whole route, however level the rest of it is.
The ruling gradient
That hardest stretch has a name: the ruling gradient. It is the steepest gradient on a section of line that a train has to climb without help, and it decides the maximum load a given locomotive can be booked to haul over that section. A line that is level for fifty miles and then has one mile at 1 in 75 is, for loading purposes, a 1 in 75 railway.
Engineers had three ways to deal with a hill:
- Go round it. Follow the valley, accept extra miles and curves, and keep the gradient gentle. Cheapest to build and cheapest to run.
- Go through it. Cuttings, embankments and tunnels flatten the line at a heavy cost in construction.
- Go over it. Accept a steep incline and either run shorter trains or add a second engine — a banker — to push on the climb.
The third option is the cheapest to build and the most expensive to operate, every day, for as long as the line exists.
Two British extremes
Isambard Kingdom Brunel's Great Western Railway is the classic river line. From Paddington it follows the Thames valley west, using the Goring Gap where the river cuts through the chalk hills, and it reaches Didcot with a ruling gradient of 1 in 1,320 — about four feet of rise per mile. It earned the nickname Brunel's billiard table. Brunel concentrated the climbing further west, at 1 in 100 near Wootton Bassett and through Box Tunnel.
The Lickey Incline near Bromsgrove, on the Birmingham–Gloucester line, is the opposite answer. It climbs for about two miles at 1 in 37.7 — 140 feet in every mile — and is the steepest sustained main-line climb in Britain. The builders took the direct route up the escarpment rather than a long detour, and for well over a century heavy trains needed banking engines to push them up. The locomotive in the table above would manage well under half its 1 in 100 load there.
Rivers also have to be crossed: Valley Rail lets you bridge a river in one of five styles.
What the river gives a railway
A river valley is a continuous route that falls one way, usually gently, and rivers cut gaps through ridges a line would otherwise have to tunnel. The price is length and curvature: valleys wind, flood plains flood, and a line that follows a river eventually has to cross it.
Valley Rail: Train Tycoon has six train models for passengers and freight, from a one-coach commuter to a streamlined express, carrying coal, wood, oil, iron ore and steel. The money each trip earns is in-game only and has no cash value. Valley Rail is in closed testing and not yet publicly available.