The motors of a tram are expected to be able to give much higher power for a short period than they could sustain continuously. This ensures rapid acceleration and good hill climbing speeds without the need for inordinately large motors.

The heat generated during these periods is gradually dissipated during the much longer periods of gentle work in between.

It is therefore the short-term power rating of a traction motor which determines its usefulness and this is the rating usually quoted.

In Bath, the steepest gradient is 1:8 (12%) on the Lansdown route and the longest hill where a minimum speed of 30 mph (50kph) must be maintained is Wellsway which has a gradient of about 1:12 (8%). From the chart below, it is possible to calculate the required power-to-weight ratio needed for the vehicles.

The horizontal axis indicates speed in mph and the diagonal lines indicate the various gradients.

In the first example, a speed of 30 mph (vertical green line) and a gradient of 1:12 (equivalent to Wellsway) is assumed. From the intercept of these lines, the horizontal green line is drawn to find the power/weight ratio required. In this example it is just over 15 hp/tonne or about **12 kw/tonne** (red spot).

A second example, the same speed of 30 mph is required up Lansdown, a gradient of 1:8 ; but the intersection of these lines is off the chart. By calculating, instead, half the speed from the 15 mph line (vertical blue line), half the power can be read-off. (horizontal blue line) and then doubled. In this example, the reading is 9.2 kw/tonne (purple spot) and by doubling we arrive at the true figure of **18.35kw/tonne**

(This takes no account of wind resistance, which is not directly proportional to speed, but at these speeds its effect can be ignored for such approximate calculations)

By suggesting about 15 kw/tonne as a target figure for Bath trams, we would be allowing spare capacity at 30 mph on all except short sections of the steepest hills. On level ground this would give good acceleration to the final speed and spare power to cope with unexpected loads. This would also allow the vehicle to comfortably exceed the road speed limit up Wellsway. Electronic governing is easy to apply to trams if required, a better system is to acknowledge that because a tram is a rail vehicle on reserved track, the road speed limit does not apply in these circumstances.

In actual practice, there is an overriding consideration which results in much greater motor power being specified. The Railway Inspectorate insists that a fully-laden tram shall be able to complete its journey with one motor out of action.

Although the operating speed under these conditions is not expected to be anything like the normal service speed, the provision of the necessary overload capacity for the motor usually results in a substantial power reserve being available under normal (two motor) operating conditions.

For a full-sized version of the chart, to permit more accurate calculations, click here

Sustainable energy sources for a tram

'Peaky' nature of tramway load

The prototype of the TPL Pullman vehicle proposed for Bath has a weight of about 22 tonnes and a pair of motors rated at 90kw continuous power and 170% for 10 minutes. This is equivalent to 8 kw/tonne continuous or 14 kw/tonne maximum.

If the body weight were reduced to (say) 18 tonnes by making a double-decked version, this would become **10 kw/tonne continuous** or **17 kw/tonne intermittent** which is more than adequate.