# Power-to-Weight Ratio

## Power-to-Weight Ratio

The Power-to-Weight ratio of a car is a measure of its ability to accelerate. A steam locomotive’s ability to accelerate is governed by its the ratio of its “power : total train weight” ratio and by its adhesive weight and adhesion coefficient (ignoring resistance factors).

The Power-to-Weight ratio of a steam locomotives is nevertheless an important meaure, however its implications are more nuanced than for a car. David Wardale explains the importance of having a high Power-to-Weight ratio on page 277 of his book as follows:

…. for high speed operation, a high Power : Weight ratio is essential. It implies the need for a small boiler, requiring highly efficient draughting, and high combustion rates, requiring an efficient combustion system. Failure to realize this means that at high speed most of a locomotive’s power is absorbed in pulling the locomotive itself. In fact any locomotive has a ‘zero drawbar power and thermal efficiency speed’ at which all its power is used to pull itself along, this speed being largely a function of its inbuilt power : weight ratio. That this ratio was not high enough in steam locomotives was the basic reason why steam was perceived as being unsuitable for the accelerated services which many railway administrations, especially in Europe, saw as essential if rail transport was to remain competitive. It was, however, only an inherent characteristic of most First Generation Steam (FGS) locomotives, not of steam traction per se.

On page 273 of his book he compares the Power-to-Weight ratio of the Red Devil with other FGS locomotives as follows:

The Drawbar Power-to-Weight ratio [of No 3450, the Red Devil] based on the engine weight only (i.e. excluding the tender) was 23.0 kW/ton calculated from the maximum recorded sustained equivalent drawbar power at 74 km/h, and 24.4 kW/ton based on the predicted maximum drawbar power at 100 km/h.

The maximum Drawbar Power-to-Weight ratio in kW per ton of engine weight for some other high power coal-fired locomotives were as follows:

• British Railways ‘Coronation’ class 4-6-2: 17.1 (best British figure based on transitory power)’
• German State Railways 45 class 2-10-2: 17.5 (approximate)1
• French National Railways 240P class 4-8-0: 23.3
• New York Central `Niagara’ class 4-8-4: 18.8 (representative of the very best American practice)
• Rio Turbio Railway 2-10-2: 20.6 (at 50 km/h, the maximum line speed)
• Porta’s experimental 4-8-0: 23.2

In respect of power capacity relative to size 3450 was therefore up to the best standards hitherto achieved despite it being a 2-cylinder simple expansion locomotive with moderate boiler pressure burning mediocre quality coal, this last factor being of great significance as very high power output from steam locomotives generally depended on burning high grade coal. Yet no-one should imagine that it represented a perform­ance ceiling for the classical Stephensonian steam locomotive. Porta’s Second Generation Steam 2-10-0 proposal was designed to give a rated Drawbar Power-toWeight ratio of 32.5 kW/ton, and even with simple expansion 29 kW/ton should have been possible for a medium-speed machine if st­arting the design with a clean sheet of paper.

The predicted Drawbar Power-to-Weight ratio for the 5AT compared well with the above figures. With a maximum sustainable drawbar power at constant speed on level tangent track (and trailing a high capacity tender) of 1890 kW and an engine weight of 80 tons, its Drawbar Power-to-Weight ratio would have been 23.6 kW/ton.

[Note: Wardale uses the word “ton” to mean “tonne” in SI units.]