Explanation and Rationale
The steam locomotive, as commonly employed, has its pistons directly attached to cranks on the driving wheels; thus, there is no gearing, one revolution of the driving wheels is equivalent to one revolution of the crank and thus two power strokes per piston (steam locomotives are almost universally double-acting, unlike the more familiar internal combustion engine).
The maximum rotational speed is fairly fixed for a given engine technology. Given the lack of any variable-ratio transmission between the piston engine and the wheels, the designer is forced to compromise between desired torque and desired maximum speed; the radius of the driving wheels determines this. The radius of the crank affixed to the wheel is of course less than this; its radius determines the length of the piston stroke. This cannot be too large, for the locomotive will be unable to generate enough steam to supply those large cylinders at speed; it cannot be too small, or the starting torque and thus tractive effort will be too small, and the locomotive will not be able to start a train.
Many applications required a low speed locomotive with ample starting tractive effort – industrial use, mines and quarries and logging operations, steeply graded lines and the like – especially when the track is cheaply built and not suited to high speeds anyway. Unfortunately, although the trade-off of speed versus torque can be adjusted in favour of torque and tractive effort by reducing the size of the driving wheels, there is a practical limit below which this cannot be done without making the piston stroke too short on a directly driven locomotive.
The solution is to separate the crank from the wheels, firstly allowing for a reasonable piston stroke and crank radius without requiring larger than desired driving wheels, and secondly allowing for reduction in rotational speed via gearing. Such a locomotive is a geared locomotive. Most were and are still single speed, but some did employ a variable-ratio gearbox and multiple ratios.
Read more about this topic: Geared Steam Locomotive
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