There is a famous question that sits at the crossroads of geography, mathematics and philosophy: “How long is the coastline of Britain?” At first glance, a pretty straightforward question – just think back to your geography textbook and dredge up the correct number. Most people say it’s around 11,000 miles – estimated from the perimeter of a triangle formed by Dover, John O’Groats and Land’s End with a ‘fudge factor’ added on for Wales.
For pub quizzes, this answer might be good enough, but is it accurate? Well, you could get all the ordnance survey maps and trace the coastline with a piece of string and eventually produce a second estimate. Certainly, the answer will be different to the first, but is it more accurate? The snag is how do you measure? Where do you trace the string for an accurate measurement? How far up the rivers do you go? Do you trace all the way to the source of the river and then back along the other bank? Do you measure the coastline at high tide or low tide? Do you trace in and out of every rock? At an extreme you would be measuring around every pebble and every grain of sand, to such an extent that the answer is very much larger than first expected. So the truly accurate answer to the question is – it depends on how you measure it.
The same kind of bizarre logic applies to shaft speed measurement. If you simply need a rough idea of how many revolutions a shaft completes in one minute, it’s pretty straightforward and even the crudest of measuring systems should deliver a fair answer. But what happens when you need to know what the speed is, say, every millisecond and then control the actual speed so that this corresponds to a tightly toleranced set point?
To borrow some terminology from the old vinyl record turntables, speed variations can be described as ‘wow’ and ‘flutter’. Wow typically refers to speed variations over relatively long periods and flutter refers to speed variations over relatively short periods, typically less than once per revolution. Often, both are important and the requirements to tightly control both wow and flutter are common in many sectors of industry: CNC machine tool motion control; aircraft flight controls; radar antennae; and weapons control systems. Such control engineering issues do not just relate to complex motion control but also to driving shafts at a constant speed (especially when there are variations in load). When one approaches the issue of a shaft that must rotate at truly constant speed, then the same logic that has us measuring around the grain of sand will quickly tell you that to get a shaft to rotate at a perfectly constant speed is – in the extreme – impossible.