Geometry and self-knowledge

For some reason, my online friends regard me as an authority on cars. I'm not sure why this is; I don't actually know all that much about cars, compared to many other people I know; but I'm the kind of person who dislikes black boxes. I want to know why cars work, and why they're made the way they are. So I seek out information. I try to learn. And occasionally, that results in me gaining a shocking insight that I hadn't thought of before. Today, that was regarding piston velocities.



The basic operating principles of a crankshaft and pistons are very simple. The shaft rotates, the offset crankpins rotate in a circle around the shaft, the connecting rods are forced up and down by the crank pins, and the pistons slide up and down. What I hadn't fully grasped is that the pistons move towards and away from the top of their travel much faster than they move away from the bottom of their travel; indeed, with some engine designs it's possible to have the piston be above the bottom of its travel when the crank pin is at its lowest, and the piston will move down on either side of "bottom dead centre". That's very counter-intuitive, but once you have the right explanation, it's obvious why it happens.

We need to consider why the piston moves up and down when the crank turns. At the sideways extremes, it's obvious why; the crank pins are moving up or down, pulling the bottom of the connecting rod, and that motion is being transferred to the top of the connecting rod, and so to the piston. But what about the upper and lower extremes? That's where it becomes all about triangles. At top dead centre, the connecting rod is pointed straight up and down; the vertical distance between the big end and the gudgeon pin is the length of the rod. As the crankshaft turns, the big end moves downwards a little, and sideways a lot. This reduces the apparent length of the rod, since it's now slanted rather than upright; the apparent length can be found by using Pythagoras's Theorem, with the actual length as the hypotenuse. The result is that the piston moves downwards rather more than the crankpin does. This effect reduces in size as the crankshaft turns, and is eliminated by the crankpin reaching the maximum sideways travel. Then, the effect begins operating in reverse; the apparent length of the connecting rod, or more correctly the vertical projection of its length, begins to get longer as the crankpin moves towards the centre line. By bottom dead centre, this apparent lengthening is dominating, and with the right connecting rod dimensions it's possible to have the final part of the approach to bottom dead centre result in the apparent lengthening (which counteracts the downward motion of the crankpin) actually pushing the piston upwards for a small part of the cycle.

What this means it that pistons connected to crankpins which are above the centre line of the crankshaft will move faster than pistons connected to crankpins below the centre line of the crankshaft. At the sideways extreme, the speed of the piston will be the same no matter which direction it's moving - and the piston will be below the half-way point of its travel.

This effect is one of many reasons it's difficult to make an internal combustion engine that's smooth-running. Both the inherent jerkiness of the power delivery and the differential movement of the mass within the engine make it a real feat to balance out all the little shakes. This effect is why four-cylinder engines are typically less than two litres in displacement; above that size, the amount of mass being moved is too much for acceptable levels of vibration. It's possible to reduce the problem with balance shafts, but they have their own problems.