To illustrate, I calculated velocity and acceleration using the position value in steps of 1, 5, and 30 degrees. As you could probably guess, only knowing the position value every 30 degrees does not give good results at all, much like how knowing the position of the runner every 40 yards doesn’t tell you much. The 5 degree increment was still pretty far off. The result of the one degree increment was pretty good with values closely matching the values calculated by derivative equations.
|Plots of velocity and acceleration using various step sizes in the calculation. The values calculated using the 1 degree step intervals pretty much matches the values from the derived equations, so the lines are basically overlapping in the graph. The lines from the 5 degree step values are a little off and the lines representing the 30 degree step are really far off.|
So there you have it, how to calculate piston position, velocity, and acceleration if you know the stroke and connecting rod lengths. You don’t even need to know calculus or physics, but you do need to know where to find the info.