> the onset of change in force is instantaneous, and is felt as a jolt by passengers
An instantaneous change of force (and thus acceleration) create a jolt, I understand that. But taking the derivative again - 'the onset of change in force' - I don't see how that is felt as a jolt.
I thought so too; but that's what I read, as what happens when Euler curves were used in practice (which they were). Unfortunately, I didn't get to the point of trying it out for myself in my game.
[BTW: Like a bob-sled track, I did find that cross-sections that were sine waves or quadratic did feel strikingly smooth - those being smooth, with smooth deviratives, smooth derivatives of derivatives, and so on.]
If you imagine an x-y graph of force over time for a track that went like (start in a straight, an Euler curve to begin the turn, some time in an circular arc, and a reverse Euler to straighten it, end in a straight), the graph would be (level, slope up, level, slope down, level):
_
_/ \_
Apparently, humans are sensitive to the change between levels and linear slopes. Lines are uncommon in nature [though gravity is constant acceleration...?]. Perhaps related to inverse kinematics in limb movement? "Jolt" may be the wrong description.
An instantaneous change of force (and thus acceleration) create a jolt, I understand that. But taking the derivative again - 'the onset of change in force' - I don't see how that is felt as a jolt.