There was a HN submission about the G forces in roller coasters. G force is acceleration, so a second derivative. Early looping roller coasters had big spikes

There was a HN submission about the G forces in roller coasters. G force is acceleration, so a second derivative. Early looping roller coasters had big spikes in G force rather than a steady G force. This made them horrible to ride on, so no one did, and was a problem to be solved (later solved by a different loop shape). Measure how spikey G forces are is the 3rd derivative.