A straight-line navigation prediction

Learning goal: On a smooth constant-speed curve, tangent prediction has a leading h² defect. A corner invalidates the smooth Taylor argument and can give first-order behavior.

h seconds R meters v m/s

Second-order prediction Use a 90° corner Exact discrepancy Taylor bound Local slope

Doubling h roughly quadruples the leading smooth tangent error. A second-order predictor can remove that term. A corner can prevent the expected higher order; results also depend on step placement.