Heun Integration

lob integrates the trajectory with Heun's method, a one-step second-order predictor-corrector, stepping in down-range distance with a caller-configurable step around a coarse default. Time of flight rides along as an integrated component, not a post-step estimate.

The method choice follows Ballistic Research Laboratory experience, via McCoy (Modern Exterior Ballistics): "The cumulative experience of the Ballistic Research Laboratory has shown that the one-step, second-order methods are, in the practical sense, optimum solutions of the point-mass trajectory problem." Higher-order methods cost roughly twice as much without earning back the step size; first-order methods need impractically fine steps to hold accuracy. We did not take McCoy's word for it: the benchmark tree pits RK4 against Heun at matched accuracy, and Heun comes out faster. Error falls as the step shrinks, at linear cost. Callers with unusual regimes measure their own trajectories rather than trusting a global number. See Integration Accuracy and Step Size for accuracy notes.