One Scottish rower's heuristic
In 1892, W.W. Naismith — founder of the Scottish Mountaineering Club — published his rule from personal pacing: three miles per hour plus an hour per 2,000 feet. No studies, no sample sizes, just a strong walker's calibrated intuition. A century of validation found it accurate within ~20% for typical hikers — a hit rate modern apps with GPS traces do not meaningfully beat.
The descendants
Book Time (Scarf's grade-based correction), the Tobler function (speed as a function of slope), and every hiking app's estimate are Naismith with refinements — terrain multipliers, fitness sliders, descent handling. The refinements matter at the margins; the two-term core does the work.
Calibrating yours
Run three known hikes through the calculator, compare planned vs actual, and fit your personal multiplier (most hikers land 0.95–1.15 on good trails). Write it down. From then on, your estimates are YOURS — which converts the rule from folklore into an instrument, and trailhead plans from hopes into schedules.