Sixty-Nine Fifty-Five: The Constants Tokyo Measured

The most-used propagation formula in electrical engineering — the Okumura-Hata urban median path-loss formula, L = 69.55 + 26.16 log10 fc − 13.82 log10 hb − a(hm) + (44.9 − 6.55 log10 hb) log10 d — contains no derived constant at all. Every coefficient is a regression number fitted by Masaharu Hata (1980) to Yoshihisa Okumura's 1968 Tokyo measurement curves. The contrast is free-space propagation, where the Friis equation derives the distance exponent as exactly 2 from geometry and energy conservation. This paper evaluates the formula in a runnable notebook: its implied distance exponent runs from 3.52 at a 30 m base antenna to 2.98 at 200 m — the law a planner gets depends on the tower; at a canonical 900 MHz link (hb = 50 m, hm = 1.5 m) the urban, suburban, and open-area fitted corrections spread the same link across 28.51 dB; and the COST-231-Hata refit moved the constants (intercept 69.55 to 46.3, frequency coefficient 26.16 to 33.9), disagreeing with the original fit by +1.33 to +4.33 dB at their shared 1500 MHz boundary. Within its validity box (150–1500 MHz, hb 30–200 m, d 1–20 km) the formula predicts well — that is what a good fit does; the paper receipts its epistemic status, not its usefulness. Grade: **A FIT SPENT AS A FORMULA — EVERY CONSTANT WEIGHED IN 1968 TOKYO, NONE DERIVED, AND THE REFIT MOVED THEM.** This paper is part of a breadth program; it touches no claim of the physics core.