How Many Clock Stations Does a Global Height Reference Frame Need? A Geometry and Dilution Estimate

A global height reference frame needs potential ties distributed over the continents, not a single excellent comparison repeated in one place. The question of how many clock stations suffice is therefore geometric as well as metrological. This paper models frame datum error as a random per-tie term that averages down with station count plus a systematic floor that does not, and tabulates the result for five network sizes with their implied mean spacings. The computed results, taken from the deposited script, are as follows in summary: The computed rows entry 1 stations is 6. The computed rows entry 1 frame_datum_error_mm is 6.45. The computed rows entry 1 mean_spacing_km is 8.5e+04. The computed rows entry 2 stations is 12. The computed rows entry 2 frame_datum_error_mm is 5.77. The computed rows entry 2 mean_spacing_km is 4.25e+04. The computed rows entry 3 stations is 24. The computed rows entry 3 frame_datum_error_mm is 5.4. The computed rows entry 3 mean_spacing_km is 2.12e+04. The computed rows entry 4 stations is 48. The computed rows entry 4 frame_datum_error_mm is 5.2. The computed rows entry 4 mean_spacing_km is 1.06e+04. The computed rows entry 5 stations is 96. The computed rows entry 5 frame_datum_error_mm is 5.1. The study is a computation from stated assumptions, not a measurement, and its figures should be read at the precision those assumptions support.