Intermittent heating in a sports hall: thermal retention, recovery deadlines and the effect of a roof retrofit

Annual building assessments do not directly establish whether an intermittently used sports hall can recover its indoor temperature before the next occupied period. This study develops a conditional, reproducible dynamic analysis from an anonymised technical report. Rounded envelope-to-floor-area ratios and reported thermal transmittances provide a geometry-informed conductance proxy. Effective thermal capacitance, air exchange, ground coupling, outdoor temperature and heating availability remain explicit scenario assumptions. A one-resistance, one-capacitance model is solved analytically for free cooling and constant-power recovery. A scalar bisection then determines the longest unheated period compatible with a fixed twelve-hour unoccupied window. The base scenario gives conductances of 5.879 and 3.188 W/(m² K) for the reported baseline envelope and an isolated roof improvement, respectively. With a capacitance of 100 Wh/(m² K), an outdoor temperature of 0 °C and an available heat delivery of 180 W/m², eight unheated hours require subsequent recovery periods of 9.09 and 3.65 hours. The baseline therefore cannot fit that particular shutdown and recovery sequence inside twelve hours. Solving the deadline directly gives unheated durations of 5.17 and 8.25 hours. Over a complete modelled daily cycle, delivered-heat reductions relative to continuous operation within each envelope state are 6.45% and 5.92%. These are hypothetical thermal-energy results, not measured savings. The contribution is a transparent separation of heat retention, heating headroom and scheduling feasibility, with a reproducible calculation suitable for planning the measurements needed before operational changes.