Deadband, Differential, and Equipment Cycling Rate

DEADBAND AND CYCLING ARE INVERSELY PROPORTIONAL, which makes the tuning trade completely explicit: halving the band to hold a tighter temperature EXACTLY DOUBLES the number of starts. Starts are what wear equipment, cost efficiency through repeated warm-up and purge, and in a compressor risk liquid slugging on a short restart. Control tightness is bought in equipment life, and the exchange rate is one for one. THE DUTY CYCLE DOES NOT DEPEND ON THE DEADBAND AT ALL, and that is the fact that makes the whole picture legible. The device runs for the fraction of time the load demands regardless of how the band is set -- the band decides how that runtime is chopped up, not how much of it there is. A narrow band does not make equipment run more; it makes it START more, which is a different and more damaging thing, and it is the distinction that gets lost in an argument about comfort. OVERSIZING IS THE MOST COMMON CAUSE OF SHORT CYCLING AND IT WORKS THROUGH THE MAXIMUM RATHER THAN THE AVERAGE. A larger device satisfies the load faster, so its on time shortens while the off time is unchanged, and the peak cycling rate -- capacity divided by four times capacitance times deadband -- scales DIRECTLY with capacity. Double the equipment and you double the worst case. AND THE WORST CASE MOVES TO A COLDER DAY, NOT A MILDER ONE, which inverts the usual intuition. The peak occurs at fifty percent duty, and an oversized unit reaches fifty percent duty at a lower outdoor temperature than a right-sized one does. Both figures are computed here, and the comparison shows something stronger than the folklore: an oversized unit cycles more than a right-sized one at EVERY load, not only in mild weather. This is a first-order model for understanding the trade, not a simulation. A real space is not a single capacitance with a single loss coefficient -- internal mass, solar and internal gains, infiltration and the distribution system all matter, and effective capacitance is not measurable with any precision. Equipment is not instantaneous either: start-up transients, purge and post-purge, compressor pull-down and anti-short-cycle timers all change the real cycle, and a timer enforcing a minimum off period decouples the rate from this relation entirely. It does not address modulating, staged or variable-speed equipment, which is the usual answer to oversizing and does not cycle this way at all. It does not evaluate the efficiency penalty of cycling or the comfort consequence of a given deadband, size equipment, or diagnose an oversizing problem. Most equipment wants no more than about 6 cycles per hour. The equipment manufacturer's minimum cycle and off-time requirements and the controls engineer govern.

load = UA x (setpoint - outdoor); on = C x deadband / (Q - load); off = C x deadband / load; cycles per hour = load (Q - load) / (C x deadband x Q); duty = load / Q; the maximum is Q / (4 C x deadband), at 50% duty.

A first-order two-position cycling model: one thermal capacitance, one loss coefficient, and a fixed-output device. Not a simulation.

A first-order thermal relation.

Estimate. AHJ and licensed professional govern.

Field names used by the API: capacitance_btu_f, ua_btu_hr_f, setpoint_f, outdoor_f, capacity_btu_hr, deadband_f, alt_deadband_f, alt_capacity_btu_hr, load_btu_hr, on_min, off_min, cycles_per_hour, duty_pct, max_cycles_per_hour, outdoor_at_max_f, alt_deadband_cycles_per_hour, alt_capacity_cycles_per_hour, alt_capacity_max_cycles_per_hour, alt_capacity_outdoor_at_max_f

• First-order space one capacitance, one UA; internal mass, gains and infiltration are not modelleda teaching model, not a simulation
• Instantaneous equipment no start-up transient, purge, pull-down or minimum off timerthe equipment manufacturer's data
• Two-position control only modulating, staged and variable-speed equipment do not cycle this waythe sequence of operation