Greenhouse Heat Loss & Ventilation Calculator: 24-Hour Climate

A one-zone sensible heat balance is derived here from conservation of energy:

For the gable house, exposed area is the two sidewalls, two end walls, triangular gables and both roof slopes. $H_0=UA_c+\psi P+\rho c_p V(n_{leak}+n_{min})/3600$, with rates entered in h⁻¹. The edge term uses outdoor temperature as a simplifying reference. $C=\rho c_pV+C_AA_f$.

The overall-cover heat-transfer method and separation of infiltration follow Aldrich & Bartok, Greenhouse Engineering, 3rd edition (1994), as summarized by the Cornell worksheet (s4), and Purdue HO-327-W, p. 6 (s1). Cover U-values include surface-film effects; a second radiation loss is not added.

Solar geometry reuses the NOAA/Meeus Julian-day and ephemeris functions from the catalog's Sun Position calculator. Declination is held at noon for a representative 2026 date. $G=G_{noon}\max(\sin\alpha,0)/\max(\sin\alpha_{noon},10^{-6})$. The user supplies the noon irradiance. Outdoor temperature follows a sinusoid peaking at the entered solar hour.

Pad supply is $T_s=T_o-\eta(T_o-T_{wb})$, consistent with UF AE069 (s2). Background exchange remains uncooled. The heater and additional fan are ideal continuously modulated controls with finite capacities; the fan runs only if intake air would lower the freely evolving temperature. The controls target the next temperature at the heating minimum or cooling setpoint, without simultaneous heating and controlled fan cooling.

Weather and equipment settings are held constant over each of 480 intervals of 180 s, with weather sampled at interval midpoints. Each interval is integrated analytically: for $K=H_0+\rho c_p\dot V_f$ and equilibrium temperature $T_e=(H_0T_o+\rho c_p\dot V_fT_s+Q_s+P_h)/K$, $T_{end}=T_e+(T_{start}-T_e)\exp(-K\Delta t/C)$. Heating power is solved from the exact endpoint response; fan flow is bounded and solved to reach the cooling setpoint where possible. Loss powers use the exact interval-mean indoor temperature, so the daily energy balance uses consistent interval integrals. The exponential cooling check tests accuracy independently of the conservation residual. With defaults, halving the weather interval changes the temperature curve by less than 0.001 K. This does not bound errors for every weather or control scenario.

UF AE030 (s3) supplies a one-air-change-per-minute summer comparison. Purdue HO-327-W p. 3 supplies a separate floor-area comparison of 8 cfm/ft². These are context, not guarantees that a particular temperature will be held.

Pad-state validation uses the unclipped humidity-ratio equation and water/ice saturation-pressure equations published in PsychroLib 2.5.0, implementing ASHRAE Handbook—Fundamentals (2017), Chapter 1, equations 5/6, 33/35 and 36 (s7). At each interval in which an active pad draws air, a negative implied outdoor humidity ratio rejects the inputs. The user supplies absolute atmospheric pressure. This checks physical feasibility of the inlet state; it does not predict greenhouse humidity. For detailed design, check against the standard in force.

• One well-mixed freestanding gable house, constant U-value, constant leakage and minimum ventilation; no wind model. Additional fan airflow is independent of background exchange.
• Default U = 4 W/m²/K is an illustrative double-film case; leakage = 0.75 h⁻¹ is a scenario. Extension values differ with construction and exposure. Enter measured or project-specific values.
• Density 1.2 kg/m³ and specific heat 1005 J/(kg·K), held constant. The older 0.02 imperial infiltration coefficient is a rounded rule and is not forced onto this air-property model.
• External, ventilated shade with a constant blocked fraction. Internal shade can return absorbed heat to the greenhouse and is not equivalent.
• Default transmittance 0.75, sensible solar fraction 0.65 and effective storage 40 kJ/(m²·K) are editable scenario assumptions, not fitted crop data. No plant transpiration or humidity balance is solved.
• Constant outdoor wet-bulb depression and pad effectiveness throughout the day. Bypass air and poorly wetted pads require a lower effectiveness or separate airflow allowance.
• The initial indoor temperature is imposed at midnight; there is no repeated-day warm-up. The heater can operate whenever needed, including daytime.
• No fan/pump heat, combustion moisture, fuel-efficiency conversion or explicit night-sky temperature. Useful heater output is specified.
• Atmospheric pressure is used for pad inlet feasibility. The heat balance still uses the stated fixed air density and specific heat; it is not a pressure-dependent moist-air energy model.

For comparative daily scenarios and preliminary equipment sizing. The simulated daily minimum is not automatically a winter design temperature. Use local design weather and appropriate equipment margins for heater selection. A control-limit exceedance means the modeled equipment cannot meet the target; it is not a numerical error.

The lumped storage and solar sensible fraction strongly influence transients. There is no validation of the complete daily model against a measured greenhouse. Check the response against site logs; a single-zone result cannot predict pad-to-fan temperature gradients, leaf/root temperatures, humidity or disease conditions. The exponential update remains accurate for constant-forcing intervals even with air-only thermal storage. Weather and equipment are still represented in three-minute intervals, so rapid weather changes or switching within an interval are not resolved. The step-size comparison is for the defaults.

UF AE024 (s6) emphasizes maintained delivered airflow, tight pad fit and calibrated sensors. Specify fans at the actual system pressure loss. Natural vent area or opening angle is not inferred from fan flow. Electrical, mechanical and combustion-system installation belongs to qualified people; use safely vented heating equipment.

Reference cases verify published envelope heat loss and airflow sizing, not the full weather or crop model. In the UAF case (s5), the published roof length is rounded to 6.7 ft. This tool uses the geometric value 6.7082 ft, so its area and heat loss are slightly higher; the tolerance allows that stated rounding.