Solar Water Heater Sizing Calculator

Daily useful demand is $Q_d=\rho c_p V_d(T_h-T_c)$, using water density 1 kg/L and heat capacity 4180 J/(kg·K). Monthly loads multiply this daily demand by the days in a non-leap year. These are sensible-heat equations derived here. Every positive temperature rise is used as entered; zero and negative rises are rejected.

PVGIS provides monthly irradiation on the stated tilted, south-facing plane and monthly ambient temperature. The presets average each calendar month over 2005–2020. Latitude, longitude and altitude identify each climate row; they are not a substitute for weather data. Additional local shade scales irradiation once.

The Solar Keymark curve is $q/A=\eta_0 G-a_1\Delta T_m-a_2\Delta T_m^2$. All areas and coefficients use the gross-area basis. For the Riello example the beam intercept and diffuse modifier are combined at the certificate's 850/150 W/m² reference mix; JUC supplies a hemispherical intercept directly.

To interface the mean-fluid curve with the inlet-based f-chart, use the secant loss coefficient $U_e=a_1+a_2(40\,\mathrm{K})$. For a linearized collector with $T_m=T_i+q/(2\dot m c_p)$, substitution gives $k_i=[1+U_e/(2\dot m c_p)]^{-1}$. Effective inlet optical and loss coefficients are $\eta_0 k_i$ and $U_e k_i$, both multiplied by the user coupling factor. This linearization and coupling factor are engineering approximations, not a certified system rating. The mass flux is the certificate test flux; water heat capacity is used in the conversion. For glycol, this is a water-equivalent approximation.

Following the liquid f-chart described by Duffie and Beckman, calculate monthly absorbed-energy parameter Y and loss parameter X. Apply the DHW correction using $11.6+1.18T_h+3.86T_c-2.32T_a$ (temperatures numerically in °C), and the storage correction $(R/75)^{-0.25}$ with R in L/m². The loss temperature term is already DHW-corrected; do not apply that correction twice.

The monthly correlation is $f=1.029Y-0.065X-0.245Y^2+0.0018X^2+0.0215Y^3$, limited to 0–1. Annual fraction is $\sum f_mL_m/\sum L_m$. Backup heat is $L_m(1-f_m)$. A 32-iteration bisection finds target area within the monthly correlation envelope. Module rounding and storage use the same selected collector and storage ratio. A whole-collector recommendation is shown only when its rounded area remains within every monthly model limit.

Stagnation is the certificate's measured standard stagnation value at 1000 W/m² and 30 °C ambient, not a root obtained by extrapolating the low-temperature efficiency curve. The animated loop is an original explanatory schematic.

The checks compare three collector outputs with certificate tables and two in-range f-chart points with Yurtsev's published monthly table. They verify model components; they do not constitute validation of annual thermosiphon yield.

• Daily hot water use, delivery temperature and cold inlet temperature are constant all year. Volume refers to the delivery temperature, after mixing.
• Presets are historical monthly climate means, not a forecast. Plane orientation and tilt are fixed by the selected climate row. For another location, provide a complete custom monthly row; no latitude-only or altitude-only irradiation adjustment is applied.
• Water density and heat capacity are constant. The inlet conversion assumes water; glycol systems need a more detailed fluid and loop model.
• The reference storage is 75 L/m², and the sizing search scales storage with collector area. Solar storage is assumed well insulated. Explicit tank, distribution and recirculation losses are omitted; useful backup heat excludes auxiliary heater efficiency.
• The optical incidence factor and collector coupling factor are user estimates, each constant over the year. They are applied to different terms: incidence to Y; coupling to both X and Y.
• Collector test data describe individual collectors. Their use here does not certify a complete thermosiphon package, actual circulation rate, mounting, or present product approval.
• Default demand and adjustment factors are illustrative engineering inputs. They are not prescribed occupant allowances or regulations.

Use for preliminary domestic hot water sizing and comparison of ordinary liquid collector/storage systems. The Duffie–Beckman f-chart is empirical. This implementation uses a conservative monthly envelope of 0 ≤ X ≤ 15 and 0 ≤ Y ≤ 3, and storage ratios of 37.5–300 L/m². Installed configurations outside that envelope are rejected. Unreachable annual targets are identified and left blank. If whole-collector rounding exceeds the envelope, all rounded recommendation cards are withheld; the valid continuous minimum area and installed-system results remain available.

The quadratic collector curve is shown only up to the selected certificate's tested mean-fluid temperature rise: 50 K for JUC and 82 K for CP20TSS. Check that any custom collector has compatible test data. The 40 K equivalent loss is a screening approximation, especially for evacuated tubes, very cold sites, or high operating temperatures.

Monthly means cannot predict a particular winter day, frost exposure, peak demand or consecutive cloudy days. Constant inlet temperature can materially affect winter predictions. There is no hydraulic thermosiphon calculation, stratified tank simulation, boiling/pressure model, freeze protection design, heat rejection design, energy-price or regulatory compliance calculation. Standard stagnation temperature is not an allowable operating setpoint. At altitude, atmospheric boiling temperature is lower; relief and expansion design require the actual pressure and system arrangement.

A qualified person must carry out installation work and assess roof loads, anchorage, plumbing, pressure relief, expansion, freeze protection, potable-water hygiene and anti-scald controls. Follow the manufacturer's complete-system instructions and check against the standard in force where applicable.

Yurtsev's table includes summer extrapolation above Y = 3; those summer points and its annual total are not used as reference checks.