☀️ Solar Radiation & Position
Calculate solar angles and direct, diffuse, and albedo radiation components on tilted flat collectors.
⚡ Fortran 90 Engine
Double Precision (IEEE 754)
✓ ISO / ASME Validated
Heat Transfer
📊 Solver Telemetry
● ACTIVE
Panel Orientation & Solar Angles
The orientation of the receiving plane relative to the solar path determines the amount of direct energy ($I_{beam}$) captured:
- Tilt ($\beta$): Angle of panel above the flat ground. $0^\circ$ is horizontal, $90^\circ$ is vertical wall.
- Azimuth ($\gamma$): Panel heading direction. $0^\circ$ is facing South, $90^\circ$ facing West, $-90^\circ$ facing East.
- Angle of incidence ($\theta$): Angle between sun rays and panel perpendicular. Lower is better.
📝 Configuration
📊 Results & Solar Decomposition
Configure geographical/panel options and click "Compute Solar Radiation" to display positioning and solar heat flux calculations.
📘 Calculation Methodology (Haurwitz Clear Sky Model)
Mathematical Model
Solar positioning is resolved first using seasonal orbital parameters, before calculating direct beam, diffuse sky, and albedo components incident on the panel surface:
Apparent Solar Time (AST):
$$AST = H_{local} + \frac{4 \cdot (15^\circ \cdot TZ - L_{loc}) + E}{60}$$
Solar Altitude ($\alpha$) & Azimuth ($\gamma_s$):
$$\sin \alpha = \sin \phi \cdot \sin \delta + \cos \phi \cdot \cos \delta \cdot \cos \omega$$ $$\cos \gamma_s = \frac{\sin \alpha \cdot \sin \phi - \sin \delta}{\cos \alpha \cdot \cos \phi}$$
Incidence Angle on tilted plane ($\theta$):
$$\cos \theta = \sin \alpha \cdot \cos \beta + \cos \alpha \cdot \sin \beta \cdot \cos(\gamma_s - \gamma)$$
$$AST = H_{local} + \frac{4 \cdot (15^\circ \cdot TZ - L_{loc}) + E}{60}$$
Solar Altitude ($\alpha$) & Azimuth ($\gamma_s$):
$$\sin \alpha = \sin \phi \cdot \sin \delta + \cos \phi \cdot \cos \delta \cdot \cos \omega$$ $$\cos \gamma_s = \frac{\sin \alpha \cdot \sin \phi - \sin \delta}{\cos \alpha \cdot \cos \phi}$$
Incidence Angle on tilted plane ($\theta$):
$$\cos \theta = \sin \alpha \cdot \cos \beta + \cos \alpha \cdot \sin \beta \cdot \cos(\gamma_s - \gamma)$$
Irradiation Components
Direct Solar Normal ($I_{dn}$):
$$I_{dn} = 1367 \cdot \left[1 + 0.033 \cdot \cos\left(360 \cdot \frac{n}{365}\right)\right] \cdot \exp\left(-\frac{0.128}{\sin \alpha}\right)$$
Direct Beam on tilted panel ($I_{beam}$):
$$I_{beam} = I_{dn} \cdot \cos \theta \quad (\text{if } \cos \theta > 0)$$
Diffuse Sky Component (Liu & Jordan):
$$I_{diffuse} = I_{dn} \cdot \sin \alpha \cdot 0.3 \cdot \left(\frac{1 + \cos \beta}{2}\right)$$
Ground Albedo Component:
$$I_{albedo} = I_{dn} \cdot \sin \alpha \cdot \rho_g \cdot \left(\frac{1 - \cos \beta}{2}\right)$$
$$I_{dn} = 1367 \cdot \left[1 + 0.033 \cdot \cos\left(360 \cdot \frac{n}{365}\right)\right] \cdot \exp\left(-\frac{0.128}{\sin \alpha}\right)$$
Direct Beam on tilted panel ($I_{beam}$):
$$I_{beam} = I_{dn} \cdot \cos \theta \quad (\text{if } \cos \theta > 0)$$
Diffuse Sky Component (Liu & Jordan):
$$I_{diffuse} = I_{dn} \cdot \sin \alpha \cdot 0.3 \cdot \left(\frac{1 + \cos \beta}{2}\right)$$
Ground Albedo Component:
$$I_{albedo} = I_{dn} \cdot \sin \alpha \cdot \rho_g \cdot \left(\frac{1 - \cos \beta}{2}\right)$$