1. Solar Radiation Basics
Problem 1: Solar Constant Calculation
The solar constant is given as 1367 W/m².
Find the total solar power received by Earth if its radius is 6.37 × 10⁶ m.
Solution
Formula:
𝑃 = 𝑆 × 𝜋𝑅2
Substitute:
𝑃 = 1367 × 𝜋(6.37 × 106 )2
𝑃 ≈ 1367 × 3.14 × 4.06 × 1013
𝑃 ≈ 1.74 × 1017 W
Problem 2: Radiation Components
If total radiation = 800 W/m²
Diffuse = 200 W/m²
Find beam radiation.
Solution:
Beam = Total − Diffuse
= 800 − 200 = 600 W/m²
2. Solar Geometry (VERY IMPORTANT)
Problem 3: Declination Angle
Find declination angle on March 21 (n = 80)
Formula:
360(284 + 𝑛)
𝛿 = 23.45∘ sin ( )
365
360(284 + 𝑛)
𝛿 = 23.45∘ sin ( )
365
Solution:
360(284 + 80)
𝛿 = 23.45sin ( )
365
= 23.45sin(360)
𝛿 ≈ 0∘
Expected answer (equinox)
Problem 4: Hour Angle
,Find hour angle at 3 PM.
Formula:
𝜔 = 15∘ × (time − 12)
𝜔 = 15∘ (𝑡 − 12)
Solution:
𝜔 = 15(15 − 12) = 45∘
Problem 5: Zenith Angle
Latitude = 20°
Declination = 0°
Hour angle = 0°
Formula:
cos 𝜃𝑧 = sin 𝜙sin 𝛿 + cos 𝜙cos 𝛿cos 𝜔
cos 𝜃𝑧 = sin 𝜙sin 𝛿 + cos 𝜙cos 𝛿cos 𝜔
Solution:
cos 𝜃𝑧 = cos 20∘
𝜃𝑧 = 20∘
3. Solar Time Calculation
Problem 6: Local Solar Time
Standard time = 2 PM
Longitude difference = 15°
Each degree = 4 minutes
Solution:
15 × 4 = 60 min
Solar time = 2 PM ± 1 hr
= 1 PM or 3 PM (depending on direction)
4. Solar Radiation Measurement
Problem 7: Pyranometer Reading
If a pyranometer records 700 W/m², what does it measure?
Solution:
Measures global solar radiation
Includes:
• Beam radiation
, • Diffuse radiation
(No calculation — concept question)
5. Energy Units Conversion
Problem 8: Convert kWh to Joules
1 kWh = ?
Solution:
1 kWh = 1000 × 3600
= 3.6 × 106 J
6. Efficiency Problems
Problem 9: Collector Efficiency
Input = 1000 W
Output = 600 W
Find efficiency.
Formula:
Output
𝜂= × 100
Input
Output
𝜂= × 100
Input
Solution:
600
𝜂= × 100 = 60%
1000
7. Flat Plate Collector Heat Gain
Problem 10
Area = 2 m²
Radiation = 800 W/m²
Efficiency = 50%
Find heat output.
Solution:
𝑄 =𝐴×𝐼×𝜂
𝑄 =𝐴×𝐼×𝜂
𝑄 = 2 × 800 × 0.5
𝑄 = 800 W
8. Load Estimation Problem
, Problem 11
A house needs 5 kWh/day.
Solar panel produces 250 W for 5 hrs/day.
Find number of panels.
Solution:
Energy per panel:
250 × 5 = 1250 Wh = 1.25 kWh
Panels required:
5
=4
1.25
Answer: 4 panels
1. Declination Angle Problems
Problem 1
Find the declination angle on April 15 (n = 105).
360(284 + 𝑛)
𝛿 = 23.45∘ sin ( )
365
Solution:
360(284 + 105)
𝛿 = 23.45sin ( )
365
= 23.45sin(384∘ )
= 23.45sin(24∘ )
𝛿 ≈ 23.45 × 0.407
𝛿 ≈ 9.55∘
Problem 2
Find declination angle on December 21 (n = 355).
Solution:
360(284 + 355)
𝛿 = 23.45sin ( )
365
= 23.45sin(630∘ )
= 23.45sin(270∘ )
𝛿 ≈ −23.45∘
2. Hour Angle Problems
Problem 3
Find hour angle at 10 AM.
Problem 1: Solar Constant Calculation
The solar constant is given as 1367 W/m².
Find the total solar power received by Earth if its radius is 6.37 × 10⁶ m.
Solution
Formula:
𝑃 = 𝑆 × 𝜋𝑅2
Substitute:
𝑃 = 1367 × 𝜋(6.37 × 106 )2
𝑃 ≈ 1367 × 3.14 × 4.06 × 1013
𝑃 ≈ 1.74 × 1017 W
Problem 2: Radiation Components
If total radiation = 800 W/m²
Diffuse = 200 W/m²
Find beam radiation.
Solution:
Beam = Total − Diffuse
= 800 − 200 = 600 W/m²
2. Solar Geometry (VERY IMPORTANT)
Problem 3: Declination Angle
Find declination angle on March 21 (n = 80)
Formula:
360(284 + 𝑛)
𝛿 = 23.45∘ sin ( )
365
360(284 + 𝑛)
𝛿 = 23.45∘ sin ( )
365
Solution:
360(284 + 80)
𝛿 = 23.45sin ( )
365
= 23.45sin(360)
𝛿 ≈ 0∘
Expected answer (equinox)
Problem 4: Hour Angle
,Find hour angle at 3 PM.
Formula:
𝜔 = 15∘ × (time − 12)
𝜔 = 15∘ (𝑡 − 12)
Solution:
𝜔 = 15(15 − 12) = 45∘
Problem 5: Zenith Angle
Latitude = 20°
Declination = 0°
Hour angle = 0°
Formula:
cos 𝜃𝑧 = sin 𝜙sin 𝛿 + cos 𝜙cos 𝛿cos 𝜔
cos 𝜃𝑧 = sin 𝜙sin 𝛿 + cos 𝜙cos 𝛿cos 𝜔
Solution:
cos 𝜃𝑧 = cos 20∘
𝜃𝑧 = 20∘
3. Solar Time Calculation
Problem 6: Local Solar Time
Standard time = 2 PM
Longitude difference = 15°
Each degree = 4 minutes
Solution:
15 × 4 = 60 min
Solar time = 2 PM ± 1 hr
= 1 PM or 3 PM (depending on direction)
4. Solar Radiation Measurement
Problem 7: Pyranometer Reading
If a pyranometer records 700 W/m², what does it measure?
Solution:
Measures global solar radiation
Includes:
• Beam radiation
, • Diffuse radiation
(No calculation — concept question)
5. Energy Units Conversion
Problem 8: Convert kWh to Joules
1 kWh = ?
Solution:
1 kWh = 1000 × 3600
= 3.6 × 106 J
6. Efficiency Problems
Problem 9: Collector Efficiency
Input = 1000 W
Output = 600 W
Find efficiency.
Formula:
Output
𝜂= × 100
Input
Output
𝜂= × 100
Input
Solution:
600
𝜂= × 100 = 60%
1000
7. Flat Plate Collector Heat Gain
Problem 10
Area = 2 m²
Radiation = 800 W/m²
Efficiency = 50%
Find heat output.
Solution:
𝑄 =𝐴×𝐼×𝜂
𝑄 =𝐴×𝐼×𝜂
𝑄 = 2 × 800 × 0.5
𝑄 = 800 W
8. Load Estimation Problem
, Problem 11
A house needs 5 kWh/day.
Solar panel produces 250 W for 5 hrs/day.
Find number of panels.
Solution:
Energy per panel:
250 × 5 = 1250 Wh = 1.25 kWh
Panels required:
5
=4
1.25
Answer: 4 panels
1. Declination Angle Problems
Problem 1
Find the declination angle on April 15 (n = 105).
360(284 + 𝑛)
𝛿 = 23.45∘ sin ( )
365
Solution:
360(284 + 105)
𝛿 = 23.45sin ( )
365
= 23.45sin(384∘ )
= 23.45sin(24∘ )
𝛿 ≈ 23.45 × 0.407
𝛿 ≈ 9.55∘
Problem 2
Find declination angle on December 21 (n = 355).
Solution:
360(284 + 355)
𝛿 = 23.45sin ( )
365
= 23.45sin(630∘ )
= 23.45sin(270∘ )
𝛿 ≈ −23.45∘
2. Hour Angle Problems
Problem 3
Find hour angle at 10 AM.
