Seasons Over Detroit: Sun Angle & Heating
Why a lower Sun means a colder Detroit winter — modeled with a lamp and calculated from Detroit's latitude.
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Standards
HS-ESS2-4 — Use a model to describe how variations in the flow of energy into and out of Earth's systems result in changes in climate.
MS-ESS1-1 — Develop and use a model of the Earth-Sun system to describe the cyclic patterns of seasons.
Why Does This Matter?
Detroit sits near 42.3°N. At noon on the summer solstice the Sun is about 71° above the horizon and the day lasts roughly 15 hours; at the winter solstice it reaches only about 24° and the day lasts about 9 hours. That difference in sunlight — not Earth's distance from the Sun — drives Detroit's warm summers and cold winters, and it decides how well solar panels and sunny windows work.
Objective
Model how the angle of incoming light changes the heating of a surface, then calculate the Sun's noon altitude over Detroit on key dates of the year.
Materials
- Desk lamp or bright flashlight (kept at the same distance for every trial)
- Black construction paper taped to a piece of cardboard
- Thermometer or temperature probe
- Protractor and ruler
- Graph paper (1 cm squares)
- Stopwatch or timer
- Computer or tablet for the Seasons Over Detroit simulation
Safety: Lamp bulbs and shades get hot — do not touch them. Never look directly at the Sun, and do not use this lab to observe the Sun outdoors without proper solar viewing equipment.
Procedure
- Tape the black paper to the cardboard and tape the thermometer bulb flat against the paper. Place the lamp 20 cm away so its light hits the paper straight on (90° to the surface). Record the starting temperature.
- Turn the lamp on. Record the temperature every 30 seconds for 3 minutes, then switch the lamp off and let the paper cool back to the starting temperature.
- Tilt the cardboard so the light strikes at 60° to the surface, keeping the lamp the same distance away. Repeat step 2. Then repeat for 30°.
- At each angle, trace the lit spot on graph paper (with the lamp or flashlight pointing at the paper) and count the squares it covers.
- Calculate the Sun's noon altitude for Detroit (latitude 42.3°N) using: altitude = 90° − latitude + declination. Use declination = 0° (equinox), +23.4° (summer solstice), and −23.4° (winter solstice).
- Open the Seasons Over Detroit simulation and check your calculated altitudes. Record the day length it reports for each date.
Data Table
Table 1: Lamp model
| Light angle on surface | Start temp (°C) | Temp at 3 min (°C) | Change (°C) | Lit area (squares) |
|---|---|---|---|---|
| 90° | ||||
| 60° | ||||
| 30° |
Table 2: Sun over Detroit
| Date | Declination | Noon Sun altitude | Day length (h) |
|---|---|---|---|
| Equinox (~Mar 20, Sep 22) | 0° | ||
| Summer solstice (~Jun 21) | +23.4° | ||
| Winter solstice (~Dec 21) | −23.4° |
Analysis Questions
- How did the temperature change and the lit area change as the angle of the light decreased? Use the idea of energy per unit area to explain.
- Show your calculation of Detroit's noon Sun altitude on the equinox and both solstices.
- Earth is actually closest to the Sun in early January. Why is January still Detroit's coldest month?
- A rooftop solar panel in Detroit is fixed in place. Based on your results, what tilt would you choose and why? What would you change between summer and winter if the panel could move?