The three formulas
Everything on this page comes from three lines of trigonometry.
- Solar noon altitude = 90° − latitude + declination. Declination is the sun's angle north or south of the equator. It runs from −23.44° on December 21 to +23.44° on June 21.
- Shadow ratio = 1 ÷ tan(altitude). Multiply by a wall's height to get the length of its noon shadow.
- Floor-lit fraction = max(0, 1 − D ÷ (W × tan(altitude))), where D is pit depth and W is pit width measured north to south.
Wichita's latitude is 37.69°N. For December 21: 90 − 37.69 + (−23.44) = 28.87°. tan(28.87°) = 0.552, so the shadow ratio is 1 ÷ 0.552 = 1.81.
Month-by-month table for Wichita (37.69°N)
Two pit shapes are compared. The deep pit is 8 ft deep and 16 ft wide, close to the classic walipini section. The shallow-and-wide pit is 4 ft deep and 20 ft wide. Values are for the 21st of each month at solar noon.
| Month (21st) | Declination | Noon sun altitude | Shadow ratio | Deep pit shadow (8 ft wall) | Deep pit floor lit | Shallow pit shadow (4 ft wall) | Shallow pit floor lit |
|---|---|---|---|---|---|---|---|
| Jan | −20.1° | 32.2° | 1.59 | 12.7 ft | 21% | 6.3 ft | 68% |
| Feb | −11.2° | 41.1° | 1.15 | 9.2 ft | 43% | 4.6 ft | 77% |
| Mar | 0.0° | 52.3° | 0.77 | 6.2 ft | 61% | 3.1 ft | 85% |
| Apr | 11.6° | 63.9° | 0.49 | 3.9 ft | 76% | 2.0 ft | 90% |
| May | 20.1° | 72.4° | 0.32 | 2.5 ft | 84% | 1.3 ft | 94% |
| Jun | 23.44° | 75.8° | 0.25 | 2.0 ft | 87% | 1.0 ft | 95% |
| Jul | 20.4° | 72.7° | 0.31 | 2.5 ft | 84% | 1.2 ft | 94% |
| Aug | 11.8° | 64.1° | 0.49 | 3.9 ft | 76% | 1.9 ft | 90% |
| Sep | 0.0° | 52.3° | 0.77 | 6.2 ft | 61% | 3.1 ft | 85% |
| Oct | −11.8° | 40.5° | 1.17 | 9.4 ft | 41% | 4.7 ft | 77% |
| Nov | −20.2° | 32.1° | 1.59 | 12.7 ft | 20% | 6.4 ft | 68% |
| Dec | −23.44° | 28.87° | 1.81 | 14.5 ft | 9% | 7.3 ft | 64% |
Three things stand out.
First, the deep pit's floor is mostly in shade from November through January. At the December solstice, only about 1.5 feet of a 16-foot floor sees direct noon sun.
Second, the shallow pit never drops below 64%. Halving the depth halves the shadow, and the extra 4 feet of width spreads what is left over more floor.
Third, the gap between the two shapes is widest exactly when you need light most. In June the difference is 8 percentage points. In December it's 55.
How Wichita compares at the December solstice
The same two pits, moved to other latitudes. For La Paz, Bolivia, we use June 21, its winter solstice, so the comparison is winter to winter.
| Location | Latitude | Winter-solstice noon sun | Shadow ratio | Deep pit floor lit | Shallow pit floor lit |
|---|---|---|---|---|---|
| La Paz, Bolivia | 16.4°S | 50.2° | 0.84 | 58% | 83% |
| Wichita | 37.69°N | 28.87° | 1.81 | 9% | 64% |
| Kansas City | 39.1°N | 27.5° | 1.92 | 4% | 62% |
| Minneapolis | 45.0°N | 21.6° | 2.53 | 0% | 49% |
La Paz matters because most walipini plans come from there. The source is Walipini Construction, a 2002 bulletin from the Benson Agriculture and Food Institute at BYU, written for the La Paz area at 16.4°S. It describes a pit 6 to 8 feet deep. At La Paz's winter sun of about 50°, an 8-foot pit still keeps more than half its floor lit at noon. That design was tuned for a high-sun latitude.
In Wichita, the same pit keeps 9%. In Minneapolis it keeps none. Wichita does have an edge over Kansas City: 1.4° more sun and roughly 6% shorter shadows.
What this means for glazing angle
The glazing on a pit greenhouse usually spans from the top of the north berm down to the south edge. Its angle sets how much winter light goes in rather than bouncing off.
Perpendicular to the December noon sun. Glazing tilted at 90° − 28.87° = 61.1° from horizontal meets the solstice noon sun head-on. That's the same rule the Benson bulletin used. Its text sets the roof perpendicular to the winter-solstice sun by adding about 23° to latitude, giving 39–40° for La Paz. Apply it at Wichita: 37.69 + 23.44 = 61.1°. Same answer.
Rule of thumb: latitude + 10 to 15°. A common rule for winter-focused glazing is a tilt of latitude plus 10 to 15 degrees. In Wichita that's 48° to 53°. It's a compromise that gives up a little December gain for better performance in February, March and October, when the sun is higher and you may be starting seedlings.
| Glazing tilt (from horizontal) | Basis | Angle of incidence at Dec 21 noon | Angle of incidence at Mar 21 noon |
|---|---|---|---|
| 61.1° | Perpendicular to Dec noon sun | 0° | 23.4° |
| 53° | Latitude + 15° | 8.1° | 15.3° |
| 48° | Latitude + 10° | 13.1° | 10.3° |
Angle of incidence is how far the sun is from hitting the glazing straight on. For a south-facing surface at noon, it equals the absolute difference between the tilt and (90° − sun altitude). All three options keep noon incidence low from December through March. The bigger differences show up in morning and afternoon sun, which this noon-only table doesn't capture. For material choice, see polycarbonate vs. glass.
What about cloudy days?
Geometry tells you where the sun lands when it's out. Wichita sees sunshine about 58% of possible daylight hours in January, per NCDC comparative climatic data. That's the same as Kansas City and below Dodge City's 67%. On cloudy days, diffuse light comes from the whole sky. A deep pit sees less of the sky than a shallow one, so it loses on overcast days too.
Practical design rules for 37.7°N
From the tables above, here's how we approach a pit greenhouse in the Wichita area:
- Keep depth to about 3–4 ft unless you only grow in spring and summer.
- Make the pit wide north to south. Width spreads the same shadow over more floor. A 20-ft width with a 4-ft wall leaves 12.7 ft lit at the solstice.
- Put tall crops and storage on the north side, where the floor is always lit, and use the shaded south strip for paths, water barrels or seed storage.
- Paint or line the north wall white or reflective to bounce light back to the south beds.
- Check your water table before you pick a depth. Parts of the Arkansas River valley and the Equus Beds area can have shallow groundwater. See our Equus Beds water guide.
Methods
- Latitude: Wichita, 37.69°N (WorldAtlas). Kansas City 39.1°N, Minneapolis 45.0°N, La Paz 16.4°S (the figure the Benson bulletin uses).
- Declination: approximate values for the 21st of each month: Jan −20.1°, Feb −11.2°, Mar 0°, Apr 11.6°, May 20.1°, Jun 23.44°, Jul 20.4°, Aug 11.8°, Sep 0°, Oct −11.8°, Nov −20.2°, Dec −23.44°.
- Altitude: 90 − latitude + declination (northern hemisphere). For La Paz at its June solstice: 90 − 16.4 − 23.44 = 50.2°.
- Floor-lit model: pit of width W (north–south) and depth D; south wall shadow D ÷ tan(altitude); lit fraction = max(0, 1 − D ÷ (W × tan(altitude))).
- Assumptions: south wall only; solar noon only; flat floor; no shading from glazing frames, end walls, berms above grade, snow or nearby trees; the wall top is at the sun-facing edge of the glazing. Morning and afternoon sun is lower, so real daily light on the floor is less than these noon figures.
- Calculated in Python by Wichita Greenhouse Builders, October 2026. Rounded to one decimal or whole percent.
Frequently asked questions
What is the sun angle in Wichita on December 21?
The solar noon altitude is 28.87°: 90 − 37.69 (latitude) − 23.44 (declination). It's the lowest noon sun of the year.
How long is the shadow from a pit greenhouse wall in Wichita in winter?
On December 21 at noon, 1.81 times the wall's height. A 4-ft wall shades 7.3 ft of floor; an 8-ft wall shades 14.5 ft. In January it's 1.59 times; by March, 0.77.
Why do walipini plans recommend 6–8 ft deep?
The widely copied plans come from a 2002 Benson Institute bulletin written for La Paz, Bolivia, at 16.4°S. There the winter-solstice sun is about 50° high and a wall shades only 0.84 times its height. At Wichita's 28.87°, the same depth puts most of the floor in shade.
What glazing angle is best for a Wichita winter greenhouse?
Perpendicular to the December noon sun is 61.1° from horizontal. A common rule of thumb, latitude + 10–15°, gives 48–53°, which trades a little December gain for better spring and fall performance.
Is Wichita better than Kansas City for an underground greenhouse?
Slightly. Wichita's solstice sun is 28.87° vs. about 27.5° in KC, so shadows are roughly 6% shorter. Our 4 ft × 20 ft model pit keeps 64% of its floor lit at noon in Wichita vs. 62% in KC.
Ready to build?
- Underground and earth-sheltered greenhouses — we design and build pit greenhouses shaped for Wichita's sun, soils and water table.
- Passive solar greenhouses — above-grade solar designs with steep south glazing and thermal mass.
- Geothermal and climate battery greenhouses — store daytime heat underground for winter nights.
- Polycarbonate vs. glass glazing — choosing glazing that transmits light and survives Kansas hail.
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