August 3rd, 2011 - I receive on a regular basis questions about the slope angle determination for some locations in Europe. Before, I used a web application where I could determine the hight of the sun in midwinter for a limited number of locations. So I began a quest to make it easier to determine..
I had already noticed that the latitudes are related to the height of the Sun, annd that moving one degree up north made the slope angles increase by 1 degree. I decided to examine this relationship more profoundly.
Relevant here are the tropics on Earth. In the northern hemisphere, we know the Tropic of Cancer, where the midsummer sun is at its highest position and in a perpendicular state. In the southern hemisphere, during our midwinter, the sun is directly above the Tropic of Capricorn. In spring and autumn the sun is directly above the equator. Thus far our brief geography lesson.
These tropics are relevant in determining the angle of the windows in an earthship. Indeed, when the sun is directly above the Tropic of Capricorn we have midwinter in the northern hemisphere. What we want to know is where the sun is at its highest point that day. Our windows are to stand perpendicular to the sun, so if for example the sun that day is 15o above the horizon, our windows should be in an angle of 75o.
Position of the tropics, equator, polar circles and poles in degrees - Illustration: W. Raets
Suppose we want to determine the slope angles for an earthship at 55o N. The midwinter sun in the north is directly above 23o27' south of the equator. So the distance from the Sun to the earthship is 55o from earthship to equator and 23o27' from equator to the Tropic of Capricorn.
If you take 55o + 23o27 you get 78o27' as result. Next, you take 90o - 78o27' = 11o33 ' what is the maximum height of the sun at midwinter at 55o north. Now the corner of your window is 90o - 11o33 '= 78o27', which we already calculated.
A little overview:
55o - 23o27' = 78o27' -> 78o what is your slope angle for your window
90o - 78o27' = 11o33' -> 12o which the highest position of the sun at midwinter 55o N
So all you need to know is what latitude you want to build yourself. Next you can calculate what the slope angle should be. For the Southern Hemisphere this also works. More information about slope angles is found in the article 'Slope angles for an earthship in Belgium'.
Text: Willy Raets
Illustrations: Willy Raets
Slope angles for a few European locations
(from South to North):1
Greece
- Heraklion (35°20′NB): 35°20′ + 23°27' = 58°47' → 59°
- Athens (38°00′NB): 38°00′ + 23°27' = 61°27' → 61°
- Halkida (38°28′NB): 38°28′ + 23°27' = 61°55' → 62°
- Thessaloniki (40°38′NB): 40°38′ + 23°27' = 64°05' → 64°
Portugal
- Porto (41°09'NB): 41°09' + 23°27' = 64°36' → 65°
France
- Marseille (43°18′NB): 43°18′ + 23°27' = 66°45' → 67°
- Bordeaux (44°50′NB): 44°50′ + 23°27' = 68°17' → 68°
- Lyon (45°46′NB): 45°46′+ 23°27' = 69°13' → 69°
- Strasbourg (48°58′NB): 48°35′+ 23°27' = 71°02' → 71°
- Paris (48°52′NB): 48°52′+ 23°27' = 71°19' → 71°
Belgium
- Charleroi (50°25'NB): 50°25' + 23°27' = 73°52' → 74°
- Brussel (50°50'NB): 50° 50' + 23° 27' = 74° 13' → 74°
- Gent (51°03'NB): 51°03' + 23°27' = 74°30' → 75°
- Antwerpen (51°13'NB): 51°13' + 23°27' = 74°40' → 75°
The Netherlands
- Maastricht (50°51'NB): 50°51'+ 23°27' = 74°18' → 74°
- Utrecht (52°05'NB): 52°05' + 23°27' = 75°32' → 76°
- Groningen (53°13'NB): 53°13' + 23°27' = 76°40' → 77°
Denmark
- Odense (55°24′NB): 55°24′+ 23°27' = 79°01' → 79°
- Copenhagen (55°43′NB): 55°43′ + 23°27' = 79°10' → 79°
- Aarhus (56°09′NB): 56°09′ + 23°27' = 79°36' → 80°
Sweden
- Malmö (55°35′NB): 55°35′ + 23°27' = 79°03' → 79°
- Gothenburg (57°42´NB): 57°42´ + 23°27' = 81°09' → 81°
- Norrköping (58°36′NB): 58°36′ + 23°27' = 82°03' → 82°
- Uppsala (59°51′NB): 59°51′ + 23°27' = 83°18' → 83°
- Sundsvall (62°23′NB): 62°23′ + 23°27' = 85°50' → 86°
1. Always check latitude and calculation before using in real life situsations
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