i have a house, three metres high, with a window 1m from the ground, and 0.5m from the roof. i need to work out how long the eaves have to be to shade the window in summer (dec 21, noon) and allow the solar radiation to pass through in winter (june 21, noon).
i have worked out that i need to determine the solar altitude of the sun:
sin(alpha)= cos(L)cos(delta)cos(w)+sin(L)sin(delta)
where L= latitude = melbourne = 38 deg
delta = declination angle = 23.45 deg (+ve for winter, -ve for summer)
but i still dont understand how to work out the hour angle (w) for noon on these days? :(
i know the hour angle is w=0 at solar noon.. however we're given local time as 12 noon in melbourne on these days. so i wasnt sure how to work out what the solar time when local time is noon? and therefore the hour angle at this solar time? i think i need the equation of time or something? and a reference latitude and stuff? but i'm a bit lost.
thanks for any help you can offer!
i have worked out that i need to determine the solar altitude of the sun:
sin(alpha)= cos(L)cos(delta)cos(w)+sin(L)sin(delta)
where L= latitude = melbourne = 38 deg
delta = declination angle = 23.45 deg (+ve for winter, -ve for summer)
but i still dont understand how to work out the hour angle (w) for noon on these days? :(
i know the hour angle is w=0 at solar noon.. however we're given local time as 12 noon in melbourne on these days. so i wasnt sure how to work out what the solar time when local time is noon? and therefore the hour angle at this solar time? i think i need the equation of time or something? and a reference latitude and stuff? but i'm a bit lost.
thanks for any help you can offer!
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The information that you need is the precise longitude for your location. When the clock reads 12 noon for your time zone, it is actually 12 noon local mean time (LMT). That is the sun is really directly over the central longitude in your time zone. Each time zone covers 15 degrees of longitude.
You take the difference in degrees and minutes from your location to the central longitude for your time zone, and you can convert the time difference between 12 noon (LMT) and solar noon (local apparent noon, LAN) for your location.
So if you are east of the central longitude for your time zone, LAN for your location is actually before LMT noon. And if you are west of the central longitude, LAN is later than LMT noon.
Melbourne, AU, is located at 144-degrees 57-minutes 47-seconds east longitude. The central longitude for Melbourne's time zone would be 142-degrees 30-minutes east longitude.
So when it is 12 noon LMT for you, the sun is directly over 142-degrees 30-minutes east longitude for your time zone. Given the longitude for your exact location, you can work out the time for LAN.
You take the difference in degrees and minutes from your location to the central longitude for your time zone, and you can convert the time difference between 12 noon (LMT) and solar noon (local apparent noon, LAN) for your location.
So if you are east of the central longitude for your time zone, LAN for your location is actually before LMT noon. And if you are west of the central longitude, LAN is later than LMT noon.
Melbourne, AU, is located at 144-degrees 57-minutes 47-seconds east longitude. The central longitude for Melbourne's time zone would be 142-degrees 30-minutes east longitude.
So when it is 12 noon LMT for you, the sun is directly over 142-degrees 30-minutes east longitude for your time zone. Given the longitude for your exact location, you can work out the time for LAN.