One thought on that gray posting, Roger: I may remember incorrectly, but I thought illuminance on a surface was proportional to the square of the cosine of the incidence angle.
Dave Sent from my iPhone On Jan 2, 2014, at 8:07 PM, "Roger Bailey" <[email protected]> wrote: > Hello Marcelo, > > Many on this list empathize with your problem. We know what we want to do but > the math is unfamiliar. In reality the trigonometry here is very simple, as > you have laid out the problem. The ratio of the height of the shadow caster, > G to the shadow length, L is the Tangent of the altitude, H. Tan H = G/L. Or > rearranging L = G/Tan H. The shadow length is equal to the height of the > shadow caster divided by a simple number. the Tangent of the solar altitude > angle H. > > This assumes you know the altitude angle. At solar noon when the sun is on > the meridian, this is an easy calculation as the Noon altitude equals the > co-latitude minus the solar declination or H = 90-Lat-Dec. > > This assumes you know your latitude and solar declination. Latitude is easy > from maps, websites, GPS etc. Solar declination is not as quite as easy but > many tables, almanacs, programs and websites can give it to you. Google > solar declination. > > What if it is not noon? The altitude and azimuth are still relatively easy to > calculate using the classical formulae of spherical trigonometry used by > navigators with sextants. Sin Sin Sin Cos Cos Cos is the first equation to > know. Sin H = Sin Dec x Sin Lat + Cos Dec x Cos Lat x Cos t. Input your > latitude, declination and time as an angle from noon to calculate H, the > altitude angle that determines the shadow length. These intimidating trig > expressions are just numbers, simple numbers that you can add, subtract, > multiply and divide. > > But have you considered the Sine effect of the incident light? Light straight > down on a surface such as a flowers leaves is fully effective. As the angle > tilts from straight down to a lower angle, the effective incident light is > diminishes. How much? By the Sine of the altitude. Straight on the > altitude is 90° and Sin 90° = 1. At altitude = 45°, Sin 45 = 0.707, so the > light is 70% as intense. At 30° altitude, the intensity is halved as Sin 30 = > 0.5. > > Many on this mailing list have found the a little geometry, trigonometry and > even spherical tri can be very useful in solving problems like yours. > > Regards, Roger Bailey > -------------------------------------------------- > From: "Marcelo" <[email protected]> > Sent: Thursday, January 02, 2014 11:37 AM > To: "Sundial List" <[email protected]> > Subject: Garden planning problem > >> Hello fellow dialists, how are you? >> I'm with a problem here which doesn't concern exactly to sundials, but >> since it deals with sun's position and his shadows, I couldn't think >> of anyone better than you to help me. >> I have a little garden here at home, a walled area where I grow some >> plants in pots. I've found that, depending on the place, teher's a >> difference greater than 2.5 hours in the sunlight a plant receives, >> and that affects greatly its development. >> I've measured the shadows cast before and after true noon during >> summer solstice (I live slightly south to the Tropic of Capricorn). I >> could repeat the process during equinox and winter solstice, but >> that's a boring task, and above all, if the weather is cloudy I'll >> miss the chance. >> So, can you tell me some trigonometrical method for calculating the >> shadows, using sun's altitude and azimuth? I couldn't devise one by >> myself. >> Thanks in advance, and Happy New Year! >> >> Marcial >> --------------------------------------------------- >> https://lists.uni-koeln.de/mailman/listinfo/sundial >> >> >> >> ----- >> No virus found in this message. >> Checked by AVG - www.avg.com >> Version: 2014.0.4259 / Virus Database: 3658/6969 - Release Date: 01/02/14 > > > ----- > No virus found in this message. > Checked by AVG - www.avg.com > Version: 2014.0.4259 / Virus Database: 3658/6971 - Release Date: 01/02/14 > > --------------------------------------------------- > https://lists.uni-koeln.de/mailman/listinfo/sundial > --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
