Calculate Shadow Casting: Length, Height, Altitude of the Sun
A simple calculator for shadow casting: height of the Sun, height of the object or shadow length, as well as the ratio between shadow length and object height can be determined. The height of the Sun is given in degrees. Object height and shadow length have the same unit, e.g. feet or meters. See also shadow length and direction by coordinates and time, where the position of the sun can be determined from location and time. However, if you already know the angle of the sun's position or want to calculate it from height and shadow length, then this calculator is better.
Formulas:
l = h * cot(α)
α = arccot(l/h)
Example: when the sun is at 40 degrees, an object twelve meters high casts a shadow that is 14.3 meters long. The ratio of length to height is 119.18 percent, so the shadow is about nineteen percent longer than the height of the object casting the shadow. It should be noted that this is the theoretical length of the shadow, which starts from the point to which the tip of the object is extended downwards.
If, for example, you take a regular, straight pyramid with a square base as the object casting the shadow, the length of the shadow calculated here is the distance from the center of gravity of the pyramid on the ground to the end of the shadow. If you want to know the length of the shadow behind the pyramid on the ground, you have to subtract half the side length of the pyramid or more up to half the diagonal from this value.
A clear shadow can of course only be seen when the sky is clear. Even light cloud cover makes the shadow diffuse, and with heavier cloud cover it quickly disappears completely. Under very good conditions, even the moon, especially the full moon, can cast shadows. In this case, of course, the angle does not refer to the position of the sun, but to the altitude of the moon.
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