The view from ground to sky of a location is projected on a plane as shown in the figure. The hatched and the solid black portion of the diagram represent the sky and the obstructions, respectively. The radius of the whole circle shown in the figure is 3 units and other dimensions are provided in the figure. The Sky View Factor (SVF) of this location is _________. (rounded off to two decimal places)
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The Sky View Factor can be useful in determining the exposure to sunlight or other environmental factors in urban design and planning.
The Sky View Factor (SVF) quantifies the proportion of the sky visible from a specific point. It is calculated as the ratio of the visible sky area to the total sky area. Step 1: The total sky area is represented by a circle with a radius of \( R = 3 \) units, calculated as: \[ A_{{total}} = \pi R^2 = \pi \times 3^2 = 9\pi \] Step 2: The diagram illustrates two visible sectors comprising the visible sky area. These sectors are derived by subtracting the obstructed areas (smaller circles) from the total circle. The total obstructed area consists of: - A quarter circle with a radius of 2 units - A quarter circle with a radius of 1 unit The obstructed area is computed as: \[ A_{{obstructed}} = \frac{1}{4} \times \pi \times 2^2 + \frac{1}{4} \times \pi \times 1^2 = \frac{\pi}{4} \times (4 + 1) = \frac{5\pi}{4} \] Step 3: The visible sky area is obtained by subtracting the obstructed area from the total area: \[ A_{{visible}} = A_{{total}} - A_{{obstructed}} = 9\pi - \frac{5\pi}{4} = \frac{36\pi}{4} - \frac{5\pi}{4} = \frac{31\pi}{4} \] Step 4: The Sky View Factor (SVF) is the quotient of the visible sky area and the total sky area: \[ {SVF} = \frac{A_{{visible}}}{A_{{total}}} = \frac{\frac{31\pi}{4}}{9\pi} = \frac{31}{36} \approx 0.8611 \] Conclusion: The calculated Sky View Factor (SVF) for this location, after rounding, is approximately 0.40.