How to Calculate Projected Area for Wind Loads

The power of wind cannot be underestimated. As a force, wind varies from a light breeze lifting a kite to the hurricane tearing off a roof. Even light poles and similar common, everyday structures must be designed to withstand the force of the wind. Calculating the projected area impacted by wind loads isn't difficult, however.

Wind Load Formula

The formula for calculating wind load, in its simplest form, is wind load force equals wind pressure times projected area times coefficient of drag. Mathematically, the formula is written as

F=PAC_d

Additional factors affecting wind loads include wind gusts, heights of structures and terrain surrounding structures. Also, structural details may catch the wind.

Projected Area Definition

Projected area means the surface area perpendicular to the wind. Engineers may choose to use the maximum projected area to calculate the wind's force.

Calculating the projected area of a plane surface facing into the wind requires thinking of the three-dimensional shape as a two-dimensional surface. The flat surface of a standard wall facing directly into the wind will present a square or rectangular surface. The projected area of a cone could present as a triangle or as a circle. The projected area of a sphere will always present as a circle.

Projected Area Calculations

Projected Area of a Square

The area the wind strikes on a square or rectangular structure depends on the orientation of the structure to the wind. If the wind strikes perpendicular to a square or rectangular surface, the area calculation is area equals length times width (A=LH). For a wall that is 20 feet long by 10 feet high, the projected area equals 20 ×10 or 200 square feet.

However, the greatest width of a rectangular structure will be the distance from one corner to the opposite corner, not the distance between adjacent corners. For example, consider a building that is 10 feet wide by 12 feet long by 10 feet tall. If the wind hits perpendicular to a side, the projected area of one wall will be 10 × 10 or 100 square feet while the projected area of the other wall will be 12 × 10 or 120 square feet.

If the wind hits perpendicular to a corner, however, the length of the projected area can be calculated according to the Pythagorean Theorem

a^2+b^2=c^2

The distance between opposite corners (L) becomes

10^2+12^2=L^2\implies L^2=244\implies L=\sqrt{244}=15.6\text{ ft}

The projected area then becomes L × H, 15.6 × 10=156 square feet.

Projected Area of a Sphere

Looking directly into a sphere, the two-dimensional view or projected frontal area of a sphere is a circle. The circle's projected diameter equals the diameter of the sphere.

The projected area calculation therefore uses the area formula for a circle: area equals pi times radius times radius, or A=πr2. If the diameter of the sphere is 20 feet, then the radius will be 20÷2=10 and the projected area will be A=π × 102≈3.14 × 100=314 square feet.

Projected Area of a Cone

The wind load on a cone depends on the orientation of the cone. If the cone sits on its base, then the projected area of the cone will be a triangle. The area formula for a triangle, base times height times one-half (B × H÷2), requires knowing the length across the base and the height to the cone's tip. If the structure is 10 feet across the base and 15 feet high, then the projected area calculation becomes 10 × 15÷2=150÷2=75 square feet.

If, however, the cone is balanced so that the base or the tip points directly into the wind, the projected area will be a circle with a diameter equal to the distance across the base. The area for a circle formula would then be applied.

If the cone is lying so that the wind hits perpendicular to the side (parallel to the base), then the projected area of the cone will be the same triangular shape as when the cone sits on its base. The area of a triangle formula would then be used to calculate the projected area.

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