Mathematics in Aviation Maintenance

The formula for the area of a circle is:

Formula: area = π × radius2 = π × r2

Example: The bore, which is “inside diameter,” of a certain aircraft engine cylinder is 5 inches. Find the area of the cross section of the cylinder.

First, substitute the known values in the formula:

Formula: a = π × r2

The diameter is 5 inches, so the radius is 2.5 inches.

Formula: (diameter = radius × 2) ; a = 3.1416 × (2.5 inches)2 = 3.1416 × 6.25 square ; inches = 19.635 square inches

An ellipse is a closed, curved, plane figure and is commonly called an oval. [Figure 3-21] In a radial engine, the articulating rods connect to the hub by pins, which travel in the pattern of an ellipse (i.e., an elliptical or orbital path).

are required. To calculate wing area, it is necessary to know the meaning of the terms “span” and “chord.” The wingspan, S, is the length of the wing from wingtip to wingtip. The chord is the average width of the wing from leading edge to trailing edge. If the wing is a tapered wing, the average width, known as the mean chord (C), must be known to find the area. The formula for calculating wing area is:

Formula: area of a wing = span × mean chord

Example: Find the area of a tapered wing whose span is 50 feet and whose mean chord is 6'8". First, substitute the known values in the formula.

Formula: a = s × c ; = 50 feet × 6 feet 8 inches ; (Note: 8 inches = 8/12 feet = 0.67 feet) ; = 50 feet × 6.67 feet ; = 333.5 square feet

Formula: inches by 12 inches. Therefore, one square foot also equals ; 144 square inches (that is, 12 × 12 = 144). To convert square ; feet to square inches, multiply by 144. To convert square

inches to square feet, divide by 144.

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