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Aviation Maintenance Technician Handbook–General

FAA-H-8083-30B Version 2023
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Chapter 3

Mathematics in Aviation Maintenance

Formula: 3 y--- 3 ; = 3 ÷ 8 = 8 3.000 Therefore, = 0.375 ; 8 ; 8 ; – 24

60

  • 56 40
  • 40 0
Formula: Calculator tip: numerator (top number) ÷ denominator ; (bottom number) = the decimal equivalent of the fraction.

Some fractions when converted to decimals produce a repeating decimal.

Example:

Formula: . ; 33 ; - ; - ; = 1 ÷ 3 = 3 1.00 = 0.3 or 0.33 ; 3 – 9 This decimal can be ; 10 represented with a bar, or can ; – 9 be rounded. (A bar indicates ; that the number(s) beneath it ; 1

Other examples of repeating decimals:

Formula: 0.212121… = 0.21 ; 0.6666… = 0.7 or 0.67 ; 0.254254… = 0.254

Decimal Equivalent Chart

Figure 3-6 is a fraction to decimal to millimeter equivalency chart. Measurements starting at 1⁄64 inch and up to 3 inches have been converted to decimal numbers and to millimeters.

Ratio

A ratio is the comparison of two numbers or quantities. A ratio may be expressed in three ways: as a fraction, with a colon, or with the word “to.” For example, a gear ratio of 5:7 can be expressed as any of the following:

5⁄7 or 5:7 or 5 to 7

Aviation Applications

Ratios have widespread application in the field of aviation.

Example: Compression ratio on a reciprocating engine is the ratio of the volume of a cylinder with the piston at the bottom of its stroke to the volume of the cylinder with the piston at the top of its stroke. For example, a typical compression ratio might be 10:1 (or 10 to 1).

Aspect ratio is the ratio of the length (or span) of an airfoil to its width (or chord). A typical aspect ratio for a commercial airliner might be 7:1 (or 7 to 1).

Air-fuel ratio is the ratio of the weight of the air to the weight of fuel in the mixture being fed into the cylinders of a reciprocating engine. For example, a typical air-fuel ratio might be 14.3:1 (or 14.3 to 1).

Glide ratio is the ratio of the forward distance traveled to the vertical distance descended when an aircraft is operating without power. For example, if an aircraft descends 1,000 feet while it travels through the air for two linear miles (10,560 feet), it has a glide ratio of 10,560:1,000 which can be reduced to 10.56: 1 (or 10.56 to 1).