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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

Figure 3-21. Ellipse.
Figure 3-21. Ellipse.

Since each of the smaller boxes has a volume of 1 cubic foot, the large carton holds 27 boxes.

Cylinder

A solid having the shape of a can, a length of pipe, or a barrel is called a cylinder. [Figure 3-26] The ends of a cylinder are identical circles. The formula for the volume of a cylinder is:

Formula: volume = π × radius2 × height of the cylinder = π r2 × h

One of the most important applications of the volume of a cylinder is finding the piston displacement of a cylinder in a reciprocating engine. Piston displacement is the total volume (in cubic inches, cubic centimeters, or liters) swept by all of the pistons of a reciprocating engine as they move in one revolution of the crankshaft. The formula for piston displacement is given as:

Formula: Piston Displacement = ; π × (bore divided by 2)2 × stroke × (# cylinders)
Figure 3-22. Wing planform.
Figure 3-22. Wing planform.

The bore of an engine is the inside diameter of the cylinder. The stroke of the engine is the length the piston travels inside the cylinder. [Figure 3-27] Example: Find the piston displacement of one cylinder in a multi-cylinder aircraft engine. The engine has a cylinder bore of 5.5 inches and a stroke of 5.4 inches. First, substitute the known values in the formula.

Formula: v = π × r2 × h = (3.1416) × (5.5 ÷ 2)2 × (5.4) ; v = 23.758 × 5.4 = 128.29 cubic inches

The piston displacement of one cylinder is 128.29 cubic

Formula: Figure 3-23 formula reference: Trigonometric equations: sin(A) = opposite / hypotenuse; cos(A) = adjacent / hypotenuse; tan(A) = opposite / adjacent. Pythagorean theorem: a² + b² = c². The companion visual also contains searchable length, area, volume, weight, and temperature conversions. Source text: Conversion Factors ; Length Area ; 1 inch 2.54 centimeters 25.4 millimeters 1 square inch 6.45 square centimeters ; 1 foot 12 inches 30.48 centimeters 1 square foot 144 square inches 0.093 square meters ; 1 yard 3 feet 0.9144 meters 1 square yard 9 square feet 0.836 square meters ; 1 mile 5,280 feet 1,760 yards 1 acre 43,560 square feet ; 1 millimeter 0.0394 inches 1 square mile 640 acres 2.59 square kilometers ; 1 kilometer 0.62 miles 1 square centimeter 0.155 square inches ; 1 square meter 1.195 square yards ; 1 square kilometer 0.384 square miles ; Volume ; 1 fluid ounce 29.57 cubic centimeters ; 1 cup 8 fluid ounces ; 1 pint 2 cups 16 fluid ounces 0.473 liters ; 1 quart 2 pints 4 cups 32 fluid ounces 0.9463 liters ; 1 gallon 4 quarts 8 pints 16 cups 128 ounces 3.785 liters ; 1 gallon 231 cubic inches ; 1 liter 0.264 gallons 1.057 quarts ; 1 cubic foot 1,728 cubic inches 7.5 gallons ; 1 cubic yard 27 cubic feet ; 1 board foot 1 inch x 12 inches x 12 inches ; Weight Temperature ; 1 ounce 28.350 grams °F to °C Celsius = ⁵/9 × (°F − 32) ; 1 pound 16 ounces 453.592 grams 0.4536 kilograms I °C to °F I Fahrenheit = ⁹/5 × (°C + 32) I ; 1 ton 2,000 pounds ; 1 milligram 0.001 grams ; 1 kilogram 1,000 grams 2.2 pounds ; 1 gram 0.0353 ounces

inches. For an eight-cylinder engine, then the total engine displacement would be:

Formula: Total displacement for 8 cylinders = 8 × 128.29 = ; 1026.32 cubic inches of displacement

Sphere

A solid having the shape of a ball is called a sphere. [Figure 3-28] A sphere has a constant diameter. The radius (r) of a sphere is one-half of the diameter (d). The formula for the volume of a sphere is given as:

Figure 3-23. Applied mathematics formula sheet.
Figure 3-23. Applied mathematics formula sheet.
Formula: Figure 3-23 formula reference: Trigonometric equations: sin(A) = opposite / hypotenuse; cos(A) = adjacent / hypotenuse; tan(A) = opposite / adjacent. Pythagorean theorem: a² + b² = c². The companion visual also contains searchable length, area, volume, weight, and temperature conversions. Source text: Order of Operation for Algebraic Equations ; 1. Parentheses ; 2. Exponents ; 3. Multiplication ; 4. Division ; 5. Addition ; 6. Subtraction ; Use the acronym PEMDAS to remember the order of ; operation in algebra. PEMDAS is an acronym for parentheses, ; exponents, multiplication, division, addition, and subtraction. ; To remember it, many use the sentence, “Please Excuse My ; Dear Aunt Sally.” ; Trigonometric Equations ; B ; c a ; A b C ; opposite side (side a) ; Sine (sin) of angle A = hypotenuse (side c) ; adjacent side (side b) ; Cosine (cos) of angle A = hypotenuse (side c) ; opposite side (side a) ; Tangent (tan) of angle A = adjacent side (side b) ; Pythagorean Theorem ; c ; a ; b ; a2 + b2 = c2

Example: A pressure tank inside the fuselage of a cargo aircraft is in the shape of a sphere with a diameter of 34 inches. What is the volume of the pressure tank?

Figure 3-24. Rectangular solid.
Figure 3-24. Rectangular solid.