Computing Volume of Three-Dimensional Solids (Part Three) Cylinder

in Aviation Mathematics

A solid having the shape of a can, or a length of pipe, or a barrel is called a cylinder. [Figure 1-26] The ends of a cylinder are identical circles. The formula for the volume of a cylinder is:

Volume = π × radius2 × height of the cylinder = π r2 × H
Figure 1-26. Cylinder.

Figure 1-26. Cylinder.

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:

Piston Displacement =
π × (bore divided by 2)2 × stroke × (# cylinders)

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 1-27]

Figure 1-27. Cylinder displacement.

Figure 1-27. Cylinder displacement.

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.

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

Total Displacement for 8 cylinders = 8 × 128.29 =
1026.32 cubic inches of displacement

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