Shop maths and physics

Mechanics use a handful of formulas again and again. The area of a circle is π × r² (or 0.7854 × d²), and a cylinder's volume is that area times its length. An engine's displacement is the volume one piston sweeps (piston area × stroke) times the number of cylinders.

Piston area 20 sq in, stroke 4 in, 6 cylinders
Displacement = 20 × 4 × 6 = 480 cubic inches

Pressure is force spread over an area: pressure = force ÷ area, so force = pressure × area. This is why hydraulics work: pressure applied to a trapped liquid is passed equally in every direction (Pascal's law), so 1,000 psi on a piston of 3 square inches pushes with 3,000 pounds.

Work is force times distance (foot-pounds), and power is work done per unit of time. One horsepower is 550 foot-pounds per second, or 33,000 foot-pounds per minute.

Gases follow simple rules if you use absolute temperatures (kelvin or Rankine). Boyle's law: at the same temperature, squeeze a gas to half its volume and its pressure doubles. Charles's law: at the same pressure, volume rises with absolute temperature. That's why tire and strut pressures are checked cold.

Air gets thinner when it is hot, high or humid (water vapor is lighter than the air it replaces). Pilots call this density altitude: on a hot day at a high airport, wings make less lift, propellers less thrust and engines less power. And Bernoulli's principle: where a moving fluid speeds up, its pressure drops. It's how a carburetor's venturi pulls fuel in, and part of how a wing makes lift.