Lighthill Jet Acoustic Power & U⁸ Law Calculator

In 1952, Sir James Lighthill formulated the acoustic analogy, discovering that turbulent aerodynamic fluid flow without solid boundaries radiates sound as a field of acoustic quadrupoles.

The radiated acoustic sound power increases with the 8th power of fluid velocity (W ∝ U⁸), making exhaust velocity by far the dominant driver of aircraft noise.

Turbulent eddies shear against stationary ambient air, creating fluctuating Reynolds stresses that radiate sound.

Acoustic conversion efficiency scales with the 5th power of Mach number: ηac ∝ M⁵. For low-speed flows, only a tiny fraction of mechanical energy becomes noise; at high subsonic speeds, noise radiation becomes enormous.

Sound Power Level LW (dB re 1 pW) represents total acoustic energy emitted in all directions.

Because of the U⁸ dependence, reducing jet velocity by just 20% slashes radiated noise power by more than 80% (~7 dB reduction).

• Jet velocity: The overwhelming factor; modern high-bypass turbofans reduce velocity by extracting core energy to drive huge fan stages.
• Nozzle chevrons/serrations: Enhance perimeter mixing to break up large turbulent noise-producing eddies.

• Evaluating jet engine takeoff noise and airport noise contours.
• Sizing industrial steam blowoff and gas relief valve silencers.

• Valid for unchoked subsonic turbulent round jets (M < 1).