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Fan Noise Estimate

Far-field noise of a fan or propeller from its thrust, shaft power, speed, diameter, blade count and blade area: the rotational (tonal) noise of the first harmonics of the blade-passing frequency by Gutin's theory in the engineering form of NACA TN 2968, and the vortex (broadband) noise by Yudin's sixth-power law with Hubbard's constant from the same report. The levels are given at the observer's distance and angle from the thrust axis, summed to an overall level, and charted against distance and angle. The estimate is for an unducted rotor in still air; a duct shields part of the tonal field and adds its own sources, so the result is a starting point and an upper bound for the rotor alone.

  • Gutin rotational noise: sound pressure and level of harmonics 1 to 4 of the blade-passing frequency at the observer

  • Vortex noise by Yudin's law, energy ∝ blade area × (velocity at 0.7 R)⁶, NACA TN 2968 constant

  • Overall level, thrust and torque contributions, ground-reflection option, inverse-distance propagation

  • Charts of level against distance and against angle from the thrust axis

Fan Noise Estimate

Unit System: /

Fan Operating Point








Observer




Gutin and Vortex Noise | Method page
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Fan Noise Estimate

Gutin and Vortex Noise

Rotational noise

A rotor's steady thrust and torque are carried by blades that sweep past a fixed observer B times per revolution; to the observer the pressure field is periodic at the blade-passing frequency B Ω/2π and its harmonics. Gutin (1936) derived the far-field sound pressure of each harmonic of a static propeller from the thrust and torque alone. In the engineering form of NACA TN 2968 the rms pressure of harmonic m is

pm = (m B Ω / (2√2 π c s)) [−T cos β + c Q / (Ω Re²)] JmB(m B (Ω Re / c) sin β)

with Ω the rotor speed, c the speed of sound, s the distance, β the angle from the forward thrust axis, Q the torque and Re = 0.8 R the radius at which the loads are concentrated. JmB is the Bessel function of order mB; its argument is the order times the Mach number of the effective radius times sin β. On the axis (β = 0 or 180°) the argument vanishes and so does the rotational noise; the maximum lies a little behind the rotor plane, near 105°, where the thrust and torque terms add. Because the Bessel order grows with the blade count, more blades push the sound into higher harmonics and cut the level sharply at low tip Mach numbers, which is why many-bladed fans are quiet. The level is 20 log10(p / 20 µPa).

The tool evaluates the first four harmonics and sums them by energy. NACA TN 2968 doubled the pressures for ground reflection in its charts and tables (+6 dB); the checkbox reproduces that, and the tool's own check cases are its Table I.

Vortex noise

The broadband hiss of a rotor comes from the vortices shed by the blade sections. Yudin found its energy proportional to the blade area and to the sixth power of the section velocity; Hubbard evaluated the constant from a helicopter blade and wrote the level at 300 ft as Lv = 10 log10(k AB V0.7⁶ / 10⁻¹⁶) with k = 3.8 × 10⁻²⁷ for AB in square feet and the velocity at 0.7 R in feet per second. He rated the result as tentative, accurate to about ±10 dB. Other distances follow the inverse-distance law.

What is not included

Forward flight (the static formula is used; TN 1358 found flight levels about 6 dB lower), atmospheric absorption, the duct's shielding and its own inlet and tip-gap noise, unsteady loading from inflow distortion, and the thickness noise that becomes important above a tip Mach number of about 0.9. The figures are the rotor's own far-field contribution in still air and should be read as an upper bound for the rotational part of a ducted fan.



References

Hubbard, H. H. (1953). Propeller-Noise Charts for Transport Airplanes. NACA Technical Note 2968, National Advisory Committee for Aeronautics, Washington, D.C.

Gutin, L. (1948). On the Sound Field of a Rotating Propeller. NACA Technical Memorandum 1195 (translation of the 1936 paper), National Advisory Committee for Aeronautics, Washington, D.C.

Deming, A. F. (1940). Propeller Rotation Noise Due to Torque and Thrust. NACA Technical Note 747, National Advisory Committee for Aeronautics, Washington, D.C.

Hubbard, H. H., and Regier, A. A. (1947). Propeller-Loudness Charts for Light Airplanes. NACA Technical Note 1358, National Advisory Committee for Aeronautics, Washington, D.C.

Yudin, E. Y. (1947). On the Vortex Sound From Rotating Rods. NACA Technical Memorandum 1136, National Advisory Committee for Aeronautics, Washington, D.C.

Worked Examples

Published examples this tool reproduces; each page lists the inputs to enter and the printed answers.

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