**bill@flutter.tv.tek.com (William K. McFadden)** (03/08/91)

Someone on the net asked about an equation for duct dimensions of a ported speaker enclosure. Having grown tired of tables and nomograms that never have the sizes I need, I decided to go back to the original technical papers by Thiele and Small to arrive at some equations. I have verified them against the examples used by Thiele and Small. First, in Small's paper, there is an equation that specifies the minimum port diameter necessary to prevent excessive vent noise. The equation is: Dv >= (Fb*Vd)^0.5, where Dv is the inside diameter of the duct in meters, Fb is the enclosure tuning frequency in Hz, and Vd is the driver displacement volume in cubic meters. Using information from Thiele's paper, I determined the equation for the length of the duct: Lv = 2362*Dv^2/(Fb^2*Vb) - 0.85*Dv, where Lv is the duct length in meters, Vb is the enclosure volume in cubic meters, and the other variables are the same as above. In english units, the two equations become: Dv >= 0.159*(Fb*Vd)^0.5 where Dv is the inside diameter of the duct in inches, Fb is the enclosure tuning frequency in Hz, and Vd is the driver displacement volume in cubic inches. Lv = 2118*Dv^2/(Fb^2*Vb) - 0.85*Dv, where Lv is the duct length in inches, Vb is the enclosure volume in cubic feet, and the other variables are the same as above. To use with the HP48SX solver, enter the following list: { 'Dmin=\v/(Fb*Vd*1_s/m)' 'Lv=(2362_m^2/s^2)*Dv^2/(Fb^2*Vb)-.85*Dv' } where \v/ is square root. You can enter the variables using any units and the 48SX will convert to the units of the variable being solved. References: A.N. Thiele, "Loudspeakers in Vented Boxes, Parts I and II," J. Audio Eng. Soc., vol. 19, pp. 382-392 (1971 May); pp. 471-483 (1971 June). R.H. Small, "Vented-Box Loudspeaker Systems," J. Audio Eng. Soc., vol. 21, (four parts, starting in the June 1973 issue). Reprints of these papers can also be found in the first volume of the AES loudspeakers anthology. -- Bill McFadden Tektronix, Inc. P.O. Box 500 MS 58-639 Beaverton, OR 97077 bill@videovax.tv.tek.com, {hplabs,uw-beaver,decvax}!tektronix!videovax!bill Phone: (503) 627-6920 "SCUD: Shoots Crooked, Usually Destroyed"