Please Define Flare Rate Frequency

[1audiohack]

Thank you Peter. This is now making some sense.

I hope to get some real time to work on this, this weekend. I am sure more questions will follow.

Thank you all for your patience! Folks like you make this a great place.
Barry.

[Steve Schell]

The flare rate (or flare constant) of a horn refers to its rate of expansion, which determines how low in frequency it will load the driver for efficient output. Theoretically, at the calculated flare frequency the output has dropped by 3dB and falls off rapidly below that as the horn no longer loads the driver effectively. At frequencies much above the flare frequency the loading provided by the horn is essentially constant, though the response of a horn/driver combination will eventually droop higher up due to several things working in combination, mainly the driver's moving mass overcoming the motor strength.

There are many types of horn flare expansions, from conical (straight sided) to exponential to hyperbolic. Exponential has long been thought to be a good compromise for bass horns, and I have found them to work very well. In a pure exponential horn the cross sectional area will continue to double, i.e. 1,2,4,8,16, etc, in a given distance. The equation I use to calculate the flare constant (Fc) in inches of an exponential horn goes like this:

4 x Pi(3.1416) x Fc... divide the result by 13,200... take that answer and divide .7 by the answer to obtain the Fc.

Using Big Ed as an example, 4 x 3.1416 x 15 = 188.496

188.496 divided by 13,200 = .01428

.7 divided by .01428 = 49.0196

So, the cross sectional area of Big Ed (the horn, not my brother whom it is named after) doubles every 49 inches. It begins with a 66 square inch throat, has expanded to a cross section of 132 square inches after 49 inches, has expanded to a cross section of 264 sq." after another 49 inches, and so on.

If you run the numbers, you will find that a horn with twice the Fc of another horn will have half the doubling distance, same as the wavelengths of the frequencies involved.

There, that's more than I know about the math involved, never a strong subject of mine. Calculations of other flare types get more complicated, which I think is reason enough to avoid them. Main points to consider are that in general the longer horns are, and the larger their mouths are, the better their performance will be. Whenever a room corner can be exploited for a bass horn the performance is improved due to the 1/8th space loading provided; sort of an acoustical free lunch.

[whizzer]

A. To determine throat area: At = (2Pi)(Fs)(Qts)(Vas)/c
where At = throat area in sq. ft.; Fs = driver's resonance frequency in Hz;
Qts = driver's total Q factor; Vas = compliance as equivalent volume of air in cu. ft.

B. To determine mouth area: Am = [1/(SF)(4Pi)](c/Fc)(c/Fc)
where Am = mouth size in sq. ft.; SF = Size Factor (SF1 is free space--like hanging above a cornfield; SF2 is half space--on a floor; SF4 is quarter space--on a floor and next to a wall; and SF8 is 1/8th space--in a corner); c = speed of sound in feet per sec. (1130); Fc = desired cutoff frequency (-3 dB).

The horn length should be at least 1/4 wavelength--in practice, the distance from the throat to the calculated mouth size using the contour formula below.

C: To determine contour (flare rate or flare frequency): Ax is equal to At times e raised to the power of 2x divided by xo.
where Ax is the area of the expansion at distance x from the throat; xo is equal to 2/k where k = (4Pi)(Fc)/c, where Fc is the desired cutoff and c is the speed of sound; e = a constant (like Pi, or 3.1416....); e = 2.71828....

So, for an example, using a Pioneer 10-inch instrument loudspeaker, A25GC40-51-F-Q, with an Fs of 30 Hz, a Qts of 0.15, and a Vas of 5.08 cubic feet, and figuring an exponential horn with a cutoff of 50 Hz with a size factor of 8 and a cabinet width (internal) of 16 inches, we find a throat area of 24 square inches, a mouth area of 730.4 square inches, a length of 73.6 inches; the distance in which the cross-sectional area doubles is about 14.94 inches.

[1audiohack]

You all have been a great help! I think I've got it.

I have modeled some of my old simple JBL horns in David McBeans HORNRESP program and need to set up the TEF and check myself against reality.

Steve I also finally swept your old corner horns in "The Big Corner" (38 feet tall, 50+ foot long walls of 6 inch thick concrete, outdoors) I will PM you when I get it off my laptop if your interested.

I am dying to cut wood!!!

Thanks again,
Barry.