I have a design for a compact full range speaker cabinet that is based on a cone.

Greetings,

The length of a rear loaded horn is base on three factors.

1 ) The parameters of the driver.

2) The volume of the chamber it resides in.

3) The throat area.

The combination of the chamber volume and throat area result in an acoustical low-pass filter.

First, the acoustical parameters of the driver and chamber need to be considered, as they become half of the circuit. The driver Cas, and the chamber Cab are both an acoustical compliance. Think of the acoustical compliance analogy as an electrical capacitance analogy.

The throat area constitutes an acoustical mass, or Mat. Think of that analogy as an electrical inductance analogy.

The values of an acoustical analogy and electrical analogy are treated the same when calculating filter math. The acoustical Compliance is in Farrad, and the acoustical Mass is in Henry.

What do you get when you resonate the reactive element of a capacitor, and the reactive element of an inductor? A low-pass filter circuit. The slope will be that of a 1st Order filter network. 6dB / Octave.

Once that frequency has been determined, the length of a rear loaded horn is calculated by multiples of half wavelengths in order for the horn mouth and speaker cone to be in acoustic phase. The phasing will only occur at the low-pass frequency. As the frequency increases the horn ceases to radiate. Below that frequency the horn is the primary radiator. The cut-off frequency of a rear loaded horn does not determine it's length.

For example. If the low-pass frequency is 300 Hz, the length of your horn will be 22.6 inches, 67.8 inches, 113 inches, etc...

Another parameter to consider is the Efficiency Bandwidth Product. fs / Qes.

Cone drivers with EBP values lower that 150 IMO, make for questionable horn drivers. Those with values of 100 and lower are best suited for bass reflex and sealed enclosures. Speakers with low EBP values typically require large enclosures.

Drivers with EBP values of 175 and greater are better suited for horn loading, and also bass reflex enclosures. The higher the EBP value, the smaller chamber volume is required.

Other factors for horn loading will be high motor strength, and light cone weight.

The best equation I have found to use is Vincent Salmon's equation for a hyperbolic horn. It allows you a degree of latitude when choosing a mouth area while maintaining the proper length. That latitude being the 'T' in the equation. A 'T' of .6 is typical. As the number decreases the flare becomes Catenoidal. At that point the horn behaves more like slightly flared a tube, which will cause distortion. When the number approaches 1, the flare becomes more Exponential. A number greater than 1 is not desirable, as the horn would flare too rapidly.

A word of advise. Just because a speaker has a cone doesn't mean it is suitable for horn loading. Stuffing a speaker with a low EBP into a small chamber will produce mushy, ill-defined bass, flawlessly.

The EICO enclosure is certainly a unique enclosure. I own a pair. Not audiophile grade, but pleasant to listen to for background music.

Now, a word about compound horns. The length of both horns, not including the chamber between them must be multiples of a half wavelength. For example, if your bass horn is 67.8 inches, and you wish to make your mid horn 6 inches, then the combined length of both horns will be 67.8 inches. What ever you add in the front horn length must be subtracted from the bass horn length. That way the acoustic phasing between the two horns will be at unity at the low-pass frequency.

Also. Choosing drivers with an fs lower than 35 Hz becomes problematic. A proper cut-off frequency for a cone driven horn is within 5 Hz below fs in order to achieve proper reactance annulling. Designing a horn based on very low fs frequencies will result in a very long horn with an unwieldly mouth area. Shortening a horn with a very low cut-off in order to make it suitable for domestic use will result in what is called a discontinuity. Your horn is no longer a horn, but a tapered tube.

H.F.