Hyperbolic bass horns

If I remember the GRC paper it is discussing "complete" horns, in that the mouth area is large enough to support the horn path length with constant expansion. The first thing I would do is double check that is the case in your simulations.

As I remember the real part of acoustic load of a hyperbolic can rise faster from cutoff to its steady state level vs an exponential. But this is not the only factor when calculating total horn output. It is a multiplying factor I would have thought. Think in electrical analog terms, if you want to know the power dissipated in a load, you have to multiple it by current squared. The analog to current in the driver side of a cabinet model is volume of air moved per second, or average(driver excursion*Sd)^2/time

Just a thought, might be off base but it is the first thing that occurs.

After some more reading and experimenting, I think I am starting to understand it better now. As you said T is linked to a number of other elements in the system. You cant just change T and watch what happens, it will throw the reactance annulling off. Vb, St and throat area need to be changed compensate. There are limits to this, where reactance annulling cant be achieved without impractical chamber volumes or compression ratio. If you adjust it all as one system, lower T values = a little bump near cutoff. T is linked to the rest if this system via this formulae (M=T): 

This is good reading if you're looking for stuff! - https://www.grc.com/acoustics/an-introduction-to-horn-theory.pdf

Edited by smoore - 02 June 2020 at 10:14am

The horn stops loading the driver completely when Ra = 0, or the real part of the acoustic impedance is nothing. That means there is no in-phase pressure and air volume movement and so no power transfer occurs.

The red line is the horn reactance, when this is non-zero it means there is air movement in the horn but it is not in phas with driver pressure so a proportion of electrical power delivered to the driver is not converted into acoustical output.

If your ignore the peaks due to horn resonances and trace a line through the black data outside the resonance and the black data betweeen the resonances, you get an idea of when it is going to cross through zero. Zooming in the y-axis would help see this.

My money would be on somewhere between first and second resonance. You can see under the first resonance frequency that the impedance is pretty much all reactive, so that is a definite cut off there.

It is hard to tell from the graph, but that is what the Ra value is suggesting. You have to zoom into see it properly. Looks like the real part of the first resonance goes down to about 40Hz but you're talking one pixel on a screen at that point.

I suspect there is more to total output than that just value, there will be scaling factors with frequency etc involved. I have never done the detailed analysis for deeper understanding myself, it is on the one day list (along with everything else).

has anyone worked out the maximum efficiency design procedure from Leach's paper? He say it 'invloves slightly more complicated expressions'. I can't see how you find Qec or Vat without specifying an additional driver paramter.