In Reply to: Tomservo, validity of Leach's math model - conical horn? posted by M on June 13, 2003 at 08:35:35:
HiYes, the math is based on an exponential horn, the idea here is that this kind of horn (exponential) has a more or less constant load impedance vs frequency and so if presented with a constant radiator velocity, produces a flat response.
While an exponential horn is a hyperbolic horn of "m" or "t"=1, going over 1 (towards conical) or under 1 (more hyperbolic) changes the shape of the radiation resistance curve near the low cutoff (on a "long enough" horn).I do know that M. Leach and an old friend (Richard Long, a horn designer from NY who did big nightclub horns like studio 54 back when) went back and fourth when the paper came out on the hyperbolic part.
I ended up incorporating Richards formula for this part in the Leach math I use.
I think the final version of the Leach paper is in the AES loudspeaker anthology, these are a great and humbling set of books for the speaker enthusiast.Hypothetically speaking, I probably can’t tell one how to copy products we sell.
On the other hand, I can hypothetically speaking, suggest a DIY’r do the following.
Locate some "nothing special" 4†or 5 ¼ inch sealed back mid drivers with a resonance around 500Hz.
Make a scratch horn of the size and angles you want, mount the drivers near the apex but on the horn walls with say 2, ¾ inch holes at the horn corners for each driver, entering the horn about 1/4 wl forward of the apex at the intended Xo.
Measure the actual response and HF cutoff.
In addition to the normal horn stuff, one also has a hf limit set by the distance of the holes to the apex.
When this is about 1/4 wl away or more one gets a hf attenuation (acoustic low pass filter effect starting with a deep notch).
Adjust this distance so that this roll off you measured is just above where you want to crossover to be.Make the real horns (same size etc), mount the drivers and go to work on the xover.
This is where it may be a bit tough, the drivers are very close acoustically so instead of just steering the radiation pattern around the room as in a normal speaker at xo (where the drivers are significantly further apart), phase problems cause big effects.
Your best bet here is to use a program like LSPcad pro which one can enter the measured response for each section (all measured from one point) as well as the impedance and then solve for a good response curve.
On the other hand, I know there are people who did DIY versions without LSPcad and the front back spacing will automatically be pretty close to that needed to compensate for the Xo and driver delays with the LF part in front of the HF part.
Hope this helps a bit.Tom
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Follow Ups
- Re: Tomservo, validity of Leach's math model - conical horn? - tomservo 06/14/0309:37:40 06/14/03 (1)
- Tomservo, validity of Leach's math model - conical horn? Thank you. - M 19:02:29 06/15/03 (0)