I beg to opine differently! After realigning my diaphragms (very easy to do) I can state that I actually like this construction. It allows one to realign the diaphragm without removing the back cover. Much safer!
Maybe I should explain... It is a trial and error process while you measure with REW. Untighten screws, wiggle diaphragm, retighten screws, measure and repeat. Wether the screws are the diaphragm screws or the back cover screws, the process is the same. Just safer if the diaphragm is not exposed to the screwdriver.
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@marco_gea Thank you very much for your thorough explanation in post #85. 
Your post answers some of my questions, but of course raises others.
You've made it clear in point 2 that there can be only one ideal match between the conical horn throat expansion and an expo or hypex horn, but that we try to get as close a match as possible. In the paper above by Marcel Batík, he writes of the effects of reflections that occur from the mismatches in the expansion rate. This is easy to understand. What is more difficult to understand is how to determine the flare rate. You posted this:
Sx is the area of the duct?
m is the flare rate
what is "d"? the distance from the origin of the duct? If so, why do we have "at distance x from the origin"? Are x and d the same thing? Please clarify d
"If the expansion of the duct is exponential (T = 1 in Salmon's equation), then m is constant throughout." Is m constant throughout for a conical horn?
Does a conical horn have a cutoff frequency? Obviously this is confusing to me, and I'd like to know more about the steps.
Once that is clear (at least to me and some other readers) we can move on to practical matters of how we determine these things on existing devices and make wise choices.
Your post answers some of my questions, but of course raises others.
This is often mentioned and I believe well understood by many builders. And shouldn't this already be taken care of when we find an optimum match to the flare rates?
You've made it clear in point 2 that there can be only one ideal match between the conical horn throat expansion and an expo or hypex horn, but that we try to get as close a match as possible. In the paper above by Marcel Batík, he writes of the effects of reflections that occur from the mismatches in the expansion rate. This is easy to understand. What is more difficult to understand is how to determine the flare rate. You posted this:
Can you explain this further for those of us who don't know the maths? That way we can perhaps work on these calculations ourselves. What does each part mean and how do we use it?
Sx is the area of the duct?
m is the flare rate
what is "d"? the distance from the origin of the duct? If so, why do we have "at distance x from the origin"? Are x and d the same thing? Please clarify d
"If the expansion of the duct is exponential (T = 1 in Salmon's equation), then m is constant throughout." Is m constant throughout for a conical horn?
That can by nearly impossible for most of us. We will always know S2, and if we are lucky we will know L, but throat Length is rarely stated in driver specs or shown in mechanical drawings. But does it matter? If we know S2 and the exit angle, we can calculate S1 at any give L. The part that I don't understand is why does L matter if it's a cone?
Does a conical horn have a cutoff frequency? Obviously this is confusing to me, and I'd like to know more about the steps.
Once that is clear (at least to me and some other readers) we can move on to practical matters of how we determine these things on existing devices and make wise choices.
On page 21 of Marcel Batík's paper, he says: "However, many compression drivers contain a segment of a conical duct as their exit section and even if the slopes of the walls match at the driver/waveguide interface, there will be a wave reflection from this curvature discontinuity." He shows this image which is similar to the graphics I posted earlier in the thread.
To solve this discontinuity he proposes inserting a ring into the driver throat that will effectively extend the horn's profile down to the driver's phase plug. This has occurred to me from time to time, but in somewhat less sophisticated terms.
Not necessarily. Matching the flare rates (first priority) could still lead to some discontinuity in the wall angles.
Only ONE exponential horn (same Fc as driver's internal throat equivalent exponential Fc), but multiple hypex horns if one can change both T and Fc to match the horn's initial flare rate m at its throat to that of the driver's internal throat (eq. exp).
Sx ( more rigorously written: S(x) ) is the area of the wavefront surface at distance x from the origin.
dSx/dx ( more rigorously written: d[S(x)]/d[x] ) is the first derivative of the equation for the surface area, relative to the distance x.
m (flare rate) is NOT constant in a conical horn. The only horns for which m is constant are pure exponentials.
Also, no cutoff frequency (Fc) is strictly defined for a conical horn. In conical horns, driver loading is determined by its solid angle (wider angle = less loading at lower frequencies).
L matters if one wants to calculate the flare rate (and Fc) of the equivalent exponential duct that shares the same S1, S2 and L as the driver's actual conical internal throat. All three values are required to identify a specific exponential expansion profile.
I'm afraid the only way to calculate the equivalent exponential parameters m and Fc, starting from measurements of S1, S2 and L is to actually use the appropriate/correct maths:
Fc = c/(4*Pi*L)*ln(S2/S1)
m = 4*Pi*Fc/c
where:
ln = natural logarithm (base e)
Pi = 3.141...
c = speed of sound = 343 m/s @ 20ºC
(L is likewise given in metres)
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This solution addresses the wall angle discontinuity, but not necessarily the mismatch in flare rates.
If there's a discontinuity in wall angles, real wavefront curvatures will be different and so will be the actual flare rates.
It actually solves both at the same time.
Absolutely, correct.
What I meant was: "matching wall angles is necessary but not sufficient to ensure a match in flare rates"
Ah ha, thanks. I may have accidentally demonstrated that early in the thread. ✅
OK, yes. This can easily be seen Hornresp sims. ✅
Sorry to me thick, but I do not understand this. Perhaps it is the word "rate" that is confusing me, I don't understand the meaning of rate. I'll have to run some numbers to understand it.
Understood. I was thinking area of the duct section, but Sx is the area of the wavefront surface. ✅
"rate" as in "rate of change", i.e., how quickly something changes, along a specified variable dimension (which can be distance, time, etc.)
Mathematically, the "flare rate" m of a horn at each distance x from the throat is defined as the first derivative of the equation for the surface area, relative to the distance x, divided by the value of the surface area itself, measured at the same distance x.
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Hi marco_gea,
Kindest regards,
M
Could this be solved by the adapter with the correct flare rate extending from the adapter-to-horn interface into the (conical) opening of the driver? Or, would this disturb the wave shape generated by the phase plug?
Kindest regards,
M
Hi Pano,
Kindest regards,
M
If one is willing to remove the protective screen, one can measure the depth (L) by e.g., a caliper or micrometer. The diameter (and then calculating S1) can be accomplished by either measurement, e.g., bore gauge, internal diameter caliper, and the like, or alternatively, if the included angle is known by simple math form diameter at S2 and L.
Kindest regards,
M
Yes, it shouldn't be too hard when you have the driver and want to remove the bug screen. Unfortunately we don't know these dimensions for most drivers and the info isn't supplied but the manufactures. Currently we have to do a best guess off the info we do have.
This might be seen as the second part of the problem. Even if you know how to figure out what driver geometry might but fit our horn - or vice-versa - we don't know the geometry of the many drivers available.
This might be seen as the second part of the problem. Even if you know how to figure out what driver geometry might but fit our horn - or vice-versa - we don't know the geometry of the many drivers available.
Hi Pano,
Saying that, such a situation may be very likely, hence my question in post # 111.
Kindest regards,
M
You are, of course, correct. I made the (inappropriate) assumption that one has the driver, a horn, or both and is trying to find the "best match" as described by marco_gea.
Saying that, such a situation may be very likely, hence my question in post # 111.
Kindest regards,
M
Potentially, yes. I imagine it may be tricky to manufacture such an extended adapter to the required tolerances, though.
That would depend on the specific geometry of the phase plug itself - which sadly is rarely (if ever) disclosed by the manufacturers.
Thanks Marco, but isn't that showing a horn entrance the same size as the driver exit? The angle is very different, that's true.
Of course you might truncate the horn and build an adapter than fits into the driver throat. If the driver opening is larger than the horn opening, you could also build your adapter to do down into the throat, which might be possible. Or use a ring adapter inside the driver throat.
But if you had to stay external to the driver, the driver exit would need to be smaller than the horn entrance.
Of course you might truncate the horn and build an adapter than fits into the driver throat. If the driver opening is larger than the horn opening, you could also build your adapter to do down into the throat, which might be possible. Or use a ring adapter inside the driver throat.
But if you had to stay external to the driver, the driver exit would need to be smaller than the horn entrance.
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Hi Pano,
I was contemplating the adapter to be inserted into the driver throat, in which case it would actually be better to have as large an included angle as possible. In fact, if one were really lucky, the adapter would end at the same diameter as the phasing plug, thus avoiding the problem of interference that I was alluding to.
Hm, perhaps the driver's exit could be re-machined if such an operation would not affect the magnetic circuit.
Hi Marco,
Kindest regards,
M
I was contemplating the adapter to be inserted into the driver throat, in which case it would actually be better to have as large an included angle as possible. In fact, if one were really lucky, the adapter would end at the same diameter as the phasing plug, thus avoiding the problem of interference that I was alluding to.
Hm, perhaps the driver's exit could be re-machined if such an operation would not affect the magnetic circuit.
Hi Marco,
My friend has printed a gauge for measuring external screws' diameters, and it is amazingly accurate.
Kindest regards,
M
OK, Marco, we are making good progress. Are you willing to walk us thru this with a few examples that we can learn from?
For example
- Take whatever driver you for which you have data (even imaginary) and show us an example of calculating its flare rate and other needed parameters.
- From that calculation, determine a horn expansion or flare that would match well to the driver.
- Start with a horn, try to determine its m and then we can figure if a certain driver is a good match or not.