Acoustic Horn Design – The Easy Way (Ath4)

For anyone's interest, this is the radius of curvature of the OS profile for the first 100 mm - for 1" and 2" throats, 90 deg coverage.

Code:
# Gnuplot code

set terminal pngcairo size 1200,1000 font "Helvetica,12"
set output "oswg.png"

rt = 25
alpha = 45

set angles degrees
k = rt*rt
q = tan(alpha)
q = q*q
pow3(x) = x*x*x

wg(x) = sqrt(k + q*x*x)		                # OS profile
wg1(x) = atan(q*x / (sqrt(k + q*x*x)))          # first derivative
wg2(x) = q*k / sqrt(pow3(k + q*x*x))            # second derivative
rk(x) = sqrt(pow3(k + (q + q*q)*x*x)) / (q*k)   # radius of curvature

set title sprintf("OSWG radius of curvature: dt=%g mm, alpha=%g deg", 2.0*rt, alpha)
set xrange [0:100]
set xtics 10
set xlabel "x [mm]"
set logscale y
set ylabel "R [mm]
set grid

plot rk(x) lw 2 not
 

Attachments

  • oswg1.png
    oswg1.png
    41.5 KB · Views: 650
  • oswg2.png
    oswg2.png
    40.8 KB · Views: 672
This is for a throat entry angle of 25 deg (wall to wall) - some drivers do have exit angle this large. I still wonder whether it helps in shaping a spherical wavefront in the end (?). I guess it should but then a spherical wave at the throat entrance would be assumed. And that may be the catch.
 

Attachments

  • oswg_profile_25deg.png
    oswg_profile_25deg.png
    66 KB · Views: 134
The question is where to cut a clothoid to be joined to a hyperbola, A and B are the two possible places. In the current release of the tool it is allways cut in the middle (between A and B) and connected to a hyperbola disregarding curvature of the latter - that is wrong. I need to find a point of the same curvature on the clothoid and take if from there. I can do it either in point A or in point B, the curvature is the same.

I would tend to choose B but it could be made as an option.
 
  • Like
Reactions: 1 user
What would be a better junction point, A or B?


For point B (if I'm interpreting the illustration correctly) the curvature starts at some non-zero value (matching the OS section), decreases to zero, then increases again. I'm not sure why this would be useful, but it would be interesting to see what the difference in performance is. I use point A in my waveguide script.
 
I would expect better directivity control...

I expect that the differences would be very small except that the optimal transition point would move quite a bit.
So for option B there would be nominally a small OS section then the section of the curve from B to A would be almost an extension of the OS curve anyway.
For option A the transition point could be further towards the mouth because it starts to curve more quickly.
I'll bet there would be damn all difference if both were optimised.

Best wishes
David
 
I would expect better directivity control for bigger throats and smallish conic section ratios. The clothoid itself doesn't hold the pattern. This way it would mimic a conic section for at least few more inches. The differences may be small however - let's see.


Shouldn't that be up to the user? If point B enforces that a certain part of the waveguide always is conical you loose some design freedom.

I think it makes sense to use point A and then let the user have full control over how much of the WG actually is conical.
 
I would expect better directivity control for bigger throats and smallish conic section ratios.

True if the mouth diameter stays the same. But a wider throat and narrower angle means a much longer device for the same mouth size. But if the length stays constant and the mouth is smaller, then the directivity control will not take hold until higher frequencies. Again, it's all in the tradeoffs.
 
The question is where to cut a clothoid to be joined to a hyperbola, A and B are the two possible places. In the current release of the tool it is allways cut in the middle (between A and B) and connected to a hyperbola disregarding curvature of the latter - that is wrong. I need to find a point of the same curvature on the clothoid and take if from there. I can do it either in point A or in point B, the curvature is the same.

I would tend to choose B but it could be made as an option.

Don't the two curves have to match slope, not curvature? With slope only A works.