Easy horn, quadrant horn?

[Hentai]

Hello,

It's been some time since i've been thinking of a horn contour thats very easy to build with handheld tools besides conicals.
So it came to mind the arc that describes a quadrant of a circle. In the picture below it would be the green part:



The circles have their centers on the same plane with the horn’s
throat so x coordinate of the center will always be 0.
In practice it can differ as other segments can be added between the throat and the driver to provide a better match between the driver and horn.
Using a hand operated router its very easy to make the contour since its part of a circle.

In the drawing we have Rt - Throat Radius, Rc- Radius of the circle, this is the radius you will need to set for your router and it will also be the length of the horn, Rm - Mouth Radius.

The equation to determine the diameter of an axisymmetric horn is:
y(x)=2*[(Rc+Rt)-sqrt(Rc^2-x^2)], with x=[0,..,Rc]

From here its easy to determine S(x). I could use help with the wave equation, i got it up to a point but im stuck.

Attached there is a excel sheet that will generate AxiDriver baffle input numbers in 5mm steps and Akabak script lines with conical sections of 5mm length.
The akabak scripting will require some adjustments.
Below are axidriver simulations for mouth diameters ranging from 10cm to 35cm with 1cm increment. 25mm throat.

[Hentai]

[Hentai]

looking forward to your opinnion.

Soon i will build one and measure it.