Hello all.
I am having a devil of a time trying to convert the various horn equations into something that allows me to plot the profile of a curve. I am trying to come up with an equation I can put into solidworks to generate a model for a CNC machine, but nothing I am doing looks right in the software.
Here is my approach.
I am using the equation S(x) = S(t)*e^(mx). I know that S(x) is the cross sectional area of the horn, and since I am building a square horn, I know that I need to take the square root of this equation in order to get the line height from the bottom of the horn to the stop of the horn.
If I take that number and divide by 2, I should get the line height from the X axis to the top of the horn. Finally I can add the radius of the horn throat (H(t)) to get the equation for the profile of a single side of the horn.
It should look something like this.
(0.5*(sqrt(S(t)*(e^(mx))))+H(t)
Is my math right here? Or am I making this way harder than it needs to be? Your thoughts are appreciated.
I am having a devil of a time trying to convert the various horn equations into something that allows me to plot the profile of a curve. I am trying to come up with an equation I can put into solidworks to generate a model for a CNC machine, but nothing I am doing looks right in the software.
Here is my approach.
I am using the equation S(x) = S(t)*e^(mx). I know that S(x) is the cross sectional area of the horn, and since I am building a square horn, I know that I need to take the square root of this equation in order to get the line height from the bottom of the horn to the stop of the horn.
If I take that number and divide by 2, I should get the line height from the X axis to the top of the horn. Finally I can add the radius of the horn throat (H(t)) to get the equation for the profile of a single side of the horn.
It should look something like this.
(0.5*(sqrt(S(t)*(e^(mx))))+H(t)
Is my math right here? Or am I making this way harder than it needs to be? Your thoughts are appreciated.
The last square horn (actually rectangular) I built, I modelled in Hornresp and used the exported dimensions to draw my horn up in cad.
hth,
Rob.
hth,
Rob.
For a square cross-section exponential horn, the half-height HH at distance x along the axis from the horn throat will be given by:
HH(x) = 0.5 * Sqrt((S1 * e ^ (m * x ))
Where:
S1 = throat area
S2 = mouth area
L12 = horn axial length
m = Ln(S2 / S1) / L12
Oops, make that:
HH(x) = 0.5 * Sqrt(S1 * e ^ (m * x ))
(The original expression has one bracket too many).
I think I may have misinterpreted what you are looking for. You will need to use calculus to determine the length along the curved side wall, and then apply the HH values at the appropriate points to determine the "flattened" profile of the wall. Or you can simply use Hornresp to do all the hard work for you...