Modeling a Double-Uneven-Length BLH with AkAbak
Ever since I have been working on the Cornu horn with its double uneven length horn segments, I have been curious about how to design one from scratch. The idea is that the two horn lengths will have offset resonances such that the combined output has a smoother frequency response. I wanted to do it using a single driver rather than two separate drivers and two separate horns. This is where it gets tricky because when you combine horns with a single common chamber and throat, there are non-linear interactions. Luckily, AkAbak can handle all of this.
I needed a good design for a single BLH to start with and since I had just modeled the very nice BK12 horn as a rear firing BLH, I decided to start there. I am using the geometry of the horn from the BK12, but modified the driver chamber to a smaller volume to accommodate the FF105WK driver which has more xmax.
The model of the horn has 8 segments (see code section below). The first segment is the throat from the driver chamber and last segment is the mouth opening.
First I doubled up the horn paths splitting them off right after the initial 1 in throat section into two equal paths. After doing this, I ran the sim to see if it matches the original single horn to double check for any errors in setting up the geometry.
Then I went in and slowly started reducing some of the key length segments of the second horn and observed the frequency response. I found that in the two longest segments, by reducing the length of the second horn (segment 2 by 5 inches, and segment 6 by 3 inches), it started to produce some offset overlaps that should help smooth the response.
I also found that if I increased the mouth of the original horn by 1 inch and increased the length of segment 8 (mouth) by 1.5 inches, it helped to balance out the SPL levels between horns 1 and 2 and filled in a rather big dip that was there before.
Anyhow, plotted below are the results: first plot is the original single horn combined driver + horn (black) & horn only (red), second plot is the uneven length double horn with combined (black) & horn 1 (red) horn 2 (green), the cone displacement, the impedance, and a plot of both responses superimposed.
The tradeoff of smoothness is less bass extension.
Code:
| Define Horn Segments (need to multiply by Width for area): S_Throat, S_Mouth, Length
| Shared Throat Segment
S1T=1.00*0.0254; S1M=2.32*0.0254; L1=1.00*0.0254;
| First Horn
S2T=2.32*0.0254; S2M=4.90*0.0254; L2=12.52*0.0254;
S3T=4.90*0.0254; S3M=4.91*0.0254; L3=2.19*0.0254;
S4T=4.91*0.0254; S4M=4.92*0.0254; L4=2.77*0.0254;
S5T=4.92*0.0254; S5M=4.93*0.0254; L5=2.19*0.0254;
S6T=4.93*0.0254; S6M=11.72*0.0254; L6=18.33*0.0254;
S7T=11.72*0.0254; S7M=13.50*0.0254; L7=4.90*0.0254;
S8T=13.50*0.0254; S8M=15.51*0.0254; L8=8.75*0.0254; | Enlarge mouth on Horn 1 by 2 in, extend length by 1.5 in
| Second Horn
S2T2=2.32*0.0254; S2M2=4.90*0.0254; L22=7.52*0.0254; | Reduced by 5 in
S3T2=4.90*0.0254; S3M2=4.91*0.0254; L32=2.19*0.0254;
S4T2=4.91*0.0254; S4M2=4.92*0.0254; L42=2.77*0.0254;
S5T2=4.92*0.0254; S5M2=4.93*0.0254; L52=2.19*0.0254;
S6T2=4.93*0.0254; S6M2=11.72*0.0254; L62=15.33*0.0254; | Reduced by 3 in
S7T2=11.72*0.0254; S7M2=13.50*0.0254; L72=4.90*0.0254;
S8T2=13.50*0.0254; S8M2=13.51*0.0254; L82=7.24*0.0254;