Tom Danley Tapped horn volume optimization equation
Hello and Happy New Year to you!
Got a whim and did a bit of reverse engineering on Tom Danleys
all tapped horns. If anyone thinks it's inappropriate or
company secrets I can say that all the data are in
data sheets and the elements I have adopted are listed below.
The horns sorts out in two groups.
1) TH115 - TH112 - TH Spud - DTS20
2) TH221 - TH28 - TH mini - TH118 - TH212 - TH412 - TH812 - DTS10
It becomes very good correlation between the net cabinet volume and total
driver area (Sd). Actually, I believe that the group 2 is closest
the optimum and group 1 is the detour where the enclosure volumes actually
are too large to be optimal, but in a regular manner.
The following graph shows the relationships. There are some assumptions that have to be taken into account.
- Birch plywood weighs 700 kg / m3
- The driver density is 4000 kg / m3
- 8 '6 kg 220 cm2
- 12 "12NW100
- 15 "15SW115
- 18 "18SW115
- 21 "21SW152
The correlation between the model and Tom Danleys tapped horns are surprisingly good.
The conclusion is that the optimal net cabinet volume of group 2 is the following:
Volume [liters] Lower freq. -3dB [Hz], Sd membrane area [cm2]
Edit: See new equation futher down.
'Volume' = (-0.00913 * 'f-3dB' + 0.61487) * 'Sd' * 'number of drivers'
Example with 2 x 12" drivers tuned to 35 Hz
285 = (-0.00913 * 35 + 0.61487) * 531 * 2
Example 1 pcs 15" driver tuned to 40 Hz
213 = (-0.00913 * 40 + 0.61487) * 855 * 1
Example with 2 x 21" driver tuned to 20 Hz
1480 = (-0.00913 * 20 + 0.61487) * 1680 * 2
One, for example, THAM15, 156 liters, provides optimum tuning at about 47 Hz, which is the type f-3dB. What a coincidence🙂
http://www.martinsson.cc/blog/images/THAM15_VS_MKII.jpg
HiFiForum.nu - martinssons horn - THAM15
The interesting thing is that the theory is correct from 2x8" tuned close to 50 Hz to single 18", double 21" down to almost to 20 Hz and double 12" all way down to 15 Hz. The data spans a large space of possible horn which gives legitimacy to the model.
I guess Danley optimized for maximum SPL while dips and peaks just above the pass band can be kept under control. A smaller box has too little juice and a greater will be not enough efficient compared to the additional enclosure volume. Doubling the enclosure volume provides about 3 dB extra but doubling the number of cabinets provide approximately 6 dB extra.
Use this data in your simulations and builds if you wish to learn from the tapped horn founder.
Comments, thoughts or concerns are of course welcome🙂
/Petter
Hello and Happy New Year to you!
Got a whim and did a bit of reverse engineering on Tom Danleys
all tapped horns. If anyone thinks it's inappropriate or
company secrets I can say that all the data are in
data sheets and the elements I have adopted are listed below.
The horns sorts out in two groups.
1) TH115 - TH112 - TH Spud - DTS20
2) TH221 - TH28 - TH mini - TH118 - TH212 - TH412 - TH812 - DTS10
It becomes very good correlation between the net cabinet volume and total
driver area (Sd). Actually, I believe that the group 2 is closest
the optimum and group 1 is the detour where the enclosure volumes actually
are too large to be optimal, but in a regular manner.
The following graph shows the relationships. There are some assumptions that have to be taken into account.
- Birch plywood weighs 700 kg / m3
- The driver density is 4000 kg / m3
- 8 '6 kg 220 cm2
- 12 "12NW100
- 15 "15SW115
- 18 "18SW115
- 21 "21SW152
The correlation between the model and Tom Danleys tapped horns are surprisingly good.
The conclusion is that the optimal net cabinet volume of group 2 is the following:
Volume [liters] Lower freq. -3dB [Hz], Sd membrane area [cm2]
Edit: See new equation futher down.
'Volume' = (-0.00913 * 'f-3dB' + 0.61487) * 'Sd' * 'number of drivers'
Example with 2 x 12" drivers tuned to 35 Hz
285 = (-0.00913 * 35 + 0.61487) * 531 * 2
Example 1 pcs 15" driver tuned to 40 Hz
213 = (-0.00913 * 40 + 0.61487) * 855 * 1
Example with 2 x 21" driver tuned to 20 Hz
1480 = (-0.00913 * 20 + 0.61487) * 1680 * 2
One, for example, THAM15, 156 liters, provides optimum tuning at about 47 Hz, which is the type f-3dB. What a coincidence🙂
http://www.martinsson.cc/blog/images/THAM15_VS_MKII.jpg
HiFiForum.nu - martinssons horn - THAM15
The interesting thing is that the theory is correct from 2x8" tuned close to 50 Hz to single 18", double 21" down to almost to 20 Hz and double 12" all way down to 15 Hz. The data spans a large space of possible horn which gives legitimacy to the model.
I guess Danley optimized for maximum SPL while dips and peaks just above the pass band can be kept under control. A smaller box has too little juice and a greater will be not enough efficient compared to the additional enclosure volume. Doubling the enclosure volume provides about 3 dB extra but doubling the number of cabinets provide approximately 6 dB extra.
Use this data in your simulations and builds if you wish to learn from the tapped horn founder.
Comments, thoughts or concerns are of course welcome🙂
/Petter
Last edited:
Pretty interesting. I'd love to see some of the more established community designs put on the scatter plot as well. 3015lf loaded SS15, 18tbw100 loaded Keystone, and maybe for fun perhaps some of the more popular speakerplans scoops.
Thanks ! It's a good guide to stop trying optimizing. With a 12" 45-400hz project, i'm just between both lines 🙂
Welcome, I tried to calculate the net volume for some other popular well
designed tapped horns aswell. See green markers. The Gjallerhorn ans SS15
are larger than the Danley equivalent line, the Othorn is smaller while the
Keystone and Xo1 Flat35 are both bery close to the Danley equivalent line.
A small correction of the mathematics were also done to this graph, but it
only impact the volume by a fraction of a percentage.
Input data, please correct if it may be improved. Copy and paste into excel or similar...
Danley Sd -3 dB External volume [dm3] Internal volume [dm3] Net weight [kg] dm3/cm2
TH221 1680x2 22 1652 1403 174 0,42
TH 28 220x2 47 103 81 16 0,18
TH mini 112 531 48 142 105 25 0,20
TH118 1210 35 420 336 59 0,28
TH212 531x2 38 319 252 46 0,24
TH412 531x4 33 879 700 126 0,33
TH 812 531x8 28 1652 1377 192 0,32
DTS10 212 531x2 15 686 528 111 0,50
TH115 855 38 420 339 57 0,40
TH112 531 33 339 259 55 0,49
TH Spud 28 220x2 19 389 305 59 0,69
DTS20 112 531 16 516 387 91 0,73
Gjallerhorn 1210 18 796 654 100 0,54
Othorn 1680 28 510 385 87 0,23
SS15 856,3 50 260 223 26 0,26
Keystone 1210 37 440 347 65 0,29
Xo1 Flat35 1210 35 420 344 53 0,28
/Petter
designed tapped horns aswell. See green markers. The Gjallerhorn ans SS15
are larger than the Danley equivalent line, the Othorn is smaller while the
Keystone and Xo1 Flat35 are both bery close to the Danley equivalent line.
A small correction of the mathematics were also done to this graph, but it
only impact the volume by a fraction of a percentage.
Input data, please correct if it may be improved. Copy and paste into excel or similar...
Danley Sd -3 dB External volume [dm3] Internal volume [dm3] Net weight [kg] dm3/cm2
TH221 1680x2 22 1652 1403 174 0,42
TH 28 220x2 47 103 81 16 0,18
TH mini 112 531 48 142 105 25 0,20
TH118 1210 35 420 336 59 0,28
TH212 531x2 38 319 252 46 0,24
TH412 531x4 33 879 700 126 0,33
TH 812 531x8 28 1652 1377 192 0,32
DTS10 212 531x2 15 686 528 111 0,50
TH115 855 38 420 339 57 0,40
TH112 531 33 339 259 55 0,49
TH Spud 28 220x2 19 389 305 59 0,69
DTS20 112 531 16 516 387 91 0,73
Gjallerhorn 1210 18 796 654 100 0,54
Othorn 1680 28 510 385 87 0,23
SS15 856,3 50 260 223 26 0,26
Keystone 1210 37 440 347 65 0,29
Xo1 Flat35 1210 35 420 344 53 0,28
/Petter
Last edited:
I'm confused how you can find the othorn "smaller" vs the danley equivalent.
The th221 is smaller per driver and has a lower f3 than thr othorn.
The th221 is smaller per driver and has a lower f3 than thr othorn.
Sine134, please correct me if i'm wrong but The th221 is 60x60x28" and the othorn is 36x36x24". This makes about 1403 dm3 vs 411 dm3 (14.5 ft3) net volume. The th221 is tuned to 22 Hz and the othorn to 28 Hz. I found the internal othorn volume on data-bass recently and the th221 volume is calculated from birch density, driver weight and horn total weight and size. The new othorn volume results in 0.244 dm3/cm2 but it is still far below the Danley equivalent of about 0.35. If so, the othorn would be 589 dm3 net volume.
/Petter
/Petter
That's an interesting correlation you found there, particularly is it's influenced by Sd rather than Vas.
On the DIY designs:
1. The TH18 (The "Flat35") design I believe was designed to have the same external dimensions as Danley's TH118. It also has a higher Fb and F3, so it's interesting to see that it correlates well.
2. The THAM15 is a somewhat compromised TH design, trading a lower volume requirement for a significant notch in the response just above the passband. It's also interesting to see that this design correlates well.
3. The Gjallerhorn looks like an attempt at a wide-bandwidth TH (20 Hz to 100 Hz), so some of the design considerations may have been different to "normal" TH designs.
4. The SS15 shares a similar fold to the Danley TH11* designs, and from your graph it looks like it will sit quite close to the line representing those systems, if you extend that line downwards.
FWIW, I ran my POC's specs through your original equation. Vb = (-0.00913 *42.4 + 0.61487) * 530.9 * 1 = 120.9 liters. Actual Vb for my POC3 is 126.9 liters. Not too bad...
On the DIY designs:
1. The TH18 (The "Flat35") design I believe was designed to have the same external dimensions as Danley's TH118. It also has a higher Fb and F3, so it's interesting to see that it correlates well.
2. The THAM15 is a somewhat compromised TH design, trading a lower volume requirement for a significant notch in the response just above the passband. It's also interesting to see that this design correlates well.
3. The Gjallerhorn looks like an attempt at a wide-bandwidth TH (20 Hz to 100 Hz), so some of the design considerations may have been different to "normal" TH designs.
4. The SS15 shares a similar fold to the Danley TH11* designs, and from your graph it looks like it will sit quite close to the line representing those systems, if you extend that line downwards.
FWIW, I ran my POC's specs through your original equation. Vb = (-0.00913 *42.4 + 0.61487) * 530.9 * 1 = 120.9 liters. Actual Vb for my POC3 is 126.9 liters. Not too bad...
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