Vertically pair symmetric 15” woofers with BMS Co-axial M/T,
a practical approach.
As with most design decisions, rubber meets the road, eventually. This project has culminated a few years of planning and gone through at least a half dozen design decisions prior to execution. Life gets in the way sometimes, and it's not just analysis paralysis.
What is practicality with regards to loudspeakers? In short, the ability to move from location to location without problems, and easy integration into different rooms and situations with similar performance characteristics.
Fully horn loaded loudspeakers can exhibit polar performance that is boundary independent, however their sheer physical size can limit placement, movement and practicality. Small direct radiator loudspeakers of the domestic type exhibit poor distortion performance, a trade-off of small size, yet are easily moved and installed in various locations and room sizes.
Larger, professional speakers intended for sound reinforcement work exhibit better distortion performance than small domestic bass limited loudspeakers, albeit some trade off smoother polar response for sheer output levels.
Lately, the trend in the DIY world has been gravitating to larger loudspeakers with horns or 'waveguides' that exhibit smoother frequency response, well defined polars, with less trade-offs than a typical small domestic type loudspeaker.
Beam steering: Typical TMM layouts have lobe steering effects that exhibit frequency dependent polar tilt. On the other hand, the woofers will exhibit better coupling at the high end of their response.
In this MTM application, the polar radiation will start out omni-directional at low frequencies, smoothly transitioning to a 60 degree wide by 50 degree vertical pattern.
Trade-offs are with the 21” deep +-boxes, a sheet of rockwool will be installed to fill in the space between the speaker baffle and the room corner, without, there will be a null in the 60-80 hz area from a 1/4 wave reflection.
The low frequency drivers are neodymium motor, 3” AL coil Faital Pro 15PR400's, in 4 ohm configuration, wired in parallel for 2 ohm nominal load, with an EBP of 106.1. DC Re is 3.3 ohms, and Bl^2/Re falls at 56.7.
No inductance countermeasures, however overall inductance of 0.6 mh is low, a result of the short coil winding depth and thickness. Le/Re from the manufacturers reported numbers is 0.182 milliseconds. Not a lot of steel in this lightweight 8 pound woofer. The low frequency drivers will cover approximately 4 octaves of sound.
Simulation of a 9.5 cu ft vented box shows that in the range of interest, between 40 hz and 160 hz, the minimum impedance result would be 4 ohms, 2 ohms with woofers in parallel. This drops to 1.65 ohms in parallel from 160 hz up to the crossover point. Impedance maxima occurs at 66.67 hz with a 40 hz tune and as a result, with parallel woofers, 16.589 ohms.
At a drive level of 300 watts, we can see that in band between 160hz and crossover point, this results in 6.742 amps through each voice coil. At the impedance maxima of 66.7 hz, 3 amps of current.
Lower the drive level to 50 watts, 160 hz + would result in 2.75 amps through each coil. 40-160hz average 2.5 amps, with only 0.86 amps through each coil at the impedance maxima.
Horn is an 18 Sound XT1464, and the 1.4” throat co-axial compression driver is the BMS 4594, with 8 ohm diaphragms. The elliptical horn mouth circumference as measured by string is 43”, and depth to the bug screen on the driver is 10”.
18 sound recommends an 800 hz crossover, albeit from their graphs it is mostly "usable" to 500 hz.
In the range of transition from horn to woofers, there are 3 distinct radiating elements, with center to center distances of 13.5 inches. 600 hz has a wavelength of 20.86 inches, and this inter-driver spacing is less than 2/3rds of a wavelength. If the crossover is pushed down to 500 hz, acoustically the drivers are even closer together.
A High Power Satellite Speaker, Joeseph D'Appolito, Speaker Builder, April 1984.
In dissecting the work of Electrovoice, D'Appolito, and Keele, for a c-c distance of 13.5 inches and a crossover frequency of 600 hz, this will result in a vertical beam width of 80 degrees widening below 600 hz towards omni, and tighter beam width above, likely resulting in a mostly smooth transition from omni to 50 degree beamwidth over approximately an octave.
Bracing of some sort is required to keep the large panel surfaces from radiating sound on their own. 3” deep Roxul Safe N' Sound will reside in the cavities formed by the bracing, along with a sheet in the middle of the enclosure behind each woofer. Care has been taken to ensure a clear path from top to bottom around the rear brace windows.
External size has been set in stone at 60” tall, 21 inches deep and 17.75” wide, resulting in a gross internal volume of 10.727 ft3. Bracing is extensive, with small spans. The front baffle, as the rest of the enclosure is single layer, each brace is 3” deep. The rear and front are connected together, as are the sides. In short, every side is connected to the opposite and at least one adjacent side.
The prototype has been constructed with butt joints and PL Premium adhesive, utilizing many pocket screws for both mechanical strength and clamping during assembly. 3/4” birch B3 plywood was used. Assuming the prototype measures well, it will become the center channel in an L/C/R triplet, with only the center residing behind an AT screen.
Why MTM? I chose MTM to minimize ceiling and floor reflections, and minimize the effect of lobe steering at different frequencies compared to a TMM layout. I have had experience with both the Yorkville Unity U215, and JTR's Noesis 215HT, both MTM configuration.
A visual representation by Patrick Bateman of the MTM alignment is visible here:
One higher profile MTM build with the 18 sound XT1464 horn for the Atlanta DIY meet, Paul W's “Raptor”:
Why vented? Some would argue there is no need for ports in a main loudspeaker, especially with this much radiation area. I disagree. Many prefer a limited bandwidth sealed box, and it can ease placement woes. The 12 db slope from an 80 hz f3 will match up well with the slope built into AVR's, and give you 24 db total slope.
With a decent vented design, you can have your cake and eat it too. Of course, this results in other trade-offs. Keeping the baffle surface as narrow as possible, and using the largest ports that are practical results in a slightly deeper depth cabinet. If I want to emulate a sealed 80 hz f3, I can do that actively.
I model for worst case Ontario ( Trailer Park Boys ) and adjust accordingly. Even a modest average drive level will increase the motor temperature above ambient, and as the motor strength drops, the woofers 'like' a larger box.
Standing waves calculated from internal enclosure size
Top to bottom 116 hz ~ 58.5 inches
Front to back 348 hz ~ 19.5 inches
Side to side 417 hz ~ 16.25 inches
The ports consume a large amount of space inside the enclosure, with an I.D. of 7.625”, 2 per enclosure. Port cross sectional area >91 in2.
Group delay approaches 18 ms @ 40 hz, below 1 cycle, with an appropriate Butterworth high pass filter in place. At 300w PIN, the velocity in the ports will be 7.061 meters per second, or 23.166 ft/s, comparatively low with regards to commercial designs. Tuning is for the moment, going to be a variable. For the moment, they will be removable through the lower woofer opening. Once tuning is confirmed, they can be glued in place.
Port self resonance should fall within a range of 520-660 hz, depending of course on how short they must be trimmed for tuning to be close to 40 hz.
BMS C8-8 passive crossovers will handle the midrange to tweeter crossover, with the aid of a UT3636 Autoformer to attenuate the level and reduce hiss from the BMS co-axial compression driver, and better make use of the gain in the system.
Each loudspeaker enclosure will have it's own dedicated QSC PLXII 2502 amplifer, with both Faital Pro woofers in parallel on one channel, and the other channel reserved for the BMS co-axial compression driver. Active crossover duties from woofer to compression driver will be handled by a Behringer DCX 24/96 unit.
Measurement will consist of a Behringer ECM 8000 microphone, phantom power supply and sound card. Horn data will be derived from 1m measurement, woofers from 4 meters, adjusting with offset in RoomEQ wizard. Acoustic crossover will be 3rd order.
The use of 2 15” direct radiators in a 9.5 cu ft 40 hz tuned cabinet affords low diaphragm displacement for relatively high sound pressure levels.
Achieving low FM and AM distortion should not be a problem. Kellogg in 1931 proposed 0.1 cm as a maximum amplitude of motion. At a sound pressure level of 110 db / 1m on axis, the diaphragm motion is approximately 1 mm as simulated.
A moving diaphragm alters the pitch of a high frequency sound, modulating it up or down in frequency.
The frequency deviation by of itself is not that deleterious, however if the diaphragm is reproducing simultaneous 50 hz and 440 hz signals, the result will be 440 hz [+- 0.4 hz], plus additional side bands of 440 hz [+-50 hz].
In other words, the transducer will be producing 390 hz, 440 hz, ( +-0.4 hz modulation ) and 490 hz output.
This active loudspeaker project shall be known as Väinämöinen.