This is the third part of our series focusing on subwoofers. The first and second parts are available here and here.
Woofer Array Types
In pro audio, we find several kinds of woofer arrays. In this third installment we’ll discuss flown and gradient arrays.
7. Flown Arrays
Flown subwoofer arrays are usually one box, or at most two boxes, wide.
Thus, they have very broad horizontal coverage. At the same time, the arrays are usually long, which leads to vertical coverage that is often too narrow.
In particular, there may be a lack of subbass in the first few rows of seats. Solutions are:
1. Curve the arrays in the vertical plane, as is shown for the horizontal case in Figure 10 and Figure 12.
Curving is often visually desirable, in that it tends to align the face of the woofer stack with the face of the high-mid stack. However, it only works well for very tall stacks.
2. Add a few groundstacked woofers at center stage. Make them just loud enough to cover the affected area.
Adjust the delay and level for even coverage over the front 10 to 20 rows. This is a common approach, but it’s tricky to tune it for even coverage.
3. Use beamforming. This is usually the most effective technique for flown arrays.
Figure 17 through Figure 19 are results from the LAPS line array modeler that show a flown bass line array (eight EV XLC-215 woofers) in a typical two-balcony theater) with various solutions applied.
The charts show vertical coverage patterns for one stack only, so they don’t include any of the horizontal lobing effects that will be present, but they do give an idea of the vertical challenge.
Figure 17 shows a simple flown array with no curving, tilting, or beamforming. The bass problem in the front rows is evident.
Figure 18 shows the same array as in Figure 17, but with two additional XLC-215 woofers stacked on or in front of the stage.
The front-fill woofers are delayed by 2.0 mSec.
The shape of the curves is quite sensitive to the delay value. Performance is better, but not excellent.
Figure 19 shows how a bit of simple beamforming can give good results.
The bottom two boxes in the stack are delayed by 4 mSec. No other processing is applied.
In all of these scenarios, there is an overall bass level difference of 12-14dB from front to back. This will not be satisfactory for most applications. A perfect solution to the problem is difficult.
Where venue dimensions permit, high trim is the single most effective technique for evening out bass SPL from front to back.
In the preceding illustrations, trim height was 32 feet (~10m) to top of stack. Figure 20 shows the same beamformed array as in Figure 19, but with a trim height of 65 feet (~20m) to top of stack. The level shift from front to back is much less.
Flown Center Subbass Line Arrays.
Where staging and rigging considerations permit, a flown center stack of subwoofers can give excellent results.
There is zero lobing, the horizontal coverage is essentially 360°, and the vertical coverage can be controlled well by beamforming.
Figure 21 shows the coverage of a flown center cluster of 12 EV Xsub woofers in an arena venue. The woofers are hung in a straight line, an optimized set of beamforming delays are applied. As well, level shading has been applied.
The result is a subbass coverage pattern that maintains constant tonal balance over the entire listening area and
In this example, the delays have been applied in pairs. That is, each adjacent pair of woofers has a drive channel. This is more economical than having a separate drive and amplifier channel for each woofer.
However, should a separate drive channel per woofer be available, even better coverage would be possible.
8. Gradient Arrays
A gradient array is an arrangement of loudspeakers driven at different amplitudes and phases in such a way as to cancel sound radiation in unwanted directions.
Gradient arrays only work when their dimensions are small with respect to wavelength. They are the opposite of beamformed and endfire arrays, which must be large in order to work.
The reason for this is that gradient loudspeakers work by controlling pressure differences between the different parts of the sound wave, and must therefore be small enough to work “within” the wave.
Gradient loudspeakers are the loudspeaker counterparts of ordinary directional microphones, which work by picking up pressure differences between different parts of the sound wave.
The gradient technique is the only practical way to implement subbass pattern control with small arrays.
When set up carefully and correctly, gradient arrays can provide a range of useful patterns that will give significantly better bass coverage than could be achieved using simple arrays of comparable size.
8.1. Example
Figure 23 shows a pair of EV Xsub subwoofers in a basic gradient configuration. Each loudspeaker box has its own drive.
The boxes are positioned back to back, 4” (10cm) apart. The rear box is driven in reverse polarity and is delayed by 4.65 mSec. The resulting array has a cardioid directional pattern.
Although in this example the loudspeakers are mounted back to back, it need not always be so. As long as the there is enough space between front and rear cabinets to allow the rear loudspeaker’s sound to emerge, the rear cabinet can be mounted facing forward or backward.
The gap should be at least 18 inches (50cm). In all cases, the delay value must always be adjusted to match the spacing between loudspeaker cones.
If each Xsub shown in Figure 23 were a column of Xsubs instead of a single Xsub, we would have a gradient line array. Gradient line arrays have useful properties and will be discussed further below.
8.2. Characteristics of Gradient Arrays
Pattern Options
For a given gradient pair, the pattern can be varied by changing the rear-element delay.
Available patterns are similar to those of microphones: cardioid, hypercardioid (various types), and figure-8.
Figure 24 and Figure 25 show four pattern options for the back-to-back Xsub pair from the example above.
Element Spacing, Output, and Bandwidth
When constructing a gradient pair, it is important to understand the role of element spacing.
By “element spacing”, we mean the distance between front and rear loudspeaker cones.
Larger element spacing increases subbass output, but decreases maximum operating frequency. Smaller element spacing decreases output but increases maximum operating frequency.
In our example, the element spacing is 62 inches (157 cm), which gives a maximum operating frequency of approximately 90 Hz. The pattern deteriorates rapidly above the high-frequency limit, as Figure 26 shows.
Effect of Nearby Surfaces
Gradient pairs do not function correctly when they are situated in front of walls or other reflecting surfaces.
Figure 27 shows what happens when our Xsub pair is placed two feet (60cm) in front of a wall.
The wall is shown by the vertical line in the center of the graph. The two woofer boxes on the left are virtual boxes—acoustic images created by the reflection in the wall.
The two boxes on the right are the actual woofers.
Reverberant Field Tonal Balance
Most subwoofer arrays become less directional at lower frequencies. Thus, as the frequency goes down, they send proportionately more of their output into the reverberant field of the venue.
This causes an excess of subbass (sometimes called “bass bloom”) in the reverberant field.
Unlike almost all other kinds of loudspeakers, gradient loudspeakers maintain pattern control down to the lowest frequencies. Thus, they can be helpful in applications where a full subbass experience is needed, but without too much reverberant low-frequency energy.
Element Drive Level and Woofer Count
In practical gradient arrays, it has been found that minimum rear radiation occurs when the output of the rear element (it is often called the “steering element”) is approximately 6dB less than that of the front element. This result is due to cabinet shape effects. In practical terms, this means that the number of rear woofers can be half of the number of front woofers.
8.3. Advanced Gradient Drive
Using delays to create directional patterns is an effective technique at low frequencies, but it does not take into account the effects of loudspeaker cabinet shapes on the sound waves. The result is that at the upper end of an array’s frequency range, its radiation pattern can deviate from the expected shape.
When front and rear loudspeakers are combined in a single cabinet, such as in EV’s XCS-312 cardioid subwoofer, it is possible to develop advanced drive processing methods that correct for these effects, so the loudspeaker maintains its specified directivity over its entire frequency range.
These drive systems use frequency-dependent delays (also called “all-pass filters”) to offset the effects of sound propagation around the cabinets.
8.4. Gradient Line Arrays
When gradient pairs are assembled into a line array, the resulting directivity exhibits both gradient and broadside characteristics.
Figure 28 shows the radiation pattern of a gradient line array that is only two boxes tall, which is too short to exhibit broadside array behavior.
The pattern is a simple cardioid of rotation.
Figure 29 shows the pattern of a gradient line array that is long enough to exhibit broadside behavior.
Its pattern is a flattened cardioid of rotation.
In practice, gradient line arrays can be constructed from purpose-built gradient loudspeakers such as the EV XCS-312 subwoofer, or from two columns of conventional loudspeakers, stacked or flown one behind the other.
Beamformed Gradient Line Arrays
Beamforming delays can be applied to a gradient line array to tilt its pattern.
The beamforming delays must be applied equally to front and rear elements of each gradient pair in the array.
Figure 30 shows a the pattern of a gradient line array with added beamforming delay to create downtilt.
The pattern could be described as a flattened, tilted cardioid of rotation.
With advanced delay profiles, more complex vertical pattern shapes can be realized.
8.5. Gradient Array Applications
As noted above, gradient arraying is useful for small subwoofer arrays and for line arrays which, while large in the vertical dimension, are small in the horizontal.
The problems of small arrays fall into two categories:
As well, gradient arrays are useful in cases where rearward bass radiation is a problem. The most common issues are:
Left-Right Arrays
For a stacked or flown left-right subwoofer system, using gradient arrays pointed offstage helps reduce lobing.
Figure 31 compares the coverage of a single-wide Xsub stack on either side of the stage with that of a gradient configuration of the same size.
Bass on Stage
Although Figure 31 doesn’t show it, the angled-hypercardioid configuration puts a good deal less bass onto the stage than the simple one.
For the simple configuration on the left, performers at center stage hear the summed output of both subbass stacks from a relatively short distance away. Nowhere in the venue is the subbass louder than this.
For the right-hand configuration, however, the gradient woofers’ hypercardioid nulls are pointed directly across the front of the stage. In typical configurations, this reduces the subbass level at downstage center by 15dB or more.
Coverage Control for Smaller Arrays
For small venues with flat floors, stacked subwoofers usually create excessive bass levels in the audience areas near the stage. While this might be fine for a dance club, it is not fine for a corporate AV presentation. In such cases, using a small center-flown subwoofer can provide excellent coverage without excessive levels anywhere.
However, if a conventional woofer is used, it will be essentially omnidirectional, which means that (a) large amounts of bass energy will be radiated into the reverberant field, which will make for muddy sound, and (b) the bass on stage will be quite loud.
In contrast, hanging a cardioid or hypercardioid woofer above the stage will put the bass energy where it’s needed—in the audience—and keep it out of the reverberant field and away from the stage.
Figure 32 shows a 120° hypercardioid woofer. If you think of the diagram as a horizontal polar plot, you’ll see that it puts most of the bass energy out front and not into useless directions. If you think of it as a vertical plot, you’ll see that the hypercardioid null points at the stage.
Large Central Clusters
Although large central woofer line arrays tend to provide excellent sound on their own, they can still benefit from gradient techniques in shows that do not require 360° subbass coverage.
In such shows, implementing the woofer cluster as a gradient line array means that less bass energy is radiated into the reverberant field. The result is a clearer subbass experience, with more definition, impact, and sense of pitch.
According to acoustic theory, using gradient woofers will reduce reverberant subbass energy by 4 to 6 dB, compared to omnidirectional woofers.
Delay Clusters
In large venues, especially outdoor stadiums and fields, the use of delay clusters is common for augmenting sound level and quality in the more distant listening positions.
The primary purpose of these clusters is to boost high-frequency level, to offset the air’s relatively high absorption of high-frequency energy. However, it is sometimes necessary for the delay clusters to provide additional low-frequency energy as well. In these cases, conventional loudspeakers pose a problem.
At low frequencies, normal delay clusters will be essentially omnidirectional; thus, they will radiate a considerable amount of sound back toward the stage. This rear radiation will be radically out of time synchronization with the direct sound from the main loudspeaker system, and detrimental interference will occur.
The solution for this problem is to use gradient loudspeakers for low-frequency delays. The pattern of choice in this case is the cardioid, since it has the lowest level of rearward radiation.
8.6. Endfire arrays
An endfire array is a row of boxes aligned on a common axis and driven so that the primary sound radiation is in the direction of the axis.
Each box is driven from a separate delay. All the boxes are in the same polarity. In the simplest case, the boxes are equally spaced and the interbox delay time is equal to the time that a sound wave takes to get from one box to the next. Figure 34 shows performance of an example.
In the graphs used here, maximum output is arbitrarily shown as 0dB. In fact, with long endfire arrays, it is possible to project powerful, directional bass over long distances.
This is the third part of our series focusing on subwoofers. The first and second parts are available here and here.
Jeff Berryman served as the director of Jasonaudio, a touring sound company based in Canada, and is a senior scientist with Electro-Voice.
Related Articles by Jeff Berryman:
What Really Defines Good Bass In Sound Reinforcement?
Discussion & Analysis Of A Variety Of Bass Coverage Patterns
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