Untitled Document

By Engineering Director Bill Webb

Early in 2002, Martin Audio entered the competitive line array market with the W8L. One year on, its compact sibling — the W8LC is about to enter production. This article explains how, in parallel with actual product development, the Engineering Department at Martin have been developing mathematical tools that can predict line array performance and give a greater insight into how line arrays really work in practice.

WHAT IS A LINE ARRAY?

The principle of configuring a vertical column made up of closely-spaced loudspeakers has been around for decades. Because of increased coupling, line arrays increase directivity in the vertical plane and produce a narrow vertical beam, while the horizontal coverage remains the same as for a single device.

The increased coupling is due to:

1. Much smaller distances between each element (either horn or direct radiator), and

2. Much flatter wavefronts produced by those elements.

To illustrate this, the difference between three closely spaced horns and three horns spaced 1m apart is shown in Figs 1a and 1b.

Fig 1a: W8L 3 x 1” HF at 8kHz (vertical dispersion)

Fig 1b: Three 30º horns 1m apart at 8kHz (vertical dispersion)

In straight line arrays, this increased directivity can result in coverage angles of less than 1 degree at high frequencies. Whilst this narrow beam might be fine for aiming voice announcements in transportation facilities, it is of little use in live performance applications where both the audience and tour manager demand high quality sound in every seat.

To achieve the wider vertical pattern required to cover an audience area, practical line arrays are nearly always physically curved in the vertical plane. Curving the array in this manner has very important implications for the design and use of practical systems, and challenges some of the simplistic ideas associated with first generation line arrays.

3dB OR 6dB PER DOUBLING OF DISTANCE?

In line array folklore, much has been made of the notion that a line array produces a cylindrical wavefront with an output that falls off at 3dB per doubling of distance rather than the 6dB associated with a spherical wavefront. The increased throw gained by extending the ‘cylindrical’ nearfield out to a greater distance has been promoted as one of the key benefits of line array technology.

There are two problems with this notion. The first is that, if it were true, a cylindrical wavefront would require a floor to ceiling column in a typical stadium to cover both the floor and the highest seat.

The second is that only an infinitely tall line could produce such a cylindrical wavefront. The wavefront produced by a line source with a finite length will only approach ‘cylindrical’ for a certain distance, after which it will disperse in the vertical plane. This distance will depend on the length of the line and the frequency. Theoretically, with a continuous array 3m high the transition from 3dB to 6dB will occur at the following distances:

100Hz 500Hz 1kHz 5kHz 10kHz

1.3m....6.5m ...13m.. 65m.. 130m

While perhaps of academic interest, this effect is largely useless as it only really comes into play at high frequencies. Also, if we remember that in a straight line array the vertical coverage may be less than 1 degree, it is clear that only a very few members of the audience could ever benefit from such a narrow beam.

In fact, whilst many believe it to be a key feature of line array, the cylindrical wavefront notion has little or no practical value.

CURVING THE ARRAY

Given that the line array must be curved in the vertical plane to cover the entire audience, we needed a way of determining exactly what shape of curvature was necessary to achieve the desired coverage for a particular venue.

Since this question was much too complex to be answered by simple reasoning alone, we embarked on the development of a computer model, incorporating the acoustic and electro-mechanical characteristics of each individual low, mid and HF element and with each element driven by a virtual crossover. The phenomenon of air absorption of high frequencies over distance was also taken into account.

To validate the model 12 WL8HF horns were arranged in a line with zero splay between them as shown in Fig 2. The SPL was measured every 20cm on a 12m path normal to the line positioned at the centre and the measured and predicted responses compared. Fig 3 shows that the response predicted by the mathematical model correlates very well with the measured response.

Fig 2: Validation set-up

Fig 3: Comparison of model prediction vs measured response

With this model, it was possible to predict the frequency response curves at various points in the audience and use the results to optimise the curvature of the array. In nearly all cases, the computer model yielded a progressive curvature array profile (Fig 4), where the curvature increases gently and gradually going down the array. This produces a more consistent frequency response from front to rear seats than J-shaped arrays (Fig 5), having a straight section at the top and a curved lower section.

Fig 4: Progressive Curvature Array

Fig 5: J-Shaped Array

FRONT OR REAR HINGE?

Not only is it important to curve the array correctly in order to achieve consistent frequency response at any point in the audience, the position of the hinge point is also important. The W8L and W8LC hinge points are at the front of the cabinet which keeps the spacing between each cabinet the same, irrespective of splay angle. This makes a significant difference as splay angle increases, usually toward the bottom of an array (Fig 6). With a hinge point at the rear, as in some first generation line array systems, noticeable drops in output occur towards the upper end of the frequency spectrum when the listener is in-between cabinets (Fig 7).

Fig 6: Front hinge, 8 cabinets 5.6kHz

Fig 7: Rear hinge, 8 cabinets 5.6kHz

As well as the cylindrical/spherical argument, which has little or no practical value in real-world line arrays, other ideas which have found their way into line array folklore include so-called criteria for wavefront curvature and the step distance between sources.

Contrary to popular belief, a perfectly flat wavefront is not essential and can indeed cause problems in curved arrays where the situation is complex and important trade-offs have to be made.

Too much wavefront curvature will adversely affect coupling and therefore output at the top of the array where there is typically very little or no splay between each cabinet.

No wavefront curvature will give noticeable high frequency hot-spots where inter-cabinet splay angles are large, typically in the short throw region at the bottom of the array. This is made much worse when the hinge point is at the rear of the cabinet.

The acoustic devices within the W8L and W8LC generate low curvature wavefronts, which, together with the advantages of a front hinge point, provide a combination of excellent projection over distance and smooth coverage right up close to the array.

The other so-called ‘criteria’ regarding what constitutes a line array calls for the step distance between drivers to be less than a wavelength at the highest frequencies.

This is one area where the performance of horns and direct radiators differ: a horn can be driven by drivers which are greater than one wavelength apart at the highest frequency that they reproduce and still produce a low curvature wavefront, as shown in Fig 8.

Fig 8: W8L mid horn – measured wavefront curvature @ 2.5kHz

Using specially-designed toroidal phase bungs (patent pending), which act in conjunction with the shape of the horn flare, the W8L mid horn produces a low curvature wavefront in the vertical plane, all the way to the upper end of its passband. Note the curvature from left to right is due to the 90º horizontal dispersion of the horn.

Fig 9: ViewPoint™

During the summer of 2002, the progressive curvature rules established by the mathematical model were built into ViewPoint™ (Fig 9), a proprietary Martin Audio optimisation programme. Venue dimensions and number of cabinets are entered into ViewPoint™, which will automatically optimise the curvature of the array to suit the venue. Designs can be saved to disk and printed out ready to give to the crew assembling the array.

AIR ABSORPTION AND BAND ZONING

Whilst line arrays have greater high frequency output capabilities than cluster based systems, all sound systems are still limited by the phenomenon of air absorption, which is a function of temperature, humidity, atmospheric pressure and frequency (Fig 10). The relationship between these quantities is quite complex, but losses always increase as frequency rises and distance from the source increases. Note this effect is in addition to the overall SPL loss as distance increases.

For instance, weather conditions can attenuate output at 8kHz by 12dB at a distance of only 50m from thesource. On another day the same system could throw over 200m!

Fig 10: Temperature and humidity effects

To offset the affects of air absorption, progressively more EQ is required as the distance from the array increases. Since air absorption primarily affects high frequencies, it is of most benefit to split the drive to the HF devices into a number of separate channels (typically three) so that optimal EQ can be added to suit the requirements of the short, medium and long throw sections of an array.

By using this ‘HF band zoning’, people near the front don’t have to listen to the extra EQ that the people at the back must have in order for them to hear high frequencies adequately. This simple technique helps to deliver remarkably consistent sound quality over the whole audience (Fig 11).

Fig 11: HF band zoning accurately compensates for air absorption

CONTROLLER PRESETS

Up to now, it has been common practice to use a single digital controller preset or analogue crossover for a particular loudspeaker system, with users adding their own preferred EQ and crossover tweaks.

Whilst the simplicity of this approach may have some appeal, line arrays benefit greatly from specific controller presets that take into account variables such as line length and degree of curvature.

Using our mathematical model, we have determined a family of presets that are optimised for different array configurations, curvatures and also take into account the highly variable effect of air absorption.

The presets are called up by ViewPoint™ during the array design process and ensure consistent sound quality over the whole audience whatever the size or shape of the array and atmospheric conditions prevailing on the day.

The development of a mathematical model that will predict line array performance has brought a greater insight into the ways that real-world, touring line arrays actually work. It has also provided the basis for everyday, practical tools such as ViewPoint™ and the band zoning techniques that enable users to get consistently good performance out of the W8L and W8LC in all configurations and atmospheric conditions.