Sunship Audio

How to Measure the Directivity Index of a Horn

A horn loudspeaker does more than increase acoustic output from a compression driver. Its flare controls how widely sound spreads, how consistently that coverage is maintained, and how much energy reaches the room rather than the ceiling, floor and side walls. The directivity index, or DI, turns that behaviour into a useful frequency-dependent measurement.

For a horn, DI is never a single permanent number. A bi-radial wooden horn may maintain a relatively stable coverage pattern through the midrange, then widen at lower frequencies as the wavelength becomes comparable with the mouth. At the top of its range, the driver diaphragm, throat geometry and diffraction from the mouth can produce narrower or irregular radiation.

A reliable measurement therefore requires more than placing a microphone in front of the horn and recording a frequency response. You need angular data, a defined reference axis, adequate distance, controlled reflections and a method for converting polar output into an estimate of radiated acoustic power.

Define The Quantity Before Measuring

Directivity factor, written as Q, compares sound intensity on the chosen reference axis with the average intensity radiated over a sphere. The directivity index is the logarithmic form:

DI = 10 log₁₀(Q)

For a perfectly omnidirectional source, Q equals 1 and DI is 0 dB. If the source radiates into a smaller solid angle while retaining the same on-axis level, Q increases and the DI rises. A horn with a nominal 90-degree horizontal pattern will therefore have a higher directivity index than a 180-degree radiator, although real horns rarely maintain a simple geometric pattern at every frequency.

The measurement should state whether it represents full three-dimensional radiation or a practical estimate based on horizontal and vertical polar data. A full spherical integration is the most rigorous approach. In loudspeaker development, a sequence of horizontal and vertical measurements, or a dense three-dimensional spin, is usually more practical. The result is often reported as DI versus frequency, alongside the response and beamwidth.

Prepare A Suitable Measurement

Mount the horn and compression driver in its normal working orientation, including the grille, phase plug arrangement and any adjacent cabinet surfaces that affect diffraction. Choose the acoustic reference point near the horn throat or the apparent origin used by the loudspeaker design. Mark the zero-degree axis carefully; a small tilt can create misleading asymmetry at high frequencies.

The microphone must sit in the far field for the frequencies being assessed. A useful starting condition is several times the mouth dimension, but the required distance also depends on wavelength, flare profile and the desired angular resolution. If the measurement distance is too short, the microphone samples a complex near-field pattern rather than the stable radiation pattern of the complete horn.

Indoors, reflections from the floor, walls and ceiling can corrupt the impulse response. A time-windowed measurement can remove later reflections, but the window also limits the lowest usable frequency. A large outdoor space, an elevated platform or a proper anechoic chamber extends the low-frequency limit. In Australia, a quiet industrial site outside Melbourne may provide useful space, while a Sydney suburban location often requires careful scheduling around traffic, aircraft and construction noise.

Use the same excitation level for every angle and monitor the amplifier for clipping. For compression drivers, a protective high-pass filter is essential during testing below the intended operating band. Temperature, humidity and wind also matter outdoors: hot Brisbane air and humid coastal conditions alter sound speed and high-frequency absorption, while wind can disturb repeated measurements.

Capture The Polar Response

Begin with an on-axis frequency response using the selected microphone distance and level. Then rotate either the horn or the microphone through a known angular sequence. Ten-degree increments provide a reasonable development view; five-degree steps are preferable when examining sharp lobes, crossover interference or a narrow high-frequency beam.

Measure both sides of the horizontal axis and repeat the process vertically. Keep the microphone height, distance and acoustic centre fixed. For a complete directivity map, use a motorised turntable or a spherical measurement system, recording azimuth and elevation coordinates for every response. The data should be gated consistently so that each angular trace shares the same frequency limits.

Convert each trace to an angular level relative to the on-axis response at each frequency. For example, if a point 30 degrees off-axis is 6 dB lower at 2 kHz, that reduction contributes to the spatial average. Do not average decibels directly. Convert the levels back to linear power ratios before integrating, because acoustic energy rather than logarithmic level is being summed.

At the crossover region, measure the horn with the actual low-frequency section operating. A woofer, horn and passive network can change the vertical pattern substantially. This is especially important in a time-aligned loudspeaker, where the crossover phase relationship is intended to preserve useful forward energy and smooth the transition between drivers. Listening tests, such as comparing live versus recorded piano, can then help relate the polar data to perceived attack, presence and room interaction.

Calculate And Interpret The Index

For each frequency, calculate the average radiated power over angle. In a full spherical measurement, the power is proportional to:

P = ∫₀²π ∫₀π I(θ, φ) sinθ dθ dφ

Here, θ is the vertical angle and φ is the horizontal angle. After normalising the intensity to the on-axis value, directivity factor is:

Q = 4π / Ω

where Ω is the equivalent radiated solid angle. In practical software, the angular samples are weighted by the sine of the elevation angle. This weighting is important because a five-degree ring near the equator covers more spherical area than a five-degree ring near the pole.

If only horizontal data is available, do not present the result as a complete three-dimensional DI without qualification. A horizontal directivity index can still show useful pattern changes, but it assumes or estimates the missing vertical behaviour. A horn that is narrow horizontally but wide vertically can appear more directional than it really is if the data is interpreted carelessly.

Measurement approach Strength Main limitation Best use
Full spherical spin Most complete DI estimate Slow and equipment-intensive Final loudspeaker validation
Horizontal and vertical polars Practical and informative Requires assumptions between planes Horn and crossover development
Single-axis response Fast and repeatable Cannot calculate DI Sensitivity and equalisation checks
Outdoor far-field sweep Good low-frequency extension Weather and background noise Large horns and cabinet systems
Gated indoor measurement Convenient and controlled Low-frequency resolution is limited Midrange and high-frequency work

A smooth DI curve generally indicates controlled coverage, but a high number is not automatically better. Abrupt directivity changes can make a room sound uneven as frequency rises. A well-designed horn often aims for pattern consistency, allowing reflected sound to retain a similar tonal balance to the direct sound.

Use The Results In A Real System

The value of directivity measurement is its connection to placement, crossover design and room acoustics. In a large Australian living room, a horn with controlled horizontal coverage can reduce strong side-wall reflections and preserve vocal clarity. In a compact apartment in Sydney or Melbourne, the same behaviour may reduce the need for heavy acoustic treatment. In a Brisbane room, where open windows and reflective hard surfaces are common, vertical control can be equally valuable.

Compare DI with the intended listening distance and room dimensions. A stable pattern can support even coverage across several seats, while a very narrow beam may produce an impressive central image but rapid tonal change away from the axis. Australian high-end buyers often use dedicated rooms, yet the same loudspeaker may also need to work in a converted living room rather than a purpose-built studio. The measurement should describe that practical trade-off.

A manufacturer such as Sunship Audio can use polar data alongside cabinet construction, passive crossover behaviour and listening tests to shape a complete system. The goal is not simply maximum efficiency; it is controlled energy distribution that remains musically convincing at realistic listening levels.

Practical Measurement Checks