The 3:1 Rule-of-Thumb for Designing with Point-source Loudspeakers

Example

Acoustic Simulations help demonstrate the effect of the 3:1 Rule-of-Thumb. In the following example, a loudspeaker (R.15-3696) has been placed with a downward tilt angle to “aim” for a particular furthest audience position. The on-axis aiming is marked by Receiver Flag #2. Receiver Flag #1 was placed taking note of the Frequency Response near the beginning of the coverage area. It represents a position where the broadband response includes frequency response uniformity.  Receiver Flag #3 has been placed to mark the position that retains the most similar Frequency Response to Flag #1 within the range of frequencies well controlled by the loudspeaker’s waveguide and also maintaining 6dB or less drop in SPL relative to Receiver Flag #1.

Using a simulation program

How to approximate coverage using the “3:1 Rule”?

1. Measure the available trim height above listeners

2. Place Loudspeaker and adjust aiming axis to point to the desired furthest listener

3. Measure distance to first listener using the hypotenuse of a right triangle (who is receiving broadband coverage) This is “D1” (Distance 1)

4. Calculate 3 x D1  = D2 (Distance 2)

5. Using a trigonometry app or other method, use the D2 value and the tilt angle of the loudspeaker to find distance along listening plane to farthest listener. Mark this as D2.

6. Evaluate coverage with simulation mapping and/or frequency response plots.

7. Make minor adjustments to the aiming and loudspeaker choice to optimize coverage.

Applying the rule without a simulation

If not using a simulation program, the coordinates can be devised in any drafting program or even just by sketching the vertical coverage and using the above computations. In the example below, the following coordinates can be determined based on a specific loudspeaker trim height 12 units above the audience listening plane. The type of units do not matter (imperial or metric) as the relationship scales based on the spherical radiation of the loudspeaker.

• D1 = 13.42

• D2 = 35.09

• Interval from D1 to D2 on the listening plane = 26.97

Why does the 3:1 Rule method matter?

These steps optimize the effective coverage of a single loudspeaker

• Identifying the beginning and ending points of the coverage reduces errors in over-lapping or under-lapping coverage from other nearby loudspeakers

• Optimizing the number of loudspeaker devices to keep the quantity to a minimum usually improves Speech Intelligibility (STI) and Music Clarity (C80)

• Other conventional methods (often taught for paging applications) do not consider the spherical radiation, defined coverage, or inverse square law functions of a given loudspeaker. This method for the above reasons is superior to methods like the following which yield far more coverage overlap than is likely necessary in most cases:

Limits of the rule

• Actual SPL variation depends on the actual dispersion pattern of the loudspeaker. A narrower pattern for example will often yield slightly different results

• Overhead ceiling and pendant loudspeakers usually exhibit a coverage dispersion closer to about 90 degrees of broadband coverage. That’s a broad approximation and actual dispersion will vary by model. Be mindful that ultra-wide specified dispersion patterns greater than 100degrees usually do not translate into greater coverage capability with appropriate uniformity.

• Line Sources, Asymmetrical Horns, Constant Beamwidth, and digitally steered loudspeakers offer a variety of specialized coverage patterns that generally exceed the limits of conventional loudspeaker radiation patterns. For those types of loudspeakers usually its essential to use the associated acoustic simulator to devise the best coverage for a given application.

Further reading

• R-Series Throw Chart: R Series speaker throw distance chart - Biamp Cornerstone

• Using the 6:1 Technique and CCA-80