Here’s a calculator for determining vertical loudspeaker aim and nominal coverage.
It’s common to point loudspeakers at the back of the audience to get the least level variance. The Yamaha Sound Reinforcement Handbook and other sources suggest this approach as a starting point, and for good reason – in examples, they use the loudspeaker polar data and information about the venue to find that pointing the loudspeaker at the back delivers a more consistent response than pointing the loudspeaker in the middle would.
We can cover an audience area with a single loudspeaker so long as the back is less than or equal to twice as far as the front. Where the back is exactly twice as far, we’ll point the loudspeaker at the back, and overcome the distance discrepancy with axial attenuation, i.e., we’ll pick a loudspeaker whose vertical coverage makes the high frequencies 6dB quieter at the front than at the back. Distance (inverse square law) makes the back 6dB quieter than the front would be if there weren’t axial attenuation, so the two work out at the same level.
If the front and back are the same distance from the loudspeaker, we’d point the loudspeaker at the middle – it will be louder in the middle than at the front or back, but if the distance to the middle of the plane isn’t much smaller to the distance to the front/back, we can still get consistent coverage with one loudspeaker. Think venues that require extremely high loudspeaker positions such as arenas.
What happens between these two extremes? Well, as the ratio of distance-to-back verse distance-to-front increases, we should gradually aim the loudspeaker more toward the back until we reach the most extreme case: twice as far to the back as to the front. Bob discussed this in an article last month, and some people have brought up the limitations of a previous vertical aiming excel calculator I made for the extreme 2x case, so here’s another calculator that might be a helpful starting point in more cases. Note: it assumes that all loudspeakers having a very linear rolloff, and it breaks if the back is at least twice as far as the front.