(Updated 6/11/08)
How loud is your airplane? That's a somewhat loaded question, because sound intensity depends on a number of factors. To understand the subject better, let's talk a little about sound, and then about how its intensity is measured.
Sound is simply the movement of air. When we hear a sound, what we're really hearing is the air between our ear and a sound source vibrating back and forth rapidly. The human ear is incredibly sensitive to this vibration. At the level of the loudest sounds that the ear can tolerate, right at the threshold of damage, the air at the ear is vibrating back and forth only four ten-thousandths of an inch (0.0004”). At the lowest level of hearing, where a person can just detect that there is a sound, the air at the ear is moving back and forth only 4 billionths of an inch (0.000000004”). That's significantly smaller than the diameter of an atom!
This vibratory movement of air transmits power from the sound source out into the air surrounding the source. We sense the level of that power as intensity, the loudness of the sound. The measurement of sound power is usually made as a measure of “power density”, with a typical unit of measurement of watts-per-square-meter (W/m2). That's a measure of the amount of power that the vibration of the air would transmit into a 1 square-meter surface. The incredible sensitivity of the human ear makes measuring sound levels in this manner somewhat cumbersome. The loudest human-tolerable sound has an intensity that is two-trillion times, or 2x1012 times, that of the weakest human-detectable sound. And so, when measuring sound intensity for a human, measurements can fall into a very large range of numbers. To make measurements of human sound perception easier to grasp, scientists have taken the power density measurement and remapped it. Here is how it works: we take the measured power density, divide it by a reference power density (that of the lowest detectable sound), and then take the base-ten logarithm of that ratio. The resulting value is the Bell, named for Alexander Graham Bell, and it does a pretty good job of reflecting the human perception of sound. The Bell's value ranges from 0 at the threshold of hearing to about 13 at the level where the ear can be damaged. Typically, we're interested in a slightly finer measurement, and so we usually describe sound intensity at tenths of a Bell, or decibels (dB). Because of the mathematical nature of the logarithmic remapping, a doubling of a sound's power raises its intensity by 3 dB. Cutting the sound's power in half reduces its intensity by 3 dB. Table 1 illustrates the typical intensity levels for a variety of sounds:
| Sound | Intensity Level (dB) |
|---|---|
| Threshold of hearing | 0 |
| Rustle of leaves | 10 |
| Average whisper (at 3 feet) | 20 |
| City street without traffic | 30 |
| Office or classroom | 50 |
| Normal conversation (at 3 feet) | 60 |
| City street with traffic | 70 |
| 10-watt stereo (at 10 feet) | 110 |
| Threshold of pain | 120 |
| Jet Engine | 130 |
Our airplanes' engines produce sound from a number of sources: the exhaust stack, the carburetor intake, the propeller, and transmission of internal mechanical vibration and metal contact to the air by the cooling fins. Of these, the exhaust and intake are usually the dominant sources. Two members of the Montrose Model Aircraft Association have made measurements of an engine operating at full throttle. With a sound meter, they measured the sound produced by an O.S. .46 engine, with the O.S. muffler installed but with the internal baffle removed. At seven feet from the running engine, the sound level was 96 dB. (That corresponds to a power density of about 4x10-3 W/m2, or 4 milliwatts per square meter.)
One phenomenon that we are all familiar with is the reduction in sound level as we move away from a source. In air, this reduction is affected by a number of factors: wind direction, humidity, presence of snow, objects between the source and the observer and objects opposite the source from the observer. However, on a dry, calm day, with no large trees in the area, the sound power density drops off by 1 divided by the square of the distance from the source (1/r2). And so, doubling the distance between you and a sound source reduces the power density to one-quarter of its original value. That corresponds to an intensity reduction of 6 dB. Cutting the distance between you and a sound source in half increases its power density by a factor of 4, raising the intensity by 6 dB. So, how loud is this engine? Table 2 illustrates the sound level of this O.S. .46 at various distances.
| Distance from engine (ft.) | Power Density (W/m2) | Sound Intensity (dB) |
|---|---|---|
| 7 | 3.98x10-3 | 96 |
| 20 | 4.88x10-4 | 87 |
| 50 | 7.80x10-5 | 79 |
| 100 | 1.95x10-5 | 73 |
| 200 | 4.88x10-6 | 67 |
| 500 | 7.80x10-7 | 59 |
| 1,397 | 3.5x10-8 | 50 |
| 1/2 Mile | 2.8x10-8 | 44 |
| 1 Mile | 7.00x10-9 | 38 |
Compare these levels with the values in Table 1. At a distance of 500 feet, the sound of the engine is at normal conversation levels. At 1/2 mile, the sound level has dropped below that of an office or classroom, essentially relegating it to the same level as other background noise.
What if there are two engines running? With two of these same engines running, the amount of power being transmitted into the air will be doubled, adding another 3 dB to the total intensity. And so two of these O.S. .46 engines running together will produce a total sound intensity of 99 dB. Each additional engine will add another 3 dB to the total.
And so, how loud is your flying field? Let's look at a worst-case scenario. At our current field, five airplanes in the air at one time is about as much as anyone can deal with. Even at this level of crowding, it's not uncommon to sometimes mistake another aircraft for one's own. At a short distance from the field, these engines will merge to become a single sound source. Using five of these same O.S. .46s, without the muffler baffle, Table 3 illustrates the sound level at various distances from the flying field.
| Distance From Flying Field (ft.) | Power Density (W/m2) | Sound Intensity (dB) |
|---|---|---|
| 500 | 3.92x10-6 | 71 |
| 1,758 | 3.17x10-7 | 60 |
| 1/2 Mile | 1.41x10-7 | 56 |
| 1 Mile | 3.50x10-8 | 50 |
Compare these values with those in Table 2. You can see that the sound level is considerably higher with five airplanes up than it is with only one. Note how much farther away you need to be before the sound intensity drops to low levels. With a single airplane, at a distance of 500 feet, the sound has dropped to normal conversation levels. With five airplanes flying, this point has moved out to 1,758 feet, or about 1/3 of a mile. The 50 dB point, the point at which the sound level has dropped to that of an office or classroom, has moved from 1,397 feet, or about 1/4 mile, all the way out to a distance of one mile.
If your flying field is on a flat plain, level with inhabited areas, and the surrounding area is free of trees, it may be best to keep a buffer zone of one mile between the field and its neighbors. If trees or terrain block the line-of-sight to the flying aircraft, this distance is reduced, sometimes dramatically. Another good option is to limit the number of aircraft flying to four. With four aircraft flying, the 50 dB point is located 3,936 feet, or 3/4 of a mile, from the field. Of course, the easiest factor to control is the sound level of the individual aircraft, by using the best muffler you can find. The O.S. .46 with the muffler baffle removed is a good, conservative choice for this analysis, as this modification puts it on the louder side. With the baffle in place, it's significantly quieter, and a very neighbor-friendly engine.
References:
Halliday and Resnick: Fundamentals of Physics, Second Edition, John Wiley & Sons, Inc., 1981, ISBN 0-471-03363-4
Copyright © 2008, Richard C. Wagner
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