Laku Landing Sound Level Analysis

April 1990

By Phil Yastrow

[ Note to the reader: I can't believe I went to the trouble to write this, but it shows how desperate we were in trying to get approval for our lakes. You are very astute if you realize that we must have had one neighbor complaining about noise! PY- 11/98]

Click here for a javascript program to calculate sound levels as described in this paper.

The purpose of this paper is to present theoretical and experimental data that will approximate the sound levels at properties surrounding Laku Landing tournament water ski site to be developed in Windsor, Colorado. Sound levels have been an area of much public concern during the permitting phase of this project, so it is necessary to study this topic in further detail. Because most people think of boats with loud outboard motors and other unmuffled engines when water skiing comes to mind, it is important to distinguish these boats from tow boats approved by the AWSA for use in sanctioned tournaments and practice. Also because we are not a commercial mining operation and expect no profits from mining, we will have as short of a construction period as possible. Therefore the sound levels caused by construction will not last nearly as long as a commercial operation.

The physics of sound propagation outdoors will first be examined, and then these results will be applied to the sound levels present during lake construction and competitive type water skiing to determine worst case sound limits to be expected at locations near the property boundary. Finally, conclusions will be drawn concerning Colorado Revised Statute 25-12-102 which addresses noise abatement.

Sound Propagation Outdoors

Attenuation Due To Distance

As in most sound contol problems, both the source and the receiver are near the ground. The discussion here is concerned with this configuration. The loudness, or decible level (abbreviated dB) of a sound decreases inversely with the distance from the source. In other words, the farther the receiver is from the source, the less sound there is at the receiver. To determine the amount of sound reduction or attenuation (A) of a source caused by distance between two locations each a distance d₁ and d₂ from the source, the following formula is used.

A=20 * log₁₀ ( d₂/d₁ )

Where A is the attenuation in decibels (A scale) and d₂/d₁ is the relative distance from the source. If d₂ is greater than d₁ then the attenuation A is positive, or the sound level is less. Otherwise A is negative and the sound is greater. When applying this equation, the sound level a given distance from the source (d₁) is usually known and the attenuation of the sound level at a different distance (d₂) is desired in order to calculate the sound level at that location. For example, if at 100 feet a given source has a sound level of 80 decibels and the sound level at 1000 feet is needed, the attenuation would be

A=20 * log₁₀ ( 1000/100 ) = 20 decibles

Therefore the sound level at 1000 feet would be 60 dB.

Excess Attenuation

The equation and calculation above are only valid for a source in a perfect, loss free atmosphere. In reality, considerations must be made for the factors which will cause excess attenuation, or attenuation beyond that due to increasing distance from the source. Some examples of excess attenuation are:

1.                                                                                                      Sound absorption in air, which is dependent on temperature and humidity

2.                                                                                                      Presence of trees, shrubs and other foliage

3.                                                                                                      Screens and rigid barriers

4.                                                                                                      Wind

5.                                                                                                      The acoustic effect of the presence of the ground and any ground cover

All causes of attenuation are additive, that is, each component of attenuation is added together to arrive at the total attenuation. In the following section, the various contributions of the above factors will be examined from a quantitative and practical point of view. Because most phenomena related to sound propagation and attenuation are frequency dependent, it is important to take this into consideration. The calculations in this paper will use the worst case frequency possible.

Air Absorption and Temperature. Air absorption is strongly dependent on temperature, relative humidity and frequency because air molecules behave differently as these parameters change. Table 1 shows the attenuation of a 4000 cycle per second sound level per 100 feet due to air absorption as a function of temperature and humidity. It is interesting to note that as the humidity decreases, the attenuation increases. In other words, dry air is a poor conductor of sound compared to humid air.

Table 1. Air Absorption Attenuation

Presence of Trees, Shrubs and Other Foliage. The foliage surrounding the Cache la Poudre River is quite dense, and therefore needs to be considered as a cause of excess attenuation. The literature available on this subject suggests that attenuation due to plantings corresponds somewhat to visibility through the same. The densest foliage surrounding the property in question occurs on the North and East sides, between the proposed lake areas and the town of Windsor.

During the summer months when activities on the site will be the greatest, trees will provide the most effective barrier to sound propagation because of their leaves. Table 2 describes this type of attenuation and assumes foliage through which there is fairly poor visibility, or that in the range of 50 to 100 feet. For this study, we will neglect attenuation caused by trees and tall foliage in order to arrive at worst case noise levels and to account for the fact that there could be some construction activity during the winter months when the trees have no leaves.

Table 2. Dense Foliage Attenuation

Screens and Rigid Barriers. This component of excess attenuation must be considered for two reasons. First, the water level in the lakes will typically average two feet below ground level, and second, we may have earthen berms surrounding the lakes. For the purposes of this study, we will assume, for a worst case situation, that there are no berms and this type of attenuation is due only to the water level being below the ground level.

The basic formula (5) to determine the attenuation in dB for a sound of frequency 400 cps caused by an effective screen of height H which causes a diffraction angle of q (theta) with a receiver is

A = 8.2 * log₁₀(44 * H/0.275 * tan q/2)

Figure 1 illustrates the parameters used to compute attenuation due to screening from the shoreline due to the water level being lower than the ground level. The first situation occurs when the boat is 150 feet from the shore (X=150 feet), and the receiver is 600 feet from the shore (Y=600 feet). This scenario occurs when the boat travels close to the center of the lake, which is always the case except for when the boat is turning close to shore at either end. If the water level is two feet below the ground level, H is 1.6 feet and q (theta) is 0.76 degrees. This yields an attenuation of 1.9 dB caused by the depressed water level.

Figure 1. Parameters for Computing Attenuation Caused by Water Level

The other possible situation when X=20 feet and Y=200 feet, when a boat is at the end of the lake turning around. Here, the attenuation caused by the depressed water level is 9.5 dB.

The Acoustic Effect of the Presence of the Ground. When the sound source and the listening position are within a few feet of the ground there will actually be a sound increase if the surface is hard and reflective, like concrete. On the other hand, if the ground is absorbent as as the case with grass and other foliage, there is an appreciable attenuation of the sound level. Table 3 (6) shows the attenuation of sound caused by absorption over grass in terms of distance and frequency. This assumes the grass is kept fairly short with regular mowings, because the attenuation is greater for longer grass.

 

Table 2. Grass Absorption Attenuation

 

 

The Application of Sound Propagation Theory

The information presented in the previous section will now be applied to the topic under consideration: Sound level occurring during tournament water ski lake construction and use. In order to do this, knowledge is needed of sound levels a given distance from the sources in question, and then the sound level for any other distance can be inferred from the attenuation discussion above.

 Referring to Figure 3, six key receiver locations have been picked surrounding the property, numbered one through six. The receiver locations are: The Francis farm (locations 1 and 2), the closest surrounding residence which is owned by the Kadlubs (location 3), a future planned subdivision, also owned by the Kadlubs (location 4), Poudre Park (location 5) and a residential neighborhood (location 6). A sound level analysis will be made for each of these receiver locations during construction and water ski activities.

Figure 3. Receiver Locations

During this section there will be reference to multiple sources producing sound at the same time. The procedure for dealing with this is not straightforward due to the logarithmic nature of sound propagation and addition. In other words, if two sources are each capable of producing a sound of 50 dB at the location of a receiver while acting alone, both sounds acting together would produce a total sound level of 53dB at the receiver. An increase of 3 dB is therefore an exact doubling of sound. If individual, different sources have sound levels at a receiver that are not identical, the following formula can be used to compute the total sound, S produced by the combination of two sounds each of magnitude x and y.

S = 10 * log₁₀(10^x/10 + 10^y/10)

As an example the 'logarithmic sum' of 40 dB and 30 dB is 40.41dB.

Ski Lake Construction

The construction phase of Laku Landing Ski Center will be typical of a small scale gravel mining operation capable of producing crushed, sorted aggregates for use as road base, structural fill or other construction needs. Therefore, the construction phase will require use of multiple pieces of equipment for excavating and processing the gravel extracted from the lakes. For the purposes of this study, we need to consider multiple pieces of equipment operating at different locations at the same time. Using the additive properties of sound levels described above, we can the calculate the total sound levels at the different receiver locations during construction phase.

Table 4 shows the distances from the lake area and processing are to the various receiver locations, each measured 25 feet from the property line.

Table 4. Distance to Receiver Locations From Excavation and Processing Equipment (all distances measured 25 feet from property line)

The equipment used during lake excavation will initially be at ground level, and slowly penetrate below ground level as the lakes are dug. The worst case sound level at any receiver location will be when the equipment is at ground level because of the screening effect caused when operating the equipment below ground level. The basic type of equipment to be used during excavation will be excavators for the dewatering trenches, scrapers for the removal and transportation of overburden (topsoil), front end loaders and excavators for gravel removal and dump trucks for gravel transportation to the processing and stockpile areas. Processing of the gravel will be done by first crushing the material in a rock crusher and then sorting it in a screening system. In addition to the crusher and screens, a loader will be used to feed material into the processing equipment. Sound levels taken a distance of 50 for these different pieces of equipment are shown in table 5.

Table 5. Sound Levels for Various Pieces of Excavation and Processing Equipment

To determine the sound level due to construction at any particular receiver location, we will assume that at a given time there are two pieces of excavation equipment and a dump truck operating simultaneously at a point in the lake area closest to the receiver. For a worst case situation, this would be an excavator, front-end loader and a dump truck. If we combine the sound levels of these pieces of equipment according to the discussion above, we will have a sound level at 50 feet of 81 decibels. In addition, we will assume that either the screens or crusher are operating at the same time. The sound level caused by the excavation equipment and the processing equipment will then be added logarithmically to arrive at the total sound level at the receiver locations. Table 6 shows the components used to reach the final value. A temperature of 77^O F and a relative humidity of 30% are used for the air absorption attenuation to give a worst case value.

 

 Table 6. Sound Levels (dBA) at Receiver Locations Due to Lake Construction

Once the lakes are started, the excavation equipment will penetrate below ground level and further attenuation will be realized due to screening. This component of attenuation is not considered in the above table in order to describe the worst case sound levels.

Ski Lake Use

Laku Landing will be used primarily for practice and training for competitive water skiing. This effectively means that there will be only one boat in operation on a lake at a time. Table 7 shows the distances from the actual boat locations to the various receiver locations, each measured 25 feet from the property line. It is important to note that at locations 2,3 and 4, the boat will be about 20 feet from the shoreline as it makes its turn, and at the other locations the boat will be travelling in the center of the lake areas shown in figure 3.

 Table 7. Distance to Receiver Locations from Boat (all distances in feet, measured 25 feet from property line)

To determine the sound levels at the designated receiver locations caused by the boats, we need to apply the attenuation results we have worked with so far. Table 8 lists some of the most commonly used competitive towboats along with their respective sound levels. These levels are what is referred to as the drive-by noise, or the sound level measured by a sound meter from 100 feet away while the boat drives by at 36 miles per hour, the maximum speed of any tournament event.

 

Table 8. Selected AWSA Approved Tow Boat Sound Levels

It can be shown in the field that the sound level caused by any of these boats while accelerating is too insignificant to be discerned by a basic commercially available sound meter. For the purpose of this study, we will use a drive-by noise of 70 dB measured at 100 feet to calculate the sound levels to be expected at the receiver locations. Table 9 shows these sound levels and how they are arrived at. Note that for receiver locations 2,3 and 4 the attenuation due to screening caused by the water level being lower than ground level is different. The reason for this is described in the screening section above.

If two identical boats are identical distances from a receiver, the sound level would increase by three decibels. Again, a temperature of 77^OF and a relative humidity of 30% are used for the air absorption attenuation.

 

Table 9. Sound Levels (dBA) at Receiver Locations Due to Boats

 

 Conclusion

According to the scope of this sound level analysis, the maximum noise level to be expected within 25 feet of the property line is 65.3 decibels. This would occur at the very beginning of excavation at receiver location 2. The nearest residence, location 6, would experience a sound level of 23.8 dB at the same time. Once construction is reasonably underway, and especially when it is finished and water skiing activities commence, the sound levels will be much less. As stated in our written Use by Special Review Application material,

The maximum permissible noise level at any surrounding residence shall not exceed 55 decibels as measured according to 25-12-102 CRS (Colorado Revised Statute)

This is intended to apply during the special end use of tournament water skiing, not the construction phase. It is also intended to be at actual home locations, not property lines. Although we have looked into the ability to comply with this standard during the construction phase of our project, we feel that Colorado Revised Statute 25-12-102 allows for 'significantly greater' level during construction. Furthermore, we wish to maintain as low of sound levels as possible at all times, but to impose a standard which may be impossible to meet is not what we desire. We therefore request the construction portion of our project to have a maximum permissible noise level of 80 decibels as measured according to 25-12-102 CRS, with the restriction that we do not blatantly ignore our rational construction plans.

The depth of our lakes will be more than 10 feet, which is more than the basement of a house. Residential construction is usually allowed this noise level even though it can take place less than 20 feet from an occupied residence. Also, 95% of the excavation of our lakes will take place farther from the receiver locations than we have accounted for in this study.

The farm where the noise level is the greatest belongs to Tom Francis. This should not affect him because his actual home site is another 1500 feet away from the property line. Also, the noise generated from his farm equipment is similar to that occurring during the construction phase of our project, and he has stated that he plans to open a gravel mine on his property in the future. The Town of Windsor thinks we have a carefully thought out plan which will have no negative impact, and they have recommended its approval to Weld County. This sound level analysis should mitigate any concerns of noise levels from people who are opposed to our project for this reason.