(1) A jet ski is a vessel, usually less than 16 feet in length (measured from end to end over the deck excluding sheer) which uses an inboard, internal combustion engine powering a water jet pump as its primary source of propulsion. The vessel is intended to be operated by a person or persons positioned on, rather than within, the confines of the hull. Jet skis are high-performance vessels designed for speed and maneuverability and are often used to perform stunt-like maneuvers. (Adapted from U.S. National Park Service, 1998).

(2) All terms such as “noise costs” and all findings are explained and derived in the text, particularly in Sections 3 through 6.

(3) That is, the opposite of amenity; the reduction or destruction of what would otherwise be an amenity.

(4) Due to legal considerations, the Lake Tahoe ordinance was drafted to ban all two-stroke engines rather than just jet skis. It permits two-stroke engines as an ancillary power source (for sailboats), or engines that use electronic fuel injection meeting advanced federal and state air emission standards, or that are less than 10 horsepower (the latter through Oct. 31, 2001 only).

(5) Arbitrarily characterizing a lake as an ellipse twice as long as it is wide, a 300-acre lake is roughly 5,770 feet long and 2,885 feet wide. Under the Vermont rule, then, lakes under half a mile across are off-limits to jet skis.

(6) The Monroe County ordinance applies to 14 beaches from Key West to Key Largo, and limits speeds to 5 mph until jet skis reach a distance of 1200 feet. (New York Times, 1998)

(7) See Personal Watercraft Industry Association (2000), for example.

(8) Bluewater Network, 1998, p. 28.

(9) Their relative magnitudes depend on the “demand elasticity”; for a detailed discussion see the sidebar “Constant Demand Elasticity” on p. 66.

(10) An alternative approach, discussed in Part 4 of the Appendix, involves estimating consumer surplus, based on “contingent valuation” surveys that ask, essentially, “For how much money would you be willing to forgo a day at the beach?”

(11) The California Air Resources Board estimates that the average jet ski is operated for 41 hours a year. (CARB 1998, Tables 6 and 7) We assume that the average jet ski is used 3 hours a day on 15 days a year, or 45 hours a year.

(12) If the jet skier and the beachgoer each spend their three hours distributed randomly and independently over the assumed six-hour beach day, the beachgoer would have the jet ski’s presence half of the time. A more likely scenario is that each would spend their respective three hours as a contiguous block of time. Assuming that the timing of these blocks is distributed uniformly and independently of each other, a probabilistic computation indicates that the beachgoer will have the jet ski’s presence two-thirds of the time.

(13) While “centering” the jet ski’s lateral position is a “worst case” assumption (i.e., it maximizes total beachgoer exposure to the noise), it is plausible or even likely. Moreover, its non-conservatism is partially offset by distributing beachgoers evenly between the shoreline and the back edge of the beach in our model, rather than concentrating them more realistically closer to shore.

(14) The 2.04 dBA increment is derived as 10 x log (1.6). This calculation is conservative since it assumes identical sound profiles for each jet ski in a cluster.

(15) At 44¢, the per-person noise cost at this beach is slightly less than the 50¢ shown in Table 3 for a popular ocean beach. This is because average distances from the jet ski are greater at this huge beach.

(16) The National Marine Manufacturers Association (1998) estimated the number of jet skis in use to be 1.0 million in 1997 and 1.1 million in 1998, suggesting 1.2 million in 1999 and a current (2000) figure of 1.3 million, based on annual sales of 150,000 units and estimated scrappage of 50,000. Separately, according to a survey of jet ski owners by the main manufacturer trade group (see next footnote), the average jet ski is used 7 times a month during the “riding season.” Allowing for the likelihood that survey respondents had higher than average use, we assumed an average of 15 days of use a year.

(17) Data in text are from Bombardier Motor Corporation of America (1996), p. 10 (for place of use) and p. 11 (for frequency of use). The survey was mailed to 10,500 holders of warranties from five jet ski manufacturers for jet skis purchased during 1991-95, and generated 2,800 usable responses, a reply rate of 26%. See also Saluck, 1999.

(18) To be sure, noise can impose health-related costs through cardiovascular strain, mental and emotional stress, etc. Not all of these costs are captured through our Noise Depreciation Index derived from studies of noise-related property-value loss. Jet skis in particular may also create economic losses by discouraging beach visits and non-motorized activity. These costs are beyond the scope of this report.

(19) Delucchi & Hsu, 1996. The authors state, “We find that the external damage cost of direct motor-vehicle noise could range from as little as $100 million per year to approximately $40 billion per year (1990 data, 1991 dollars), although we believe that the cost is not likely to exceed $5 billion.” (pp 1-2) Adding 10% to reflect growth to 1999 vehicle levels and 27% to adjust to 1999 dollars, for a combined increment of 40%, yields figures in text.

(20) Personal Watercraft Industry Association (2000).

(21) Yamaha claims that its Yamaha Sound Suppression “reduces the sound intensity level of the XL1200 Ltd. [three-person Wave Runner model] by 70 percent of last year’s XL1200.” (Yamaha, undated.) A 70% reduction in sound intensity equates to a 5.2 reduction in dBA. Bombardier (1997) and Polaris (undated) assert that their respective new SEA-DOO and Genesis product lines deliver reductions in sound pressure of 50% and 60%, respectively; these correspond to respective dBA reductions of 6.0 and 8.0. However, a spokesman for Polaris acknowledges that its new Genesis Watercraft produces a noise level of 73 dBA at a distance of 25 meters. (Polaris, 2000) Adjusted to our “reference” distance of 20 feet, this is equivalent to 83 dBA. We were unable to obtain estimates of actual noise levels for the Yamaha and Bombardier machines, despite repeated phone calls to both manufacturers. The above were the sole noise reduction claims posted on the PWIA web site.

(22) Realistically, bans would lead to a diminution of total usage. In addition, beachgoers with high noise sensitivities would gravitate to jet-ski-free beaches, while those with greater noise tolerance would tend to remain at areas where jet skis are permitted. Both phenomena would heighten the reduction in noise costs resulting from bans. Conversely, bans would have a smaller effect on national noise costs if, as we consider likely, they were applied disproportionately to smaller and/or less-frequented beaches. These considerations were beyond our analytical range here but are deserving of further study.

(23) Recall that we assume a 67% duty cycle, with a jet skier impinging on a beachgoer for two-thirds of the beachgoer’s day rather than 100%. With the “time sharing” scenario in the text, and under a worst-case assumption in which the total number of jet skis is unchanged, the duty cycle would fall, but only to one-half, making a 25% reduction from 67% (since 0.50 / 0.67 = 0.75). Note that the average size of a jet ski cluster would rise from the “base level” of 1.6, adding to the source noise level and shrinking the reduction in noise costs.

(24) One could say equivalently that assessments of jet ski noise that ignore out-of-water operation overlook 84% of the overall impact of jet ski noise.

(25) Even enthusiasts may suffer reduced real estate values, as jet ski noise makes their property less attractive to a large segment of potential buyers and renters.

(26) The calculation is: 2,000,000 x ½ x ½ x 7.6 dBA x $100,000 x 6% x 1.0%, yielding $228 million. The figure of 2 million beachfront houses was derived from an estimate of 60,000 lakes in the U.S., each fronted by an assumed average of 30 houses, yielding 1.8 million lakefront houses. We added 200,000 houses on rivers, bays, canals and oceans for a total of 2 million. The figure of 60,000 lakes was derived from known numbers of lakes in MN (15,000), WI (10,000), ME (5,000), and MA (1,500), plus estimates of 5,000 for MI and 4,000 for NY. Assigning roughly 20,000 to the other 44 states yields a national total of around 60,000.

(27) The added noise level from a jet ski on the open ocean is much higher than on ocean beaches, due to the absence of background surf noise. In any event, since 92% of jet ski use is on lake-type waters, the 37 dBA noise increment on secluded lakes is a good approximation of the average noise increment imposed by a jet ski cluster on sailboaters, kayakers, swimmers, etc.

(28) Walsh, 1992. The mean value of a recreation day of non-motorized boating was 112% greater than (i.e., slightly more than double) their mean value for a day of swimming, consistent with the expense associated with use of boats.

(29) The calculation is: 12.2 million x ½ x 2 x 37 dBA x $40 x 1.0% x 0.67 duty cycle factor, yielding $120 million.

(30) U.S. annual fuel use by jet skis is around 180 million gallons, based on per-jet ski daily fuel use of 9.2 gallons (PWIA survey, or Bombardier, 1996) and 19.5 million “jet ski days” estimated earlier. In comparison, U.S. motor vehicles annually consume approximately 125 billion gallons of gasoline, of which almost all in light-duty gasoline vehicles. The ratio of the respective gallon figures is around 700 to 1.

(31) McCubbin & Delucchi, 1996, Table 11.7-6. The cost range, 0.58¢ to 7.71¢, exclude visibility and ecosystem damage from air pollution (these are treated in other reports by Delucchi in the series), “upstream emissions” (e.g., from oil refining) and road dust (treated in the same report). The wide range reflects uncertainties in the rates of pollutant emission, dispersion, human exposure, and disease generation.

(32) U.S. Coast Guard, 1997. Data are from Boating Accident Reports for recreational boats. Of 5,089 vessels in collisions, 2,486 were PWC (personal watercraft, i.e., jet skis), and 310 were unknown (see p. 30); excluding the latter, jet skis were 52% of the total.

(33) Ibid., pp. 4 and 5. The Coast Guard estimated that there were 12.3 million “numbered [registered] boats” in 1997, of which 0.5 million were jet skis. However, the latter figure excluded 25 states, including some with the most jet skis (see p. 24), and is only half the 1997 figure reported by trade associations and others. We therefore added 0.5 million jet skis to the Coast Guard 1997 figures, for 1.0 million jet skis, making an 8% share of a 12.8 million total. If 8% of boats (the jet skis) were in 52% of serious accidents (see prior footnote), and the remaining 92% of boats were in 48%, then jet skis were in accidents 12.5 times as often as other boats.

(34) Ibid., p. 16.

(35) For a detailed description of the full range of jet ski damage to people and the natural environment, see Bluewater Network, op. cit.

(36) In 1987, the National Marine Manufacturers Association measured an average reduction in sound levels from motorboats of 4.8 decibels with a doubling of distance from 50 to 100 feet, and 5.1 decibels with a further doubling to 200 feet. (NMMA, 1987) These figures hold over a wide variety of types of powerboat with remarkable consistency (standard deviations of only 0.6 dBA in the first case and 1.0 dBA in the second). Our attenuation model is based on a noise level loss of 5 dBA per doubling of distance over water and 6 dBA per doubling of distance over land, or inverse power laws with exponents of 1.661 and 1.993, respectively.

(37) At the somewhat high-end frequency of 1000 hertz, the typical value for this additional attenuation is only 1 dBA at 4000 feet and is much less at 1000 feet. These figures increase at higher frequencies, and could be as high as 6 dBA and 2 dBA, respectively. On this basis, we conclude that exponential attenuation can be safely ignored over the distance regimes under consideration here. Hubbard, 1952.

(38) Wagner, 1994 and 1999.

(39) We quote from an uncredited, but apparently industry-based document, identified as PIANC SPN Working Group No. 6, Discussion of Personal Watercraft Noise-Related Issues, undated: “Current PWC models are virtually all below 78-80 dBA at a distance of 15 meters (50 feet) [while] older models may be as loud as 84-86 dBA and modified PWC … may be much louder [by] 10 dBA or more.” We added 6-7 decibels to these ranges to adjust from the 50-foot distance to our base distance of 20 feet.

(40) Noise Unlimited Inc., 1995. Readings were taken at 50 feet for two Kawasaki Jet Skis: model 750 STS (81 dBA) and model 900, High Performance 3 Cylinder 100 hp (76 dBA). Text figures are 6-7 dBA higher to adjust for difference in reference distance from our 20 feet.

(41) The usual mean and median are not defined on the infinitely long interval [1, ¥), i.e., from 1 to infinity. In this situation, a “natural” measure often used is the “harmonic” measure, which is induced by the reciprocal map y = 1/x (which maps [1, ¥) onto the “unit interval” [0, 1], with the standard “uniform” measure ). This induces the measure dy = (1/x^2) dx on [1, ¥); under this measure, the median is 2.0. The mean is still undefined on [1, ¥), although the value 2.0 corresponds to the mean 0.5 of [0, 1] under uniform measure.

(42) McConnell, 1977. McConnell used a semilog regression to estimate consumer surplus. We assumed values of $20K for family income (in the 1974 dollars used in his regression), air temperature of 85· F, beachgoers averaging 10 beach visits per season, and beachgoer density of 1 person per 100 square feet corresponding to a popular beach. These values yield a consumer surplus of $4.50 (adjusted to 1999 dollars), which must be doubled to derive total beachgoer utility. Assuming 5 beach visits per season instead of 10 would raise this result by one-third.

(43) Silberman & Klock, 1988. Although Silberman & Klock did not specify the population density of the beaches they surveyed, their location, on the Jersey Shore within the New York metropolitan area, suggests high usage rates. In addition, their efforts to correlate beachgoer utility to beach “congestion” were inconclusive.

(44) Walsh et al., op. cit.

(45) The “power law” equation is the solution to the “constant elasticity = E” differential equation: (dQ/Q) / (dP/P) = - E .

(46) McConnell, op. cit., reports that the federal Bureau of Outdoor Recreation’s 1974 beach standard equated to 75 square feet per person, with 100 square feet “as a more appropriate standard for environmental concern.” (pp. 191-192) McConnell also reports that Ohio, Nebraska and California promulgated standards in the early 1970s that ranged between 75 and 109 square feet per person, while Vermont recommended 25-50 square feet. (p. 192n)

(47) The Wall Street Journal, 1998, reports that Italy’s bagnini (beach workers) place beachgoers’ uniform umbrellas exactly 6 feet apart. Since each umbrella effectively commands a 6-foot square, each beachgoer occupies 36 square feet.

(48) Delucchi & Hsu, op. cit.

(49) E. I. Feitelson et al., 1996. These ranges include valuations inferred from respondents who indicated that no price or rent reduction could induce them to live in the noisier district.

(50) National Marine Manufacturers Association, 1998, reports average retail prices for jet skis of $6,328 in 1996, $6,454 in 1997 and $6,681 in 1998, suggesting that $6,000 is a reasonable estimate of the sale price of jet skis in service in 1999.

(51) Respondents to the PWIA survey (Bombardier, 1996, op. cit.) reported average daily fuel use of 9.2 gallons.

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