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HomeMy WebLinkAboutSaint Mary's - Pitka Point Wind Energy Project - Pitka's Point Wind Resource Report - Apr 2012 - REF Grant 7040017Pitka’s Point, Alaska Wind Resource Report Pitka’s Point met tower, photo by Doug Vaught April 25, 2012 Douglas Vaught, P.E. V3 Energy, LLC Eagle River, Alaska Pitka’s Point, Alaska Met Tower Wind Resource Report P a g e | 2 Summary The wind resource measured at the Pitka’s Point met tower site is outstanding with measured wind power class 6 by measurement of wind power density and wind speed. Extensive wind resource analysis has been conducted in the Saint Mary’s region, with met towers at a lower elevation site closer to the village of Saint Mary’s and near Mountain Village in addition to the Pitka’s Point met tower. Documented in another report, the wind resource measured at the nearby Saint Mary’s met tower site is less robust than that measured at Pitka’s Point and appears to experience similar icing problems. The Mountain Village wind resource classification appears to be between those measured at Pitka’s Point and Saint Mary’s. Considering the inland location of Saint Mary’s/Pitka’s Point, the wind resource measure at the Pitka’s Point met tower site is highly unusual, and very favorable, with its combination of a high annual average wind speed, relatively low elevation, likely good geotechnical conditions, and proximity to existing roads and infrastructure. Met tower data synopsis Data dates October 26, 2007 to February 12, 2009 (16 months) Wind power class Class 6 (excellent), based on wind power density Wind power density mean, 38 m 558 W/m2 Wind speed mean, 38 m 7.62 m/s (17.0 mph) Max. 10-min wind speed 29.5 m/s Maximum 2-sec. wind gust 26.3 m/s (81.2 mph), January 2008 Weibull distribution parameters k = 1.93, c = 8.63 m/s Wind shear power law exponent 0.176 (low) Roughness class 2.09 (description: few trees) IEC 61400-1, 3rd ed. classification Class II-c (at 38 meters) Turbulence intensity, mean (at 38 m)0.076 (at 15 m/s) Calm wind frequency (at 38 m)20% (<4 m/s)(16 mo. measurement period) Test Site Location A 40 meter NRG Systems, Inc. tubular-type meteorological (met) tower was installed on Pitka’s Point Native Corporation land on the bluff immediately above the Yukon River with excellent exposure to northeasterly winds down the Andreafsky River, northerly winds from the mountains and southerly winds from the flat, tundra plains leading toward Bethel. The met tower site is near an active rock quarry and visual inspection of that quarry indicates the likelihood of excellent geotechnical conditions for wind turbine foundations. Also of advantage for the site is near proximity of the road connecting Saint Mary’s to Pitka’s Point, the airport and Mountain Village. A two-phase power distribution line (connecting the St. Mary’s powerplant to Pitka’s Point as one phase and to the airport as the second phase) routes on the south side of the road. This line could be upgraded to three-phase at minimal cost to connect wind turbines to the system. Pitka’s Point, Alaska Met Tower Wind Resource Report P a g e | 3 Photo of St. Mary’s from Pitka’s Point site, view to NE, Andreafsky River in background Site information Site number 0066 Latitude/longitude N 62° 02.252”W 163° 14.820” Time offset -9 hours from GMT (Yukon/Alaska time zone) Site elevation 177 meters (580 ft.) Datalogger type NRG Symphonie, 10 minute time step Tower type Tubular tall tower, 8-inch diam., 40 meter height Tower sensor information Channel Sensor type Height Multiplier Offset Orientation 1 NRG #40C anemometer 38.0 m 0.765 0.35 NNE 2 NRG IceFree III anemometer 28.2 m 0.572 1.0 WNW 3 NRG #40C anemometer 28.8 m 0.765 0.35 NNE 4 NRG #40C anemometer 21.0 m 0.765 0.35 NNE 7 NRG #200P wind vane 38 m 0.351 260 080° T 8 NRG IceFree III wind vane 29 m 0.351 350 350° T Pitka’s Point, Alaska Met Tower Wind Resource Report P a g e | 4 9 iPack Voltmeter 0.021 0 10 NRG #110S Temp C 2 m 0.136 -86.383 N/A 12 RH-5 relative humidity 2 m 0.097 0 Google Earth image, Pitka’s Point and Saint Mary’s Topographic maps St. Mary’s Pitka’s Point, Alaska Met Tower Wind Resource Report P a g e | 5 Data Quality Control Data was filtered to remove presumed icing events that yield false zero wind speed data and non-variant wind direction data. Data that met criteria listed below were automatically filtered. In addition, data was manually filtered for obvious icing that the automatic filter didn’t catch, and invalid or low quality data for situations such as logger initialization and other situations. Anemometer icing – data filtered if temperature < 1°C, speed SD = 0, and speed changes < 0.25 m/s for minimum 2 hours Vane icing – data filtered if temperature < 1°C and vane SD = 0 for minimum of 2 hours Tower shading of 29 meter and 28 meter (IceFree) paired anemometers – refer to graphic below Because the met tower site is a known rime icing environment, it was thought that installation of a heated anemometer and wind vane would result in much better data recovery than from standard non- heated sensors, but that did not prove entirely true. As one can see in the table below, data loss due to icing was actually higher from the IceFree anemometer than the standard anemometers, although data loss due to icing from the IceFree wind vane is not quite half that from the standard vane. It is not clear why data recovery from the heated anemometer was so poor. One possible explanation is excessive voltage drop from the power line tie-in to the sensor on the met tower. Another explanation is simply the difficult nature of the rime icing environment at the site. Note also that all data was lost for the period from December 27, 2008 to January 7, 2009. The tower itself collapsed during a severe rime icing event on February 12, 2009, although temperature and relative humidity data collection continued for two additional weeks until March 1, 2009. The February 12 ice storm also resulted in the collapse of the nearby St. Mary’s met tower. The St. Mary’s met tower was replaced in order to continue that study but with more than one year of Pitka’s Point data obtained, it was decided not to replace the Pitka’s Point met tower. Pitka’s Point, Alaska Met Tower Wind Resource Report P a g e | 6 Sensor data recovery table Sensor Possible Records Valid Records <Unflagged data> Icing Invalid Low quality Tower shading Recovery Rate (%) Speed 38 m 74,016 52,519 52,519 15,962 2,702 0 0 70.96 Speed 28 m IceFree 74,016 47,014 47,014 17,676 2,706 648 6,252 63.52 Speed 29 m 74,016 51,775 51,775 14,605 2,702 0 4,294 69.95 Speed 21 m 74,016 54,025 54,025 13,971 2,702 0 0 72.99 Direction 38 m 74,016 51,528 51,528 17,608 2,772 0 0 69.62 Direction 29 m IceFree 74,016 58,876 58,876 9,803 2,772 0 0 79.54 iPack Voltmeter 74,016 69,122 69,122 0 245 0 0 93.39 Temperature 74,016 68,694 68,694 0 673 0 0 92.81 RH-5 Relative Humid. (installed on 1/8/2009) 74,016 7,344 7,344 0 62,023 0 0 9.92 Sensor data recovery rate by month anemometers vanes Year Month 38 m 28 m IceFree 29 m 21 m 38 m 29 m IceFree 2007 Oct 86.9 75.4 88.3 88.3 79.2 28.1 2007 Nov 53.7 82.9 51.9 54.0 44.5 100.0 2007 Dec 74.1 69.3 80.1 82.7 77.5 79.0 2008 Jan 28.7 23.8 27.6 43.2 54.8 72.5 2008 Feb 76.3 73.5 79.2 78.5 65.8 86.7 2008 Mar 89.5 78.0 92.7 96.6 77.7 89.6 2008 Apr 39.3 71.1 49.1 42.4 66.9 76.5 2008 May 98.5 85.5 89.5 97.3 96.3 98.2 2008 Jun 100.0 89.8 89.3 100.0 100.0 100.0 2008 Jul 100.0 93.6 93.7 100.0 100.0 100.0 2008 Aug 100.0 92.6 97.0 100.0 100.0 100.0 2008 Sep 100.0 89.6 99.0 100.0 96.7 100.0 2008 Oct 97.9 88.2 98.3 97.9 93.8 95.6 2008 Nov 62.3 28.1 58.0 56.4 54.9 79.0 2008 Dec 65.4 31.9 65.5 64.6 46.6 72.6 2009 Jan 53.6 36.7 50.1 58.0 45.2 51.1 2009 Feb 40.9 22.7 42.3 42.3 37.9 36.6 2009 Mar 0.0 0.0 0.0 0.0 0.0 0.0 All Data 71.0 63.5 70.0 73.0 69.6 79.5 Pitka’s Point, Alaska Met Tower Wind Resource Report P a g e | 7 Data loss due to icing conditions Tower shading filter plot Documentation of Icing Rime icing is more problematic for wind turbine operations than freezing rain (clear ice) given its tenacity and longevity in certain climatic conditions. For this reason, wind power at the Pitka’s Point site should be developed with consideration to the possible need for anti-icing and de-icing measures. These may include redundant control sensors, air-heated rotor blades, leading edge blade heaters, and active operational intervention during winter months to visually detect and de-ice the turbines. 0.0% 10.0% 20.0% 30.0% 40.0% 50.0% 60.0% 70.0% 80.0% 90.0% 100.0%Anemometer Icing Data Loss 38 m 28 m IceFree 29 m Pitka’s Point, Alaska Met Tower Wind Resource Report P a g e | 8 An icing event leading to data recovery loss from the sensors is indicated in the January 15, 2009 photographs below, which clearly indicate the presence of icing conditions. This icing event is also shown in the data graphs of January 15 below. Note that temperature is below freezing, relative humidity is high, wind speed standard deviation equals zero, and the wind speeds are stopped at their offset values of 0.4 m/s. These conditions met the criteria of icing conditions and were automatically flagged by the wind analysis software. Pitka’s Point Icing Event Photographs, 1/15/2009 Pitka’s Point Icing Event Data, 1/12/2009 to 1/16/2009 Pitka’s Point, Alaska Met Tower Wind Resource Report P a g e | 9 Wind Speed Anemometer data obtained from the met tower, from the perspectives of both mean wind speed and mean wind power density, indicate an outstanding wind resource. Note that cold temperatures contributed to a higher wind power density than standard conditions would yield for the measured mean wind speeds. Anemometer data summary Variable Speed 38 m Speed 29 m Speed 28 m IceFree Speed 21 m Measurement height (m) 38 28.8 28.2 21 Mean wind speed (m/s) 7.68 7.29 7.33 6.83 MoMM wind speed (m/s)7.62 7.24 7.33 6.78 Median wind speed (m/s) 7.20 6.80 7.00 6.40 Max wind speed (m/s) 29.50 29.20 27.50 28.40 Weibull k 1.94 1.89 2.22 1.88 Weibull c (m/s) 8.64 8.20 8.26 7.68 Mean power density (W/m²) 573 502 441 414 MoMM power density (W/m²)559 490 441 404 Mean energy content (kWh/m²/yr) 5,015 4,396 3,861 3,627 MoMM energy content (kWh/m²/yr)4,897 4,294 3,861 3,541 Energy pattern factor 1.95 2.00 1.73 2.01 Frequency of calms (%) (< 4 m/s) 20.4 21.9 17.6 24.7 MoMM = mean of monthly means Time Series Time series calculations indicate high mean wind speeds during the winter months with more moderate, but still relatively high, mean wind speeds during summer months. This correlates well with the Saint Mary’s/Andreafsky/Pitka’s Point village load profile where winter months see high demand for electricity and heat and the summer months have lower demand for electricity and heat. The daily wind profiles indicate relatively even wind speeds throughout the day with slightly higher wind speeds during night hours. 38 m anemometer data summary Mean Median Max 10- min avg Max gust (2 sec) Std. Dev. Weibull k Weibull c Month (m/s) (m/s) (m/s) (m/s) (m/s) (-) (m/s) Jan 10.17 10.70 29.5 35.9 5.34 1.97 11.45 Feb 9.21 9.20 20.1 23.3 4.07 2.41 10.36 Mar 8.62 8.50 21.8 26.3 4.33 2.07 9.71 Apr 7.98 7.80 16.9 20.6 2.83 3.05 8.90 May 7.27 6.90 21.8 27.1 3.67 2.06 8.19 Jun 5.70 5.80 13.2 15.3 2.62 2.28 6.40 Pitka’s Point, Alaska Met Tower Wind Resource Report P a g e | 10 Jul 7.98 7.70 21.7 26.3 3.33 2.55 8.99 Aug 5.89 5.70 15.3 17.9 2.95 2.05 6.62 Sep 6.37 6.70 12.5 16.8 2.44 2.85 7.11 Oct 6.80 6.60 20.1 24.8 3.81 1.80 7.62 Nov 7.32 6.40 24.1 29.8 4.48 1.72 8.23 Dec 8.97 8.90 22.9 27.5 4.69 1.95 10.07 Annual 7.62 7.20 29.5 35.9 4.09 1.94 8.64 Monthly time series, mean wind speeds Daily wind profiles (annual) Pitka’s Point, Alaska Met Tower Wind Resource Report P a g e | 11 Probability Distribution Function The probability distribution function (PDF), or histogram, of the Pitka’s Point met tower site wind speed indicates a shape curve dominated by moderate wind speeds and is reflective of a “normal” shape curve, known as the Rayleigh distribution (Weibull k = 2.0), which is defined as the standard wind distribution for wind power analysis. As seen below in the wind speed distribution of the 38 meter anemometer, the most frequently occurring wind speeds are between 5 and 10 m/s with very few wind events exceeding 25 m/s (the cutout speed of most wind turbines; see following wind speed statistical table). PDF of 38 m anemometer (17months’ data) Weibull k shape curve table Pitka’s Point, Alaska Met Tower Wind Resource Report P a g e | 12 Weibull values table, 38 m anemometer Weibull Weibull Mean Proportion Power R k c Above Density Squared Algorithm (m/s) (m/s) 7.678 m/s (W/m2) Maximum likelihood 1.940 8.644 7.666 0.452 543.6 0.990 Least squares 1.898 8.692 7.713 0.454 566.8 0.988 WAsP 1.998 8.725 7.732 0.461 541.3 0.990 Actual data 7.678 0.461 541.3 Occurrence by wind speed bin (38 m anemometer) Bin Endpoints (m/s) Occurrences Bin Endpoints (m/s) Occurrences Lower Upper No. Percent Cumul. Lower Upper No. Percent Cumul. 0 1 955 1.82% 1.82% 15 16 893 1.70% 96.52% 1 2 1,918 3.65% 5.47% 16 17 615 1.17% 97.69% 2 3 3,409 6.49% 11.96% 17 18 373 0.71% 98.40% 3 4 4,050 7.71% 19.67% 18 19 306 0.58% 98.98% 4 5 4,141 7.88% 27.56% 19 20 181 0.34% 99.33% 5 6 4,982 9.49% 37.04% 20 21 133 0.25% 99.58% 6 7 5,320 10.13% 47.17% 21 22 93 0.18% 99.76% 7 8 4,975 9.47% 56.65% 22 23 58 0.11% 99.87% 8 9 4,911 9.35% 66.00% 23 24 29 0.06% 99.92% 9 10 3,976 7.57% 73.57% 24 25 11 0.02% 99.94% 10 11 3,177 6.05% 79.62% 25 26 7 0.01% 99.96% 11 12 2,681 5.10% 84.72% 26 27 11 0.02% 99.98% 12 13 2,246 4.28% 89.00% 27 28 5 0.01% 99.99% 13 14 1,707 3.25% 92.25% 28 29 5 0.01% 100.00% 14 15 1,349 2.57% 94.82% 29 30 2 0.00% 100.00% Wind Shear and Roughness Wind shear at the Pitka’s Point met tower site was calculated with the three standard (non-heated) anemometers installed on the met tower. The calculated power law exponent of 0.176 indicates relatively low shear at the site. Calculated surface roughness at the site is 0.11 m (the height above ground where wind speed would be zero) for a roughness class of 2.08 (description: few trees). Pitka’s Point, Alaska Met Tower Wind Resource Report P a g e | 13 Vertical wind shear profile Comparative wind shear profiles Wind shear by direction sector table Time Mean Wind Speed (m/s) Best-Fit Surface Direction Sector Steps Speed 38 m Speed 29 m Speed 21 m Power Law Exp Roughness (m) 345° - 15° 7,444 8.55 8.02 7.61 0.197 0.1777 15° - 45° 5,176 7.53 7.08 6.63 0.214 0.2655 45° - 75° 7,501 9.62 9.06 8.66 0.176 0.0973 75° - 105° 5,627 8.93 8.30 7.57 0.280 0.7842 105° - 135° 3,004 7.71 7.38 7.00 0.165 0.0645 135° - 165° 2,779 8.28 8.04 7.71 0.121 0.0070 165° - 195° 2,364 7.42 7.21 6.95 0.111 0.0035 195° - 225° 456 3.83 3.57 3.35 0.224 0.3280 225° - 255° 1,636 4.73 4.45 4.27 0.172 0.0857 255° - 285° 1,478 4.86 4.59 4.42 0.161 0.0572 Pitka’s Point, Alaska Met Tower Wind Resource Report P a g e | 14 285° - 315° 2,821 6.24 6.00 5.88 0.098 0.0011 315° - 345° 4,845 6.92 6.54 6.38 0.136 0.0189 Extreme Winds A modified Gumbel distribution analysis, based on monthly maximum winds vice annual maximum winds, was used to predict extreme winds at the Pitka’s Point met tower site. Sixteen months of data though are minimal at best and hence results should be viewed with caution. Nevertheless, with data available the predicted Vref (maximum ten-minute average wind speed) in a 50 year return period (in other words, predicted to occur once every 50 years) is 41.6 m/s. This result classifies the site as Class II by International Electrotechnical Commission 61400-1, 3 rd edition (IEC3) criteria. IEC extreme wind probability classification is one criteria – with turbulence the other – that describes a site with respect to suitability for particular wind turbine models. Note that the IEC3 Class II extreme wind classification, which clearly applies to the Pitka’s Point met tower site, indicates relatively energetic winds and turbines installed at this location should be IEC3 Class II rated. Site extreme wind probability table, 38 m data Vref Gust IEC 61400-1, 3rd ed. Period (years) (m/s) (m/s) Class Vref, m/s 3 29.2 35.5 I 50.0 10 35.4 43.1 II 42.5 20 37.0 45.0 III 37.5 30 39.6 48.2 S designer- specified5041.6 50.6 100 44.2 53.8 average gust factor:1.22 Extreme wind graph, by annual method Pitka’s Point, Alaska Met Tower Wind Resource Report P a g e | 15 Temperature, Density, and Relative Humidity The Pitka’s Point met tower site experiences cool summers and cold winters with resulting higher than standard air density. Calculated mean-of-monthly-mean (or annual) air density during the met tower test period exceeds the 1.204 kg/m 3 standard air density for a 177 meter elevation by 5.7 percent. This is advantageous in wind power operations as wind turbines produce more power at low temperatures (high air density) than at standard temperature and density. Temperature and density table Temperature Air Density Mean Min Max Mean Min Max Mean Min Max Month (°F) (°F) (°F) (°C) (°C) (°C) (kg/m³) (kg/m³) (kg/m³) Jan 4.7 -20.2 39.0 -15.1 -29.0 3.9 1.325 1.204 1.416 Feb 4.1 -24.7 32.4 -15.5 -31.5 0.2 1.343 1.264 1.430 Mar 11.0 -14.3 38.8 -11.7 -25.7 3.8 1.275 1.204 1.397 Apr 19.5 -6.3 44.2 -7.0 -21.3 6.8 1.299 1.235 1.372 May 39.4 13.8 65.5 4.1 -10.1 18.6 1.247 1.185 1.314 Jun 49.2 29.5 70.2 9.5 -1.4 21.2 1.223 1.174 1.272 Jul 50.5 37.9 81.9 10.3 3.3 27.7 1.220 1.149 1.250 Aug 51.3 33.1 70.9 10.7 0.6 21.6 1.218 1.173 1.263 Sep 45.1 30.0 64.6 7.3 -1.1 18.1 1.233 1.187 1.270 Oct 22.7 5.0 37.2 -5.2 -15.0 2.9 1.290 1.252 1.339 Nov 16.3 -14.6 44.6 -8.7 -25.9 7.0 1.308 1.234 1.398 Dec 13.9 -16.2 45.0 -10.1 -26.8 7.2 1.307 1.204 1.403 Annual 27.4 -24.7 81.9 -2.5 -31.5 27.7 1.273 1.149 1.430 Pitka’s Point temperature boxplot graph Pitka’s Point, Alaska Met Tower Wind Resource Report P a g e | 16 Wind Speed Scatterplot The wind speed versus temperature scatterplot below indicates cold temperatures at the Pitka’s Point met tower site with a preponderance of below freezing temperatures. During the met tower test periods, temperatures were often below -20° C (-4° F), the minimum operating temperature for most standard-environment wind turbines. Note that arctic-capable (ratings to -40°C) wind turbines would be required at Pitka’s Point. Wind speed/temperature Wind Direction Wind frequency rose data indicates that winds at the Pitka’s Point met tower site are primarily bi- directional, with northerly and east-northeasterly winds predominating. The mean value rose indicates that east-northeasterly winds are of higher intensity than northerly winds, but interesting, the infrequent south-southeasterly winds, when they do occur, are highly energetic and likely indicative of storm winds. Calm frequency (the percent of time that winds at the 38 meter level are less than 4 m/s, a typical cut-in speed of larger wind turbines) was a very low 20 percent during the 16 month test period. Pitka’s Point, Alaska Met Tower Wind Resource Report P a g e | 17 Wind frequency rose (38 m vane) Mean value rose (38 m anem.) Wind energy rose (38 m anem.) Scatterplot rose of 38 m wind power density Pitka’s Point, Alaska Met Tower Wind Resource Report P a g e | 18 Wind density (38 meter height) roses by month (common scale) Turbulence The turbulence intensity (TI) is acceptable with a mean turbulence intensity of 0.076 and a representative turbulence intensity of 0.105 at 15 m/s wind speed, indicating quite smooth air for wind turbine operations. This equates to an International Electrotechnical Commission (IEC) 3rd Edition (2005) turbulence category C, which is the lowest defined category. These data are shown in the turbulence intensity graph below. As seen, representative TI (90th percentile of the turbulence intensity values, assuming a normal distribution) at 15 m/s is well under IEC Category C criteria at the Pitka’s Point met tower site. Turbulence synopsis 38 m anem. 29 m anem. Legend Sector Mean TI at 15 m/s Repres. TI at 15 m/s IEC3 Category Mean TI at 15 m/s Repres. TI at 15 m/s IEC3 Category IEC3 Categ. Mean TI at 15 m/s all 0.076 0.105 C 0.088 0.117 C S >0.16 315° to 045° 0.060 0.084 C 0.067 0.094 C A 0.14-0.16 045° to 135° 0.079 0.105 C 0.093 0.119 C B 0.12-0.14 135° to 225° 0.089 0.119 C 0.093 0.117 C C 0-0.12 045° to 135° 0.074 0.099 C 0.071 0.084 C Pitka’s Point, Alaska Met Tower Wind Resource Report P a g e | 19 Turbulence rose, 38 m anemometer, 38 m vane Turbulence rose, 29 m anemometer, 29 m vane Pitka’s Point, Alaska Met Tower Wind Resource Report P a g e | 20 Turbulence intensity, 38 m, all direction sectors Turbulence intensity, 29 m, all direction sectors Pitka’s Point, Alaska Met Tower Wind Resource Report P a g e | 21 Turbulence table, 38 m data, all sectors Bin Bin Endpoints Records Standard RepresentativeMidpoint Lower Upper In Mean Deviation Peak (m/s) (m/s) (m/s) Bin TI of TI TI TI 1 0.5 1.5 1,336 0.403 0.185 0.640 1.833 2 1.5 2.5 2,692 0.197 0.105 0.331 1.111 3 2.5 3.5 3,834 0.139 0.070 0.228 0.600 4 3.5 4.5 4,076 0.114 0.059 0.190 0.917 5 4.5 5.5 4,528 0.100 0.051 0.165 0.827 6 5.5 6.5 5,278 0.091 0.041 0.144 0.364 7 6.5 7.5 5,126 0.085 0.039 0.135 1.169 8 7.5 8.5 5,027 0.079 0.034 0.122 0.637 9 8.5 9.5 4,538 0.073 0.030 0.112 0.449 10 9.5 10.5 3,503 0.074 0.028 0.110 0.255 11 10.5 11.5 2,881 0.074 0.026 0.108 0.229 12 11.5 12.5 2,488 0.074 0.024 0.105 0.271 13 12.5 13.5 1,966 0.075 0.023 0.105 0.197 14 13.5 14.5 1,519 0.075 0.022 0.104 0.191 15 14.5 15.5 1,054 0.076 0.022 0.105 0.241 16 15.5 16.5 777 0.079 0.022 0.107 0.177 17 16.5 17.5 484 0.082 0.022 0.111 0.163 18 17.5 18.5 322 0.089 0.023 0.118 0.203 19 18.5 19.5 260 0.086 0.020 0.112 0.144 20 19.5 20.5 148 0.085 0.018 0.109 0.138 21 20.5 21.5 113 0.088 0.012 0.103 0.130 22 21.5 22.5 75 0.087 0.013 0.104 0.112 23 22.5 23.5 49 0.085 0.010 0.098 0.107 24 23.5 24.5 11 0.092 0.010 0.105 0.105 25 24.5 25.5 8 0.097 0.014 0.114 0.127 26 25.5 26.5 7 0.089 0.024 0.119 0.137 27 26.5 27.5 10 0.081 0.013 0.098 0.104 28 27.5 28.5 7 0.075 0.013 0.091 0.100 29 28.5 29.5 2 0.071 0.013 0.087 0.080 30 29.5 30.5 1 0.085 0.000 0.085 0.085