USING A COLLISION RISK MODEL TO ASSESS BIRD COLLISION RISKS FOR OFFSHORE WINDFARMS WITH EXTENDED METHOD WORKED EXAMPLE March 2012 INTRODUCTION 1. The Strategic Ornithological Support Services group (SOSS) provides advice to the offshore wind farm industry with the aim of resolving consenting challenges posed by the potential for offshore wind farms to impact bird populations. 2. SOSS has published guidance on Using a Collision Risk Model to assess bird collision risks for offshore windfarms i, which includes a spreadsheet to facilitate calculation of collision risks. The following worked example has been developed to demonstrate use of that guidance and spreadsheet, and should be read in conjunction with them. The worked example follows the six stages A F of the Collision Risk Model (CRM) guidance, at each stage explaining the choice of data input to the spreadsheet, and the outputs calculated: Stage A Flight activity Stage B Estimating number of bird flights through rotor Stage C Probability of collision for a single rotor transit Stage D Multiplying to yield expected collisions per year Stage E Avoidance and attraction Stage F Expressing uncertainty The worked example also includes a collision risk assessment using the extended model (introduced March 2012) which can take account of the skewed distribution of flight heights of seabirds. 3. The Worked Example is accompanied by a spreadsheet (comprising a set of seven worksheets 1 ) for each of the two turbine options considered. These make use of the data detailed in this example. Within each set of seven worksheets, all input data is entered on Sheet 1 Input data. The supporting sheets then perform the supporting collision risk calculations and the outputs, summarised in Table 10, appear in Sheet 2 Overall collision risk. 4. This example is entirely fictitious, including the bird density and turbine specifications used. The results are not characteristic of collision risks at any particular site. IMAGINED SCENARIO 5. An offshore wind farm is proposed in an area of the North Sea. Among the seabirds present on site and viewed as sensitive to collision risk are Northern gannet (Morus bassanus). This document describes the collision risk assessment for gannet. 1 This Worked example does not include any specific collision risk for migrating birds, hence the examples do not include the Migrant collision risk worksheet.
6. This windfarm is still at the design stage, and the results of this preliminary collision risk assessment will be used to help determine the final design. The maximum area of the site is around 48 km 2. If that full area were used the maximum generating capacity would be around 800 MW. This collision risk assessment has been undertaken for this maximum capacity. Collision risks to birds are expected to scale in proportion to windfarm capacity. STAGE A: FLIGHT ACTIVITY Bird density 7. Boat based bird survey has been undertaken where possible over two days in each month over two years. The survey has included the proposed development site, of approximately 48 km 2, and a 2km buffer around the development site, making a total study area of around 108 km 2. The survey made use of linear transects with snapshots of birds in flight within a 300m x 300m box to either side of the vessel, ie the area of sea captured within each snapshot was 0.18 km 2. The total number of birds observed in flight within these snapshots was then divided by the total snapshot area to yield the areal density of birds in flight: Total snapshot area = 0.18 km 2 x total number of snapshots Bird density per km = Total snapshot count of gannet Total snapshot area 8. Survey results for the development site are presented in Table 1: Table 1: Survey results for development site bird density in birds/km 2 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year 1 s1 0.13 0.75 1.26 1.21 0.94 1.13 0.58 2.21 2.88 0.93 n/a 0.30 s2 0.07 n/a 2.26 1.55 0.90 1.31 0.86 1.61 3.40 0.79 0.82 0.14 Year 2 s3 0.00 0.25 1.35 1.43 1.00 0.90 0.45 1.55 2.37 0.78 0.39 0.00 s4 0.00 0.40 1.09 n/a 0.68 0.82 0.39 1.81 2.49 n/a 0.29 0.02 Mean 0.05 0.47 1.49 1.40 0.88 1.04 0.57 1.80 2.79 0.83 0.50 0.12 SD 0.05 0.21 0.45 0.14 0.12 0.19 0.18 0.26 0.40 0.07 0.23 0.12 9. The bird density measurements pertaining only to the development site have been used. The data showed a generally higher bird density within the development site than for the development site and buffer zone combined. (It is preferable in a collision risk assessment to use only the bird densities recorded on the actual development site. However where the variance in survey data is high, and in circumstances where it is reasonable to assume no difference in bird density between the site and the buffer, use of data including buffer areas may improve the precision of the bird density estimate.) 10. For each month a mean and standard deviation are calculated from all surveys undertaken within that month (and across both years of survey). The collision risk model evaluates risk on
a month by month basis across the year in order to reflect changing bird abundance within and utilisation of the area. Proportion flying at risk height 11. The surveys also recorded the flight heights of birds, using bands of < 20m, 20 50m, 50 200m, and > 200m. In the absence of definitive information at the time of survey on the minimum height above the sea of the turbine rotors to be used, it was assumed that all flights between 20m and 200m height will be at risk. Little difference is seen between the results for the development site and the buffer area (Table 2), so all the flight height data for the study area including the buffer has been used, to make use of the increased accuracy provided by the larger sample size. Table 2: Survey results proportion observed flying above 20m and below 200m height Number of gannets observed Proportion above 20m height Development site 382 8.6% Development site + 2km buffer 646 8.3% 12. On behalf of SOSS, Cook et al ii have analysed flight height data for gannet, drawing from bird survey at a range of windfarm sites around the UK. Using that generic data, the proportion flying above a risk height of 20m would be 11.3%. Collision risks have been worked out using both the site survey data and the generic data. Nocturnal activity factor 13. Levels of nocturnal activity by gannet are believed to be low but significant, ascribed by Garthe and Hüppop iii a score of 2 on a range from 0 (hardly any flight by night) to 5(much flight activity at night). A nocturnal activity factor of 2 in the spreadsheet assumes that on average, nocturnal activity is at around 25% of daytime level. (Where possible local information should be obtained on nocturnal activity it is known that at some sites, levels of nocturnal gannet activity are very low iv. However there has as yet been no night time survey at this site.) Windfarm latitude 14. The windfarm latitude is 55 48 north ( entered in decimals as 55.8 ). It is used in the model by Sheet 4 daylight and night time hours to determine the total daylight and night time hours for which these bird densities may be expected to persist. Table 3: Stage A data input to spreadsheet Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Bird density (birds/km 2 ) 0.05 0.47 1.49 1.40 0.88 1.54 0.57 1.80 2.79 0.83 0.50 0.12 Proportion flying at risk height 8.3% Nocturnal activity factor 1 Windfarm latitude 55.8
STAGE B: ESTIMATING NUMBER OF FLIGHTS THROUGH ROTORS Windfarm data 15. Decisions have not yet been taken on the size or model of turbines to be used. However it is likely that these will be among the largest currently available, in the range 4 6MW. On the basis of the expected maximum site capacity of around 800 MW, CRM has therefore been undertaken for two options: 200 of 4.0 MW turbines and 133 of 6 MW turbines As collision risk is greater for the larger number of smaller turbines, the 4 MW option represents a worst case scenario and the 6 MW turbines a best case scenario for collision risk. 16. The potential number of flights through rotors depends on rotor size. The rotor radii are respectively 57.5m for the 4MW turbine option, and 65m for the 6 MW turbine. 17. To include a flight height distribution in the calculation, the height of the rotor is also relevant. The rotor hubheights are 80m for the 4MW turbine and 91.5m for the 6MW turbine. These heights are quoted relative to Highest Astronomical Tide (HAT). As the analysis of flight heights is undertaken relative to the sea surface, a tidal offset is added to the height so as to give the turbine hub height relative to Mean Sea Level. For this site, HAT is 5.4m and Mean Sea Level is 2.9m so the tidal offset added is the difference of 2.5m. Bird data 18. Typical gannet flight speed is taken as 14.9m/sec (Pennycuick 1987 v ). Table 4: Stage B data input to spreadsheet Windfarm data 4 MW option 6 MW option Number of turbines 200 133 Rotor radius 57.5m 65.0m Hub height 80m 91.5m Tidal offset 2.5m 2.5m Bird data Gannet flight speed 14.9 m/sec Output 19. The output from Stage 2 is shown in Sheet 2 Overall collision risk as the potential number of bird transits through rotors, per month and per annum: 4MW turbines 6 MW turbines Option 1 492,504 birds/annum 370,234 birds/annum Option 2 Option 3 154,180 birds/annum 60,793 birds/annum
20. Results have been evaluated for three options: Option 1: using the basic model, assuming 8.3% of birds flying at risk height with equal probability at any height between minimum and maximum rotor height Option 2: using the basic model, assuming 5.7% (for the 4MW turbines) and 3.0% (for the 6MW turbines) flying at risk height with equal probability at any height between minimum and maximum rotor height. These percentages are the figures derived from the generic flight height distributions, taking the lowest point of the turbines as 25m (4MW turbines) and 29m (6MW turbines) after allowing for the tidal offset (lowest height = hubheight radius tidal offset). Option 3: using the extended model, using the generic data on gannet flight heights but using the site data for the overall density of birds. 21. Note that at this stage, non operational time for the turbines has not yet been factored in. STAGE C: PROBABILITY OF COLLISION FOR A SINGLE ROTOR TRANSIT Bird data 22. Typical dimensions for gannet have been taken from BTO Bird facts vi : wingspan 172 cm, length 94 cm. As above (paragraph 17), typical flight speed is taken as 14.9m/sec. It should be noted that the same flight speed is used in this CRM for flights upwind and downwind. 23. Typical gannet flight is a mix of gliding and flapping : flapping flight has been used in this collision risk modelling, which will give a slightly more precautionary estimate (ie a higher collision estimate) than for gliding flight. 24. The orientation of the wind turbines may be expected to have a distribution across many directions, according to the wind rose for the site. It has been assumed that gannet flights through rotors of the windfarm are equally split as between upwind and downwind. Turbine data 25. The number of blades, rotor radius and maximum blade width are derived directly from manufacturers specifications. Average pitch 26. A pitch of 15 degrees is estimated as an average when the turbine is operating at around its mean rotational speed, and this is used throughout the CRM. The variation of pitch along the length of the blades is not provided by manufacturers, nor is data available for the pitch at different wind speeds. Rotation speed 27. Collision risk depends on rotor rotation speed, which in turn depends on wind speed. If simplicity is sought, one can use the maximum rotor speed when the turbine is generating full power for collision risk analysis. However it should be recognised that that will be precautionary, ie it will lead to a higher collision risk than if the risk were more accurately based on mean rotor speed.
28. Calculating a mean rotor speed is quite straightforward if one has a wind frequency distribution, and turbine manufacturer s data (see Table 5) on operational rotor speeds, and cut in and cutout wind speeds. The Annex describes how to calculate a mean rotor speed, and sets out the calculation for the 6 MW turbine option. The information available from the turbine manufacturer will usually specify an operational rotor speed range, a cut in wind speed below which the rotor does not operate, a cut out wind speed above which the turbine is shut down for protection, and a rated wind speed which is the minimum wind speed at which the turbine will generate full power. Table 5: Information on rotation speeds Manufacturer s data: 4 MW model 6 MW model Rotation speed 5 13.6 rpm 7.1 rpm Cut in wind speed 4 m/sec 3.5 m/sec Cut out wind speed 25 m/sec 30 m/sec Rated wind speed 12.5 m/sec 14.8 m/sec Derived mean rotation speed at this site (see Annex) 9.9 rpm 9.3 rpm Table 6: Stage C data input to spreadsheet: Bird data Bird length Wingspan Flight speed Flight style Proportion of flights upwind 94 cm 172 cm 14.9 m/sec Flapping 50% Turbine data 4 MW model 6 MW model No of blades 3 3 Rotor radius 57.5m 65.0m Maximum blade 4.21m 5.35m width Average pitch 15 15 Rotation speed 9.9 rpm 9.3 rpm Output 29. Sheet 3 of the spreadsheet Probability of collision for single bird transit through rotor calculates the risk of collision during in a single transit. The result is expressed as a percentage risk for upwind and downwind flight respectively, and the average 8.1% for the 4 MW turbine and 8.3% for the 6 MW turbine is automatically copied back to Sheet 2 Overall collision risk. STAGE D: MULTIPLYING TO YIELD EXPECTED COLLISIONS PER YEAR 30. In this stage, the output from Stage B (number of potential transits through rotors) is multiplied by the output of Stage C (collision risk for a single rotor transit) to yield the projected number of bird collisions per month or year. However, allowance must first be made for the proportion of time that rotors are not operational. Proportion of time operational
31. Monthly proportion of time operational refers to the proportion of time when a turbine is rotating. It excludes time when the wind is below cut in wind speed, when the rotors may be stationary or idling; time when the rotors are stopped and feathered for protection in very high wind speeds; and down time for operations and maintenance (O&M). These proportions vary over the year, reflecting different wind conditions in different seasons, and the increased opportunities for maintenance access in summer. The data in Table 7 has been acquired from the developer for the two turbine options and is based on the wind frequency distribution at the site and experience of O&M requirements at similar operational sites. Proportion of time operational = Proportion of time available x Proportion of time wind speed is (ie excluding maintenance shutdown) above cut in and below cut out Table 7: Proportion of time turbine operates Prop of time available Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 0.94 0.94 0.92 0.94 0.85 0.85 0.85 0.92 0.92 0.94 0.94 0.94 4 MW turbine Prop of time above cut in and below cut out 0.90 0.90 0.90 0.84 0.77 0.75 0.76 0.78 0.80 0.84 0.87 0.90 Prop of time operational 0.846 0.846 0.846 0.773 0.655 0.638 0.646 0.718 0.736 0.790 0.818 0.846 Prop of time available 0.94 0.94 0.94 0.92 0.85 0.85 0.85 0.92 0.92 0.94 0.94 0.94 6 MW turbine Prop of time above cut in and below cut out 0.96 0.94 0.93 0.90 0.90 0.82 0.86 0.87 0.92 0.64 0.96 0.96 Prop of time operational 0.902 0.884 0.874 0.828 0.765 0.697 0.731 0.800 0.846 0.884 0.902 0.902 Large array correction 32. If the full site is developed, the area of the windfarm would be approximately 48 km 2. For the purpose of applying a large array correction, the windfarm is taken as occupying a circular site of area 48 km 2, of which the diameter gives an average width dimension of 7.8 km. No specific assumptions are made as to the number of turbine rows; the model assumes by default that the number of turbine rows will be the square root of the number of turbines. Table 8: Stage D data input to spreadsheet Proportion of time operational Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 4 MW turbine 0.846 0.846 0.846 0.773 0.655 0.638 0.646 0.718 0.736 0.790 0.818 0.846
6 MW turbine 0.902 0.884 0.874 0.828 0.765 0.697 0.731 0.800 0.846 0.884 0.902 0.902 Large array correction Width of windfarm Output 7.8 km 33. The output from Stage D shown in Sheet 2 Overall collision risk is the expected number of collisions assuming no avoidance: No of collisions (no avoidance) 4 MW turbines 6 MW turbines Option 1 27,954 23,986 Option 2 18,054 8,770 Option 3 5,455 3,463 34. Sheet 5 Large array correction factor has calculated the correction factor which should be applied to take account of any depletion of bird density because of collisions. A figure close to 100% means little correction. For either of the turbine options, the factor is greater than 99.7% for any of the avoidance rate assumptions made below, that is to say the adjustment required is less than 0.3%. Such a minor adjustment is insignificant in relation to the other uncertainties in the collision risk estimate, and can be disregarded. STAGE E: AVOIDANCE AND ATTRACTION Avoidance rates 35. The review for SOSS by Cook et al (2011) ii identified a single study observing avoidance of wind farms by gannet, indicating a figure of 96% macro avoidance, that is long range avoidance of the wind farm site as a whole. No information is available on micro avoidance, ie behaviour of gannet while within the envelope of a wind farm. An overall avoidance rate of 98% (based on macro avoidance of 96%, and at least 50% taking micro avoiding action within the windfarm) is considered a highly precautionary assumption, at least in the basic model. True avoidance rates are likely to be in excess of 99 or 99.5%. Collision risks have been calculated for avoidance rates of 96%, 98%, 99%, 99.5%. The central result, still regarded as precautionary, is taken to be that for 99% avoidance, where applied to output from the basic model. 36. The extended model already takes account of the high proportion of low flying birds which will miss the rotor discs without taking avoidance action, but which may have contributed to avoidance statistics calculated on the basis of the basic Band model. Therefore 98% is therefore taken as the central result for application to the results of the extended model. Attraction 37. There is no reason to expect the site once constructed to attract a higher density of gannets than at present. Table 9: Stage E data input to spreadsheet Avoidance rates 96%, 98%, 99%, 99.5%
OUTPUTS 38. The results of the CRM may be summarised as follows. The central results, ie those judged most realistic, are those in bold: Table 10: Outputs using SOSS Collision risk spreadsheet Option 1 Option 2 Option 3 200 x 4MW 133 x 6MW 200 x 4MW 133 x 6MW 200 x 4MW 133 x 6MW Stage B Potential annual bird transits through rotors 469533 352967 154180 60793 Stage C Risk for single rotor transit 8.1% 8.3% 8.1% 8.3% 4.8% 3.03% Collisions allowing for nonoperational time: Stage D assuming no avoidance 27954 23986 18054 8770 5455 3463 96% avoidance 1118 959 722 351 218 139 Stage E 98% avoidance 559 480 361 175 109 69 99% avoidance 280 240 181 88 55 35 99.5% avoidance 140 120 90 44 27 17
STAGE F: EXPRESSING UNCERTAINTIES 39. There are uncertainties in the input data and at several stages in the calculation, and these must be combined to give an understanding of the uncertainty (and hence the likely accuracy) of the estimated collision risk. 40. The potential number of bird transits through rotors is, in essence, a product of Bird density x No of hours active x Proportion flying at risk height x Total area of rotors x Proportion of time operational and the total collision risk is Potential number of transits x Risk during a single transit Therefore the errors in each of these elements must be combined to estimate the total error or uncertainty. Each error or uncertainty (e 1 to e 5 ) is first expressed as a relative error, ie expressed as a fraction or percentage of the value to which it refers. 41. All the errors here are based on seeking 95% certainty. Thus the range of uncertainty in bird density is taken as two (more strictly 1.96) standard deviations from the mean, and the assessment of the accuracy of flight height observations is based on an expectation that flight height will have been categorised correctly in 95% of cases. 42. The errors are assessed as follows: Bird density (e 1 ). Bird density survey measurements showed variability between surveys. In Table 1 a standard deviation has been calculated from all survey results available for each month. We want to know the error in the collision estimate for a full year, which is the sum of the collision estimates for each of twelve months. If we ignore the variation across the year in deriving collisions from bird density (for example because of changes across the year in turbine operational time), the annual collision rate approximately depends on the sum of the bird densities for each month. The standard deviation for the sum is obtained by summing the twelve standard deviations, but taking the square root of the sum of squares, to allow for the fact that errors in one month may be offset by errors in the other direction in other months. Sum of monthly bird densities = Mean Jan + Mean Feb + Mean Mar.. + Mean Dec SD year = ( SD 2 Jan + SD 2 Feb +.. SD 2 Dec ) The relative error is then 1.96 x SD year Sum of monthly bird densities which calculates to e 1 =0.13. Nocturnal activity (e 2 ). The number of daylight hours may be assumed to be accurate. However there is considerable uncertainty in the use of a nocturnal activity factor of 25%, which accounts for around one fifth of all flights at risk. In the absence of night time survey data, it is judged that nocturnal activity might be anywhere in the range 15 35% of daytime activity. That means that for every 100 daytime flights, a mean of 25 nocturnal flights has been used, but they may in fact number between 15 and 35. This translates to an uncertainty of around ± 8% in the total number of flights. e 2 = 0.08 Proportion at risk height (e 3 ). The most significant error in relation to flight height is that inherent in requiring observers to classify flight height in bands <20m, 20 50m, 50 200m
and >200 m. Though observers were fully trained and check comparisons undertaken from time to time, it is very possible that some birds below 20m may have been classed as 20 50m, and vice versa. If the visual estimate were out by ±5m it is estimated that the proportion flying above 20m would vary by around ±25%. e 3 = 0.25 For collision assessment by Option 3, ie using the extended model, the flight height distribution data published in Cook et al ii includes upper and lower 95% confidence intervals. Substituting that data in turn in place of the median data used in sheet 5 Flightheight indicates that the confidence range for bird density generates a range of uncertainty in collision estimates which is ±19% for the 4MW turbine option, ±25% for the 6MW turbine option. (That difference no doubt reflects that the 6MW turbine is more at the upper tail of the distribution where relative errors are larger.) Turbine size and time operational (e 4 ). It is assumed that the calculation of the area of the rotors is reasonably precise, and also the estimate of the proportion of time operational (though this may be subject to year to year variation according to wind conditions). e 4 = 0. Collision model (e 5 ). The collision risk model itself involves a number of simplifications, such as the shape of the bird, and the use of an average pitch, etc. Its author (SOSS Guidance, paragraph 47) assesses an uncertainty of ±20%. e 5 =0.20 These errors arise independently and so in combining errors it is appropriate to take a root mean square approach, to allow for the likelihood that some errors will offset others, ie E = (e 2 1 + e 2 2 + e 2 3 + e 2 4 + e 2 5 ) which calculates to E = ± 0.35 ( ie ± 35%) Table 11: Sources of uncertainties (before avoidance is considered) e1 uncertainty in bird density ± 0.13 e2 uncertainty in level of nocturnal activity ± 0.08 e3 uncertainty in proportion flying at risk height ± 0.25 e4 uncertainty in operational time 0 e5 Uncertainty due to simplifications in the model ± 0.20 E Combined uncertainty ± 0.35( ie ± 35%)
CONCLUSION OF THE COLLISION RISK ASSESSMENT 43. The final turbine options are not as yet decided, but the CRM has been undertaken for a worst case (in terms of likely collision risk) of 200 x 4MW turbines as well as one of the leading options, 133 x 6MW turbines which is likely to be a best case in terms of likely collision risk. Table 12: Best estimate of annual collision risk assuming that flight distribution is similar to national generic profiles, and using a 98% avoidance rate Turbine option 200 x 4 MW 133 x 6 MW Annual collision estimate (birds/annum) assuming 99% avoidance 109 ± 35% 69 ± 35% 44. While the range of uncertainty shown is sizeable, there is a substantially greater uncertainty over avoidance rates for this species. In this regard 99% is a fairly precautionary figure to use; if macro avoidance accounts for 96% avoidance, then it only requires 75% micro avoidance to attain an overall avoidance rate of 99%. 45. Where generic data on flight heights is used for this estimate, care is needed to check that observations of flight height on the site in question are sufficiently in accord with generic data to justify its use. In this case, the figure from site survey of 8.3% of birds flying above a risk height of 20m is somewhat less than the figure of 11.3% above 20m from the generic data, so the generic data may present a precautionary perspective. Using more precise estimates of height of the rotor above sea level for each turbine type, the proportions derived from the generic data reduce to 5.5% for the 4MW turbine and 3.1% for the 6MW turbine. It is concluded that use of the generic data is well justified and provides a more realistic view of noavoidance collision risk than use of the basic model which assumes no variation of bird density with height.
ANNEX : CALCULATING A MEAN ROTOR SPEED A1. This annex describes how to calculate a mean rotor speed. To do this one needs: the expected wind speed frequency distribution for the site the cut in and cut out wind speeds for the turbine the rotor speed range for the turbine the rated wind speed s for thee turbine, ie the minimumm wind speed at which full power is generated A2. The expected distribution of wind speeds is based on wind data collected from the site over two years. Graph 1 below shows the smoothed frequency wind distribution 2 for the site in question. Graph 1: Site wind speed distribution A3. Modern offshore turbines usually operate with a range of operating rotor speeds, between cutis in, at the lowest wind speed enabling operation, and maximum operating speed, which achieved when wind speed first enabless full power to be generated. At increasing wind speeds above this operating wind speed, s rotor speed is maintained at this maximum, until at a high wind speed the turbine is shut down forr protection, at a cut outt speed which is usually around 25m/sec or 30m/sec. Between minimum and maximum rotor speeds, for simplicity it iss assumed that rotor speed increases linearly with wind speed. Graph G 2 indicates schematically how rotor speed varies with wind speed. 2 To smooth out the variability in the observed data, the observed data has been fitted by a Weibull probability distribution, which is controlled by a shape factor k (equal to or close to 2.0) and a scale e factor λ (proportional to overall wind speeds). A Weibull distribution function is available within Excel. E
Graph 2: Rotor speed as a function of wind speed Rotor speed max min Wind speed cut in operating cut out A4. These two sets of data wind speed frequency and rotor speed as a function of wind speed must be brought together to calculate a mean rotor speed. Graph 3 shows both the site wind speed distribution, and also the rotor speed (axis at right) as a function of wind speed for each of the two selected turbine options. A5. If a turbine has rotor speed Ω(w) at wind speed w, and wind speed w occurs with frequency f(w), then the mean rotor speed is Sum of (frequency x rotor speed) Sum of (frequency) where the sums are over all wind speeds between cut in and cut out. cut out cut out ie Σ Ω(w) f(w) / Σ f(w) cut in cut in The denominator here is just the proportion of time for which the wind speed is in operational range. A6. For the purpose of collision risk analysis it is sufficient to do this calculation by scaling off a graph like Graph 3, taking values for each frequency range of width 1 m/sec (eg from 7.5 m/sec to 8.5 m/sec). The accuracy of a graphical method is quite adequate within the context of the various other uncertainties in the calculation. If desired, a more refined calculation may be done using a spreadsheet, using an interpolation formula to evaluate the rotor speed at any given wind speed. A spreadsheet also facilitates comparison of a range of turbine options.
Graph 3: Bringing together wind frequency distribution and rotor speed data to calculate a mean rotor speed Table 13: Calculation of mean rotor speed for 6MW turbine The wind speed frequency and rotor r speed are read off from Graph 3. Proportion of time wind speed iss in operational range 3 30m/sec = 89.9% Mean rotor speed = 8.351 / 0. 899 = 9.3 rpm Wind speed w Wind speed frequency f(w) Rotor speed Ω (w) 0 1 1 2 0.011 0.035 Below cut in 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 24 24 25 25 26 26 27 27 28 28 29 29 30 >30 Sum Σ f(w) 0.054 0.070 0.083 0.089 0.092 0.090 0.084 0.077 0.068 0.057 0.048 0.038 0.029 0.022 0.016 0.012 0.008 0.005 0.004 0.003 0.002 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.899 7.1 7.5 7.9 8.3 8.8 9.2 9.6 10.0 10.4 10.8 11.3 11.7 Above cut out Sum Σ Ω (w) f(w) Mean operational rotor speed Σ Ω (w) f(w) / Σ f(w) Product Ω (w) f(w) 0.497 0.617 0.709 0.768 0.792 0.782 0.742 0.679 0.601 0.515 0.428 0.345 0.264 0.194 0.139 0.097 0.066 0.044 0.028 0.018 0.011 0.007 0.004 0.002 0.001 0.001 0.000 8.351 9.3 rpm
REFERENCES i Using a collision risk model to assess bird collision risks for offshore windfarms. Bill Band on behalf of The Crown Estate (2011). SOSS Website http://www.bto.org/science/wetland and marine/soss/projects, see SOSS 02. ii A S C P Cook, L J Wright, N H K Burton. A review of flight heights and avoidance rates of birds in relation to offshore windfarms. BTO on behalf of the Crown Estate (2012). SOSS Website http://www.bto.org/science/wetland and marine/soss/projects, see SOSS 02. iii Garthe, S. and Hüppop, O. (2004). Scaling possible adverse effects of marine wind farms on seabirds: developing and applying a vulnerability index. J. Appl. Ecol. 41: 724 734 iv Hamer, K.C., Humphreys, E.M., Magalhaes, M.C., Garthe, S., Hennicke, G., Peters, G., Gremillet, D. & Wanless, S. (2009). Fine scale foraging behaviour of a medium ranging marine predator. Journal of Animal Ecology 78: 880 889. v Pennycuick 1987: http://jeb.biologists.org/content/128/1/335.full.pdf vi BTO Bird Facts: northern gannet. http://blx1.bto.org/birdfacts/results/bob710.htm.