EDDF-1 data have been analysed by Deutsches Zentrum für Luft- und Raumfahrt (DLR) to study wake vortex transport out of ground effect (approach 1), while the EDDF-2 database where the majority of the vortices developed in ground proximity has been analysed by Université catholique de Louvain (UCL, approach 2) and Deutsche Flugsicherung (DFS, approach 3). Different assumptions regarding level of probability, corridor size and crosswind computation are used by these approaches when analysing the data. However, the different analyses for similar assumptions were also compared. Crosswind data from different instrumentation and different height ranges are employed. However, the paper focuses on wind data measured at 10 m height as this altitude is used by default for airport operations. The different approaches will now be described in detail.
3.1. Approach 1: computation based on sonic anemo-meter wind measurements using the EDDF-1 database
During 7 days of Lidar measurements 147 departures of heavy aircraft have been measured. The measurements confirm that vortex behaviour and displacement strongly depend on meteorological conditions. A distinct correlation of crosswinds with horizontal displacement of the vortices was observed. The period in which the vortices could be observed was limited during the measuring days in January because the vortices were displaced out of the measurement range by the strong crosswind before they dissipated. As expected, all of the vortex pairs are descending with time.
First, the distance that wake vortices have to be displaced laterally to clear the area of concern was determined. In contrast to the approach phase where the adherence to the Instrument Landing System (ILS) limits aircraft deviations a definition of a safety corridor for departing aircraft is more arbitrary. This is due to the different rotation points and varying climb rates of the various aircraft types.
Besides the definition of a corridor half width of 100 m, which allows for the comparison to the other approaches in Sections 3.2 and 3.3 a corridor width from the distribution of lateral aircraft positions within the Lidar observation plane is estimated. Only for this purpose and to avoid artificial increase of the flight corridor caused by vortex drift the initial (y, z)-positions (with y perpendicular to the runway and z being the vertical axis) of the wake vortices were extrapolated to the time of vortex generation and the resulting distributions were fitted by Gaussian distributions. The required clearance distance is then calculated as the sum of the mean vortex spacing (b0 = 50.6 m) plus two times the 2σ-value (95%) of the estimated distribution of lateral aircraft positions (Δac = 49.0 m). The resulting corridor half width:
amounts to roughly 75 m. The first line of Table I summarizes the required drift velocities needed to clear the flight corridor for different aircraft separation times by using with tsep being the aircraft separation time. Additional safety distances between vortex centre and follower aircraft (Schwarz and Hahn, 2006) are not considered in this study.
Table I. Drift velocities obtained by approach 1 needed to displace the vortices by 150 m for given aircraft separation times
|Clearance time (s)||50||60||90||120|
|vreq (m s−1) for clearance||3.0||2.5||1.67||1.25|
|uc (m s−1)||4.1||3.7||3.1||2.8|
The measured vortex drift velocities show considerable variation due to e.g. effects of turbulence and vortex deformation. The mean observed wake vortex drift speed, vdrift is calculated from the Lidar data through:
where yinitial is the initial vortex position at the first time of detection tinitial, ylast denotes the vortex position at the time of last measurement tlast. The larger the times and distances the more accurate the calculated average vortex drift speed.
A linear approach was used to estimate the crosswind thresholds needed to clear the 2d = 150 m corridor. Only luff vortices are considered since those have to drift a longer distance to leave the corridor. In the coordinate system used (Figure 1) and the take-off direction to be east, the left (right) vortex is the luff vortex if the crosswind is positive (negative).
Figure 3 shows the observed vortex drift velocity of the luff vortices depending on the crosswind measured at 10 m above ground including a linear fit and the respective 95% envelopes. The calculated drift velocity of each measured vortex is represented by a single data point. The linear fit allows deriving a relation between the 10 m crosswind and the resulting mean vortex drift velocity. Based on the lower 95% envelope of the vortex drift velocity vdrift a crosswind threshold uc can be determined which assures the advection of 95% of the vortices out of the flight corridor. The aircraft separation time specifies the required vortex drift velocity, vreq, to clear a certain corridor from wake vortices. The resulting crosswind threshold fit can then be calculated according to:
Figure 3. Drift speed vdrift, required vortex speed, vreq of upwind (luff) vortices (triangles) and crosswind at 10 m height measured by the SONIC. The linear fit is shown by the solid line surrounded by the 95% envelopes (dotted lines). The horizontal and vertical lines explain the use to estimate a crosswind threshold for a 60 s separation (see text)
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The crosswind thresholds needed to clear a corridor with half width of 75 m from wake vortices for different aircraft separation times according to Equation (3) are listed in Table I (second line). In Figure 3 the method is illustrated exemplarily: assuming a separation time of 60 s a required vortex drift speed of 2.5 m s−1 is needed (Table I). Following the horizontal line in Figure 3 to the intersection with the lower boundary of the 95% envelope a crosswind threshold of 3.7 m s−1 needed to clear the flight corridor on a 95% probability is obtained.
The same analysis was done without distinguishing between luff and lee vortices meaning that all vortices were used for the linear fit. The crosswind thresholds obtained were only about 0.1 m s−1 lower which is negligible. This result is not unexpected since the vortices measured within EDDF-1 developed at altitudes where no ground effects were observed that could influence the luff and lee vortices in different ways.
Figure 4 gives a schematic illustration of this approach. The wake vortices shed by the leading aircraft can be found within the grey shaded area with a probability of 95%. This area is advected from the average flight track by the crosswind. The position of the leading aircraft shown is the extreme situation where the luff vortices are generated at the upwind edge of the area of interest. For a given separation time tsep the described approach then results in a crosswind threshold needed for the following aircraft to avoid wake vortex encounters. The described method is in principle applicable to any flight level above b0 since all wake vortices used in the analysis developed out of ground effect. This is the key difference to the other approaches described next.
Figure 4. Schematic illustration of approach 1. The grey shaded area shows the corridor of the leading aircraft which includes the wake vortices with a 95% probability level. Leading and following aircraft with defined separation time tsep, average flight track and direction of crosswind are indicated. The dashed and solid thick lines starting at the wing tips of the leading a/c indicate exemplary positions of the wake vortices
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The probability of not encountering the vortices is actually much higher than 95% because firstly only the missing 2.5% on one side of the symmetric distribution is critical (the 2.5% on the other side correspond to vortices that have moved farthest from the centreline) and secondly, on average, the leading heavy aircraft take off late and climb slowly whereas the following medium weight class aircraft take off early with a steep climb rate. Thereby, the respective flight tracks are well separated. Additionally, wake vortex descent increases the vertical separations between the vortices and the follower aircraft.
3.2. Approach 2: computation based on Lidar wind measurements using the EDDF-2 database
During the 6 months of the EDDF-2 measurement campaign, 10 442 cases of tracked vortices have been collected. Since this database is very large it was first screened using well-defined criteria in order to retain 6950 cases which are considered relevant for further analysis. Cases for which only one of the two vortices was measured were excluded. Cases with a too low or too high initial measured vortex spacing and bank angle were also discarded. Finally, the WindTracer algorithm used to compute the circulation does not calculate circulation values above ∼750 m2 s−1. For larger values the algorithm sets the circulation data to exactly 800 m s−1 (Section 3.3). Since this is an arbitrary limit of the algorithm, those cases were also excluded.
Next, the wake vortex lateral transport has been correlated with the crosswind uc using three different definitions of the crosswind measured by the Lidar:
the crosswind measured at 10 m, uc(h = 10 m);
the averaged crosswind from 0 to 100 m altitude; uc, mean, and;
the crosswind measured at the mean altitude of the measured vortices, uc(hmean).
Figure 5 shows a schematic view of the different crosswind definitions. The present study mainly focuses on the crosswind measured at 10 m with the Lidar. This height has also been used in the two other data analyses approaches described here. It is worth noticing that the Lidar measures the wind exactly within the plane where the measured vortices evolve. It is thus the best measurement of the wind as experienced by the vortices. Consequently, for an anemometer at some further distant location the crosswind will deviate more from the crosswind sensed by the vortices and the resulting crosswind thresholds will be somewhat higher.
Figure 5. Schematic description of the crosswind velocities. The black crosses indicate the port vortex trajectory. The bullets indicate the three crosswind definitions used in approach 2
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For five vortex ages, from 40 to 120 s, and for each individual departure, the net lateral displacement of the vortices, Δy = ylast − yinitial, is correlated to the measured crosswind uc. From the 13 900 measured vortices (6950 vortex pairs), one computes, for each vortex age, the mean correlation coefficient α between displacement and crosswind and the envelopes containing 90, 95, and 99% of the measurements. The linear fit used on the data points for respectively the upwind, the downwind and both vortices, is then given by Equation (4):
Figure 6 presents the correlation between uc(h = 10 m) and Δy of all vortices for a vortex age of 60 s. The mean behaviour and the 95% envelope are also shown. The values of the fit parameters for the different times are provided in Table II. The mean value of α = 1.15 indicates that the lateral transport of the wake vortices (both due to wind and ground effects) is on average 15% higher than the crosswind measured at 10 m height. Without wind the left and right vortices move a finite distance due to ground effect. If left and right vortices are averaged the net displacement is zero.
Figure 6. Evolution of the vortex net lateral displacement as a function of the crosswind uc at 10 m for a time separation of 60 s. The triangles (resp. the dots) show the displacement of the starboard (resp. the port) vortices. A linear fit shows the mean evolution (dashed line). The envelope containing 95% of the total examined vortices is denoted by solid lines. Six thousand and nine hundred and fifty measured vortex pairs are used
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Table II. Averages of α parameter of the linear fit of approach 2, Equation (4), for the different vortex ages
A slow decrease of the α factor with time is observed. This behaviour can be explained by considering three steps. In the first step, the vortices are not IGE yet and sink progressively. Assuming a typical wind profile, the crosswind experienced by the vortices is initially higher than the crosswind at 10 m height and decreases as the vortices sink. The α value decreases thus accordingly. In the second step, the vortices are IGE and interact with the secondary vorticity generated at the ground. With crosswind, the upwind (resp. downwind) vortex travels slower (resp. faster) than the wind. The average displacement speed of the down- and upwind vortices is slightly smaller than the local wind speed. Finally, in the third step, the vortices rebound and move again with the local wind speed. Since the α factor represents an accumulated effect of the wind on the vortex displacement after a certain time, it is to be expected to observe a slow decrease of α until it reaches a plateau.
Moreover, the (90, 95 or 99%) envelope half width, W, is seen to grow linearly in time, at least for the time window of interest. A linear fit is thus also used for W given by Equation (5):
According to this database analysis, after a certain time t, the wake vortices, experiencing a crosswind uc, would have travelled a net lateral distance Δy comprised of the interval:
One can thus compute the crosswind needed for the vortices to travel a certain distance within a certain time when using the prescribed envelopes (respectively 90, 95 and 99%). Alternatively, one can compute, for a given crosswind value, the time needed for the vortices to travel a certain distance.
Likewise, one can compute the crosswind threshold needed for the vortices to be at least at a distance d from the runway centreline after a time tsep. Figure 7 shows a schematic view of the use of such envelopes. In this figure, for graphical purpose, the envelopes are extrapolated for time separations shorter than 40 s. However, the envelopes were built and are used for times between 40 and 120 s. The obtained crosswind thresholds are reported in Table III, for three aircraft separations and three corridor half widths d. Two additional corridor half widths defined by d1 = 0.5*× runway width + wingspan ≈ 100 m and d2 = wingspan ≈ 50 m have been included in Table III. The study has been performed separately considering the wake vortices generated by medium aircraft, by heavy aircraft and by the combination of both. For instance, using the 95% envelope, a crosswind uc(h = 10 m) = 3.5 m s−1 is required for the vortices, generated by heavy aircraft, to be at least at a distance d = 75 m from the runway centreline for an aircraft separation of 60 s.
Figure 7. Schematic illustration of approach 2. The solid envelope contains the port vortices while the dashed envelope contains the starboard vortices. The envelopes have been extended to times below 40 s but, at these times, the results are not used
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Table III. Crosswind uc(h = 10 m) in m s−1 obtained by approach 2 and needed to move the WV generated by medium (top), heavy (middle) and all aircraft (bottom) respectively 50, 75 and 100 m away from the runway centreline when using the 95% probability envelopes
|tsep (s)||50 m||75 m||100 m|
Further, Table III indicates that the crosswind thresholds for the heavy aircraft are consistently higher or at least equal to those of the medium aircraft. This is related to the fact that wake vortices of the heavies were mostly measured IGE. The ground effect tends to reduce the lateral transport of the upwind vortex and to increase the lateral transport of the downwind vortex. In the Lidar scan plane, the vortices, generated by heavy aircraft, were on average lower because those aircraft rotate, on average, later and climb less steep. Moreover, the height at which the ground effect starts to play a role depends on the vortex separation b0. Since the wing span, and thus b0, is higher for heavy aircraft, the vortices shed by those aircraft enter in ground effect at higher altitudes than those generated by medium aircraft. In the database, more vortices generated by heavy aircraft are IGE than those generated by medium aircraft.
Finally, this analysis highlights also the benefits of using a more sophisticated definition of the crosswind than uc(h = 10 m). In that respect, the crosswind averaged over the first 100 m, uc, mean, is of special interest as it is still operationally feasible and can be obtained, for instance, by a Lidar or a SODAR/RASS instrument installed at the airport. Using the 95% envelope, a crosswind uc, mean = 3.9 m s−1 is required for the vortices, generated by heavy aircraft, to be at least at a distance d = 75 m from the runway centreline for an aircraft separation of 60 s. It is important to stress that, due to the wind profile shape, the altitude-averaged wind, uc, mean, is on average 17% higher than the 10 m height crosswind (see scheme in Figure 5). This ratio has been established based on the EDDF-2 measurements and is also verified to be consistent with the typical turbulent wind profile (i.e. using the logarithmic profile which is valid up to 100 m). Thus, an altitude-averaged crosswind uc, mean = 3.9 m s−1 corresponds to a 10 m height crosswind uc(h = 10 m) = 3.3 m s−1. Operationally, for the same wind conditions, the wind threshold to be used will be lower when using a more sophisticated wind measurement since it best represents the wind as experienced by the vortices.
3.3. Approach 3: computation based on WTR/RASS, sonic anemometer and Lidar wind measurements using the EDDF-2 database
Similar to the previous analysis different crosswind definitions are used:
crosswind measured at 10 m height with any of the anemometers displayed in Figure 2;
the crosswind average between 60 and 200 m as determined by WTR/RASS;
the average in-plane wind between 0 and 200 m as measured by the Lidar, and,
the average in-plane wind from the Lidar restricted to the altitude where the vortices evolved.
Recall that the Lidar is scanning in a cross-plane of the runway centreline, thus in-plane wind is almost equal to the crosswind. A small difference arises from the fact that the lidar beam is scanning and generally not measuring parallel to the surface. For the setup used in EDDF-2 and the highest measurement altitude this error is 2% of the crosswind in 200 m above ground disregarding the contribution of vertical wind speeds. This error is neglected as well as the fact that the Lidar measurement involves effectively a weighted average over a distance on the order of the laser pulse length.
The correlation of crosswind with vortex transport is quantified by the following procedure: for any of the vortices the lateral (y-coordinate) position at a given vortex age has been combined with a crosswind for this very event. Hereby, vortices from heavy aircraft and medium aircraft are analysed in separate classes as well as left and right vortices are analysed independently from each other. Vortex ages of 0, 20, 40, 60, 80, 100 and 120 s have been chosen. In that manner 112 different sets of vortex position and crosswind pairs have been obtained.
An example of such sets showing the effect of the different methods to determine crosswind is given in Figure 8. Figure 8 depicts the lateral distributions of the left vortices of heavy aircraft 60 s after generation. It can be seen immediately that the various methods of measuring crosswind do have an impact on the observed distributions of vortex displacement at a given crosswind. Obviously, the best correlation between vortex transport and crosswind is achieved when the wind is measured close to the air mass which actually advects the vortices (filtered in-plane Lidar).
Figure 8. Vortex position versus crosswind contours for different methods to measure crosswind: (a) Crosswind at 10 m, (b) mean crosswind from WTR between 60 and 200 m, (c) averaged in-plane wind between 0 and 200 m measured by the Lidar and (d) filtered in-plane Lidar wind restricted to the altitude where the vortices evolve
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For any of the 112 different sets of crosswind and vortex position pairs some parameters characterizing the distribution have been computed:
the number of cases contributing to the set under consideration;
a least squares straight line has been fitted through the data points; for this line:
–the position offset, i.e. the value of the regression line at zero crosswind, and,
–its slope have been determined;
the correlation coefficient between crosswind and lateral position and
the minimum (maximum) crosswind required to ensure that only a 2.5% fraction (corresponding to roughly the 2σ boundary for a normal distribution) of the leftmost (rightmost) vortices remain within a corridor (d) of 50 or 100 m to either side of the runway centreline.
Before discussing the results for the different methods to measure crosswind in more detail, the working hypotheses are summarized:
there should be a mirror symmetry in the behaviour of left and right vortices;
in this experimental setup, ground effect should have less of an impact on medium aircraft vortices (since they are less frequent and shorter in ground effect) than on heavy aircraft;
ground effect is independent of crosswind and
the slope should equal vortex age; a wind of speed u impacting on the vortices for a time t should transport the vortices the distance u × t; note that ground effect becomes manifest in the slope changing with time ( = vortex age).
Figure 9 shows the characteristic parameters when the surface measurement is used as the characteristic crosswind. In the case of surface wind as a means to determine crosswind, the offset (Figure 9(a)) is not showing the expected symmetry. The slope (Figure 9(b)) is exceeding the vortex age considerably and it is different for heavy and medium aircraft. Correlation (Figure 9(d)) is hardly exceeding 0.8. Note that the percentiles are related to the number of vortices observed at the given age t (Figure 9(c)). Figures 9(e) and (f) show crosswind thresholds with different widths of the corridor. The asymmetry of the offset, which is most pronounced in Figure 9(a) is due to the fact that the crosswind has been measured at different altitude and some distant location from where the vortices evolved. Since the vortices move at altitudes considerably higher than 10 m, where the wind is measured, this asymmetry may also result from the Ekman spiral, i.e. the change of wind direction with altitude in the atmospheric boundary layer. This asymmetry will be different at other airports or runways. In order to simplify the results, crosswind thresholds are symmetrized, i.e. only the maximum of the absolute values of the respective thresholds for left and right vortices are listed in Table IV.
Figure 9. Parameters characterizing the relation between lateral vortex transport and surface crosswind at 10 m height: (a) offset, (b) slope, (c) number, (d) correlation, (e) 2.5% within ± 50 m and (f) 2.5% within ± 100 m. Properties of heavy aircraft vortices' are shown as black lines, those of medium aircraft vortices as grey lines. Right vortices are shown as full lines, left vortices as dashed lines. Heavy aircraft, left vortex , heavy aircraft, right vortex , medium aircraft, left vortex , medium aircraft, right vortex 
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Table IV. Crosswind thresholds for surface wind measurements at 10 m height estimated by approach 3
| ||50 (m)||75 (m)||100 (m)||50 (m)||75 (m)||100 (m)|
Symmetry in the offset, the slope and correlation are improving when crosswinds at higher altitudes are included. Figure 10 shows that these indicators improve even further, when the crosswind as measured by the WindTracer is used and in particular when the crosswind is averaged only in the height band where the vortices have evolved. However, at the present stage these additional crosswind definitions are not used in airport operations.
Figure 10. Parameters characterizing the relation between lateral vortex transport and crosswind measured by Lidar in the altitude range where the vortices evolve: (a) offset, (b) slope, (c) number, (d) correlation, (e) 2.5% within ± 50 m and (f) 2.5% within ± 100 m. Heavy aircraft, left vortex , heavy aircraft, right vortex , medium aircraft, left vortices , right vortices 
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To analyse the asymmetry between the right and left vortex the vortex motion in ground effect is discussed briefly for heavy aircraft. For any two consecutive observations of the same vortex a vortex lateral speed has been computed. The vortex self induced speed is yield after subtraction of the crosswind, here taken from the WindTracer in-plane wind profile. Taking into account the error of the vortex position measurement and considering the potentially amplifying effect of the numerical differentiation involved, a considerable statistical error can be expected.
Again, the technique to superimpose a large number of such data points with relatively large error was employed to obtain an estimate of the average behaviour with much smaller error than the single measurement. The vortices' self-induced speed as a function of altitude in non-dimensional form is shown in Figure 11. These plots represent more than 100 000 data points. Above one wingspan, b, the distributions are symmetric, suggesting that there is no effect of ground vicinity. Below half a wingspan, the ground effect shifts the right vortices' distributions towards positive velocities and likewise the left vortices towards negative velocities. In addition to that the distributions broaden. Thus, the vicinity to the ground may not be the only factor that determines the self-induced velocities of the vortices. Note that in Figure 11 the wake vortices reach very low altitudes above the ground. This may be related, for example, to the oblate shape of the vortices close to ground. The deteriorated circular symmetry increases the error in the computation of the height of the vortex, because the algorithm assumes a circular shape.
Figure 11. Vortex self induced velocities in ground proximity for heavy aircraft as function of non-dimensional altitude after 60 s of generation: (a) left vortex and (b) right vortex
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The distributions of altitudes of EDDF-2 heavy and medium aircraft at the intersection with the Lidar scan plane showed that the majority of heavy aircraft wakes is already generated in or near ground effect. In contrast, vortices of medium aircraft were, on average, generated at higher altitudes. If they reach the ground at all they are exposed to ground effect for shorter time before dissipating.