In order to also investigate a set of realistic wind speeds and directions, automatic airport weather re- ports (METAR) from Munich airport were used as input for the autoland simulations. METARs are generated every 30 minutes (more often if significant changes of the weather conditions occur) and contain information about the mean wind speed and direction. If the difference between the average wind speed and peaks wind speeds in gusts is significant (> 5 kts) gusts are reported additionally. The month of November of the year 2012 was used as input for the simulations that included 1437 weather reports. Turbulence intensity was simulated again by applying the Dryden wind models with 2∙10-1
the probability of exceedance of high altitude intensity if the wind speed was below 10 kts, 10-1 for wind speeds above 10 kts, 10-2 if gusts were reported and remained at or below 20 kts, 10-3 if gusts were reported between 21 and 30 kts and 10-4 for gusts above 30 kts. The maximum tailwind component considered was 4 kts. Otherwise it can be assumed the approach and landing direction would have been changed. In the cases with a larger tailwind the wind direction was changed by 180° which would be equivalent to changing the landing direction on the runway. For each approach a random sample from a uniform distribution for the aircraft mass and location of the center of gravity in the specified ranges were drawn. All parameters are again summarized in Table 4-6.
Aircraft mass Aircraft CG VTAS Initial altitude Wind direction Wind speed Turbulence intensity 50-64.5 t (uniform distr.) 15-45% (uniform distr.) 70 m/s 609.6 m (2000 ft) as described as reported as described
Table 4-6 Parameter set used in autoland simulations to evaluate impact realistic wind scenarios.
Figure 29 shows the obtained touchdown points on the runway. Out of the 1437 simulation runs eight touchdowns occurred at behind the runway (seven of them outside the plot limits) and 14 touchdowns occurred outside the landing box. However, that again is considered to be a weakness of the model and those points would trigger a warning and a go-around of the aircraft in case they happened in reality. Figure 30 shows a QQ-plot (Quantile-Quantile) for the distribution of the touchdown points on the runway. The core of the distribution again appears very close to linear, however, the tails are signifi-
cantly non-linear in this representation hinting at non-Gaussian distributed data. This result is again confirmed by the Anderson-Darling and Kolmogorov-Smirnov test at a 5% significance level.
Figure 29 Touchdown points on runway and in relation to the touchdown box for recorded winds from Munich Airport in November 2012 with uniform distributed landing weight and center of gravity location between their respective maximum and minimum values.
Figure 30 Quantile-quantile plot for simulated touchdown points (recorded winds from Munich Airport in No- vember 2012 with uniform distributed landing weight and center of gravity location between their respective maximum and minimum values) with Gaussian fit for data between the 25th and 75th percentile.
The non-Gaussian distribution of the touchdown points requires again either a Gaussian overbound or the fit of a Johnson distribution to the obtained results. Both methods were applied and the results are shown in Figure 31. The Johnson SU curve with moments fitting method (
0.1987, 1.5788, 351.6510, 130.5373
γ = − δ = ξ = λ= ) again provides a better fit to the experimental data than the Gaussian overbound (µ =364.53 , 147.22m σFTE overb, . = m). Especially for the land-short case the
overbound results in a significant over-estimation of the risk of landing outside the touchdown box. On the land-long side both methods yield similar results for estimating the risk of landing long, how- ever, the Johnson curve is more shape-preserving that the Gaussian model.
10.545 10.55 10.555 10.56 10.565 10.57 10.575 Longitude [°] 52.317 52.318 52.319 52.32 52.321 52.322 Latitude [°] -4 -3 -2 -1 0 1 2 3 4
Standard Normal Quantiles 100 200 300 400 500 600 700 800 900 Input Sample [m]
Simulated touchdown points Gaussian fit to core of distribution
Figure 31 Simulated touchdown points with recorded winds from Munich airport modelled by inflated Johnson curve and Gaussian overbound.
In summary of the discussion of the wind and turbulence influence, it was shown that wind and turbu- lence intensity have a significant impact on the touchdown point of the aircraft. With a certain prevail- ing steady wind direction and wind speed the nominal touchdown point varies substantially. For the given aircraft and autopilot model the variation of the touchdown point for a headwind and a tailwind scenario with a steady wind of 5 m/s were in the range of about 200 m. Considering also turbulence in addition to the steady wind causes the touchdown points to vary additionally about the respective nominal touchdown points. In the requirement derivation process this variation is described as stand- ard deviation of a Gaussian distribution. It was, however, found that only the core of the resulting dis- tribution of the touchdown points was close to Gaussian while for the tails the Gaussian distribution was not a good fit (visible in the QQ plots). Thus, an overbound was determined in order to not under- estimate the tail probability that is of special interest in this kind of integrity evaluations. Furthermore, it was also found that the touchdown points are more spread out for the land long case than for the land short case (floating of the aircraft in the ground effect) and the overbound of σFTE is thus usually driven by the land-long case. For all cases it is challenging to define an NTDP. While based on simula- tions an NTDP can be found by not simulating any wind influence, this may not in general be a good and valid assumption for a specific approach with a steady wind component.
Finally, modelling the touchdown errors by a Johnson distribution yielded significantly better results in terms of goodness of fit. The shape of the distribution was matching the shape of the actual distribu- tion better than a Gaussian distribution. It is therefore preferable to use a Johnson distribution to model the touchdown performance.
100 200 300 400 500 600 700 800 900
Standard Normal Quantiles 10-4
10-3 10-2 10-1 100
Quantiles of Input Sample
CDF of sample 1-CDF of sample CDF of fitted Johnson dist. 1-CDF of fitted Johnson dist. CDF of Gaussian overbound 1-CDF of Gaussian overbound