AC 20-191

AC 20-191 Appendix B Figure B-1 Headwind-Tailwind Probability of Exceedance, %

99.99 99.9 99 90 80 70 60 50 40 30 20 0.01 30 TAILWIND SPEED .KT (WIND FROM 180 DEG) 10 HEADWIND SPEED .KT (WIND FROM O DEG) -300.01 0.1 10 20 30 40 50 60 70 80 90 99 99.9 99.99 Probability of not Exceeding, %

HEADWIND-TAILWIND DESCRIPTION B-4

AC 20-191 Appendix B Figure B-2 Crosswind CROSSWIND SPEED.KT COUNTERCLOCKWISE FROM 0 DEG 99.99 99.9 99 90 Probability of Exceedance, % 80 70 60 50 40 30 10 0.1 0.01 30

0.1 20 30 40 50 60 70 80 99 99.9 99.99 _ Probability of Exceedance, %

CROSSWIND DESCRIPTION B-5

AC 20-191 Appendix B Figure B-3 Annual Percent Probability of Mean Wind Speed Equaling or Exceeding Given Values PERCENT PROBABILITY OF EXCEEDANCE 20

0.2

o. O 5 10 15 20 25 30 35 40 Wind Speed Tw kt

ANNUAL PERCENT PROBABILITY OF MEAN WIND SPEED

EQUALING OR EXCEEDING GIVEN VALUES 9-&

AC 20-191 Appendix B Figure B-4 Wind Direction Relative to Runway Heading Wind Direc tion Histog ra m Wind Direction Rela tive to Runwa y Hea ding P e r c e n t 0 2 4 6 8 10 12 180190200210220230240250260270280290300310320330340350 0 10 20 30 40 50 60 70 80 90 100110120130140150160170180

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Wind fr om the L eft Wind from the R ight B-7

AC 20-191 Appendix B Figure B-5 Selected Description for Variances of Horizontal Turbulence Components.

— f[0.177+0.823hh ¡] ‡ h≤h¡

1.0 mani

1.2

1.0

0.8 h/h j 0.6

0.2

1.0 1.2 1.6 2.0 B-8

AC 20-191 Appendix B Figure B-6 Selected Integral Scale Description.

Lw =1 d,h = hi h,h<hi LWoU h h < hj Lu ={ Ow I 10.177 + 0.823 h/t ] 1.2 d nzhi Ly=Lu hj= Altitude above which turbulence is isotropic

1.2 Г

1.0

0.8 h/h¡

0.6

0.4 L=L

0.2

0.2 0.4 0.6 0.8 1.0 Lw/h¡›Lu/h¡= Lv/h¡

SELECTED INTEGRAL SCALE DESCRIPTION В-9

AC 20-191 Appendix B B.3 Wind Model C.

This wind model is a harmonized derivative of Wind Model A incorporating the changes defined in JAA paper AWOG 904a. The changes are a result of experience from pilot-in-the-loop simulator tests for Category III HUD certification, where the wind shear and turbulence intensities defined in JAA paper AWOG 904a were found to be more representative of nominal wind conditions for Category III approaches and compatible with motion-based, pilot-in-the-loop simulators. Wind Model C is therefore more appropriate for use in Category III HUD certification programs; however, this does not preclude its use for other types of landing system.Wind Shear (Vwref).

B.3.2 The Model A equation for the Wind Shear component:

 h+ 0.15V = 0.20407 V ln wref 20  0.15  is replaced for Wind Model C with:

 h+ 0.046Vwref = 0.165 V20 ln  0.046  B.3.3 Root-Mean-Square (RMS) Turbulence Scale (σw).

The Model A equation for the RMS Turbulence Scale: σw = 0.1061V20 (ft/sec) is replaced for Wind Model C with: σw = 0.0625V20 (ft/sec) B.3.4 Turbulence Scale Factor (Lu).

The Model A establishes three values for Turbulence Scale Factor Lu depending on the altitude h, but for Model C, Lu = 600 feet, for all values of h B.4 Wind Model B.

B.4.1 Mean Wind.

It may be assumed that the cumulative probability of reported mean wind speed at landing and the crosswind component of that wind are as shown in Figure B-7.

Normally, the mean wind that is reported to the pilot is measured at a height that may be between 20 ft.(6m) and 33 ft. (10m) above the runway. The models of wind shear and turbulence given in the following paragraphs assume this reference height.

B.4.2 Wind Shear.

Wind shear should be included in each simulated approach and landing unless its effect can be accounted for separately. The magnitude of the shear should be defined by the expression:

u = 0.43 U log10 (z) + 0.57 U, for z ≥ 0.05 m u≅ 0, for z < 0.05m where z is the height in meters u is the mean wind speed at height z (meters) B-10

AC 20-191 Appendix B U is the mean wind speed at 10m (33 ft.).

B.4.3 Abnormal Wind Shear.

The effect of wind shears exceeding those described above should be investigated using known severe wind shear data.

B.4.4 Turbulence.

B.4.4.1. Horizontal Component of Turbulence.

It may be assumed that the longitudinal component (in the direction of mean wind) and lateral component of turbulence may each be represented by a Gaussian process having a spectrum of the form:

( ) 2σ2 LΦ Ω = •π 1+Ω 2 L2 where Φ(Ω) = a spectral density in (meters/sec)2 per (radian/meter).

σ = root mean square (rms) turbulence intensity = 0.15 U L = scale length = 183m (600 ft.)

Ω = spatial frequency in radians/meter.

B.4.4.2. Vertical Component of Turbulence.

It may be assumed that the vertical component of turbulence has a spectrum of the form defined by the equation above for the horizontal component with the following values:

σ = 1.5 knots with L = 9.2m (30 ft.), or alternatively σ = 0.09 U with L = 4.6m (15 ft.) when z < 9.2m (30 ft.), and L = 0.5 z when 9.2 < z < 305m (30 < z < 1000 ft.)

B-11

AC 20-191 Appendix B Figure B-7 Cumulative probability of reported Mean Wind, and Head Wind, Tail Wind Cross Wind Components when landing.

403020100 Total Wind Head Wind ComponentCross Wind Component Tail Wind Component

WIND SPEED KNOTS Cumulative probability of reported Mean Wind, and Head Wind, Tail Wind Cross Wind Components, when landing.

P R O B A B I L I T Y O F E X C E E D I N G G I V E N W I N D S P E E D

0.01

0.05

0.1

0.2

0.5 1 2 8 10 20 30 40 50 60 70 80 90 95 98 99

99.8

99.9

99.99 NOTE: This data is based on world wide in-service operations of UK airlines (sample size about 2000) B-12

AC 20-191 Appendix B B.5 Acronyms and Definitions for the Wind Models.

h Height AGL in ft.

Lu Turbulence scale factor RMS Root Mean Square VT Aircraft speed in ft/sec.

Vwref Mean wind speed measured at h ft V20 Mean Wind speed measured at 20 ft. AGL w Temporal frequency in radians/sec, σw RMS turbulence scale in knots W Spatial frequency in radians/ft.

Φw(Ω) Spectral density of the vertical component of turbulence in (ft/sec)2 B-13

AC 20-191 Appendix C APPENDIX C. GBAS PERFORMANCE MODEL FOR APPROACH AND LANDING

SIMULATION C.1 GBAS Performance Analysis.

In carrying out the performance analysis the following model of GBAS Performance may be used. The GBAS Performance Model simulates the outputs of a fault-free GBAS airborne receiver when used in conjunction with a GBAS ground station categorized as either Facility Approach Service Type (FAST) C or FAST D.

C.1.1 GBAS Performance Model.

C.1.1.1. The architecture of the GLS Model is illustrated in Figure C-1. The GLS Model includes a Navigation System Error (NSE) Generator which generates NSE representative of a GBAS providing approach service type C or D as defined by the requirements [1, 2, 3]. The Position Calculator adds NSE to the true position of the GLS Reference Point (GRP). The deviation calculator computes the deviations of the GRP given the Final Approach Segment (FAS) data. A latency model is applied to each output of the GLS Model.

C.1.1.2. Development of all components of the GLS Model is documented in [4,5] and [6]. The NSE Generator and NSE Step Generator are discussed below.

C.1.2 GBAS NSE Generator.

The GBAS NSE Generator produces NSEs in the along-track, cross-track and vertical directions in meters. The block diagram of the GBAS NSE Generator is shown in Figure C-2. The Gaussian White Noise (GWN) Generator produces three independent noise sequences with zero mean and unity variance. Each sequence is filtered by a second-order Butterworth filter. The compensation gain which brings the RMS of the filtered noise back to unity is obtained as:

2 2Gx = ∆Tωn [1] The filter output is scaled by NSE scale factors Katrk, Kxtrk, and Kvert. At the beginning of each run, the NSE generator filter must be initialized at a value sampled from a Gaussian distribution consistent with these scale factors.

C-1

AC 20-191 Appendix C Figure C-1 GBAS Signal Model NSE Generator GRP Position Calc Deviation Calc Deviations GRP Pos (LLH) GRP

P (ECEF) True Ant Pos FAS Data, GERP Flag, Dev Scale Flags FAS Attitudes, Body Rates, GRP Offset, Offset Flag GAST Seed & ∆ T NSE Horiz Dist to LTP Latency Latency Latency Figure C-2 GLS NSE Generator Σ Σ Σ GAST Limit Case Fault Mode Generator Step Event Time Malfunction Event Time Model Type (nominal vs.

Limit Geometry) Compensation Gain Compensation Gain Compensation Gain 2nd Order Filter 2nd Order Filter 2nd Order Filter GWN Generator

Seq1 Seq2 Seq3 Seed , ∆ T K Value Selector X X X σ =1 σ =1 σ =1 NSE atrk NSE xtrk NSE vert

K atrk K xtrk K vert Step Function Generator Σ Σ Σ C-2