Publication: Magyar Közlöny
Issue: MK-2009-104 (Year: 2009, Number: 104)
Era: 2004-2010
Section: 
Paragraph Index: 2428

b) and in the horizontal plane: 1) an hmd; 2) an approach angle; 3) a speed for each aircraft at closest approach; 4) a decision for each aircraft whether or not it turns; 5) the turn extent; the bank angle; and the turn end time; 6) a decision for each aircraft whether or not its speed changes; and 7) the magnitude of the speed change. Note.— It is possible for the selections made for the various characteristics of an encounter to be irreconcilable. When this occurs, the problem can be resolved by discarding either the selection for a particular characteristic or the whole encounter, as most appropriate. Chapter 4 Annex 10 — Aeronautical Telecommunications 4-35 22/11/07 4.4.2.6.1.3 Two models shall be used for the statistical distribution of hmd (4.4.2.6.4.1). For calculations of the effect of ACAS on the risk of collision (4.4.3), hmd shall be constrained to be less than 500 ft. For calculations of the compatibility of ACAS with ATM (4.4.4), hmd shall be selected from a larger range of values (4.4.2.6.4.1.2). Note.— 4.4.2.6.2 and 4.4.2.6.3 specify vertical characteristics for the aircraft trajectories in the standard encounter model that depend on whether the hmd is constrained to be small (“for calculating risk ratio”) or can take larger values (“for ATM compatibility”). Otherwise, the characteristics of the encounters in the vertical and horizontal planes are independent. 4.4.2.6.2 ENCOUNTER CLASSES AND WEIGHTS 4.4.2.6.2.1 Aircraft address. Each aircraft shall be equally likely to have the higher aircraft address. 4.4.2.6.2.2 Altitude layers. The relative weights of the altitude layers shall be as follows: Layer prob(layer) 0.13 0.25 0.32 0.22 0.07 0.01 4.4.2.6.2.3 Encounter classes 4.4.2.6.2.3.1 The encounters shall be classified according to whether the aircraft are level (L) or transitioning (T) at the beginning (before tca) and end (after tca) of the encounter window and whether or not the encounter is crossing, as follows: Aircraft No. 1 Aircraft No. 2 Class before tca after tca before tca after tca Crossing L L T T yes L L L T yes L L T L yes T T T T yes L T T T yes T T T L yes L T L T yes L T T L yes T L T L yes L L L L no L L T T no L L L T no L L T L no T T T T no L T T T no T T T L no L T L T no L T T L no T L T L no Annex 10 — Aeronautical Telecommunications Volume IV 22/11/07 4-36 4.4.2.6.2.3.2 The relative weights of the encounter classes shall depend on layer as follows: for calculating risk ratio for ATM compatibility Class Layers 1-3 Layers 4-6 Layers 1-3 Layers 4-6 0.00502 0.00319 0.06789 0.07802 0.00030 0.00018 0.00408 0.00440 0.00049 0.00009 0.00664 0.00220 0.00355 0.0027 0.04798 0.06593 0.00059 0.00022 0.00791 0.00549 0.00074 0.00018 0.00995 0.00440 0.00002 0.00003 0.00026 0.00082 0.00006 0.00003 0.00077 0.00082 0.00006 0.00003 0.00077 0.00082 0.36846 0.10693 0.31801 0.09011 0.26939 0.41990 0.23252 0.35386 0.06476 0.02217 0.05590 0.01868 0.07127 0.22038 0.06151 0.18571 0.13219 0.08476 0.11409 0.07143 0.02750 0.02869 0.02374 0.02418 0.03578 0.06781 0.03088 0.05714 0.00296 0.00098 0.00255 0.00082 0.00503 0.00522 0.00434 0.00440 0.01183 0.03651 0.01021 0.03077 4.4.2.6.2.4 vmd bins 4.4.2.6.2.4.1 The vmd of each encounter shall be taken from one of ten vmd bins for the non-crossing encounter classes, and from one of nine or ten vmd bins for the crossing encounter classes. Each vmd bin shall have an extent of 100 ft for calculating risk ratio, or an extent of 200 ft for calculating compatibility with ATM. The maximum vmd shall be 1 000 ft for calculating risk ratio, and 2 000 ft otherwise. 4.4.2.6.2.4.2 For non-crossing encounter classes, the relative weights of the vmd bins shall be as follows: vmd bin for calculating risk ratio for ATM compatibility 0.013 0.128 0.026 0.135 0.035 0.209 0.065 0.171 0.100 0.160 0.161 0.092 0.113 0.043 0.091 0.025 0.104 0.014 0.091 0.009 Note.— The weights for the vmd bins do not sum to 1.0. The weights specified are based on an analysis of encounters captured in ATC ground radar data. The missing proportion reflects the fact that the encounters captured included some with vmd exceeding the maximum vmd in the model. Chapter 4 Annex 10 — Aeronautical Telecommunications 4-37 22/11/07 4.4.2.6.2.4.3 For the crossing classes, the relative weights of the vmd bins shall be as follows: vmd bin for calculating risk ratio for ATM compatibility 0.064 0.026 0.144 0.036 0.224 0.066 0.183 0.102 0.171 0.164 0.098 0.115 0.046 0.093 0.027 0.106 0.015 0.093 0.010 Note.— For the crossing classes, vmd must exceed 100 ft so that the encounter qualifies as a crossing encounter. Thus, for the calculation of risk ratio there is no vmd bin 1, and for calculations of the compatibility with ATM vmd bin 1 is limited to [100 ft, 200 ft]. 4.4.2.6.3 CHARACTERISTICS OF THE AIRCRAFT TRAJECTORIES IN THE VERTICAL PLANE 4.4.2.6.3.1 vmd. The vmd for each encounter shall be selected randomly from a distribution that is uniform in the interval covered by the appropriate vmd bin. 4.4.2.6.3.2 Vertical rate 4.4.2.6.3.2.1 For each aircraft in each encounter, either the vertical rate shall be constant (ż) or the vertical trajectory shall be constructed so that the vertical rate at tca – 35 s is ż1 and the vertical rate at tca + 5 s is ż2. Each vertical rate, ż, ż1or ż2, shall be determined by first selecting randomly an interval within which it lies and then selecting the precise value from a distribution that is uniform over the interval selected. 4.4.2.6.3.2.2 The intervals within which the vertical rates lie shall depend on whether the aircraft is level, i.e. marked “L” in 4.4.2.6.2.3.1, or transitioning, i.e. marked “T” in 4.4.2.6.2.3.1, and shall be as follows: L T [240 ft/min, 400 ft/min] [3200 ft/min, 6000 ft/min] [80 ft/min, 240 ft/min] [400 ft/min, 3200 ft/min] [–80 ft/min, 80 ft/min] [–400 ft/min, 400 ft/min] [–240 ft/min, 80 ft/min] [–3 200 ft/min, 400 ft/min] [–400 ft/min, 240 ft/min] [–6 000 ft/min, 3200 ft/min] 4.4.2.6.3.2.3 For aircraft that are level over the entire encounter window, the vertical rate ż shall be constant. The probabilities for the intervals within which ż lies shall be as follows: ż (ft/min) prob(ż) [240 ft/min, 400 ft/min] 0.0382 [80 ft/min, 240 ft/min] 0.0989 [80 ft/min, 80 ft/min] 0.7040 [–240 ft/min, 80 ft/min] 0.1198 [–400 ft/min, 240 ft/min] 0.0391 Annex 10 — Aeronautical Telecommunications Volume IV 22/11/07 4-38 4.4.2.6.3.2.4 For aircraft that are not level over the entire encounter window, the intervals for ż1 and ż2 shall be determined jointly by random selection using joint probabilities that depend on altitude layer and on whether the aircraft is transitioning at the beginning of the encounter window (Rate-to-Level), at the end of the encounter window (Level-to-Rate) or at both the beginning and the end (Rate-to-Rate). The joint probabilities for the vertical rate intervals shall be as follows: for aircraft with Rate-to-Level trajectories in layers 1 to 3, ż2 interval joint probability of ż1 and ż2 interval [240 ft/min, 400 ft/min] 0.0019 0.0169 0.0131 0.1554 0.0000 [80 ft/min, 240 ft/min] 0.0000 0.0187 0.0019 0.1086 0.0000 [–80 ft/min, 80 ft/min] 0.0037 0.1684 0.0094 0.1124 0.0075 [–240 ft/min, –80 ft/min] 0.0037 0.1461 0.0094 0.0243 0.0037 [–400 ft/min, –240 ft/min] 0.0000 0.1742 0.0094 0.0094 0.0019 –6 000 ft/min –3 200 ft/min –400 ft/min 400 ft/min 3 200 ft/min 6 000 ft/min ż1 for aircraft with Rate-to-Level trajectories in layers 4 to 6, ż2 interval joint probability of ż1 and ż2 interval [240 ft/min, 400 ft/min] 0.0105 0.0035 0.0000 0.1010 0.0105 [80 ft/min, 240 ft/min] 0.0035 0.0418 0.0035 0.1776 0.0279 [–80 ft/min, 80 ft/min] 0.0279 0.1219 0.0000 0.2403 0.0139 [–240 ft/min, –80 ft/min] 0.0035 0.0767 0.0000 0.0488 0.0105 [–400 ft/min, –240 ft/min] 0.0105 0.0453 0.0035 0.0174 0.0000 –6 000 ft/min –3 200 ft/min –400 ft/min 400 ft/min 3 200 ft/min 6 000 ft/min ż1 for aircraft with Level-to-Rate trajectories in layers 1 to 3, ż2 interval joint probability of ż1 and ż2 interval [3 200 ft/min, 6000 ft/min] 0.0000 0.0000 0.0000 0.0000 0.0000 [400 ft/min, 3200 ft/min] 0.0074 0.0273 0.0645 0.0720 0.1538 [–400 ft/min, 400 ft/min] 0.0000 0.0000 0.0000 0.0000 0.0000 [–3 200 ft/min, –400 ft/min] 0.2978 0.2084 0.1365 0.0273 0.005 [–6 000ft/min, –3 200ft/min] 0.0000 0.0000 0.0000 0.0000 0.0000 –400 ft/min –240 ft/min –80 ft/min 80 ft/min 240 ft/min 400 ft/min ż1 for aircraft with Level-to-Rate trajectories in layers 4 to 6, ż2 interval joint probability of ż1 and ż2 interval [3 200 ft/min, 6 000 ft/min] 0.0000 0.0000 0.0000 0.0000 0.0192 [400 ft/min, 3 200 ft/min] 0.0000 0.0000 0.0962 0.0577 0.1154 [–400 ft/min, 400 ft/min] 0.0000 0.0000 0.0000 0.0000 0.0000 [–3 200 ft/min, –400 ft/min] 0.1346 0.2692 0.2308 0.0577 0.0192 [–6 000 ft/min, –3 200 ft/min] 0.0000 0.0000 0.0000 0.0000 0.0000 –400 ft/min –240 ft/min –80 ft/min 80 ft/min 240 ft/min 400 ft/min ż1 Chapter 4 Annex 10 — Aeronautical Telecommunications 4-39 22/11/07 for aircraft with Rate-to-Rate trajectories in layers 1 to 3, ż2 interval joint probability of ż1 and ż2 interval [3 200 ft/min, 6 000 ft/ min] 0.0000 0.0000 0.0007 0.0095 0.0018 [400 ft/min, 3 200 ft/min] 0.0000 0.0018 0.0249 0.2882 0.0066 [–400 ft/min, 400 ft/min] 0.0000 0.0000 0.0000 0.0000 0.0000 [–3 200 ft/min, –400 ft/min] 0.0048 0.5970 0.0600 0.0029 0.0011 [–6 000 ft/min, –3 200 ft/min] 0.0000 0.0007 0.0000 0.0000 0.0000 –6 000 ft/min –3 200 ft/min –400 ft/min 400 ft/min 3 200 ft/min 6 000 ft/min ż1 for aircraft with Rate-to-Rate trajectories in layers 4 to 6, ż2 interval joint probability of ż1 and ż2 interval [3 200 ft/min, 6 000 ft/ min] 0.0014 0.0000 0.0028 0.0110 0.0069 [400 ft/min, 3 200 ft/min] 0.0028 0.0028 0.0179 0.4889 0.0523 [–400 ft/min, 400 ft/min] 0.0000 0.0000 0.0000 0.0000 [–3 200 ft/min, –400 ft/min] 0.0317 0.3029 0.0262 0.0152 0.0028 [–6 000 ft/min, –3 200 ft/min] 0.0110 0.0220 0.0014 0.0000 –6 000 ft/min –3 200 ft/min –400 ft/min 400 ft/min 3 200 ft/min 6 000 ft/min ż1 4.4.2.6.3.2.5 For a Rate-to-Rate track, if line |ż2 – ż1| < 566 ft/min then the track shall be constructed with a constant rate equal to ż1. 4.4.2.6.3.3 Vertical acceleration 4.4.2.6.3.3.1 Subject to 4.4.2.6.3.2.5, for aircraft that are not level over the entire encounter window, the rate shall be constant and equal to ż1 over at least the interval [tca – 40 s, tca – 35 s] at the beginning of the encounter window, and shall be constant and equal to ż2 over at least the interval [tca + 5 s, tca + 10 s] at the end of the encounter window. The vertical acceleration shall be constant in the intervening period. 4.4.2.6.3.3.2 The vertical acceleration ( z ) shall be modelled as follows: z = (Aż2 – ż1) + ε where the parameter A is case-dependent as follows: A(s–1) Case Layers 1-3 Layers 4-6 Rate-to-Level 0.071 0.059 Level-to-Rate 0.089 0.075 Rate-to-Rate 0.083 0.072 Annex 10 — Aeronautical Telecommunications Volume IV 22/11/07 4-40 and the error ε is selected randomly using the following probability density: ( ) exp p ε ⎛ ⎞ ε = − ⎜ ⎟ μ μ ⎝ ⎠ where μ = 0.3 ft s-2. Note.— The sign of the acceleration z is determined by ż1 and ż2 . An error ε that reverses this sign must be rejected and the error reselected. 4.4.2.6.3.4 Acceleration start time. The acceleration start time shall be distributed uniformly in the time interval [tca – 35 s, tca – 5 s] and shall be such that ż2 is achieved no later than tca + 5 s. 4.4.2.6.4 CHARACTERISTICS OF THE AIRCRAFT TRAJECTORIES IN THE HORIZONTAL PLANE 4.4.2.6.4.1 Horizontal miss distance 4.4.2.6.4.1.1 For calculations of the effect of ACAS on the risk of collision (4.4.3), hmd shall be uniformly distributed in the range [0, 500 ft]. 4.4.2.6.4.1.2 For calculations concerning the compatibility of ACAS with ATM (4.4.4), hmd shall be distributed so that the values of hmd have the following cumulative probabilities: cumulative probability cumulative probability hmd (ft) Layers 1-3 Layers 4-6 hmd (ft) Layers 1-3 Layers 4-6 0.000 0.000 0.999 0.868 0.152 0.125 1.000 0.897 0.306 0.195 0.916 0.482 0.260 0.927 0.631 0.322 0.939 0.754 0.398 0.946 0.859 0.469 0.952 0.919 0.558 0.965 0.954 0.624 0.983 0.972 0.692 0.993 0.982 0.753 0.996 0.993 0.801 0.999 0.998 0.821 1.000 0.999 0.848 4.4.2.6.4.2 Approach angle. The cumulative distribution for the horizontal approach angle shall be as follows: approach cumulative probability approach cumulative probability angle (deg.) Layers 1-3 Layers 4-6 angle (deg.) Layers 1-3 Layers 4-6 0.00 0.00 0.38 0.28 0.14 0.05 0.43 0.31 0.17 0.06 0.49 0.35 0.18 0.08 0.55 0.43 0.19 0.08 0.62 0.50 0.21 0.10 0.71 0.59 Chapter 4 Annex 10 — Aeronautical Telecommunications 4-41 22/11/07 approach cumulative probability approach cumulative probability angle (deg.) Layers 1-3 Layers 4-6 angle (deg.) Layers 1-3 Layers 4-6 0.23 0.13 0.79 0.66 0.25 0.14 0.88 0.79 0.28 0.19 1.00 1.00 0.32 0.22 4.4.2.6.4.3 Aircraft speed. The cumulative distribution for each aircraft’s horizontal ground speed at closest approach shall be as follows: ground cumulative probability ground cumulative probability speed (kt) Layers 1-3 Layers 4-6 speed (kt) Layers 1-3 Layers 4-6 0.000 0.977 0.528 0.005 0.988 0.602 0.024 0.000 0.997 0.692 0.139 0.005 0.998 0.813 0.314 0.034 0.999 0.883 0.486 0.064 1.000 0.940 0.616 0.116 0.972 0.700 0.171 0.987 0.758 0.211 0.993 0.821 0.294 0.998 0.895 0.361 0.999 0.949 0.427 1.000 4.4.2.6.4.4 Horizontal manoeuvre probabilities. For each aircraft in each encounter, the probability of a turn, the probability of a speed change given a turn, and the probability of a speed change given no turn shall be as follows: Layer Prob(turn) Prob(speed change) given a turn Prob(speed change) given no turn 0.31 0.20 0.5 0.29 0.20 0.25 0.22 0.10 0.15 4, 5, 6 0.16 0.05 0.10 4.4.2.6.4.4.1 Given a speed change, the probability of a speed increase shall be 0.5 and the probability of a speed decrease shall be 0.5. 4.4.2.6.4.5 Turn extent. The cumulative distribution for the extent of any turn shall be as follows: cumulative probability Turn extent (deg.) Layers 1-3 Layers 4-6 0.00 0.00 0.43 0.58 0.75 0.90 0.88 0.97 0.95 0.99 0.98 1.00 0.99 1.00 Annex 10 — Aeronautical Telecommunications Volume IV 22/11/07 4-42 4.4.2.6.4.5.1 The direction of the turn shall be random, with the probability of a left turn being 0.5 and the probability of a right turn being 0.5. 4.4.2.6.4.6 Bank angle. An aircraft’s bank angle during a turn shall not be less than 15 degrees. The probability that it equals 15 degrees shall be 0.79 in layers 1-3 and 0.54 in layers 4-5. The cumulative distribution for larger bank angles shall be as follows: cumulative probability Bank angle (deg.) Layers 1-3 Layers 4-6 0.79 0.54 0.96 0.82 0.99 0.98 1.00 1.00 4.4.2.6.4.7 Turn end time. The cumulative distribution for each aircraft’s turn end time shall be as follows: cumulative probability Turn end time (seconds before tca) Layers 1-3 Layers 4-6 0.42 0.28 0.64 0.65 0.77 0.76 0.86 0.85 0.92 0.94 0.98 0.99 1.00 1.00 4.4.2.6.4.8 Speed change. A constant acceleration or deceleration shall be randomly selected for each aircraft performing a speed change in a given encounter, and shall be applied for the duration of the encounter. Accelerations shall be uniformly distributed between 2 kt/s and 6 kt/s. Decelerations shall be uniformly distributed between 1 kt/s and 3 kt/s. 4.4.2.7 ACAS EQUIPAGE OF THE INTRUDER The performance requirements specified in 4.4.3 and 4.4.4 each apply to three distinct situations in which the following conditions concerning the intruder’s ACAS and trajectory shall apply:

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