1. The Analytic Blunder Risk Model (ABRM) A computer model for predicting collision risk Kenneth Geisinger Operations Research Analyst Federal Aviation Administration (retired)

2. aircraft collisions Historically relatively rare About 10 midair collisions per year One involving an air carrier in about 10 years But increasingly likely Doubling traffic increases risk by a factor of four Risky situations are increasing 10 to 25 percent per year

3. Examples of Blunders Operational error Controller mistakenly puts aircraft on conflicting courses Controller fails to take timely intervention Pilot deviation Pilot disobeys controller instructions Pilot breaks air traffic regulations Equipment failure Radio communication blocked or garbled Aircraft mechanical failure Runway incursion Aircraft or vehicle crosses active runway without clearance.

4. Purpose of the ABRM The ABRM computes the risk of a specific blunder resulting in a collision. It considers “what-ifs”, such as: What if one the two aircraft had been at a slightly different location or on a slightly different heading when the blunder occurred? What if the controller had been slightly slower in responding? What if communication had been blocked temporarily?

5. Types of Models Step simulation models The most common type of computer model Moves aircraft through space one step at a time and computes the results. Flexible but inefficient. Fairly easy to construct. Analytic models Uses mathematical equations rather than repeated steps. Efficient but requires simplifying assumptions. Relatively difficult to develop.

6. ABRM Assumptions linear paths Aircraft are assumed to maintain a constant speed and direction between the blunder and the point where the paths cross in the horizontal plane. aircraft shape Aircraft are assumed to be discs with a specified thickness and radius, oriented parallel to the horizontal plane. two aircraft Blunderer – the aircraft experiencing the blunder Evader – the aircraft threatened by the Blunderer

7. Blind Flying Risk Pbf depends upon the speed, direction, and sizes of the aircraft, and the number of aircraft per hour on the evader’s path. In order for this to be non-zero, the paths must cross in the horizontal plane within a vertical distance permitting the discs to touch. Blind flying risk, Pbf, is defined as the probability of a collision assuming both aircraft continue on course without any avoidance action or maneuver. If a blind-flying collision can occur, the time between the blunder and the collision is computed.

8. Risk amelioration aircraft not on a collision course Because the volume of sky is so large and the size of aircraft so relatively small, the chance of a collision should be small, even if nothing is done. controller intervention If either aircraft is under ATC, a controller most likely will intervene and cause one or both aircraft to alter course. Pilot (visual and/or CAS) intervention Suppose a blunder occurs. There are a number of reasons why it won’t result in a collision: Either aircrew could detect the threat and correct for it, either by visual observation or a collision alerting device.

9. controller intervention The probability of a successful controller intervention in time to prevent a pending collision depends on the time it takes to complete three independent steps. (These are hypothetical data for illustration.) 0 2 4 6 8 10 12 seconds Probability 1.0 0.0 0 2 4 6 8 10 12 seconds Probability 1.0 0.0 Probability 1.0 0.0 Probability 1.0 0.0 Controller reaction time Airframe reaction time Aircrew reaction time total reaction time 1 3 2 Result

10. pilot intervention The probability of a successful pilot intervention in time to prevent a pending collision depends on the time it takes to complete three independent steps. (These are hypothetical data for illustration only.) 1.0 0.8 0.6 0.4 0.2 0 miles Probability 1.0 0.0 0 2 4 6 8 10 12 seconds Probability 1.0 0.0 Probability 1.0 0.0 Probability 1.0 0.0 Pilot detects the threat Airframe reaction time Aircrew reaction time total reaction time 1 3 2 Result

11. Hypothetical response time data

12. Visual detection assuming that the aircraft are on a collision course Collision point x blunderer evader apparent path evader path blunderer path Visual detection depends on: 1.Visibility 2.The size of the other aircraft 3.Time available 4.Closing rate 5.Cockpit crew size 6.Field of view Apparent position of blunderer in evader field of view x Apparent position of evader in blunderer field of view x

13. Probability of a Collision The probability of a collision, Pc, is then computed by: Pc = Pbf *(1-Pba)*(1-Pbp)*(1-Pea)*(1-Pep) Where: Pbf = probability of a blind-flying collision Pba = probability of blunderer ATC correction Pbp = probability of blunderer pilot correction P ea = probabilit of evader ATC correction Pep = probability of evader pilot correction

14. Sensitivity analyses The chance of a collision is very small and depends on the exact value of many variables which are not knowable except within a range of values. This is a graph of collision risk as a function of a combination of vertical and horizontal blunder angles computed within the ABRM for a sample problem.

15. Input data

16. Output data

17. Sample problem #1 airborne blunder - An MD-80 begins a descent across the path of an oncoming B-757 in level flight. Both are doing about 400 kts. The crossing angle is 60 degrees. The Blunderer is 6 nm from the path intersection when the blunder occurs. The visibility is 10 nm. There is one evader per hour on the evader path. results Time between blunder and collision is 55 seconds Blind-flying collision probability = 1.03x 10 –4 Probability of controller intervention on the Blunderer = 0.913 Probability of controller intervention on the Evader = 0.959 Probability of Blunderer visual detection and correction = 0.302 Probability of Evader visual detection and correction = 0.223 Probability of TCAS detection and correction = 0.976 Probability of no correction = 5 x 10 –5 Probability of collision = 4.7 x 10 - 9

18. Sample problem #2 surface blunder - A truck doing 20 kts. suddenly crosses an active runway in the path of an B757 doing 65 kts. in a take-off roll. The paths cross at a 90-degree angle. The Blunderer is 0.05 nm from the path intersection when the blunder occurs. The visibility is 2 nm. There are 35 Evaders per hour on the evader path. results Time between blunder and collision is 8.5 seconds. Blind-flying collision probability = 3.22x 10 –2 Probability of controller intervention on the Blunderer = 0.0 Probability of controller intervention on the Evader = 0.0026 Probability of Blunderer visual detection and correction = 0.012 Probability of Evader visual detection and correction = 0.0014 Probability of TCAS detection and correction = 0.0 Probability of no correction = 0.984 Probability of collision = 3.17 x 10 - 2

19. Conclusion The ABRM is a practical tool for estimating collision risk under a wide range of scenarios. The ABRM requires much data that are difficult to obtain. The ABRM allows hypothetical data to be used in the absence of real data to produce results that are approximately correct. The ABRM is relatively easy to modify and extend.