J.W. Andrews

Modeling ofAir-to-Air Visual Acquisition

A mathematical model ofair-to-airvisual acquisition has been developed and validated ina series offlight testsatLincoln Laboratory. Themodel describes thevisual acquisition process as a nonhomogeneous Poisson process in which the probability of visual acquisition per unit of time is proportional to the solid angle subtended by the target. The model has proven useful in the investigation ofactual midair collisions, as well as in the evaluation of collision avoidance systems.

The Cerritos Midair Collision takingly transcribed at the NTSB laboratory in Washington, D.C. Air traffic personnel, airline August 31, 1986 was a typical warm, sunny officials, eyewitnesses, friends, and relatives of summer dayin southern California. At 11 a.m., the pilots were interviewed. Among the many three people boarded a single-engine Piper important questions to answer was a familiar Archer airplane at the Torrance, Calif., airfield one to the NTSB investigators: why didn't the and departed on a flight to the resortarea ofBig two aircraft see each other in time to avoid a Bear, Calif. The pilot of the Piper was William collision? Kramer, a 53-year-old metallurgist who owned In pursuit ofthe visual acquisition question, the aircraft. Onboardwere his daughterandhis NTSB investigator Malcolm Brenner contacted wife. The Kramers planned a day ofvacation at Lincoln Laboratory about studies conducted as Big Bear and a return flight to Torrance later part ofLincoln Laboratory's collision avoidance thatevening. As the Piperwas climbingoutfrom work. Lincoln Laboratory had developed a Torrance, Aeromexico flight 498, a DC-9 air­ mathematical model of visual acquisition and craft, was descending into Los Angeles on the hadjustcompleteda seriesofflight tests directly last leg of a regularly scheduled flight that had applicableto Cerritos. Lincolnagreed to support originated in Mexico City. In the radar control the NTSB, and the details of the Cerritos acci­ facility at Los Angeles International Airport, air dent were soon being analyzed with the Lincoln traffic controllerWalterWhite cleared Aeromex­ model. ico to descend for the approach. No one seemed to suspect that anything was amiss until, at Origin of the Model 6,500 feet, the Piper collided with the tail ofthe DC-9 (Fig. 1). The Kramers were fatally injured Visual acquisition is not a deterministic pro­ inthe collision; thePiperspunoutofcontroland cess; iUs described bymodels thatareprobabil­ slammed into a school yard in the suburban istic in nature. For small targets, acqUisition town of Cerritos. The DC-9 plunged to earth in takes place onlywhen the direction ofthe pilot's a residentialarea, killingall 64personsonboard visual search is aligned almost exactly with the together with 15 people on the ground (Fig. 2). line ofsightto the target. Therandomness ofthe In the months that followed, investigators searchprocess, combined with the randomness from the National Transportation Safety Board of the detection probability at a given angular (NTSB) carefully reconstructed the events that offset, causes acquisition times to vary greatly, led to the tragedy. The wreckage was reas­ even under identical visual conditions. An air­ sembled, measured, and photographed. The craft on a collision course is usually well above cockpitvoice recorderwas recovered andpains- the visual resolution threshold ofthe eye before

The Lincoln Laboratory Journal Volume 2, Number 3 (1989) 475 Andrews - Modeling ojAir-to-Air Visual Acquisition

Fig. 1-lmpactgeometry for the Cerritos, Calif., midair collision between an Aeromexico DC-9 anda PiperArcher, on August31, 1986. According to eyewitnesses, neitheraircraft took anyevasive action before impact.

it is acquired. Pilots have described the phe­ The immediate question to be answered was nomenon ofacquisitionwell above the threshold the degree of benefit from the automatic traffic by saying that targets seem to "pop up outofthe advisories provided by the collision avoidance sky." In reality, the targets are visible for some equipment. At first glance, it might seem that time before the search results in acquisition. the benefits could be characterized by some The Lincoln Laboratory model originated simple statistic such as the range at which the dUring testingofa ground-based collision avoid­ approaching traffic was seen. But two difficul­ ance system known as the Automatic Traffic ties arose. The first problemwas that the visual Advisory and Collision Avoidance System. Dur­ acquisition process was highly variable and ing the flight tests, subject pilots flew near­ thus required a suitable statistical approach. collision encounters in two Lincoln Laboratory The second and more significant problem was aircraftbased atL.G. Hanscom Field in Bedford, that manyfactors affected the difficulty ofvisual Mass. Radar measured the paths ofthe aircraft, acquisition. Among these factors were the speed and radio transmission determined the time and geometry ofapproach, the size ofthe target when the pilots visually acquired each other. By aircraft, the timing and accuracy of traffic ad­ correlating the speeds and distances with the visories, and the preVailing atmospheric visibil­ times ofvisual acquisition, the flight tests pro­ ity (visual range). How could visual acqUisition duced quantitative measures of pilot visual data collected at one set of speeds against a acquisition perfonnance. single aircraft be applied to the general problem

476 The Lincoln Laboratory Journal. Volume 2. Number 3 (1989) Andrews - Modeling ojAir-to-Air Visual Acquisition

Unfortunately, the air-to-air visual acquisition process is complicated because Ais not constant with time. In fact. A increases steadily as two aircraft on a collision course approach closer together. The cumulative probability of visual acqUisition must then be written

P(acq by t,) = 1- exp[ -IA(tldtl (2)

This equation describes a nonhomogeneous Poisson process and provides a general mathe­ maticalformulation thatcanbe used to describe Fig. 2-Aftermath of the Cerritos, Calif., midair collision. many different visual search situations. Fifteen people on the ground were killed in addition to 64 To apply Eq. 2. an expression for Amust be people on the airplane. The accident occurred on a clear day when the reported visual range was 14 nmi. found. Several setsoftestdatawere examinedin addition to the Lincoln Laboratory data. The other sets of data included a classic flight test conducted in DC-3s by Wayne Howell for the involving a range of speeds and a variety of Civil Aeronautics Administration in 1957 [2], aircraft? If the conclusions were to be generally and data collected by Control Data Corporation applicable. it would be necessary to devise a dUring a series of air-to-air photographic mis­ means of extrapolating experimental results to sions in 1973 [3). When properly analyzed, all other conditions. The mathematical model of data sets supported the conclusion that the visual acquisition was developed to serve this visual acquisition rate is proportional to the purpose. angular size of the visual target. That is, The first step in developing the model was to establish a mathematical formalism that could (3) serve as a powerful yet general basis for analy­ sis. The key to such a formalism proved to be the where A is the visual area presented by the use oftheinstantaneousvisualacquisition rate. target aircraft, ris the range to the target. and f3 At any given instant. the visual acquisition rate is a constant to be determined. Acan be defined as follows: The above expression is suitable only when theatmosphere is sufficientlyclearatthe ranges ?c(t) = lim P(acq in M) . (1) ofinterest. In fog or haze. the contrast oftargets M---70 tlt can decrease rapidly with range; this depend­ This rate is the probability ofvisual acquisi­ ency must be included iff3 is to be modeled as a tion perinstant time. IfA = O.02/s. for example, constant. Laboratoryexperiments showthat the then the probability ofvisual acquisition in one detectability of a static target is actually deter­ second of search is approximately 2%. The mined bytheproductofthe target size and target cumulative probability of visual acquisition is contrast. This recognition suggests that the obtained by evaluating the acquisition proba­ size-contrast product should be substituted for bilities for each instant as the target aircraft the size expression in Eq. 3. A relationship approaches. If Awere constant. then the result known as Koschmieder's law states that. in a would be a set of simple equations that corre­ homogeneous atmosphere, apparent contrast spond to the classic Poisson process. a process degrades exponentiallywithvisual range. Thus. used widely to describe physical processes such if Co is the inherent contrast of the target with as the rate of fission of radioactive isotopes. its background, then at range r the apparent

The Lincoln Laboratory Journal. VoLume 2. Number 3 (1989) 477 Andrews - Modeling ojAir-to-Air Visual Acquisition contrast is reduced to tern for Preventing Midair Collision" on page ~). 437 in this issue). These advisories are dis­ Co exp(-2.996 played on a plan-position display located on the aircraft instrument panel. The constant -2.996 arises from the defini­ Traffic advisories improve visual acquisition tion of visual range as the range at which in two principal ways. First, they increase the apparent contrast is reduced to 5% ofthe inher­ fraction of the crew's time devoted to the visual ent contrast. search for traffic. Second, they concentrate vis­ The resulting expression for A. is ual searchin the properdirection. Aquantitative measure ofcrewperformance with such adviso­ A = f3 ~ exp ( -2.996 ~) (4) ries was an objective of Lincoln Laboratory's work in TCAS flight testing. Lincoln Laboratory where A is the visual area presented by the built and installed a prototypeTCAS in a Cessna target aircraft, ris the range ofthe target, and R 421 aircraft; the TCAS provided traffic adviso­ is the visual range. Here the inherentcontrastis ries through a special interface to a weather included in the value of (3. radar CRT. The bearing accuracy of these advi­ Numerical integration is usually required to sories was approximately 7° (one standard de­ find the cumulative probability ofvisual acqui­ viation) and the position of the traffic was up­ sition given by Eq. 2. However, in certain special dated once per second. Six different subject cases a'simple closed-form solution can be pilots flew a variety of missions that resulted in obtained. For example, consider the common data for 66 near-miss encounters. case in which the following conditions apply: The subjects were aware that, from time to (a) the visual range is so large that it plays no time, a second test aircraft would conduct an role in degrading contrast, (b) the target aircraft intercept that would trigger the collision avoid­ is on an unaccelerated collision course, and (e) ance alarms. The interceptor was vectored by the value of (3 and A are constant. Condition a ground radar to achieve a near-zero horizontal allows us to set R to infinity. Condition b allows miss distancewith an altitude separationof200 us to write the range to the target as r = to 500 ft. From the viewpoint of the subject - it where ;- is the closing rate and t is the time pilots, the intercepts presented visual acquisi­ to collision. Condition e allows the integration to tion problems similar to those ofactual collision be carried out with the following result: situations. When the subjects used the TCAS, they visually acqUired in 57 of the 66 encoun­ .~A ters. The median range ofvisual acquisition was P(acq by tz ) = 1 - exp( J. (5) 1.4 nmi. In five of the nine cases of acquisition r tz failure, the subject aircraft received a climb The Value of Traffic Advisories advisory from the TCAS and entered a nose-up attitude that prevented acquisition of the in­ Air traffic controllers assist visual acquisition truder passing below. byprovidingtraffic advisories for nearby aircraft To understand these results fully, we ana­ detected by radar. Such an advisory might be lyzed the data in accordance with the visual "American 578, you have traffic at two o'clock, acquisition model. A robust estimation tech­ three miles, reporting seven thousand feet." niquewas developed to obtain the value of(3. The These advisories are issued on a "workload technique was based on the fact that, according permitting" basis, which means that in some to the model, the probability of visual acquisi­ busy situations the air traffic controller may tion within any time interval for which (3 is curtail the service. Automatic traffic advisories constant can be determined from the time are generated by the Traffic Alert and Collision integral Q ofthe solid angle-contrast product of Avoidance System, or TCAS (see ''TCAS: A Sys- the target. Based on Eqs. 2 and 4, Q can be

478 The Lincoln Laboratory Journal. Volume 2. Number 3 (J 989) Andrews - Modeling ojAir-to-Air Visual Acquisition defined as follows: Even though the subjects had no traffic advi­ sories to alert them to the time and direction of P(acg by t) = 1 - exp[-,BQ(tl] (6) approach of the intercepts, additional care was where taken to prevent undue concentration on visual t search. The tests were conducted as a general Q(tl = f ~ exp ( -2.996 ~) dt. (7) study of single-pilot cockpit technique. Initial subject briefings stated that the experimenters Since Qrepresents the opportunityfor visual were interested in seeing each pilot's individual acquisition that the target has provided, Q is technique, that there was no single standard for called the opportunity integral. The estimated right and wrong, and that the subject should fly value off3 is obtained byplotting observed acqui­ in as normal and relaxed a manner as possible. sition probability as a function of Q and then Data were collected in the cockpit by a safety finding the value of f3 that, when inserted in Eq. pilot. Periodically this pilot would ask the sub­ 6, best fits the plotted data. Figure 3 shows the jects questions such as "Where is Worcester acquisition probabilities for TCAS flight test Airport from our present location?" At several data plotted as a function of Q. The value of f3 points during the flight, the safety pilot would that best fits this curve is 140,000/ster-s. ask subjects to rate their workload on a 1-to-9 A numerical example places the value of f3 in scale. They were also asked to call out all traffic perspective. Consider the acquisition rate for a when it was first seen; the times of sightings Boeing 727jet transport when seen head-on at were carefully recorded for later analysis. The a range of 3 nmi. The visual area of the aircraft subjects were told that other company traffic is about 430 sq ft when seen from this angle. At might be operating in the area, but that the a range of 3 nmi, the aircraft will subtend an Lincoln Laboratory control center would make angle a of 1.3 x 10-6 ster. Thus the rate ofvisual sure that this traffic knew their location and acqUisition is A. =. f3a = 0.18/s, or approxi­ kept clear of their altitude. mately 18% per each second of alerted search. Of course, the angular size of the aircraft is constantly changing, and the integration indi­ cated in Eq. 2 must be carried out in order to 1.0 compute the cumulative probability of visual acquisition over a period of time. 0.9 0.8 gc ,B =17,000/ster-s Unalerted-Search Flight Tests :i1i 0.7 ~ c- 0.6 During the experiments with collision avoid­ «u ance equipment, the focus of testing had been '0 0.5 on visual acquisition aided by automatic traffic ~ :c 0.4 advisory avionics. Because most Visual Flight ell .D Rule flights have no traffic advisory services, a 0 0.3 a..... need remained to establish a baseline for unal­ 0.2 • Unalerted Search ertedsearch. With the supportofthe FAA, anew 0.1 ... Alerted Search (TeAS) seriesoftestflights were initiated to provide this 0.0 baseline. In these tests, a group of 24 general 0 50 100 150 200 aviation pilots each flew a Beech Bonanza on a Opportunity Integral (J1steradian-s) triangular cross-country flight of about 45 minutes' duration. During this time, a Cessna Fig. 3-Measured and modeled visual acquisition proba­ 421 aircraft conducted three intercepts; it flew bilities. The probabilityis definedin terms ofthe opportunity both over and under the test route to provide a integral-a measure ofthe angularsize ofthe visual target target for visual acquisition. and the duration of the search.

The Lincoln Laboratory Journal. Volume 2. Number 3 (1989) 479 Andrews - Modeling ojAir-to-Air Visual Acquisition

The test design appeared to be highly suc­ Time to Collision (s) cessful in preventing subjects from concentrat­ 5 10 15 20 25 30 35 40 45 50 ing unduly on visual search. Only two subjects 1.0 guessed that the Cessna 421 was the "company 0.9 traffic," and in neithercase did this insight arise c 0 0.8 before the last intercept was over. :§:;::::; ::J 0.7 Datawere obtained for 64 encounters. Visual C1" U acquisition was achieved in only 36 of these ~ 0.6 co encounters (56% of the total), and the median ::J CIl 0.5 acquisition range for the 36 encounters was :> '0 0.4 0.99 nmi. Figure 3 provides a plot of the ac­ g quisition probability versus opportunity inte­ :.a 0.3 gral for these unalerted-search data. The value ell .De 0.2 of f3 that best fits the data is approximately a.. 17,OOOjster-s. 0.1 In a comparison between the unalerted­ 0.0 search results and the alerted-search results 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 from the earlierTCAS tests, the pilots who used Range (nmi) the TCAS traffic advisories exhibited a f3 value that was higher by a factor of 8.2. The higher Fig. 4-Modelprediction ofvisual acquisitionprobabilityas factor implies that the presence of the TCAS a function of separation between aircraft for the Cerritos scenario. These curves assume unalerted visual search. traffic advisory increased search effectiveness by a factor of 8. In other words, one second of search with the TCAS advisory was as effective from the Piper. The acquisition probability in­ as eight seconds of search with no alert. creases significantly over the last minute of flight. At 12 s before collision, the probability of Analysis of the Cerritos visual acquisition is 90%. Acquisition ofthe DC­ Midair Collision 9 is easier because it provides a visual target that is about eight times larger than the Piper. Because neither aircraft in the Cerritos acci­ This analysis shows that only in the last dent had received a traffic advisory, the results minute prior to collision does a significant ofthe unalerted-search flight tests were crucial probability for visual acquisition exist. Events to the analysis ofthataccident. Dataprovided by that occurred earlier (such as traffic advisories the NTSB were used to determine the closing or cockpit distractions) are unlikely to have had rate between the aircraft (271 knots) and the any effect on the failure to acquire. visual areas of each aircraft as seen from the Asecond significant resultwas to focus atten­ other (72 sq ft for the Piper and 588 sq ft for the tion on whythe pilotofthe Piperdid not acquire. DC-9). Figure 4 shows the results of the analy­ The results of the model apply only if normal sis. The bottom two curves describe the search visual search is underway. Therefore, an un­ for the Piper from the DC-9. The two-pilot curve usual factor must have existed that prevented is derived by assuming thatthe effect ofthe sec­ normal search on board the Piper. In fact, the ond pilotis to double the search performance for NTSB investigation revealed evidence that pilot the aircraft. The figure shows that the probabil­ Kramer, who was navigating by visual ground ity ofvisual acquisition is small until the last 15 references, had misidentified a freeway and had seconds or so before collision. The probabilityof strayed from his intended course. At the time of effective collision avoidance (using 12-swarning the accident, he would probably have been time as a criterion) is only 42%, even assuming looking out the left side of the aircraft for that both pilots are searching. Disneyland, a prominentvisual landmark used The top curve describes search for the DC-9 by local pilots. If this idea was correct, it might

480 The Lincoln Laboratory Journal. Volume 2. Number 3 (1989) Andrews - Modeling ojAir-to-Air Visual Acquisition explain why the DC-9. approaching from 50° to and the potential benefitsofservices such asthe the right of the nose of the aircraft. would not automatic traffic advisories available from colli­ have been seen. sion avoidance systems. In the search for ways to prevent similar Although visual acquisition is a complex accidents in the future, NTSB posed the follow­ process, a useful statistical model of pilot per­ ing question: would the Cerritos accident have formance hasbeen developed atLincoln Labora­ been prevented iftheAeromexico DC-9 had been tory. The model explains a varietyofexperimen­ equipped with a TCAS? Because the Piper was tal results that, without a common framework not equipped with an altitude-reporting trans­ for analysis, would be difficult to compare. The ponder. the TCAS would have been unable to model is currently used by the FAA to evaluate issue a resolution advisory. It would. however. collision avoidance systems. airspace regula­ have issued a traffic advisory that would have tions, and waiver requests. The NTSB has also accurately depicted the angular position and used it to provide insight into crew performance range of the Piper. A second set of calculations in accident scenarios. The model has a signifi­ were carried out under the assumption of cant limitation: it can be applied onlywhere the alerted search by the DC-9 crew. These calcula­ pilot performance level can be assumed to ap­ tions showed that if they had been alerted by a proximate that for which flight test data are TCAS traffic advisory. the crew would have had available. Extension of the model to other situ­ a 95% chance of seeing the Piper in time to ations (such as high-workload landing phase or avoid. The NTSB final report concluded that military training situations) may require pilot "had flight 498 been equipped with a TCAS. performance testing with either actual flight or the accident might not have occurred."They re­ realistic flight simulators. commended that the FAA "expedite the de­ velopment. operational evaluation. and final References certification of the Traffic Alert and Collision Avoidance System for installation and use in 1. J.W. Andrews. "Air-to-Air Visual Acquisition Perfor­ certificated air carrier aircraft (3)." mance with Pilot Warning Instruments (PWl)," Project Report ATC-73. Lincoln Laboratory (25 Apr. 1977). FAA­ RD-77-30. 2. W.O. Howell. "Determination ofDaytime Conspicuity of Conclusion Transport Aircraft." Technical Development Report No. 304. Civil Aeronautics Administration (May 1957). Maintenance of safe separation between air­ 3. A. MiIIhollon. J. Lyons. and W. Graham. "Air-to-Air craft is often dependent on the ability ofpilots to Visual Detection Data." Interim Report. Control Data Corporation (Apr. 1973). FAA-RD-73-40. see and avoid other traffic. But even when 4. J.W. Andrews. "Air-to-Air Visual Acquisition Perfor­ weatherconditionsare favorable for visual sepa­ mance with TCAS II." Project Report ATC-l30, Lincoln Laboratory (27 July 1984), DOT/FAA/PM-84-17. ration, midair collisions often occurwithout the 5. "Collision of Aeronaves de Mexico. S.A. McDonnell crewsofeithercollidingaircraftseeing the other. Douglas DC-9-32. XA-JED and Piper PA-28-181. N4891F, Cerritos. California. August 31, 1986."AircraJt This fact raises central questions concerningthe Accident Report No. NTSB/AAR-8l /07. National Trans­ performance that can be expected of air crews portation Safety Board (7 July 1987).

TIle Lincoln Laboratory Journal. Volume 2. Number 3 (1989) 481 Andrews - Modeling ojAir-to-Air Visual Acquisition

I'

JOHN ANDREWS is an as­ sistant group leader in the System Design and Evalu­ ationGroup and is currently responsible for technical management of the Termi­ nalAirTraffic ControlAuto­ mation (TATCA) Program. For 14 years. he was involved in thedevelopmentofcollision avoidancesystems. His workon the Traffic Alert and Collision Avoidance System (TeAS) resulted in contributions to aircraft-altitude tracking tech­ niques. analysis of computer logiC. human-subject flight testing. and the analysis ofpilotvisual acquisition perform­ ance. John has served as a consultant to the National Transportation Safety Board in the investigation ofmidair collisions. including the Cerritos accident. He has a B.S. degree in physics from the Georgia Institute ofTechnology. and an S.M. degree in aeronautical engineering from MIT.

482 The Lincoln Laboratory Journal. Volume 2. Number 3 (1989)