vary not with the level of traffic but, more ominously, with its square. For an analogy from the ground, consider a one-way street that has a stop sign at its intersection with a busy two-way street. Suppose that traffic increases by 20% in the area. Then, to a first approximation, one might expect the number of cars on the one-way street that violate the stop sign to increase by 20% per year. One might also foresee a 20% rise in the chance that when a violation occurs, another vehicle traveling on the busier street is so close to the intersection that an accident results. the overall effect is that accidents would grow by a factor of 1. 2x1. 2=1. 44, or by 44% Of course, intuitive arguments can go in all directions: One could defend a variety of functional relationships between traffic and risk. However, there is empirical support for the quadratic rule just stated. Barnett, Paull, and ladelucaanalyzed all 292 US runway incursions in 1997, focusing on the 40 events which(i)were described as having extremely high"accident potential by a panel of experts that included pilots and air traffic controllers and (ii) took place under conditions of reduced visibility(dawn/dusk, night, haze/fog). The researchers investigated whether the spread of these dangerous incursions across US airports was proportional to the square of 1997 traffic levels. On a per-capita basis, for example, did airports with 500,000 operations that year have roughly four times as many dangerous events as airports with 250,000? The quadratic hypothesis passed statistical tests with flying colors. Interestingly the"neighboring alternative hypotheses, namely, that dangerous events varied linearly with traffic, or instead with the cube of traffic levels, both failed statistical tests against the data. The quadratic rule-of-thumb, therefore, emerges as more credible from the data analysis. So does its unpleasant implication that increases in airport activity could cause disproportionate growth in collision risk. A 50% rise in traffic, for example, could induce a 125% increase in collisions Taking into account various phenomena, Barnett et al estimated that the runway- collision death risk per US jet flight could rise to 1 in 25 million over 2003-2022, four times the corresponding figure in Table 3. Because of increased numbers of jet passengers, the annual death toll could grow more steeply, from three per year over 1990 99 to about 30 per year over 2003-2022. It seems reasonable to fear that Western Europe-the scene of the two worst runway collisions in history (Tenerife, Madrid )- will be subject to the same general trend Midair Collisions Table 4 summarizes First-World death risk in the 1990s caused by collisions between planes in the air Table 4 goes here7 vary not with the level of traffic but, more ominously, with its square. For an analogy from the ground, consider a one-way street that has a stop sign at its intersection with a busy two-way street. Suppose that traffic increases by 20% in the area. Then, to a first approximation, one might expect the number of cars on the one-way street that violate the stop sign to increase by 20% per year. One might also foresee a 20% rise in the chance that, when a violation occurs, another vehicle traveling on the busier street is so close to the intersection that an accident results. The overall effect is that accidents would grow by a factor of 1.2x1.2 = 1.44, or by 44%. Of course, intuitive arguments can go in all directions: One could defend a variety of functional relationships between traffic and risk. However, there is empirical support for the quadratic rule just stated. Barnett, Paull, and Iadeluca8 analyzed all 292 US runway incursions in 1997, focusing on the 40 events which (i) were described as having “extremely high” accident potential by a panel of experts that included pilots and air traffic controllers and (ii) took place under conditions of reduced visibility (dawn/dusk, night, haze/fog). The researchers investigated whether the spread of these dangerous incursions across US airports was proportional to the square of 1997 traffic levels. On a per-capita basis, for example, did airports with 500,000 operations that year have roughly four times as many dangerous events as airports with 250,000? The quadratic hypothesis passed statistical tests with flying colors. Interestingly, the “neighboring” alternative hypotheses, namely, that dangerous events varied linearly with traffic, or instead with the cube of traffic levels, both failed statistical tests against the data. The quadratic rule-of-thumb, therefore, emerges as more credible from the data analysis. So does its unpleasant implication that increases in airport activity could cause disproportionate growth in collision risk. A 50% rise in traffic, for example, could induce a 125% increase in collisions. Taking into account various phenomena, Barnett et al8 estimated that the runway￾collision death risk per US jet flight could rise to 1 in 25 million over 2003-2022, four times the corresponding figure in Table 3. Because of increased numbers of jet passengers, the annual death toll could grow more steeply, from three per year over 1990- 99 to about 30 per year over 2003-2022. It seems reasonable to fear that Western Europe—the scene of the two worst runway collisions in history (Tenerife, Madrid)--- will be subject to the same general trend. Midair Collisions Table 4 summarizes First-World death risk in the 1990’s caused by collisions between planes in the air. Table 4 goes here