AbstractThe number of mid-air collisions which would occur if all pilots were flying uncontrolled and blindfolded is computed from data on the sizes, speeds and density of aircraft, and compared to the number which actually occurred over the United States during the 9-year period 1964-1972. The ratio comes out at least 32 to 1 for low-altitude en route traffic, and at least 84 to 1 in low-altitude terminal airspace (5-30 miles from the centre of an airport). Within 5 miles the density is so high that this ratio would have been far higher, and meaningless; the number of collisions at high altitudes is very small, and again less than would be predicted by the model. The model is such that it might drastically underestimate the number of collisions (and therefore the above ratios), but could not overestimate it by more than a factor of two or three. It is concluded that under conditions of moderate to high densities of air traffic, the air traffic control system and its inherent doctrine of see-and-avoid are useful in avoiding collisions.