Airport runway lengths

Our newest book, ASK A SCIENCE TEACHER, released by Experiment Publishing, contains 80 new Questions and Answers concerning science and everyday life. Below is one of the new Q & A.
How do they decide how long airport runways should be?
The length of airport runways depends on several factors, including the types of aircraft the airport will serve, the airplane’s itinerary, the altitude, winds, surrounding terrain, and the proximity of tall buildings and towers.
Large, heavy, aircraft need a longer runway to achieve the high speed required to give the wings lift. As for itineraries, more fuel is needed for longer flights, so a higher take off speed is used to lift the larger weight. Some fully loaded Boeing 747 planes weigh close to a million pounds.
Another factor is the elevation difference between airports near sea level, like the one in San Francisco, and those in the mountains, like Denver’s airport. The air in Denver, the “Mile High City,” is quite a bit less dense than the air in San Francisco, and so there’s comparatively less lift during takeoff in Denver. So an aircraft in Denver must reach a higher takeoff speed on the ground, requiring a longer runway to give the aircraft time to reach that higher takeoff speed. As a rule of thumb, the runway length is increased by seven percent for each 1,000 feet of elevation above sea level.
For Denver, the figuring goes like this: 1.07 to the fifth power equals 1.4. We can multiply 1.07 times itself five times and we come up with 1.4. So the runway lengths at Denver should be 40 percent greater than the airport runway lengths at San Francisco. That holds with reality: The new runway at Denver is 16,000 ft long, while the longest runway at San Francisco is 11,870 feet in length.. The required takeoff distance for the fully loaded Boeing 747-400 at sea level is 11,100 feet, and at Denver’s high altitude, a plane needs roughly 5,000 ft more runway to generate the required lift.
An additional need for a longer runway is based on air temperature. Warmer air is less dense than cold air, so warm air has less lift. Pilots refer to this as “density altitude.” Dry air is slightly more dense than moist air. Ideally, airplanes want to take off in air that is low (low altitude), cold, and dry.

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