Commercial pilot applicants are required to fly eights on pylons to demonstrate an intuitive control of the airplane, so it’s ironic that mastering the maneuver starts with an equation.
Pilots perform eights on pylons at pivotal altitude, a groundspeed-dependent height above ground level that constantly changes as a tailwind becomes a headwind and then a tailwind again along the figure-eight track. From a pilot’s perspective, it’s the altitude you must fly to keep a ground reference point at a fixed position off your wing.
Imagine a laser pointer mounted at eye level, perpendicular to the airplane’s centerline. Your job is to keep the dot pointed at a tree on the ground. In zero wind, you’ll fly a level circle. In a tailwind, the dot will drift above and ahead of the tree unless you adjust the controls. You must steepen the bank and climb. Turning upwind, the bank shallows and the airplane descends.
To estimate pivotal altitude, square the groundspeed in knots and divide by 11.3. But leave your calculator on the ground—not just an academic exercise, eights on pylons are a pat-your-head-rub-your-belly maneuver measuring your ability to maintain coordination and situational awareness while controlling the airplane precisely in three dimensions. Easy, right?