The commercial-pilot maneuver where you fly a figure eight around two ground points, holding your wingtip visually pinned on each pylon — not by turning harder, but by flying at exactly the right altitude. This page derives that pivotal altitude, shows why the trick works, and lets you fly the whole maneuver in wind.
At one specific height above the ground, an airplane in a turn appears to pivot around a point off its wingtip: the sight line through the wingtip stays nailed to the ground point with no effort. That height depends on groundspeed only — not bank angle, not distance from the pylon. Faster over the ground → higher pivotal altitude, and it grows with the square of speed.
Typical trainer at 100 kt → ≈885 ft AGL. Because groundspeed changes as you turn through the wind, pivotal altitude changes continuously during the maneuver — that's the whole game in section 3.
Your wingtip is bolted square to the airplane, so it swings around at whatever rate the airplane is turning. Meanwhile the direction out to the pylon is swinging around too, because you're circling it. For the wingtip to stay glued to the pylon, those two have to sweep at the same rate.
Now here's the lever: banking harder or flying slower makes the airplane turn quicker; moving closer makes the pylon sweep quicker. Slide the altitude below and watch the two rates in the meter — there's exactly one height where they line up. And it depends only on your groundspeed — not your bank, not how far out the pylon sits (change the distance slider: the match doesn't move). That height is pivotal altitude, the same V²/g ≈ GS²/11.3 from section 1.
Too high and the airplane out-turns the pylon — the pylon slides ahead of the wingtip, so you ease forward and descend. Too low and the pylon wins the race and slides behind, so you ease back and climb. You fly the whole maneuver on the elevator, chasing the pylon — never the ailerons.
The math, if you want it: the airplane turns at g·tan φ ⁄ V and the pylon sweeps at V ⁄ d. Sighting along the banked wing means tan φ = h ⁄ d, and setting the two rates equal makes both the distance d and the bank φ cancel — leaving just h = V² ⁄ g.
In wind, groundspeed rises and falls as you turn through the eight, so the pivotal altitude rises and falls with it: highest at the downwind side of each turn, lowest upwind. Flying the maneuver well means continuously climbing and descending to ride that curve. Toggle to hold a fixed altitude instead and watch the pylon drift off the wingtip exactly as section 2 predicts.
With the default 12 kt of wind at 100 KTAS the required altitude swings roughly across the eight — every lap is a gentle climb–descend cycle, twice. Entry is normally made downwind, so you arrive at the first pylon at the highest pivotal altitude with speed to trade away.