The handbook formulas
The visual line to the pylon stays fixed on the wing when you are at the pivotal altitude for your present groundspeed. The Airplane Flying Handbook writes this as:
pivotal altitude (ft AGL) ≈ (groundspeed in mph)² / 15
pivotal altitude (ft AGL) ≈ (groundspeed in knots)² / 11.3
Those constants are rounded forms of the exact identity h = V² / g. With g0 = 9.80665 m/s², the exact divisors are about 11.294 (knots) and 14.957 (mph), so the handbook figures are a few feet low — 717 ft instead of about 718 ft at 90 kt, for example.
Wind
Groundspeed changes around the pylon. You are faster, and the pivotal altitude is higher, on the downwind side; slower and lower on the upwind side. The AFH describes a slight climb and descent to keep the reference line on the pylon rather than flying a single fixed altitude.
Sources
FAA Airplane Flying Handbook (FAA-H-8083-3), Eights-on-Pylons; Commercial Pilot and CFI Airman Certification Standards for the maneuver. For bank and turn radius at a given TAS, see the turn radius calculator.
Frequently asked questions
Is it knots squared over 11.3 or 15?
Use 11.3 when groundspeed is in knots, and 15 when it is in miles per hour. They are the same height to within the rounding of the two constants. This page shows both, plus the exact V²/g value.
Should I enter TAS or groundspeed?
Groundspeed. The geometry is about the rate at which the pylon’s bearing changes over the ground. In a wind, TAS and groundspeed are not the same, and pivotal altitude changes around the figure-eight.
Why is the exact height a little higher than the handbook number?
The 11.3 and 15 constants are rounded. The exact V²/g height with standard gravity is GS(kt)² / 11.294, a few feet above the AFH figure at typical training speeds. Either is close enough for the maneuver; this page reports both so you can see the difference.