More generally, the plane flies along a spacetime geodesic, the most convenient of which is a ballistic parabola. This does require cutting the engines. Cuttin

More generally, the plane flies along a spacetime geodesic, the most convenient of which is a ballistic parabola. This does require cutting the engines. Cutting the engines is necessary but not sufficient. In level flight, air still supports the plane even without engine thrust, so the passengers would still feel "weight." The "vomit comet" could achieve the same weightless effect without climbing by cutting the engines and pointing the plane toward the ground. That's effectively the second half of the ballistic parabola. But it would only provide about 12 seconds of weightlessness instead of 25.