Boomerang style: the trick is all about lift and gyroscopic precession. Your wings are angled and a little twisted so that the faster‑moving side— the one that’s spinning forward—gets a higher airspeed. That side generates more lift and a bit less drag, so the boomerang tilts in a way that pushes it sideways. At the same time, the spin keeps the wings pointed in the right direction, like a gyroscope. The lift on the forward side pushes the whole thing toward the ground, while the lift on the back side pushes it up, and the gyroscopic precession turns that lift into a sideward motion. The result is a curved, looping flight that brings it back to you. So it’s wing shape for lift, spin for stability, and gyroscopic magic for the return. Try it—just make sure you throw it with enough speed and the right angle, and watch the circle unfold.

Sure thing—no fancy plots, just the low‑down. Imagine each wing is a tiny airfoil that generates lift \(L = \tfrac12 \rho V^2 S C_l\). Because the boomerang’s spin makes the leading edge of the front wing travel faster, it gets a slightly higher \(V\), so its lift is a bit bigger than the back wing’s. That lift difference \(\Delta L\) creates a torque \( \tau = r \times \Delta L\), where \(r\) is the radius from the spin axis to the wing’s lift center. That torque turns the whole thing in the direction of precession—basically “pushes” the faster wing forward, the slower wing backward, and the spin carries that tilt into a side‑to‑side motion. That’s the physics bite. Altitude? Air density \(\rho\) drops, so both wings lose lift. The boomerang just flies flatter and farther before the lift difference can swing it back. The return radius shrinks, and you need a faster spin or a more aggressive launch angle to get the same loop. Basically, higher up, it’s like trying to throw a boomerang in a thin‑air swimming pool—you’ll get a shorter, quicker arc. Just adjust your power, and you’ll still get that sweet come‑back.

Got it, keep it simple. At the low speeds a boomerang flies—around 20–30 mph—the Mach number is way below 0.3, so the lift coefficient is pretty constant, no big Mach effects. If you want a reference, the NACA Technical Report 1044 (Aerospace Flight Mechanics) and the AIAA Aerodynamics Handbook both give the classic lift‑coefficient‑vs‑Mach plots for flat plates and simple airfoils. Those show that up to Mach 0.3 the change is less than 5 %. So at high altitude you’re mostly losing lift because of lower density, not because the air is moving faster relative to the boomerang. That’s why a higher spin or a steeper launch angle can help—more lift, more gyroscopic torque, still all about that lift‑difference balance. No moon‑grade physics needed, just good old aerodynamics.