04-BS-7 · December 2018
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Reference texts: White, F.M., Fluid Mechanics (8th ed.) — fluid statics and hydrostatic force on plane/curved surfaces incl. gravity-dam stability (Ch. 2), buoyancy and Archimedes' principle (Ch. 2), orifice/nozzle discharge and jet momentum forces (Ch. 3, 6), viscous flow in ducts and the Moody chart (Ch. 6), open-channel flow and the hydraulic jump (Ch. 10), drag and stability of bluff bodies (Ch. 7), turbomachinery and jet propulsion (Ch. 11).
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
Given. A frisbee flies forward while spinning rapidly about its own vertical axis; its cross-section is a shallow, cambered, airfoil-like disc (curved upper surface, flatter lower surface).
Find. How airflow over/under the disc generates lift, and the aerodynamic role of the spin.
Airflow and lift generation. In forward flight the frisbee is tilted at a small positive angle of attack and its cross-section is cambered — convex on top, flatter (or slightly concave) below. As shown in the sketch, streamlines passing OVER the disc are forced into a longer, more curved path over the raised upper camber, so by continuity that air must speed up; streamlines passing UNDER the disc follow a shorter, straighter path close to the flatter lower surface and remain relatively slower. By Bernoulli's equation, the faster-moving air on top is at LOWER pressure than the slower air underneath, and this pressure difference, integrated over the disc's planform area, is exactly the aerodynamic lift force that supports the frisbee's weight and sustains its long, low-sink-rate glide.
Effect of spinning. The forward-flight lift mechanism above does not itself require spin — spin's role is almost entirely one of stability, not lift generation. A rapidly spinning disc possesses substantial angular momentum about its own axis of symmetry; by the gyroscopic principle, this angular momentum strongly resists any external torque (from a gust, an uneven throw, or a small asymmetry in the pressure distribution) that would otherwise tip the disc off its flight axis. The spin therefore keeps the disc's orientation — and hence its angle of attack relative to the oncoming flow — effectively constant throughout the flight, which is precisely what keeps the lift force steady and the flight path smooth rather than tumbling.
Horizontal (in-flight) stability. Because the spin axis stays gyroscopically fixed in space (not tied to the direction of travel), a properly thrown frisbee maintains a nearly constant, level attitude even as its flight path itself curves or descends — any momentary disturbance produces only a small, rapidly-damped precession rather than an outright tumble, exactly the behaviour a non-spinning flat disc of the same shape does NOT exhibit (a thrown non-spinning disc tumbles almost immediately, since nothing resists a disturbing torque).
