We explain how the rotation of a discus makes it into a reasonably efficient airfoil generating substantial lift at a lift/drag ratio ~ 3, thus increasing the length of the throw with 5-10 meters. The rotation makes the boundary layer turbulent which delays separation at the high angle of attack in descent.
A Discus Acts Like a Wing
Assuming that lift and drag are constant during the flight and that the discus has unit mass, it follows by elementary mechanics that the time of flight T and traveled distance d are given by the following formulas:
T = (V sin(a) + sqrt(V2sin2(a) + 2gh) )/G
d = V cos(a) T - DT2/2
where V is the initial speed, a is the launch angle, h the launch height, G = g – L the effective vertical force with g the gravitational force and L the vertical lift force and D the horisontal drag force.
The maximal lift coefficient at 30 degrees of angle of attack is ~ 1.0 with lift/drag ratio ~ 3 .
Typical values are V = 20 m/s, a = 35 degrees, h=1.5 m, G = 0.8g which gives T ~ 4 s and d ~ 80 m, see also Optimal discus trajectories.
Shortcut to the Action of a Wing
Sideview of velocity and pressure, and topview of streamwise vorticity of Naca0012 wing at aoa = 14. Observe the turbulent streamwise vorticity emanating from separation instability. Computed solution of the Navier-Stokes equations with slip boundary condition . It is possible that the rims (and holes of some frisbees) of a frisbee trigger transition to turbulence in the boundary layer and thus improves
the flight.Principle of action of a wing: Potential flow (upper left) with zero lift/drag modified by low-pressure counter-rotating rolls of streamwise vorticity from instability mechanism at separation (upper right), switching the pressure on rear wing (bottom left ) to give both lift and drag (H high, L low pressure). Viscous flow separating at the crest with low lift and large drag (bottom right).
Lift/drag ratio of a Naca0012 airfoil as function of the angle of attack
Lift (and circulation) as function of the angle of attack
Drag as function of the angle of attack
Flight of a Discus
- It stabilizes the flight into maintaining the launch angle, although it increases slightly due to precession as explained in Why a Frisbee Flies so Well.
- It makes the boundary layer turbulent which delays separation and maintains a useful lift/drag ratio.