discspeed wrote:...Making discs more gyroscopic is good. Dave Mac made the Wizard more gyroscopic than the Aviar-x, and it made it better. Not better enough to make someone a better putter or to allow Gateway players to dominate the putting green, but better in small incremental ways that nerds discuss on the internet. Now MVP made the Ion more gyroscopic than the Wizard, and in the same incremental way it flies better.

I agree that more gyroscopic is good. I'm all for it. But there are many many many factors that determine how a disc flies, and the moment of inertia only really affects the rate of change in hyzer/anhyzer angle, along with numerous other factors.

Back to physics...

The rate of change of disc hyzer/anhyzer angle (i.e., rate of turn/fade, ) is the aerodynamical pitching moment/torque

T divided by the angular momentum

L. The angular momentum

L is the product of the disc spin rate

w and the moment of inertia

I. In summary, the rate of change of hyzer/anhyzer angle is

T/(I*w).

T is the product of the component of aerodynamical force parallel to the disc axis (basically, the lift force

F_l) times the length of displacement of the center of lift/pressure from the exact center of the disc

x. So,

T=F_l*x. The lift force,

F_l, is itself a function of air density and velocity,

F_l=A_l*d*v*v (where

A_l is the dimensional* lift coefficient,

d is air density, and

v is the air speed).

In summary, the rate of change of hyzer/anhyzer angle of a disc in flight is:

T/(I*w)=A_l*d*v*v*x/(I*w).

So let's look at this list of characteristics that change the disc's rate of hyzer/anhyzer in flight:

T/(I*w)=A_l*d*v*v*x/(I*w):1)

Lift coefficient,

A_l, depends only on the radius

R and shape of the disc, and is moderately sensitive to variations in runs/plastics for a given mold.

2)

Air density,

d, is most sensitive to altitude. Relative to sea level, air density drops by 10% at 1300 m altitude (4300'), and is diminished by 20% at 2500 m (8200'). Unlike moment of inertia, air density also proportionally affects other aspects of flight, such as the aerodynamic drag force that slows the disc (thus high altitude is not strictly analogous to higher moment of inertia).

3)

Air speed,

v, is imparted to the disc by the thrower, and is additionally affected by wind. Factors affecting air speed are a combination of grip, throwing mechanics, and weather. Air speed is dissipated by the aerodynamic drag force, which is given by

F_d=A_d*d*v*v (where

A_d is the dimensional* drag coefficient).

4)

Displacement of center of lift/pressure,

x, from the center of the disc depends on the air speed, angle of attack, and is

extremely sensitive to disc shape. Variations in runs/plastics for a given mold can cause

x to change it's value by more than 100%.

5)

Moment of inertia,

I, depends on the disc mass

M, disc radius

R, and distribution of mass between the flight plate and rim. It exhibits a moderate degree of variability, it is always greater than M*R*R/2 (corresponding to all mass in the flight plate), and it is always less than M*R*R (corresponding to all mass in the rim).

6)

Spin rate,

w, is imparted to the disc by the thrower. Factors affecting spin are a combination of grip and throwing mechanics. Spin rate is dissipated by the axial resistance torque, which is a poorly constrained function of spin rate. The rate of slowing of spin rate is inversely proportional to the disc moment of inertia.

This is a big list! It is not easy to isolate all of these factors without doing wind tunnel testing to measure the forces directly, although physics-based disc flight simulations can give some insight on how changes in each factor affect flight patterns and distance. Increasing the moment of inertia helps to stabilize a disc, but the powerful influence of slight variations in disc shape is also present. I suspect that slight variations in disc shape exerts a stronger influence on flights than moment of inertia. This view is informed by simulations that show only a very slight sensitivity in flight pattern and distance (all else being equal), and is additionally informed by the fact that every run of a disc, even if the shape differences are microscopic, has a dramatically different flight. Differences between 2 similar (but different) molds and molding processes are certain to be important, and cannot be neglected, particularly in comparison to weaker effects such a moment of inertia.

So there you have it. Take it or leave it (you can lead a horse to water...).

*The lift and drag coefficients are usually non-dimensionalized by the disc cross-sectional area, pi*R*R, however, this factor is absorbed into the coefficient here for the sake of brevity.