Blake_T wrote:You guys are the experts on disc throwing (I'm relatively just an amateur), but Blake, this raises my hackles a bit as a physicist. 8-15 Hz is a variation by a factor of two. The torques acting on a disc in flight will only depend on the flight speed and orientation (i.e., nose/hyzer angle). (I think wind tunnel tests have put to rest any notion that rotation affects the torques.) A disc flying with 15 Hz spin will turn (or fade) about twice as slowly as a disc flying with 8 Hz spin given the same flight speed and orientation.
This is not conjecture, it is a law of physics.
i'm very interested in the physics equations if you have them handy. i was an engineering major for 2 years and a physics major for 2 years but i'm so far removed from it that i only remember a handful of equations.
keep in mind that the 8-15 RPS is a range that encompasses at least 2/3rds of players, possibly more. someone's ability to manipulate spin while keeping launch angles, launch velocity, etc. the same is likely more along the lines of 2-5 RPS. it's the "being able to keep everything else the same while still manipulating spin" part of things that i don't put a lot of stock in.
this is also very dependent upon speed ranges and the disc's aerodynamic properties. if you ever wonder why pro bags are often so similar in terms of their workhorse discs (and the weights), there's only a handful of discs on the market that seem to whittle their way into nearly every pro bag. these discs are usually those that are extremely HSS.
for a player who has an average launch velocity near 70mph (these guys also generally have tremendous amounts of spin), why is it that nearly every disc flips unless it's an extremely stable model and at max weight? how much spin would it take to make a disc like a sidewinder not turn over with a 70mph launch velocity and 5 degrees of nose down?
The basic law is:
where L is angular momentum, t is time, I is the moment of inertia (about the spin axis), w is the angular velocity and tau is the torque (or moment of force) acting on the disc. d/dt is the time derivative (rate of change with time).
This is a vector equation (and strictly speaking, I is a second rank tensor), so even if the rotation rate is constant, disc turn/fade amounts to a change in orientation of the angular velocity vector and hence non-zero terms in the vector equation. The magnitude of I increases as the disc mass, disc radius, and amount of disc material distributed outward toward the rim increases (it is easy to calculate). Aerodynamic forces (due to linear velocity, orientation, and disc shape) govern tau. For a disc turning in flight, tau is perpendicular to w, and causes the disc to precess even though the rotation rate doesn't change appreciably. According to the basic equation, the rate of turning is tau/I. This is why heavier discs turn over less than lighter discs for the same throw velocity/orientation/disc mold.
The answer to your question about the Sidewinder is: For a very HSS disc, tau might be nearly zero at a given high velocity and orientation (such as 70 MPH, 5 degrees nose down) owing to aerodynamic factors alone, while for a Sidewinder the aerodynamic factors might be such that tau is not zero for the same aerodynamic factors (i.e., speed, orientation). In this case the Sidewinder will turn no matter how rapidly it spins. The relative rate at which it turns will be inversely proportional to the spin rate,
Say tau_sw is the torque on a Sidewinder (with moment of inertia I_sw) at 70 MPH and 5 degrees nose down, while tau_od is the torque on "other disc" (with moment of inertia I_od) at 70 MPH and 5 degrees nose down. The relative rate of turn on the Sidewinder is given by dividing the equation for one by the other,
Calculating tau for various speeds and orientations is difficult (it involves solving the turbulent flow problem), and would require a super-computer simulation to do it properly. In a sense, what you do is a natural simulation by just going out and throwing consistently at various speeds/nose angles and judging LSS and HSS. A computer simulation can tell you the same things, but at much greater expense. Of course, your number system is somewhat subjective and works in a relative sense, while the full computer simulation would yield more objective data. It would also give a value for tau at all disc speeds, instead of just two speeds (it would be interesting to see the turning torque plotted as a function of speed for various nose angles...it is probably not linear, and could be curved this way or that way for different molds). This isn't, of course, meant to take anything away from the valuable services you provide...it is the best thing around right now.