Disc Physics

[JHern]

(Bumping a discussion into a new thread from another less-related thread...)

I've spent a lot of time thinking about the flight ratings charts, and how complicated a topic it really is to rate the flight characteristics of a disc. Here is my take on it presently, from a physical point-of-view. It is interesting to think about how this can be made more quantitative. By quantitative, I mean the potential for taking numbers from a ratings chart and doing a physical simulation of the disc's flight to predict its behavior under a number of conditions. This is the future Blake, and I think we might be able to collaborate on this, and perhaps be the first one's to do it well.

It seems to me that there are three separate physical phenomena that occur in a disc's flight:

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1. Disc Drag: This is the aerodynamic drag on the disc due to its displacement of the surrounding air, and tends to decrease the speed of the disc in flight. Disc flight is typically in the turbulent flow regime, so that the drag is proportional to the square of the disc speed. The rule of thumb is: if you throw the disc with twice the speed, you get four times the aerodynamic drag.

Drag force is a function of the shape of the disc, nose angle, and speed alone. Drag force is completely independent of the disc mass. The drag typically increases in proportion to its cross-sectional area projected along its flight trajectory. If the disc's nose angle changes, then so too will the cross-sectional area of the disc.

Off-axis torque, OAT, is induced when the disc has a component of spin about an axis that isn't exactly parallel to its axis of symmetry. This causes the disc to wobble, and creates a pocket of turbulent air around the edge of the disc that tends to cling to it instead of flowing smoothly past the disc. This causes the effective cross-sectional area of the disc to increase.

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2. Disc Lift: This is the "wing" effect of the disc in flight, an aerodynamic force that causes the disc to lift upward and fight against gravity to remain in the air.

The lift force is approximately directed along the axis of symmetry of the disc (if the disc is laying on a flat surface, the axis of symmetry will point directly upward at right angles to that surface). It increases in proportion to the square of the disc speed, the planform area of the disc (which differs little from pi times the disc radius squared), and a lift coefficient. The lift coefficient is a function of the nose angle (or "angle of attack"). The lift force on the disc in flight is not, however, always directed through the center of the disc. Rather, the center of lift, or center of pressure, can either be in front, or in back, of the disc center (front/back relative to the disc's line of motion). This leads to precession, as discussed next.

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3. Disc Precession: This is what causes the disc to change its hyzer angle leftward or rightward while in flight. This is important, because the disc tends to travel in the direction of its in-flight hyzer angle. Given a clean release (no OAT), for a given nose angle and speed, the disc orientation does one of three things...
A. It fades. Fade is defined here as the disc's natural tendency to increase its hyzer angle while in flight through precession (left for RHBH). b]Fade[/b] is caused by a center-of-pressure/lift that is in front of the center of the disc. I.e., lifting the leading edge of the disc more than the trailing edge causes the disc to precess in a manner that makes it fade.
B. It holds the hyzer angle it is currently on. A disc can hold the line/angle it is on when the center-of-pressure/lift is at the very center of the disc.
C. It turns. Turn is defined here as the disc's natural tendency to decrease its hyzer angle while in flight through precession (right for RHBH). Turn is caused by a center-of-pressure/lift that is behind the center of the disc. I.e., lifting the trailing edge of the disc more than the leading edge causes the disc to precess in a manner that makes it turn.

The disc will typically fade or turn over a range of flight speeds, always fading at low speed and only turning at sufficiently high speeds. At some magic speed the disc is neither turning or fading, but holding the line. It is useful to define a number to the turn, and take fade as negative turn (i.e., in the opposite direction as turn). Then the holding speed is the speed of the disc in flight (for a given nose angle) at which the disc has zero turn (and by extension, zero fade).

The rate of turn, how fast the disc turns or fades for a given nose angle, is inversely proportional to the angular momentum, which is itself proportional to both the disc's mass and shape (moment of inertia) and the rate of spin on the disc. If you increase the spin rate, the disc will turn more slowly. The golden rule is: spin it twice as fast, and it will turn half as quickly in flight.

As mentioned above, the tendency to turn has to do with the center-of-pressure relative to the center of the disc. The center of pressure is the center of the lift force projected onto the disc. It tends to fall along a line parallel to the trajectory of the disc that goes through the center of the disc.

Also as mentioned previously, off-axis torque causes the disc to wobble, and creates a pocket of turbulent air around the edge of the disc that tends to cling to it instead of flowing smoothly past the disc. This interferes with the flow of air around the disc in a way that pushes the center of pressure back and therefore increases the turn.

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So, that's the basic outline. I have written down a set of equations that can be used to simulate the motion of the disc, given the above assumptions and a few more. I'll probably try some simulations soon to see what it looks like.

I think there are some important numbers here. In the chart is the strength of the turn at low and high speed (LSS and HSS), and the power (speed) requirement. To me, one measure of the power requirement could be something like the power (in terms of distance is fine) needed to get a disc to hold a straight line. Speed at zero turn would be even better, but I don't think most players are cognizant of their speeds. Anyways, with some modeling, we could indeed begin to tabulate this kind of information for various discs, but there are many variables that need to be better constrained first...I'll have to think about how to do that in the best way without too much special equipment being required.

Here is a figure I whipped up to help explain how the offset between the center-of-pressure and the center of the disc causes it to turn while in flight. I hope it makes sense.

 

[TEX]

I wish you would have posted this info back when I was trying to do a project on disc flight. :lol: :lol:

 

[Dogma1]

I don't have time to read back through it, but have you read this thread: http://www.discgolfreview.com/forums/viewtopic.php?f=3&t=11666

There have been a few similar thread before that one.

 

[grizzles]

I'd like to see the equations. It'd be great if you could run some simulations. I was just thinking about this last week. It's cool that you're thinking about this.

J

 

[George1]

Thanks for creating this thread, JHern. Here's my reply copied over from the old thread.
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JHern,

Your figure is excellent, thanks for posting that!

I would add to your explanation that the weight of the disc affects the disc flight in (at least) two different ways. One is the moment of inertia (which you explain)—a lighter disc of the same shape will have a smaller moment of inertia, and, if the angular velocity is the same, will have a smaller angular momentum and therefore be subject to greater precession.

The second manner in which the weight enters is in the angle of attack. If two discs, identical except for mass, are thrown level with the same speed and the same angular velocity, the lift on the two discs will be the same, but the force of gravity will be smaller on the lighter disc. The net upward force will therefore be greater on the lighter disc, and it will rise faster. A level disc that is rising has a negative angle of attack. (I’m considering angle of attack to be slightly different from nose angle in that angle of attack is with respect to the air whereas nose angle is with respect to the horizontal ground.) Because of its faster rise, the angle of attack of the lighter disc will be more negative (than that of the heavier disc), causing the center of pressure to move farther behind the center of the disc, and thereby creating a greater torque and more precession. When a level disc is falling, the reverse is true: the center of pressure moves forward. In airfoils, I believe this effect is largely characterized by the pitching moment coefficient, which also changes with angle of attack, but I could be wrong.

Jonny Potts (who founded Discwing) measured the pitching moment of a disc (I don’t think it was a golf disc) in a wind tunnel and measured the change of pitching moment with angle of attack and described it in this paper:

http://www.discwing.com/research/flowOverRotate.html

Although the initial turn and the final fade are generally thought of solely in terms of speed by disc golfers, I think the changing angle of attack (negative in the first part of the flight, and positive in the final part) plays a major role in causing the typical S-curve flight. Of course since lift increases with increasing speed, the angle of attack and the speed are closely related.

Disclaimer: I am not an aerodynamicist but I am a physicist (and a mediocre rec masters disc golfer).

George

 

[George1]

Here are a few disc physics links I've found. --George

Frisbee Flight Simulation and Throw Biomechanics (http://mae.engr.ucdavis.edu/~biosport/frisbee/frisbee.html) Contains Sarah Hummel’s Master’s Thesis at UC Davis and other disc related research.

Discwing’s Research Page (http://www.discwing.com/research/aerodynamics.html) Papers by Jonny Potts (the founder of Discwing) and his collaborators. Includes wind-tunnel tests made on discs.

Frisbee Physics (http://web.mit.edu/womens-ult/www/smite/frisbee_physics.pdf) A paper by V. R. Morrison hosted on the MIT Women’s Ultimate page. Contains flight simulation Java code.

A Computational Study of Flow around a Rotating Disc (http://www.microcfd.com/download/pdf/dissertation.pdf) Axel Rohde’s doctoral dissertation in aerospace engineering at the Florida Institute of Technology.

“The physics related to different golf disc models” (http://www.odgc.ca/files/dg-flightphysics-mkIV.pdf) Article by Ken Darovich of the Ottawa Disc Golf Club.

 

[Jeronimo]

I was always under the impression that OAT was caused by Precession. Why is that not the case? In other words how is it precession that causes turn over?

 

[Blake_T1]

JHern:

if you want to write up an article thing i will post it on the main site.

 

[chiggins]

Speed at zero turn would be even better, but I don't think most players are cognizant of their speeds.

Perhaps they would be if that zero-turn-speed were part of the rating? I think it would be pretty interesting to find that number for some DGR staples, and then have Bradley set up the camera and radar gun and see how that plays out.

 

[Nothaz]

http://www.discwing.com/research/aerodynamics.html

 

[JHern]

JHern: if you want to write up an article thing i will post it on the main site.

Blake: Sure thing. I'm writing it up along the way, and there is definitely more to come. Is PDF ok for this purpose? It's hard to have equations and such using standard text or html, and I'm pretty sure everybody's web browser can handle PDF these days.

I'll probably need feedback, since I'm used to writing technical papers for journals and some of the stuff might need more explanation. Let's use this thread to iron out the presentation, and get feedback in case any part of the text is not clear enough.

I'd like to see the equations. It'd be great if you could run some simulations. I was just thinking about this last week. It's cool that you're thinking about this.

Jack: Great to see your interest. I was thinking of animating the solutions as well, and maybe code up disc shapes in povray or something like that to show high quality movies of the flights.

I don't have time to read back through it, but have you read this thread: http://www.discgolfreview.com/forums/viewtopic.php?f=3&t=11666
There have been a few similar thread before that one.

Dogma: Yes, this has been discussed in many threads, but they were only fleeting and lacking commitment. This thread will follow things through to the bitter end.

Here are a few disc physics links I've found. --George

George: Thanks.

 

[JHern]

Speed at zero turn would be even better, but I don't think most players are cognizant of their speeds.

Perhaps they would be if that zero-turn-speed were part of the rating? I think it would be pretty interesting to find that number for some DGR staples, and then have Bradley set up the camera and radar gun and see how that plays out.

Let's do it! Right now I'm working on analyzing the governing equations to find some tricks to tease out some of the relationships between the input parameters based on simple measurements of the disc's flight.

One thing I've been studying is that each disc has a magic cruise speed (it is nose angle dependent), and I've derived the appropriate expression. If you can measure the speed of the disc in level flight, as well as its nose angle, then it is possible to constrain the coefficient of aerodynamic lift. If this is done at several different nose angles, then the angle of attack at zero lift can also be determined. Then, when the disc is in its gliding stage, and is undergoing a steady descent, the angle of descent can be used to constrain the drag coefficient as well.

Once all these parameters are known, they can be used to define a new disc flight chart, with a set of physically based parameters instead of the subjective charts in use at the present time (you know, with the vague definition of speed, turn, fade, glide, etc.). But this disc flight chart will be awesome, because it offers predictive power: if you input the parameters, then you can calculate how the disc will fly at various speeds, angles of release, etc., without ever throwing the disc. This would offer a very cool way for people to assess how different discs would fly for them if they were to actually throw them.

 

[JHern]

I was always under the impression that OAT was caused by Precession. Why is that not the case? In other words how is it precession that causes turn over?

The basic idea is that spinning the disc gives it gyroscopic stability: a pitching moment (i.e., a force that pushes the nose/tail down or up while in flight) gives rise to left/right tilt (i.e., turn) of the disc, instead of actually pushing the nose up or down. In fact, while the air is doing its best to push the nose up or down in flight, the nose angle doesn't ever really change a great deal from the time it leaves your hand up until the point it reaches the target (at ultra-slow speeds the nose angle might change, but that's the least interesting part of the flight).

OAT=Off-axis torque. Here, axis=the axis of symmetry of the disc. If you impart a spin onto the disc that isn't exactly parallel to the axis of symmetry, the disc will appear to wobble. This is OAT.

 

[JR]

Way cool!

If some sort of flight chart is compiled a quick and dirty buyers guide paper version for stores and people going to a store without the ability to browse the simulator for different nose angles should probably have nose angle of 0 in the values for cruising speed. Cruising speed meaning the speed _range_ where the disc won't turn or fade. A broken in Roc and Teebird vary greatly from the run of the mill discs in the breadth of the speed range where they won't turn or fade.

Perhaps nose angle manipulation should be shown how it's done. For example wrestling the wrist down farther than the disc parallel to the bones of the forearm and raising the rear of the disc above the seam of the hand.

I suggest 0 degrees nose angle because not every player is able to keep the disc front lower than the rear at release on line drives. I suggest normalizing for flat releases because hyzer and anhyzer releases differ from flat throws and have easier time of having the nose down after the apex of the flight. Apex should also be defined. The point where the disc reaches the maximum altitude in the flight might be suitable.

The term nose is not widely known I suspect so defining it to be variable from the front edge of the disc facing the oncoming wind the disc sees is also a must for the understanding of the uninitiated.

 

[Blake_T1]

I suggest 0 degrees nose angle because not every player is able to keep the disc front lower than the rear at release on line drives. I suggest normalizing for flat releases because hyzer and anhyzer releases differ from flat throws and have easier time of having the nose down after the apex of the flight. Apex should also be defined. The point where the disc reaches the maximum altitude in the flight might be suitable.

a 0 degree nose angle on most of the wide winged drivers would yield some rather absurd results that are extremely far from what is required to get a disc's designed characteristics.

 

[TEX]

I don't know if this is off topic, but I don't quite understand what everybody means when you say to throw the disc with the nose down. Also, is there a thread that explains all of the different terms that you guys use so that us uninformed individuals can understan dwhat you guys are talking about.

 

[Moseley]

is there a thread that explains all of the different terms that you guys use so that us uninformed individuals can understan dwhat you guys are talking about.

http://discgolfreview.com/resources/tips.shtml#terms

 

[JR]

I suggest 0 degrees nose angle because not every player is able to keep the disc front lower than the rear at release on line drives. I suggest normalizing for flat releases because hyzer and anhyzer releases differ from flat throws and have easier time of having the nose down after the apex of the flight. Apex should also be defined. The point where the disc reaches the maximum altitude in the flight might be suitable.

a 0 degree nose angle on most of the wide winged drivers would yield some rather absurd results that are extremely far from what is required to get a disc's designed characteristics.

I should have been more thorough. The angle must be referenced and I suggest a relation to horizon at the rip. What I meant was that perhaps it's beneficial to pick an angle available to even amateurs without too much trouble and still not nose up. The front of the disc and the rear of the disc at equal height is golfable. Aka a low line drive. Additional explanation what happens when the front is higher than the rear and vice versa should help.

 

[discspeed]

I suggest 0 degrees nose angle because not every player is able to keep the disc front lower than the rear at release on line drives. I suggest normalizing for flat releases because hyzer and anhyzer releases differ from flat throws and have easier time of having the nose down after the apex of the flight. Apex should also be defined. The point where the disc reaches the maximum altitude in the flight might be suitable.

a 0 degree nose angle on most of the wide winged drivers would yield some rather absurd results that are extremely far from what is required to get a disc's designed characteristics.

I should have been more thorough. The angle must be referenced and I suggest a relation to horizon at the rip. What I meant was that perhaps it's beneficial to pick an angle available to even amateurs without too much trouble and still not nose up. The front of the disc and the rear of the disc at equal height is golfable. Aka a low line drive. Additional explanation what happens when the front is higher than the rear and vice versa should help.

Nose down orientation can be achieved simply through a proper grip. It was taught to me (either by reading what Blake wrote or Dave D., I can't remember) by describing a cocked wrist position similar to when you are pouring coffee from a coffee pot.

 

[Jeronimo]

http://www.discwing.com/research/flowOverRotate.html

That was an enlightening read. It would appear some of my earlier assumptions were in fact in error. I'll have to do some numerical analysis myself.

On the nose angle/cruise speed topic: It sounds as if the ideal nose angle is one that is low enough to account for the lift generated? Similar to how a satellite in orbit is designed to move at just the right speed to account for the force of gravity in order to keep it in orbit?