Disc Physics

[Muddyboots]

It occurs to me that measuring some of the initial properties of the throw could be achieved fairly easily with a high frame rate camera, aimed at a storyboard or green screen as a disc with ink markings is thrown in front of it. From there, couldn't you extrapolate velocity (both foward and radial?)? Some sort of timing would be important as well, for initial figures. I am still thinking on how to measure or track the pitch of the projectile, without adding a device to the disc that would skew the flight. Wonder if we could borrow the cable cams that seem so popular in football stadiums lately. I would guess that they are not fast enough. They used to have higher speed rail cams at certain racetracks too, but without some sort of frame of reference, the best you could hope for was swag (carpenter speak "scientific wild ass guess"). Seems like there would be a system wherein we could replicate the velocity of the disc, even if it wasn't moving foward, think super fast turntable or lathe. You could move the axis around which the disc rotated, but how do you make it come back to center (equilibrium) and then slow to fade? Simulated wind across above contraption? This is all an effort to get around having to track the disc in flight, in essence, keep the flight static for observation. I see possibilities here. What is everyones' best guess as to how far the axis moves during flight? I would think mms for any flight that stays up very long. Is it cms? Should I try and supercharge a record player and sneak into a variable speed wind tunnel?
KP

 

[JHern]

KP, interesting thoughts. The other possibility is to build a cheap wind tunnel, of sorts, and measure all this stuff directly.

I'm not sure what you mean by "how far the axis moves during flight?"

 

[JR]

With two cameras with known aperture/focal length placed at known positions and angles relative to some markers we could probably do some triangulation, although it is a bit more of a hassle. The accuracy will increase the more you place the camera to the side and obtain a side projection.

I think a streaky image of the disc flying is OK for a start, if you want to try a purely side projection with as straight a flight as you can manage to throw (as a starting point). With many frames we could fit a smooth parametric function through the blurred data points (i.e., x(t) and z(t) type of thing), and then use the fitting data to obtain the information we need. For starters, we don't need to capture the entire flight, maybe just the apex and the glide, which would already tell us a lot about the disc's aerodynamic parameters. The hard thing will be to determine the nose angle from the images, which is an important parameter.

If one of two cameras were used either for apex filming or as an extension to the first camera's view there's one point of the second camera's image that doesn't need triangulation and can be used as a sanity check. That point is the middle of the camera's view. I think that it wouldn't take too many attempts to get a flat throw with the front and rear of the disc equally high above the ground to get zero degree variation from horizon. Would that help?

Regarding a flat throw and you say there's one and only one cruising speed not a range of speeds where the disc holds the exact same height -it may be true. To an extent because discs aren't balls that either rise, fall or one infitestimally small period of time keeps the altitude at the apex. Which for practical purposes is a non issue because that time can be taken as limes zero in duration. A Roc may be slightly different. I just don't know if it's relevant to simulation if a spinning wide diameter disc can hold altitude for one second at say 30 mph and 29.7MPH. Or a shorter or a longer time and speed variation -I don't know. Determining that would take a high resolution high speed camera with the disc needing to pass the apex flying flat in the video in front of a vertical tape measure. Tall order.

For practical terms nobody has the height control within an inch at 200' but many can keep the disc within that one inch height window for quite a while in time, speed difference and distance from the tee. Rarely does one need such height accuracy. Even more relevantly 5" height variation or whichever figure you pick could be used. Cruising speed range +- some height window allowance for speed variation is a relevant function in shot and disc selection especially when driving with putters and mids. Discspeed would surely argue for a Buzzz for keeping height on low line drives farther out than a Roc Cruising speed range for a given height window may be able to be captured in high speed mode filming the apex. But unlikely with the resolution we have available. Or the camera guy would have to risk getting hit by the disc if shelter can't be found for him. The disc would have to pass close, few feet due to resolution limitations, at the right height showing the vertical tape measure. Even though mafa has a remote control for his camera and we can use a tripod I don't think he'd risk his camera for this

Right now I can't think of uphills that are long, wide and mild enough uphill close to me. If I threw upward a mild enough hill and the camera would lie at the side of the apex measured in distance from the throwing place we could get the apex and the glide. Until the disc hits the hill. The question is how high of an apex is relevant? The optimum height for my power changes with the disc.

Hmm I just thought of a known GPS measured place with a viewer stand that is higher than the field so flat land throwing with optimum height apexes for my limited nose down angle is filmable. Any apex is filmable from the apex height. Hitting the height flat is another matter The sports field has one line that I remember 100 % certainly to be 90 meters from on end of the field and 33 m from the other end. Viewing from the back of the thrower from the 90 m line direction I think the other lines were 40, 60 and 70 m. They can be measured for confidence but using walking measuring they seem to work.

I'd hate to complicate matters by bringing up a phenomenon that needs capturing in video and simulating. I don't know the names of physics reasons for sure and exact causes for the following flight behavior: In calm weather a purely thrown flight can hyzer flip a disc to flat and fly with no hyzer or anny then at about 250' +-? the disc turns clockwise into an anhyzer. Blake has written about it and IIRC it has to do with the spin rate going down and something else. Naturally the speed is also down but where does cruise speed fit into this? The fastest disc I've achieved this with initially 8' apex line drive is a 145 R-Pro Boss. It annied to ground higher throws have flexed back. Can't do it it full weight Bosses but have up to 160 R-Pro. And naturally slower discs.

Last week I got my best face high line drive ever with that 145 Boss staying flat until 360' fading a foot hitting the ground at about 387' skipping to two feet left 403'. I don't think it fell a foot below maxmum height (can you call out an apex with this kind of shot that is falling indetectable to the eye to at least 280'?) until about 330'-340'. Now it's colder so a repeat is unlikely before summer. Valk DX 175 line drives earlier in much warmer weather to 400' were higher. I have no clue how fast these throws were. But there's clues to my limits speed wise. And the ability to get the disc turning right after 250' line drive. What I can tell is that these late turning throws need is a few degrees less initial hyzer and a lot of power. Both 145 Boss and 175 Valk throws had full run up ad Brinster hop so I threw as hard muscle wise as I could with my limited form and timing.

 

[RAWB]

:wink:

 

[JR]

:wink:

Will nuke your caveman ass. Keep throwing sticks dildo

 

[JHern]

If one of two cameras were used either for apex filming or as an extension to the first camera's view there's one point of the second camera's image that doesn't need triangulation and can be used as a sanity check. That point is the middle of the camera's view. I think that it wouldn't take too many attempts to get a flat throw with the front and rear of the disc equally high above the ground to get zero degree variation from horizon. Would that help?

Regarding a flat throw and you say there's one and only one cruising speed not a range of speeds where the disc holds the exact same height -it may be true. To an extent because discs aren't balls that either rise, fall or one infitestimally small period of time keeps the altitude at the apex. Which for practical purposes is a non issue because that time can be taken as limes zero in duration. A Roc may be slightly different. I just don't know if it's relevant to simulation if a spinning wide diameter disc can hold altitude for one second at say 30 mph and 29.7MPH. Or a shorter or a longer time and speed variation -I don't know. Determining that would take a high resolution high speed camera with the disc needing to pass the apex flying flat in the video in front of a vertical tape measure. Tall order.

For practical terms nobody has the height control within an inch at 200' but many can keep the disc within that one inch height window for quite a while in time, speed difference and distance from the tee. Rarely does one need such height accuracy. Even more relevantly 5" height variation or whichever figure you pick could be used. Cruising speed range +- some height window allowance for speed variation is a relevant function in shot and disc selection especially when driving with putters and mids. Discspeed would surely argue for a Buzzz for keeping height on low line drives farther out than a Roc Cruising speed range for a given height window may be able to be captured in high speed mode filming the apex. But unlikely with the resolution we have available. Or the camera guy would have to risk getting hit by the disc if shelter can't be found for him. The disc would have to pass close, few feet due to resolution limitations, at the right height showing the vertical tape measure. Even though mafa has a remote control for his camera and we can use a tripod I don't think he'd risk his camera for this

Right now I can't think of uphills that are long, wide and mild enough uphill close to me. If I threw upward a mild enough hill and the camera would lie at the side of the apex measured in distance from the throwing place we could get the apex and the glide. Until the disc hits the hill. The question is how high of an apex is relevant? The optimum height for my power changes with the disc.

Hmm I just thought of a known GPS measured place with a viewer stand that is higher than the field so flat land throwing with optimum height apexes for my limited nose down angle is filmable. Any apex is filmable from the apex height. Hitting the height flat is another matter The sports field has one line that I remember 100 % certainly to be 90 meters from on end of the field and 33 m from the other end. Viewing from the back of the thrower from the 90 m line direction I think the other lines were 40, 60 and 70 m. They can be measured for confidence but using walking measuring they seem to work.

Don't risk your health or equipment for this, please. All we can do is give it a try, and see how well it works. I think there is useful information that can be gained even from simple films of the flight.

I'd hate to complicate matters by bringing up a phenomenon that needs capturing in video and simulating. I don't know the names of physics reasons for sure and exact causes for the following flight behavior: In calm weather a purely thrown flight can hyzer flip a disc to flat and fly with no hyzer or anny then at about 250' +-? the disc turns clockwise into an anhyzer. Blake has written about it and IIRC it has to do with the spin rate going down and something else. Naturally the speed is also down but where does cruise speed fit into this? The fastest disc I've achieved this with initially 8' apex line drive is a 145 R-Pro Boss. It annied to ground higher throws have flexed back. Can't do it it full weight Bosses but have up to 160 R-Pro. And naturally slower discs.

This remains to be seen. I can see that a decrease in spin would cause a disc flying flat for a while to turn over later in its flight. But the disc would not be perfectly flat for a time, instead it would be turning very very slowly and then accelerating in its turn until it becomes noticeable. The numbers for damping the spin are fairly well-known, and this hypothesis can definitely be tested with the numerical simulation for various input parameters. Sounds like a fun flight to model!

Last week I got my best face high line drive ever with that 145 Boss staying flat until 360' fading a foot hitting the ground at about 387' skipping to two feet left 403'. I don't think it fell a foot below maxmum height (can you call out an apex with this kind of shot that is falling indetectable to the eye to at least 280'?) until about 330'-340'. Now it's colder so a repeat is unlikely before summer. Valk DX 175 line drives earlier in much warmer weather to 400' were higher. I have no clue how fast these throws were. But there's clues to my limits speed wise. And the ability to get the disc turning right after 250' line drive. What I can tell is that these late turning throws need is a few degrees less initial hyzer and a lot of power. Both 145 Boss and 175 Valk throws had full run up ad Brinster hop so I threw as hard muscle wise as I could with my limited form and timing.

Yes, this sounds useful. These properties will be important for characterizing the disc's physical parameters.

For your reference, the cruise speed of the lids that Potts (wind tunnel) and Hummel (camera+simulation) measured were only around 7 m/sec. I don't know what the Valkyrie or Boss would be, probably quite a bit higher, but certainly not astronomical. So, no need to throw the disc really really far to characterize the properties of the disc flight. Just get the discs into their operating speed range, and that will be a good starting place. For the Boss this probably requires a lot of speed (i.e, 400+), but the Valk is fine at 300+ power.

 

[JR]

If one of two cameras were used either for apex filming or as an extension to the first camera's view there's one point of the second camera's image that doesn't need triangulation and can be used as a sanity check. That point is the middle of the camera's view. I think that it wouldn't take too many attempts to get a flat throw with the front and rear of the disc equally high above the ground to get zero degree variation from horizon. Would that help?

Regarding a flat throw and you say there's one and only one cruising speed not a range of speeds where the disc holds the exact same height -it may be true. To an extent because discs aren't balls that either rise, fall or one infitestimally small period of time keeps the altitude at the apex. Which for practical purposes is a non issue because that time can be taken as limes zero in duration. A Roc may be slightly different. I just don't know if it's relevant to simulation if a spinning wide diameter disc can hold altitude for one second at say 30 mph and 29.7MPH. Or a shorter or a longer time and speed variation -I don't know. Determining that would take a high resolution high speed camera with the disc needing to pass the apex flying flat in the video in front of a vertical tape measure. Tall order.

For practical terms nobody has the height control within an inch at 200' but many can keep the disc within that one inch height window for quite a while in time, speed difference and distance from the tee. Rarely does one need such height accuracy. Even more relevantly 5" height variation or whichever figure you pick could be used. Cruising speed range +- some height window allowance for speed variation is a relevant function in shot and disc selection especially when driving with putters and mids. Discspeed would surely argue for a Buzzz for keeping height on low line drives farther out than a Roc Cruising speed range for a given height window may be able to be captured in high speed mode filming the apex. But unlikely with the resolution we have available. Or the camera guy would have to risk getting hit by the disc if shelter can't be found for him. The disc would have to pass close, few feet due to resolution limitations, at the right height showing the vertical tape measure. Even though mafa has a remote control for his camera and we can use a tripod I don't think he'd risk his camera for this

Right now I can't think of uphills that are long, wide and mild enough uphill close to me. If I threw upward a mild enough hill and the camera would lie at the side of the apex measured in distance from the throwing place we could get the apex and the glide. Until the disc hits the hill. The question is how high of an apex is relevant? The optimum height for my power changes with the disc.

Hmm I just thought of a known GPS measured place with a viewer stand that is higher than the field so flat land throwing with optimum height apexes for my limited nose down angle is filmable. Any apex is filmable from the apex height. Hitting the height flat is another matter The sports field has one line that I remember 100 % certainly to be 90 meters from on end of the field and 33 m from the other end. Viewing from the back of the thrower from the 90 m line direction I think the other lines were 40, 60 and 70 m. They can be measured for confidence but using walking measuring they seem to work.

Don't risk your health or equipment for this, please. All we can do is give it a try, and see how well it works. I think there is useful information that can be gained even from simple films of the flight.

I'd hate to complicate matters by bringing up a phenomenon that needs capturing in video and simulating. I don't know the names of physics reasons for sure and exact causes for the following flight behavior: In calm weather a purely thrown flight can hyzer flip a disc to flat and fly with no hyzer or anny then at about 250' +-? the disc turns clockwise into an anhyzer. Blake has written about it and IIRC it has to do with the spin rate going down and something else. Naturally the speed is also down but where does cruise speed fit into this? The fastest disc I've achieved this with initially 8' apex line drive is a 145 R-Pro Boss. It annied to ground higher throws have flexed back. Can't do it it full weight Bosses but have up to 160 R-Pro. And naturally slower discs.

This remains to be seen. I can see that a decrease in spin would cause a disc flying flat for a while to turn over later in its flight. But the disc would not be perfectly flat for a time, instead it would be turning very very slowly and then accelerating in its turn until it becomes noticeable. The numbers for damping the spin are fairly well-known, and this hypothesis can definitely be tested with the numerical simulation for various input parameters. Sounds like a fun flight to model!

Last week I got my best face high line drive ever with that 145 Boss staying flat until 360' fading a foot hitting the ground at about 387' skipping to two feet left 403'. I don't think it fell a foot below maxmum height (can you call out an apex with this kind of shot that is falling indetectable to the eye to at least 280'?) until about 330'-340'. Now it's colder so a repeat is unlikely before summer. Valk DX 175 line drives earlier in much warmer weather to 400' were higher. I have no clue how fast these throws were. But there's clues to my limits speed wise. And the ability to get the disc turning right after 250' line drive. What I can tell is that these late turning throws need is a few degrees less initial hyzer and a lot of power. Both 145 Boss and 175 Valk throws had full run up ad Brinster hop so I threw as hard muscle wise as I could with my limited form and timing.

Yes, this sounds useful. These properties will be important for characterizing the disc's physical parameters.

For your reference, the cruise speed of the lids that Potts (wind tunnel) and Hummel (camera+simulation) measured were only around 7 m/sec. I don't know what the Valkyrie or Boss would be, probably quite a bit higher, but certainly not astronomical. So, no need to throw the disc really really far to characterize the properties of the disc flight. Just get the discs into their operating speed range, and that will be a good starting place. For the Boss this probably requires a lot of speed (i.e, 400+), but the Valk is fine at 300+ power.

I wouldn't wonder if Blake utilized a brick to the head for saying a Valk is fine at 300'. From learning and minimalism point of view his stance is defensible. Even though one can be accurate with a DX Valk at 200'. But I quote Nate Doss talking of a different thing but highly appropriate in this case: That's not allowing the disc to fly. You don't know the Valk fully until you get it to 370' minimum and 400' is even better and I expect at 450'+ it's yet again a very different animal although I haven't experienced it personally.

The simulator should be a great tool for illustrating the different characteristics a disc has at different speeds.

Late turn ain't a theory it's fact. IIRC I saw a Billy Crump interview of Barry Schulz where they talked how Barry had a late turn with a Roc over a lake last year. Dave D wrote that spin lasts 20-25 seconds. Avery Jenkins got up to about 20 revolutions per second in the vid on youtube in the folder of mfranssila.

 

[JHern]

I wouldn't wonder if Blake utilized a brick to the head for saying a Valk is fine at 300'. From learning and minimalism point of view his stance is defensible. Even though one can be accurate with a DX Valk at 200'. But I quote Nate Doss talking of a different thing but highly appropriate in this case: That's not allowing the disc to fly. You don't know the Valk fully until you get it to 370' minimum and 400' is even better and I expect at 450'+ it's yet again a very different animal although I haven't experienced it personally.

In any case, for initial data acquisition purposes, we really don't need to get a Valkyrie into the 350+ regime. A disc's aerodynamic coefficients have mostly been found to be the same at all speeds/distances (i.e., independent of Reynolds number). You're more than welcome to do long throws, of course, but it isn't absolutely necessary as a first step, and shorter flights might be easier to film. All you need to do is exceed the cruise speed, which is fairly easy to do with a Valk for most players (I am betting the cruise speed is around 15 m/sec).

The simulator should be a great tool for illustrating the different characteristics a disc has at different speeds.

That's the idea.

Late turn ain't a theory it's fact. IIRC I saw a Billy Crump interview of Barry Schulz where they talked how Barry had a late turn with a Roc over a lake last year.

The "spin-out" explanation for late turn is a hypothesis, which we will consider untested for the moment until it can be demonstrated with actual physical numbers. Don't worry, this is on my radar.

Dave D wrote that spin lasts 20-25 seconds.

If the yaw force on a disc goes linearly in rotation rate, then it is easy to get a solution for this part of the motion...it will simply be an exponential decay in speed. Each disc will therefore have an e-fold time-scale, or "half-life" of spin. This will be a parameter in the models.

According to work already done on measuring this damping force (where it was found to be very small in comparison to other forces), 20-something seconds sounds reasonable.

Avery Jenkins got up to about 20 revolutions per second in the vid on youtube in the folder of mfranssila.

20 Hz rotation is pretty darn fast. I'll have to see if this kind of rotation rate gets us into non-linear territory...if so, this can be handled relatively straightforwardly, but is more of a hassle, to be sure.

 

[mafa]

..the disc always fades out in the same direction at low speeds, and turns in the opposite direction at high speeds. The pitching moment for fade is always nose lifting in orientation, and the pitching moment for high speed turn is nose depressing in orientation. The center of pressure must therefore cross from behind the center at high speeds to in front of the center at low speeds. This corresponds to a negative pitching moment at high speeds and a positive pitching moment at low speeds. In the literature I have seen, this kind of speed dependence of the position of the center of pressure is not realized/used/written in the formulation of the pitching moment (v^2 is present and goes along with the lift but is always positive/non-negative while the change needs to be from positive to negative), and it seems to me that this could lead to big errors in modeling the flight.

Let the discussion start:

In literature pitching moment does change sign but as a function of _AoA_, not speed. This has been stated for all kind of airfoils I have this far found, not just frisbees of which there are much less research results available. In the frisbee studies ( i.e. Potts & Crowther) the change of sign was around 9 degrees nose up. This would imply the pitching moment is negative with _all_ velocities if the AoA is below the limit angle for given disc. There's also concept of aerodynamic center of a wing about which the aerodynamic torque is constant with AoA. Maybe knowing the location of aerodynamic center of disc could give some insight into stability of discs.

This approach does not contradict in my opinion with the concepts of high speed stability and slow speed stability. With high speed flight (considerably more than cruising speed) the disc tends to rise thus lowering AoA and increasing nose-down pitching moment which will lead to faster high-speed turn. In slow speed (below crusing speed) the disc will fall and and AoA increases thus leading to positive (nose-up) moment leading to fade. Fade causes the disc to fall even faster.

It would be nice to have some wind-tunnel time with contemporary discs to actually measure load data and how pitching coefficient/moment really works. With the near-finished models and simulator we just give it to Blake and dgdave to tune in all the parameters of all known discs on the planet (as someone already suggested)

I am not sure how much data we can extract from throwing drives on the field with one camera. We would need to know the launch conditions and flight path of each sample throw.

Matti

 

[JHern]

..the disc always fades out in the same direction at low speeds, and turns in the opposite direction at high speeds. The pitching moment for fade is always nose lifting in orientation, and the pitching moment for high speed turn is nose depressing in orientation. The center of pressure must therefore cross from behind the center at high speeds to in front of the center at low speeds. This corresponds to a negative pitching moment at high speeds and a positive pitching moment at low speeds. In the literature I have seen, this kind of speed dependence of the position of the center of pressure is not realized/used/written in the formulation of the pitching moment (v^2 is present and goes along with the lift but is always positive/non-negative while the change needs to be from positive to negative), and it seems to me that this could lead to big errors in modeling the flight.

Let the discussion start:

In literature pitching moment does change sign but as a function of _AoA_, not speed. This has been stated for all kind of airfoils I have this far found, not just frisbees of which there are much less research results available. In the frisbee studies ( i.e. Potts & Crowther) the change of sign was around 9 degrees nose up. This would imply the pitching moment is negative with _all_ velocities if the AoA is below the limit angle for given disc. There's also concept of aerodynamic center of a wing about which the aerodynamic torque is constant with AoA. Maybe knowing the location of aerodynamic center of disc could give some insight into stability of discs.

This approach does not contradict in my opinion with the concepts of high speed stability and slow speed stability. With high speed flight (considerably more than cruising speed) the disc tends to rise thus lowering AoA and increasing nose-down pitching moment which will lead to faster high-speed turn. In slow speed (below crusing speed) the disc will fall and and AoA increases thus leading to positive (nose-up) moment leading to fade. Fade causes the disc to fall even faster.

There is no question that the pitching moment is a function of AoA, and changes sign in the manner you suggest. However, I know very well from my experience that I can prevent a nose up disc from fading rapidly left by throwing it faster, even when that same AoA would result in fade at lower speeds. I use this kind of throw when I'm forced to throw understable plastic and get it to fade left more sharply at the end of the flight (especially mid-range left doglegs). This alone suggests a velocity dependence.

What's worse for the only-AoA-dependence is that the pitching moment scales as v^2, and at higher speeds and the disc should fade much much more quickly for the same AoA as a disc flying at low speeds with the same AoA. So this simple parameterization predicts that the kind of throw I describe above is completely impossible, and that the faster I throw the disc with a nose up orientation, the harder it will fade for a nose up throw.

I think we all probably know from experience that this must be wrong.

It would be nice to have some wind-tunnel time with contemporary discs to actually measure load data and how pitching coefficient/moment really works. With the near-finished models and simulator we just give it to Blake and dgdave to tune in all the parameters of all known discs on the planet (as someone already suggested)

I am not sure how much data we can extract from throwing drives on the field with one camera. We would need to know the launch conditions and flight path of each sample throw.

Matti

I was looking at how much it would cost to build a cheap wind tunnel. Could do it for under $300, but the speeds are limited to 30 MPH, which will be below the cruise speed for some discs.

I was also thinking about building a rig to put on my car, and drive it down a smooth road. The idea would be to use this to determine the AoA for zero lift and the AoA for minimum drag, as well as the pitching moment. If I could obtain accurate force meters, then I could in principle measure everything at speeds up to 150 MPH (well, that's probably 2X as fast as we'll need). I've already played around with this by sticking a disc out the window of my moving car and changing the AoA manually while feeling the torques with my own arm. The key to doing this well would be to mount a device that can make real measurements somewhere on the car where the streamlines are straight. I would also probably need an air speed indicator. I'm sure mounting it high above the car would work in terms of getting the disc into a smooth air stream. And, I have a sun roof (hey, its California!) which might actually make this plausible. I could set up some sort of data logging on my computer and just record the necessary data for every disc I have in my possession.

Of course, I would need a lot of molds to test them out. :wink: Maybe I could get some manufacturers to send me discs to obtain flight data, after I've demonstrated that the principle works, and can be used in the simulations.

 

[George1]

I was looking at how much it would cost to build a cheap wind tunnel. Could do it for under $300, but the speeds are limited to 30 MPH, which will be below the cruise speed for some discs.

I was also thinking about building a rig to put on my car, and drive it down a smooth road. The idea would be to use this to determine the AoA for zero lift and the AoA for minimum drag, as well as the pitching moment. If I could obtain accurate force meters, then I could in principle measure everything at speeds up to 150 MPH (well, that's probably 2X as fast as we'll need). I've already played around with this by sticking a disc out the window of my moving car and changing the AoA manually while feeling the torques with my own arm. The key to doing this well would be to mount a device that can make real measurements somewhere on the car where the streamlines are straight. I would also probably need an air speed indicator. I'm sure mounting it high above the car would work in terms of getting the disc into a smooth air stream. And, I have a sun roof (hey, its California!) which might actually make this plausible. I could set up some sort of data logging on my computer and just record the necessary data for every disc I have in my possession.

Of course, I would need a lot of molds to test them out. :wink: Maybe I could get some manufacturers to send me discs to obtain flight data, after I've demonstrated that the principle works, and can be used in the simulations.

I've been wondering about cheap wind tunnel possibilities and car rigs as well. The car rig with strain gauges or something similar might be the way to go. I don't have a sun roof and it's Wisconsin in November.

Could some of these measurements be done in moving water at slower speeds? I vaguely remember from what little fluid mechanics I've had that you get similar behavior as long as you have a similar Reynolds number. I'm doubtful that it would work--air and water are different in many ways that don't enter into the Reynolds number--but I thought I'd throw it out there for discussion.

George

 

[mafa]

There is no question that the pitching moment is a function of AoA, and changes sign in the manner you suggest. However, I know very well from my experience that I can prevent a nose up disc from fading rapidly left by throwing it faster, even when that same AoA would result in fade at lower speeds. I use this kind of throw when I'm forced to throw understable plastic and get it to fade left more sharply at the end of the flight (especially mid-range left doglegs). This alone suggests a velocity dependence.

What's worse for the only-AoA-dependence is that the pitching moment scales as v^2, and at higher speeds and the disc should fade much much more quickly for the same AoA as a disc flying at low speeds with the same AoA. So this simple parameterization predicts that the kind of throw I describe above is completely impossible, and that the faster I throw the disc with a nose up orientation, the harder it will fade for a nose up throw.

JHern, I think I see your point but please keep in mind that velocity has squared influence on lift. Throwing disc with 1.4 times its cruise speed will lead to lift force of twice that is needed to keep the disc aloft. That converts to one g of radial acceleration which rapidly renders initial nose-up throw into much more favorable in terms of AoA. When pass the apex (disc starts to fall) initial nose-up will lead to harder fade since the AoA is already more positive than with a flatter throw. This treatment was with the assumption that the disc will not turn over. It' also possible to turn over a disc with nose-up drive due to the lift-induced turn-over -favorable AoA.


We need hard data. Car-rig would be cool. It's snowing here so you should implement it

Matti

 

[Muddyboots]

JHern, my comment on axis movement was partially in response to your illustrations earlier in the thread. I think perhaps I misunderstood. To clarify for me, and please correct me, your idea is that changes in velocity influence the attitude of the disc by changing the angle (tilt) of the disc as it flies, i.e. faster radial and foward velocity turns, slower fades? And the questions about late fade seem counterintuitive when viewed as such? This phenomenon is easy to replicate with putters in my experience, but for me I always thought it resulted because of acceleration due to gravity, as the disc descends ( putters typically being thrown high for throws 300' or better) it picks up speed, and turns, despite the fact that it is losing rpms. I hope my ignorance, or at least inexperience isn't annoying, I really am interested.
The car rig sounds neat, but I think you need immediate and very controllable windspeed to replicate flight.
KP

 

[JHern]

I've been wondering about cheap wind tunnel possibilities and car rigs as well. The car rig with strain gauges or something similar might be the way to go. I don't have a sun roof and it's Wisconsin in November.

We need hard data. Car-rig would be cool. It's snowing here so you should implement it

Matti

OK, OK! So, if this happens soon it should be performed in California. I agree.

Could some of these measurements be done in moving water at slower speeds? I vaguely remember from what little fluid mechanics I've had that you get similar behavior as long as you have a similar Reynolds number. I'm doubtful that it would work--air and water are different in many ways that don't enter into the Reynolds number--but I thought I'd throw it out there for discussion.

According to Potts' work, the aerodynamical properties of the disc have been found to be independent of the Reynolds number for regimes relevant to human throwing power. Of course hings might differ for a disc shot out of a cannon, and almost certainly different at super-sonic speeds.

JHern, I think I see your point but please keep in mind that velocity has squared influence on lift.

Yes, and also on drag and all of the moments too. This comes out of the aerodynamical scaling of forces.

Throwing disc with 1.4 times its cruise speed will lead to lift force of twice that is needed to keep the disc aloft. That converts to one g of radial acceleration which rapidly renders initial nose-up throw into much more favorable in terms of AoA.

Right. That was the whole point behind the equilibrium speed vs ascent angle diagram that I posted earlier in this thread. Maybe I should put that into the first post as well, and explain it better. In most of my reasoning, I'm working on the baseline assumption that lift and gravity are approximately in balance through the flight, and this includes the ascent angle and its relation to the nose angle and AoA.

When pass the apex (disc starts to fall) initial nose-up will lead to harder fade since the AoA is already more positive than with a flatter throw.

I agree 100%. But I don't agree that AoA is the only thing affecting the pitching moment. I think that latter proposition is impossible.

This treatment was with the assumption that the disc will not turn over. It' also possible to turn over a disc with nose-up drive due to the lift-induced turn-over -favorable AoA.

No, it doesn't work that way. You can throw these discs nose up without significant lift if you initially aim low and the speed is small enough. And anyways, my point is that, at high enough speed, everything will turn over no matter what the AoA.

 

[JHern]

JHern, my comment on axis movement was partially in response to your illustrations earlier in the thread. I think perhaps I misunderstood. To clarify for me, and please correct me, your idea is that changes in velocity influence the attitude of the disc by changing the angle (tilt) of the disc as it flies, i.e. faster radial and foward velocity turns, slower fades? And the questions about late fade seem counterintuitive when viewed as such? This phenomenon is easy to replicate with putters in my experience, but for me I always thought it resulted because of acceleration due to gravity, as the disc descends ( putters typically being thrown high for throws 300' or better) it picks up speed, and turns, despite the fact that it is losing rpms. I hope my ignorance, or at least inexperience isn't annoying, I really am interested.

No, not annoying at all, this is a fun matter to discuss. From my analyses of the equations, I've come to the conclusion that the lift and gravity might be approximately in balance, and this inevitably leads to the conclusion that the apex of the flight occurs at a higher speed than the descent of the disc...the whole flight is dictated by an initial velocity greater than the cruise speed, so that the disc ascends, and then slowing of the disc by drag occurs which slows the disc to cruise speed and it apexes, and then as it slows more it descends. This one-to-one dependence of speed upon the stage of the flight is important...without it, you cannot make an equilibrium.

In any case, the point you make is from the perspective that only speed determines the disc's turn. In reality, I think the disc's speed and its angle of attack (AoA) determine this. Some think only the AoA determines it, but I think they're wrong.

 

[JR]

To reduce blurring even more than the snow on the ground increasing available light on a sunny day we can throw a putter flat. Those need the least speed for practically keeping height. If the camera and cameraman are protected by a solid object we can film the release from the distance of my follow through. How's that for capturing launch conditions? Not very useful but if Bradley protects his camera at the side of the apex filming the apex of a slowish flat putter drive measured by his radar for speed I think a flat putter throw can be assumed to have zero deviation from roll and pitch angles at the release if the disc is visually flat at the apex. Version two is using my 640x480 camera for close up of the launch angle and to hell with velocity measurements at that frame rate and having mafa filming the point where the disc starts to fall or a little earlier and call it apex. Very scientific

Kidding aside to figure out a test setup which parameters exactly you want? Speed, hyzer/anhyzer/flat and front/rear angle relative to ground at launch and apex any others?

Launch velocity is perhaps passably accurate at 60 FPS 320x240 with my camera but angles determination is gonna be very rough. That's why visual confirmation by the thrower may be equally accurate. But if apex camera shows a flat throw perhaps it's safe to assume a flat launch. Is that acceptable? I can throw a flight that lands flat roll and pitch wise and does not deviate from the initial line to the side no problem. With a putter.

Approximate cruise speed can be determined by seeing where the disc is visually dropping in the apex camera. Cruise speed is a little above that. As long as the disc is flat lift should not be an issue in determining cruise speed for the putter. Getting some vids with different speeds at the apex and different falling rates or no falling we should be able to determine at least approximate onset of falling and the speed measurement at the apex. At 250 FPS measurement of speed should be accurate enough. Any observations or wishes to the test setup?

 

[JR]

You can throw these discs nose up without significant lift if you initially aim low and the speed is small enough. And anyways, my point is that, at high enough speed, everything will turn over no matter what the AoA.

It's a balance or equilibrium thing again. In addition to the above example: If you throw down with too much speed and the nose up the disc airbounces continuing on a straight line as long as the speed is high enough but rising. Of course the fade will occur once the speed dies down. But speed and spin are related as long as the disc doesn't slip. Comparing an airbounce and a straight line throw that move as far but land in different places sideways aren't equal in speed and spin. An airbounce must start faster thus the spin rate is higher as well. Depending on the disc gyroscopics different discs give very different fades once the airbounce does fade. A lid is very different from a Boss in weight distribution and gyroscopic behavior. Nose angle and speed must be adjust to suit each other and the direction the disc is thrown at as well as initial hyzer/flat/anny angle. This is true of every flight line.

What I'm saying is that the same mold at different weight behaves differently and so do different molds from each other. From observing golf discs in flight speed above cruising speed and if the ability of the spin to counter AoA and previous momentum vector(s) fails a disc will turn. Use the same AoA and a lower speed the disc won't turn. But without using a top down camera as well determining speed to spin ratio staying the same at different speeds means there's a possible variable that can make a difference in the conclusion that speed too is relevant. We might be able to pull off a test of that for putter cruising speeds with discs landing flat on the initial line of the throw. That result may or may not help in determining the role of speed to discs turning.

What I know from having achieved late turns is that they occur with harder throws. So adding power counts but exactly what it is about the added power that turns the disc? Speed, spin, speed/spin ratio and resulting gyroscopics changes or possible non equal initial AoA and momentum vectors may be involved. Or different disc pivot in the thumb lock that tilts the front lower than the rear or failing in that with resulting momentum addition or not. And OAT to the AoA at launch and some time after it and the result of that to gyroscopics and lift/gravity directions. And possibly some other factors as well that I can't think of now as well. I don't know how to test just speed change with everything else staying the same to see if speed indeed has an effect for a model predicting the future of the flight. And not act just an explanation to past momentum direction(s). Too many variables for my head to figure out separating just speed variation without changing other factor as well.

There's probably a limit to AoA where speeds much over cruising speed will turn the disc. That may be when the disc is tilted so much that the airflow separates from the bottom of the disc. This occurs well before the disc is flying top of the flight plate first. Ain't a 30 degree AoA relative to the direction of the airfoil movement a good result in airplanes avoiding a stall? Whatever the actual figures are for discs that kind of angles are relevant in putts alone and not in every style even then. So there are limits to AoA relevant to DG but are they relevant to drives and where are the limits of linear (non stall) AoA behavior in degrees? Thinking of the possibility of speed plus AoA turning the disc. And are there other factors still? My head is spinning this is beyond my knowledge.

A wind tunnel or driving in car does not tell about the speed to spin ratio changes of any single thrower and then the form adds issues. According to the measurements of Erin Hemmings they occur when he's closing full speed and then his spin starts to separate from speed increase factor. Less spin per speed at full speed and somewhat below that. The closer to full speed he got the larger the separation of delta spin to delta speed was in favor of speed increasing faster than spin. Erin thought it was because he couldn't hold on to the disc. If mafa calculated correctly a 175 disc exerts hundreds of kilos of force with long approach speeds. Try to hold on with just index and thumb

Using a lighter version of the same disc may allow holding on to the disc for longer increasing spin more than speed. In Carlsens thesis wrist opening gave 10 % extra speed and 40 % more spin for the longest thrower. Lighter weight adds also speed by allowing the body to move faster. That's a complication I'd like to avoid. That means not using even a same weight same mold same plastic disc. For truly doing whatever we can do to preserve ceteris paribus the same disc needs to be used for the vids.

 

[JHern]

In terms of measuring disc flights, don't forget that one very useful fact is that the lift coefficient and drag coefficient are the same regardless of the speed of the throw. Potts found these to be independent of the Reynolds number, and this is a great help because it means that we can measure disc properties at low speeds and they will apply equally well to high speeds.

Note that the cruise speed in nose angle dependent. If the nose angle approaches the zero lift AoA, the cruise speed grows to infinity. For a linear variation in lift coefficient with AoA, the square of the cruise speed is given by,
2*m*g/rho*A*C_L=2*m*g/rho*A*C_La*(phi-alpha_L0),
where m is disc mass, g is gravity acceleration, rho is air density, A is area of the disc, C_L is the coefficient of lift, C_La is a constant, phi is nose angle, and alpha_L0 is the AoA at zero lift. So by getting a disc to cruise speed at different values of phi, it will be possible to determine C_La and alpha_L0, which is half the battle.

On a car this amounts to getting the disc into a balance: at a given cruise speed, some nose angle neutralizes the lift and gives the disc weightlessness. This is another way to determine these quantities directly.

Once we have C_La and alpha_L0 in hand, we can turn our attention to downward glide, which will allow us to obtain information about the drag coefficients. During downward glide at an ascent angle beta_g (which is negative, since it is descending), there is the well-known relation (which is the same for airplanes and such):
tan(beta_g)=-C_D/C_L,
where C_D is the drag coefficient. C_D is typically taken to vary as the square of AoA, such as C_D0+C_Da*(alpha-alpha_D0)^2 where C_Da is a constant. Most previous studies found alpha_D0~alpha_L0, and while this assumption would need further testing, it would be a good starting point. So, using this approximation, and knowing beta_g, C_La and alpha_L0 (~alpha_D0), we can determine C_D at the glide point, which is an important reference.

If you know the cruise speed, nose angle, and alpha_L0, then you can directly calculate what the glide speed should be at beta_g, to check that you are really measuring the glide state.

The very first determinations of disc properties by students (I think at Brown Univ) used very simple procedures like this to obtain a baseline behavior and set of parameters. A lot can be done with that, and for a long time all physical models were performed using such information.

The late turn issue is something I think will be solved once we have a believable base set of parameters in place to run a proper simulation of a given mold. I've also talked to Blake about this, and the OAT-factor was discussed. After thinking some more, it seems that wobble-type OAT will not straightforwardly make a late turn...it is something that is damped out as the disc flies (dissipation smooths the wrinkles out), and the disc turns less later rather than more. The spin, on the other hand, was found by Axel Rohde (in numerical simulations including a spinning disc) to have an increasing damping force (I'll just call this "spin damping") at very high spins...his determination is something like a cubic polynomial in rotation rate. Thus, even though the disc spin typically decays over 10-20 second e-fold time scales, at higher spin rates the disc rotation decays much more quickly. So, for example, a 20 Hz spin at release will stabilize the first phase of the disc's flight by making it go relatively straight, but after a few seconds the more rapid spin damping at high spin rate causes the spin rate to decrease to more modest values (well under 10 Hz). This decreases the angular momentum of the disc by a similar amount, and it turns faster than it did before, yielding late turn.

 

[JR]

Are you happy with a test setup of either 640x480@30FPS or 320x240@60FPS at launch and 448x336@250FPS at approximate apex? I thought that to make flat non deviating flight landing flat easier and more consistent to achieve with enough accuracy to capture a meter long vertical stick at the background of the disc with the apex cam an Aviar P&A DX 175 should be used. For ease o the test these would be approach speed throws because if I were driving from farther away to achieve dropping at the camera I might not be accurate enough for the small area to hit when the disc starts falling. I wouldn't wonder if I got even less speed than 7 m/s in Hummel's thesis. We may be able to get faster flights as well with more attempts. The resolution deficiency mandated necessary closeness of the camera to the meter stick makes the area to hit small and the higher the speed the longer the throw must be. Is a no fade flat landing throw acceptable for you?

We can't proceed until we know how we set up things and how I should throw. John is this setup ok if we film at right angles and I try to make the disc start visibly falling only when it achieves the small viewing area of the apex cam? We need specifications of the test setup so that the calculations can be correct because we might need to measure distances etc. for sanity checks. Since you're doing the simulations and calculations we need to comply to your needs which means we need a detailed plan from you. Is it ok if I threw mildly uphill to protect the camera? How wide the filming area should be at the apex cam or how many meters of flight do you need to capture and is 50FPS 1920x1080 ok for a longer portion of the flight captured from farther away with the apex cam? I was thinking of not having any zoom on the camera to avoid a possible error source there.

Mafa if you film from behind the corner of the club house at Tali both you and the camera are protected from errant throws. I was thinking of throwing along the path going by the long side of the house. Does this sound safe enough?

 

[JHern]

Regarding resolution vs. frame rate, maybe try out the various settings and see which gives the clearest image of the disc while capturing the flight. We will not need a huge number of data points (a few dozen is probably just fine), so frame rate may not need to be so high as you guys have in the drive videos. So this is more up to the film crew. If you want, you can also try another setting for comparison, but this is of course more work and it is cold out there! Resolution and exposure might be most important, since we would like to be able to measure the nose angle from the videos. So I would initially go for the highest res, fastest exposure, and slowest frame rate setting. But only doing it will give the experience to know for sure which is best. But right now I'm thinking that 50 fps is plenty fast enough.

You can film on a hillside, if you wish, but make sure you place the camera level so we know which way is "up" in the frames, or hang an object on a string from something in the background for orientation double-check.

Camera zoom should not add any error, so you could use it to film further from the side and hence get the camera away from danger. Aim to get some of the flight before the apex and after the apex. Of course, the more you can get, the better. The straighter the flight at apex, the better (i.e., zero hyzer at apex). You'll probably need to do a bunch of throws, and only keep the straight ones (you can delete the others where there is too much turn, they aren't useful right now).

At the apex of the flight, we're working with a relatively simple equation for apex speed. The square of the apex speed divided by the square of the cruise speed is equal to 1+(a_up/g), where a_up is the upward acceleration and g is the gravitational acceleration. So we need 2 things: the velocity at apex, and the change in upward velocity at apex. These can be obtained by getting a number of data points from the video, translating them to "x(t)" and "z(t)" (where x is the horizontal dimension along the flight path, and z is the altitude), and after fitting smooth functions to eliminate aliasing, we simply take the time derivative of x(t) at z_max to get apex speed and the second time derivative of z(t) at the apex to get the apex upward acceleration.

Recall that cruise speed is a function of nose angle. To better constrain this functional dependence (which in principle can tell us everything we need to know about the lift coefficients), we need to film throws with different nose angles (which will, in turn, give us different cruise speeds and drags).

From the x(t) data we can also take the second time derivative at the apex, which gives the lateral acceleration, a_lat (negative, since it should be slowing). At the apex, the equation is simple, m*a_lat=-F_D, where F_D is the drag force. We would have a_lat and m, allowing us to analyze drag. Again, F_D at the apex is a function of nose angle, so we need flights with a variety of nose angles.

If the throw is fairly straight, and a_up and a_lat are small, then: 1) we can almost ignore a_up in the correction for cruise speed, or at least its smallness from the fitting is not a big deal. 2) we will need a wider frame shot from the side to be sure we can resolve a_lat.

So, if you guys can turn out the following...
- Throw several flights in as straight a line as possible, and film from the side with the center of frame approximately at the apex. The more flights you get, and the more difference in nose angle on each flight, the better the data set.
- For each flight, obtain several dozen frames of the flight near apex, with a frame covering around 30 meters horizontally (this seems reasonable).
- The pixel positions on the video for the center of the disc need to be translated into lateral and upward distances (of course, I'm a fan of metric system). One can use horizontal markers placed at given increments of spacing on the ground along the flight track of the disc (try to throw over these as best you can) that can be seen from the camera angle.
- Try to do whatever adjustment you can so that we can directly measure the nose angle of the disc from the frames. I know the resolution is tough, but I think if you aren't too far away that you can't see the nose angle, but not so close that camera perspective distortion becomes an issue, then we will have a great data set.

Using this information, we should be able to distill quite a lot of essential flight data. We should be able to find (in order from expected easiest to constrain, to most difficult to constrain):
- Cruise Speed
- Lift Coefficient (derived from cruise speed, air density, mass, and diameter of disc)
- AoA for Zero Lift (from fitting the cruise speed function for various nose angles...more nose angle variety in data->better constraints on AoA for Zero Lift)
- Drag Coefficient (from lateral deceleration of the disc at apex, air density, mass, and diameter of disc)
- Change of Drag Coefficient with AoA (this requires big nose angle differences in different flights to resolve it well)
- AoA for Minimum Drag (this will be the toughest, since the system is expected to be quadratic...only a large number of flights and good variety of nose angles will allow for a robust constraint of this quantity)

The data should will also give us error estimates on our determinations.

This would be fantastic, and a great place to begin. The next step would be to examine the moments and begin analyzing the turn of the disc in flight, which will be another fun project...I need to do some more analysis of this part of the equations to find the key measurements to make.