Disc Physics

[JR]

Coldness is a non issue.

How much is too much turn? I thought to use perfect frozen ropes without any turn and fade whatsoever. Not even a centimeter if I can pull it off.

30 meters wide view mandate higher resolution. We have filmed drives before during summer on a sunny day and unfortunately the camera does not have the ability to manually force short enough exposure times for unblurred images at that resolution. The camera is capable of better exposure performance in automatically controlled 250 FPS mode but I'm not sure if other parameters can be manually locked. We need to check that. We probably need to try a close up250 FPS and HD 50 FPS from farther away and if necessary 50 FPS from close up as well to determine angles. We need to come up with more sticks then but I was gonna stretch a 1 m measure vertically onto a stick in the center of image anyway for height determination help.

How many meters separation for the vertical sticks do you want? I think we need a flat area and that's gonna be a problem for close up shooting over wise unless we can find a suitable yard and use a house corner. Local DG courses with corners may not be flat enough. Meilahti may do but I'm not sure of flatness and the ground is asphalt so the disc may get lighter and panting stakes may be impossible on a shoestring budget. I'll ponder on a suitable place. For a few dozen pics at 50 FPS it's a minimum of half a second flight then and looking at your bag I also have an XD that is even slower but more nose angle insensitive so it may not be a typical disc but a flat landing is easiest to achieve with it. Half a second is easily a bunch of sticks with one meter interval. My Classic Roc is so new that it fades even on full power. Thinking of weight I need to clean up the disc after each throw to maintain a constant weight.

We really need to use a string with weight.

I looked at forecasts and no windless days are near but the figures are likely averages or top wind speeds so we may get windless periods. They usually occur in the evenings if there are calm periods in a day. If I got a portable weather station with real time and peak wind speed functions and log wind direction and speed would that be ok if we logged the results for each throw? I've been toying with the idea of getting one anyway. Seeing as finding time that suits us both and getting no wind and having light may prove to be a long time coming.

Do you need airbounces for AoA and cruise speed determinations? Those fade necessarily and so will many other nose angles. I'm not sure if I get a no fade throw uphill in steep angles but I'm also haywire when it comes to accuracy of dropping rates using sticks that are planted uphill. that's why I've been stuck on flat ground thinking.

I don't know about but mafa could about camera closeness perspective distortion. In the case he doesn't how do we eliminate that? How do we determine the minimum distortion free filming distance from the disc and the sticks?

I think the disc turning experiment may need another video session unless we manage to capture unintentional but useful to you turns.

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.

 

[JHern]

Coldness is a non issue.

How much is too much turn? I thought to use perfect frozen ropes without any turn and fade whatsoever. Not even a centimeter if I can pull it off.

Just do the best you can. Most important thing is that the disc is flat as possible around the apex of the flight.

30 meters wide view mandate higher resolution. We have filmed drives before during summer on a sunny day and unfortunately the camera does not have the ability to manually force short enough exposure times for unblurred images at that resolution. The camera is capable of better exposure performance in automatically controlled 250 FPS mode but I'm not sure if other parameters can be manually locked. We need to check that. We probably need to try a close up250 FPS and HD 50 FPS from farther away and if necessary 50 FPS from close up as well to determine angles. We need to come up with more sticks then but I was gonna stretch a 1 m measure vertically onto a stick in the center of image anyway for height determination help.

How many meters separation for the vertical sticks do you want? I think we need a flat area and that's gonna be a problem for close up shooting over wise unless we can find a suitable yard and use a house corner. Local DG courses with corners may not be flat enough. Meilahti may do but I'm not sure of flatness and the ground is asphalt so the disc may get lighter and panting stakes may be impossible on a shoestring budget. I'll ponder on a suitable place. For a few dozen pics at 50 FPS it's a minimum of half a second flight then and looking at your bag I also have an XD that is even slower but more nose angle insensitive so it may not be a typical disc but a flat landing is easiest to achieve with it. Half a second is easily a bunch of sticks with one meter interval. My Classic Roc is so new that it fades even on full power. Thinking of weight I need to clean up the disc after each throw to maintain a constant weight.

Maybe 30 m wide is wishful thinking, and you will need to do a smaller window, but this will decrease the resolution of the data with respect to calculating drag. Height is not an issue, whatever you can manage is fine. We need as many different nose angles as you can manage, and to try and increase the exposure rate so that we can infer the nose angle (maybe this is possible even from blurry images?). Getting data just before and just after the apex will be most important, and for a long enough time to measure the lateral acceleration of the disc (i.e., to resolve it given the data).

I looked at forecasts and no windless days are near but the figures are likely averages or top wind speeds so we may get windless periods. They usually occur in the evenings if there are calm periods in a day. If I got a portable weather station with real time and peak wind speed functions and log wind direction and speed would that be ok if we logged the results for each throw? I've been toying with the idea of getting one anyway. Seeing as finding time that suits us both and getting no wind and having light may prove to be a long time coming.

Wind will really mess with this kind of determination if it is unsteady, even if you know the average direction and speed. This is because many of these things are scaling like square of wind speed, so fluctuations can grow to become a large effect. It really is best to have as calm a day as you can find. Temperature, altitude, and humidity will give the air density, and you can probably find this from the weather service. So unless you really want your own weather station, I'm not sure it will really help a lot with this experiment. Plus, the wind is typically different more than 10 m high above the ground, and so a ground measurement is not always reliable.

Do you need airbounces for AoA and cruise speed determinations? Those fade necessarily and so will many other nose angles. I'm not sure if I get a no fade throw uphill in steep angles but I'm also haywire when it comes to accuracy of dropping rates using sticks that are planted uphill. that's why I've been stuck on flat ground thinking.

Air bounce or not doesn't matter...the differences will have disappear around the flight apex anyways.

I don't know about but mafa could about camera closeness perspective distortion. In the case he doesn't how do we eliminate that? How do we determine the minimum distortion free filming distance from the disc and the sticks?

The minimum distortion is always at infinite distance. The further to the side, with more zoom, the smaller the distortion. For filming close, we can look up some info on the camera if we know the lens data. This could be a useful exercise anyways, but isn't extremely important to do it now.

I think the disc turning experiment may need another video session unless we manage to capture unintentional but useful to you turns.

Yes, definitely will need 2 angles...one from the side, and one from behind at the minimum.

 

[JR]

Weather station ain't gonna remove the wind so I'll drop that and try to find no wind conditions. Today on a practice field we had breaks from wind but this time of year is unsuitable for this kind of experiment. I don't know if we can throw indoors somewhere and get sticks set up as well. If you're ok with uneven ground and having to measure from each individual stick the height of the disc go right ahead. It's easier for us. Is it ok to show 1 meter in the stick with color because I don't know how deep the sticks need to be stuck into the ground and thus we need to use more than a meter long pieces.

How thick should the sticks be and at which interval for 50 FPS 1920x1080 video at which distance?

Mafa what are the specs of your camera's optics? We need to know this to figure out how wide the image is at any given filming distance so that we can pick the filming distance and plan the stick density accordingly.

We talked on the phone with mafa and he was skeptical about what and how accurate data we can obtain but the blurrs come from full force drives at the tee. Blurred images may not be a trouble at the apex with putter cruise speed.

 

[JHern]

I think we cannot plan everything in advance. It will require some experimenting, setting up the camera, taking some trial films, etc., before we can figure out all the possible issues. We need some items that can be seen in the camera that tell us the effective distance per pixel and also which way is up. If you can film inside, that would be nice, of course. Anyways, wait for calm conditions or an indoor opportunity. We aren't in a huge hurry. Meanwhile I will continue to look at the equations and understand the physics. I'm going to begin focusing more on turn after I finish working out why glide becomes unstable even in straight flights.

 

[JHern]

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, I've been looking into this possibility, and I think it should work. Consider:

1) Potts' experiments with a disc in water also needed to address the Reynolds number scaling issue. Fortunately for this technique, he found that the lift and drag coefficients did not change with Reynolds number.

2) Re=v*D/eta, where v is speed, D is length scale (disc diameter), and eta is kinematic viscosity...
Re_air=v_air*D/eta_air
Re_water=v_water*D/eta_water
...thus...
Re_water/Re_air=(v_water/v_air)*(eta_air/eta_water)
...The best scale for v is the cruise speed. The cruise speed goes as 1/sqrt(rho), where rho is the density of the surrounding medium. So in water the cruise speed is about sqrt(1000/1.3)~28X smaller than in air. Also, we have eta_air~2e-5 m^2/sec and eta_water~1E-6 m^2/sec, so...
Re_water/Re_air~(1/28)*(20)~0.7
...Therefore, the Reynolds number is, in any case, similar for a disc at cruise speed in water compared to a disc at cruise speed in air.

Both of these facts virtually ensure that measuring the disc in water will work very well as an analog for the disc in air. Viscosity can be tuned by adding some solutes (maybe not necessary). There are a few other minor differences, e.g., compressibility (this this probably not so important). I say let's go for it!

Here's a sketch for one idea:

Basic idea is to use the pressure head (rho*g*h) to drive flow while the porous membranes act as diffusers to smooth out the flow and make it approximately laminar coming at the disc. Membranes of variable porosity can be used to control the rate of flow for a given pressure head.

There would be some sort of suspension (maybe using stainless wire/rod rig?) that both holds the disc and controls its orientation and also measures the forces acting on the disc (torques can be measured using simple linear force meters if the rig is cleverly designed).

 

[George1]

Basic idea is to use the pressure head (rho*g*h) to drive flow while the porous membranes act as diffusers to smooth out the flow and make it approximately laminar coming at the disc. Membranes of variable porosity can be used to control the rate of flow for a given pressure head.

There would be some sort of suspension (maybe using stainless wire/rod rig?) that both holds the disc and controls its orientation and also measures the forces acting on the disc (torques can be measured using simple linear force meters if the rig is cleverly designed).

I hadn't thought of the porous membrane. What type of material were you thinking of?

I'm also wondering about just putting a rig in a river. (We've got one right in the middle of our campus.) Another possibility would be a boat rig similar to your car rig. The big advantage over the car rig would be much slower speed. Doing this in the lab would be much nicer and more easily repeatable, although it would require space and more construction.

No matter what the set-up, the rig will have to be very carefully aligned with the center of mass of the disc. If the pitch axis of the rig is off by a little, it could throw the torque measurement off by a fairly large fraction.

 

[JHern]

OK, getting back into this again soon, though I'm also busy figuring out whether solutes in Earth's core tend to diffuse upwards or downwards under a strong pressure gradient (my real work), which is not so simple.

I think my next step should be to post my disc physics write-up somewhere, when it is more legible. Then can take more comments/suggestions.

I hadn't thought of the porous membrane. What type of material were you thinking of?

These kinds of "diffusers" are important for wind tunnels, to damp any incoming large scale vorticity and set things on a streamlined path again. In this case, would have to experiment with whatever would regulate the flow properly, although I suppose this can also be adjusted by thinning it.

I'm also wondering about just putting a rig in a river. (We've got one right in the middle of our campus.) Another possibility would be a boat rig similar to your car rig. The big advantage over the car rig would be much slower speed. Doing this in the lab would be much nicer and more easily repeatable, although it would require space and more construction.

True. Or maybe drag a rig through a swimming pool?

No matter what the set-up, the rig will have to be very carefully aligned with the center of mass of the disc. If the pitch axis of the rig is off by a little, it could throw the torque measurement off by a fairly large fraction.

The contraption that holds the disc will indeed have to be cleverly designed, no matter what the overall strategy is. I think we could come up with something workable, with enough thought.

 

[George1]

I've made a simple web page on disc physics, including an introductory article on disc physics, a couple of projects done by my students, and a list of links to disc physics related sites. I hope to add more later. Please feel free to give me suggestions, corrections, etc.

The URL is http://www.uwec.edu/physics/stecher/gfdpp/

George

 

[JR]

Thanks for that George.

 

[JHern]

I realized just now that it has been more than a year since I last posted in this thread. This is unfortunate, since I was on a roll for a while, and there is much work yet to be completed.

Anyways, I was thinking about the different phases of the flight, and about how the disc approaches the equilibrium state I described some time back, between lift and gravity for a given nose angle and speed, with the speed increasing or slowing according to up/down trajectory and air drag. I think much of the flight of a disc is governed by nearly this kind of equilibrium when it is flying relatively straight or holding a constant hyzer or anhyzer line or is turning only very slowly in either direction...in other words, after the disc loses its wobble from OAT and goes through what I'll call the "inertial phase" of the flight.

I think this example demonstrates the inertial phase of flight I'm thinking about a bit more than other scenarios. Take your stable putter out, put it on a 45 degree hyzer line straight out in front of you, and give it a good amount of velocity with clean release (no OAT). What happens? Well, the putter will fly almost dead straight for a little while, maybe hissing like a Banshee, and only after it stops slowing down a bit from the air drag does it begin to realize that it has a 45 hyzer angle (because you threw a stable putter, recall), and then it starts to move left (or right if you throw spin up instead of spin down). (This is of course an important thing to realize if you use your putter on long hyzer approach shots, as I like to do. So I think probably most of you know what I'm talking about.)

Anyways, I call this the "inertial phase" of the flight because the dynamics are governed by a very large amount of aerodynamic drag on the disc at the point of release balanced by the inertia (mass times deceleration). Other forces are insignificant until the disc slows down a bit, dissipating its inertia. I'm going to begin analyzing this phase of the flight, since it is quite interesting and an important phase of the flight in all throws.

 

[JR]

Unfortunately i haven't been able to find a way with which to make equal height vertical yardsticks have the tops at equal height from the ground. So i haven't been able to realize the filming of the flight project we talked of. I can't measure the evenness of ground easily and with any sort of accuracy with my knowledge and equipment. So i haven't even pushed forward with manufacturing yardsticks. I did search suitable ones that were available to buy but found only too large to store traffic cones. And that would have been too short and too expensive relative to my interest.

I'm dog tired so i want to check if i got you right. Do you mean that the inertial flight portion where discs push through hyzer or anhyzer? After which when slowing down they start to turn according to the hyzer/anhyzer angle? Pushing through hyzer/anhyzer is a pre existing term. Why not use that and define it like you did?

 

[JHern]

I'm dog tired so i want to check if i got you right. Do you mean that the inertial flight portion where discs push through hyzer or anhyzer? After which when slowing down they start to turn according to the hyzer/anhyzer angle? Pushing through hyzer/anhyzer is a pre existing term. Why not use that and define it like you did?

Pushing through hyzer/anhyzer is an example of this, but doesn't tell the complete story. You can also throw the disc at a high launch angle, with the nose down, and the disc will initially fly upward but the disc will eventually track toward the equilibrium defined by the speed and orientation of the disc, and level out (or glide with forward penetration if the nose is down enough). This would be "pushing up through nose down." Another example is even more well-known, where you throw the disc downward with a flat or nose up release, and the disc appears to "bounce" back up and then find the equilibrium trajectory for its nose angle and speed. We call this "air bounce" I think universally. The "pushing up through nose down" can then be thought of as a reverse air bounce.

So pushing through hyzer/anhyzer, air bounce/reverse air bounce, are all examples of the inertial phase of the flight. This inertial phase results from releasing the disc on a trajectory that is different than the trajectory defined by the equilibrium between disc orientation and speed. It is also easy to think about releasing the disc at exactly the trajectory that is already close to the equilibrium trajectory defined by the nose angle and speed of the disc. You would have no air bounce, no pushing through hyzer/anhyzer, the disc will just start and stay on a smooth and graceful line with no kinks or funkiness immediately following the release. That is, of course, unless you have OAT-induced wobble. OAT induced wobble can also interact with the inertial phase of the flight, on some discs it will bleed off before the inertial phase ends, or maybe it will stay with it all the way to the end of the flight (depending on the mold, kind of throw, degree of wobble, etc.).

OK, I've got some new ideas, and so back to the math to make it all rigorous.

 

[Moseley]

Take a look at the disc flight 6 min out in this vid http://vimeo.com/18866399

The disc seems to turn right as it runs out of speed - well after the initial turn and fade. Any idea 'bout what happens there?

 

[jubuttib]

Disc is going downhill, either keeping a steady pace or even accelerating, while the spin dies down. Low spin + still moderately high speed -> turn?

 

[Moseley]

Disc is going downhill, either keeping a steady pace or even accelerating, while the spin dies down. Low spin + still moderately high speed -> turn?

makes sense :thumbup:

 

[JR]

That has been captured on video on more than one occasion. Check Youtube for Bob Mohl i think throwing down from a mountain in Switzerland hitting an interesting target. And having huge air time.

 

[Monocacy]

Unfortunately i haven't been able to find a way with which to make equal height vertical yardsticks have the tops at equal height from the ground.

Garden designers use clear, flexible tubing filled with water. The water line gives you a perfect level. Don't try this in Finland during winter (well, maybe with antifreeze).

 

[Moseley]

Disc is going downhill, either keeping a steady pace or even accelerating, while the spin dies down. Low spin + still moderately high speed -> turn?

makes sense :thumbup:

No wait tdk had a better idea I think: because of the height the disc can keep fading, completing a full helix,
So direction goes: forward/slight right (the turn part) then it fades left until it travels towards the thrower, and keeps up until it's fading towards the right, seen from the throwers perspective.
When I think about it, I don't think a throw can keep airborne while losing that much spin, it would just tumble out of the air...

 

[jubuttib]

No wait tdk had a better idea I think: because of the height the disc can keep fading, completing a full helix,
So direction goes: forward/slight right (the turn part) then it fades left until it travels towards the thrower, and keeps up until it's fading towards the right, seen from the throwers perspective.
When I think about it, I don't think a throw can keep airborne while losing that much spin, it would just tumble out of the air...

I could see that happening if there wasn't a great big hill there. If the disc tried to make a full helix it'd hit the side of the mountain. Depending on how much the disc manages to build up (or retain) speed affects how much of the spin it'd need to lose to turn like that. If he threw downhill and with at least a little nose down compared to the horizon (which I think he did, since the disc doesn't try to stall at any point) it didn't necessarily lose much airspeed while still losing just enough spin to fly like that.

Then there's the possibility that the disc hit a gust of wind at the end of it's flight.

I'd really like to see how a moderately overstable disc would handle on a throw for high up. As it faded it'd be in a steep dive, building up lots of speed. Would it turn again, speeding down ever faster, turning right all the time, or possibly even flattening out for a bit? Could it then perhaps just bounce between slowing down and fading and again speeding up and turning, until it loses enough spin to just start fluttering around?

Dunno, but I'd like to see it. Someone find a sheer cliff about two miles or so high and try it out.
Back to the original question, SUMMON JHERN!

What's your take on it?

EDIT: Regarding my inane ramblings, no, it could not.

The pitching moment for fade is always nose lifting in orientation, and the pitching moment for high speed turn is nose depressing in orientation.

 

[Moseley]

Wind was my first Idea as well, but as I understand it was pretty much quiet that day. I think you underestimate the way directional energy is diverted as the disc fades - the disc doesn't stop It's entirely logical that a disc can maintain air speed because mainly through gravity, while the fade keeps it turning towards the left - if it has enough room to descen, it will describe a full helix.
In the video, the disc descends much faster than it moves horisontally in this phase, so it looks as if it drops a bit, then moves a bit towards the right before it hits.
I think