Disc Physics

[JHern]

I've finally had time to think about your last figure. Treating the problem in terms of energy instead of forces certainly clarifies some things.

Yes, I need to also consider the dissipation explicitly, which adds the necessary entropic element to the whole process and the sink in the energy budget.

How does the potential energy fit in to your three different throws? I can see that the nose-down throw reaches an equilibrium point sooner than the level throw or the nose-up throw. I would assume that means that the latter portion of the flight is more energy efficient for the nose-down throw. (Or rather, that the nose-down flight makes efficient use of the gravitational energy sooner.) However, does the nose-down throw have more or less potential energy when it reaches that point? In other words, if the nose-down throw follows a very flat trajectory, it might be very energy efficient at the end but not have as much height and therefore as much potential energy to work with.

Its a good question to see how the apex of the flight trades off in this manner relative to nose angle. I haven't worked out the details of this kind of thing yet, but when I can get a good estimate for the dissipation integrated over the flight path, then I can put more secure numbers and see how all of those things trade off. Note that the actual velocity and kinetic energy for the nose down flight going down a curve from a given point in the plot is significantly higher than for the nose up flight (i.e., nose down cruise speed, around the apex, is greater than for nose up).

Even more important is the dissipation and efficiency, as you suggest. An interesting result hinted at on the figure, is that the equilibrium glide angle of descent is smaller for more nose down. Glide is where dissipation equals work done by gravity, so the disc goes at a constant speed (I put a Sidewinder into a glide today at hole 27, DeLaveaga, "top of the world," as part of my field work). So the nose down is indeed more energy efficient. The reason for this is probably that the drag force goes as a power of angle of attack that seems to be of order higher than linear according to Potts' experiments, while the lift force has been measured to be approximately linear in the angle of attack (this is also true of all sorts of airfoil shapes). This means that increasing nose up makes the angle of attack higher, and the drag force's quadratic dependence out-competes the linear lift force dependence...thus nose down=less drag upon descent, and hence feeds upon potential energy at a lower rate.

Also, how significant is the potential energy? Is it a large or small fraction of the kinetic energy? I can see the drop in kinetic energy as the disc ascends, but how much of that is work against gravity and how much is it work against drag forces? (I tried a back of the envelope calculation, guessed a flight speed of 20 m/s and an apex height of 5m, and came up with about a 1:4 potential to kinetic ratio, but I'm not sure how realistic my assumptions are.)

g*h=50, while v^2/2=200, so in this case 1:4. Probably about right, although these numbers can vary a bit. If you get the disc to apex at 10 m you will need more velocity to get it there...to know exactly how much becomes a matter of dissipation once again. It seems clear that the greatest energy cost is getting the disc to the apex...I think for big arms, this is where all the effort goes...you probably need a nose down just to keep the disc from rising up like mad, and then you aim to put it through some apex...once it is there it simply glides back down. So probably a good amount of kinetic energy is eaten up during this process, although the potential energy is still not varying a great deal.

Thinking about it, in principle this information might be obtainable from the present plot and formula via a subtle manipulation, since the rate of increase of potential energy is proportional to the square root of the vertical axis times the sine of the horizontal axis...easy breezy, no?

How does the rotational kinetic energy relate to the drag energy loss and to the linear kinetic energy? In other words, as the angular velocity of the disc gets smaller, where does the rotational kinetic energy go? My guess would be that most of the loss is to drag and to (slight) sideways motion of the disc caused by a Magnus force. I would also guess that the disc only loses a small fraction of its rotational kinetic energy during the flight. (I assumed that the kinetic energy on your vertical axis was the linear part of kinetic energy.)

I agree with this assessment. I also don't think there is much Magnus force for typical throws, and neither does the angular velocity change much over the flight (which is saying pretty much the same thing).

Overall, it seems to me that there are four relevant energy terms in the problem--linear kinetic, rotational kinetic, potential, and loss to drag. It would be interesting to see all four of those plotted as a function of time. Alternatively, if you could replot your figure with the potential plus kinetic energy on the vertical axis that would give different and helpful information as well.

Very true. The kinetic plus potential energy would have to decrease during flight, owing to continual drag loss, so I think the curves might follow a similar trajectory, but maybe not as much upward curvature of the curves around the apex to reflect the extra potential energy in the flight around the summit of the path.

I don't mean to be critical--your work and your figure are both outstanding and very helpful and I'm quite impressed. They just raise lots of interesting questions! Thanks for posting it!

Thanks for the queries. This is indeed a fun way to look at things, and I'm glad you also enjoy it. I intend to follow through with this to the bitter end (where ever that is). (In my day-to-day work in geophysics I am also a big fan of energy balances, so this is in keeping with my usual form.)

 

[George1]

I intend to follow through with this to the bitter end (where ever that is).

Physics and disc golf together? Sounds like a joyous, rather than bitter, end.

 

[Blake_T1]

for those who are unedjumacated in physics on a PHD level:

Jhern and i were talking and he explained why when the big guns throw their discs continue to lift and lift while the medium/short throwers will have their discs peak early/lower.

e.g. someone like Markus Kallstrom will throw a 10 degree upwards trajectory and his disc will peak at 50', while a 350' throwing am will throw the same 10 degree upwards trajectory and his disc will peak at 15'.

basic summary:
when a disc is launched at a velocity beyond the upper bound of its cruising speed range the disc will continue to lift until its velocity drops into the cruising speed range.

if a disc has a cruising speed range of 30mph on the lower bound and 50mph on the upper bound, a 75mph throw will continue to rise until the disc has reached 50mph.

basically, a 75mph launch may take 200'+ to decelerate to 50mph and the disc has a lot of time to rise.
a 55mph launch may only take 50' to decelerate to 50mph and the disc will not get nearly the same amount of lift before it peaks even if it was launched at the same trajectory.

i would assume throws slower than 50mph will have no additional lift and for a flat trajectory at launch, the disc would pretty much flat at the height it was released at (or have an even earlier apex peak if thrown slightly upwards). Jhern can probably verify this.

 

[chiggins]

if a disc has a cruising speed range of 30mph on the lower bound and 50mph on the upper bound, a 75mph throw will continue to rise until the disc has reached 50mph.

Okay, so is this where "nose down" compensates?

 

[Blake_T1]

no. nose down causes lift and reduces the drag on the disc.

when a disc is thrown nose down, the air passing over the top of the disc moves faster than the air passing under the disc. the result is aerodynamic lift.

basically, there's an upper and lower bound of good nose down for each model.
there has to be X amount of nose down for the disc to fly as designed.
if the nose down angle exceeds Y, the disc will dive into the ground.

"good" flights happen with the nose angle between X and Y.

 

[JHern]

Good summary, Blake.

A couple of things to clarify...

1) There is actually a single cruise speed for a given disc with a given nose angle. This is the speed at which the disc can maintain level flight (it doesn't of course, because it is slowing down from drag and doesn't have a propeller or jet to balance drag). Anything faster will ascend, and anything slower will begin to descend. I know you were speaking about a range of cruise speeds before (and in your post), but in terms of my tinkering so far there is evidence that this occurs only at this exact speed, and not a range.

2) Nose down does not give you more lift per se; it actually gives you less pure lift force. However (and you are saying something to the same effect), the efficiency of lift relative to drag is indeed better for smaller nose angles (but only up to the limit of zero lift). This is because drag increases more strongly as nose up is changed than does the lift. Therefore the disc has more ``carry'' with nose down than nose up.

 

[Blake_T1]

1) There is actually a single cruise speed for a given disc with a given nose angle. This is the speed at which the disc can maintain level flight (it doesn't of course, because it is slowing down from drag and doesn't have a propeller or jet to balance drag). Anything faster will ascend, and anything slower will begin to descend. I know you were speaking about a range of cruise speeds before (and in your post), but in terms of my tinkering so far there is evidence that this occurs only at this exact speed, and not a range.

so cruise speed for lift/descent.

how about for turning/fading vs. straight? is that a range?

 

[chiggins]

Okay. I probably don't have this exactly right, but I'm curious about what's happening with those discs where having the nose down gets it farther. I'm probably not picturing it in the right context.

I'm thinking back to a thread where the relationship between a disc's optimum max height to max distance was being discussed, and nose-down came up. So, of the several relevant planes (the ground, the trajectory its thrown at, the actual direction once it gets the additional height from lift if it's going over its speed limit), what is the nose down in relation to, and how's that change with different throw angles?

I don't even know if that made sense. When I think of nose-down on a practical level, it comes down to "have it eject at an angle that keeps it from stalling out when it gets to its apogee, and ideally doesn't allow it to fade hard left, but not so far down that it turns over and can't fight back to level." But I'm guessing that's not it.

 

[Blake_T1]

I'm thinking back to a thread where the relationship between a disc's optimum max height to max distance was being discussed, and nose-down came up. So, of the several relevant planes (the ground, the trajectory its thrown at, the actual direction once it gets the additional height from lift if it's going over its speed limit), what is the nose down in relation to, and how's that change with different throw angles?

I don't even know if that made sense. When I think of nose-down on a practical level, it comes down to "have it eject at an angle that keeps it from stalling out when it gets to its apogee, and ideally doesn't allow it to fade hard left, but not so far down that it turns over and can't fight back to level." But I'm guessing that's not it.

distance throwing uses some tricks to cheat the nose angles (and optimally ride the wind). keep in mind, here i'm referring to the types of lines people use when going for the world record.

when you are riding a crossing tail wind, thwe disc ill catch and push with like 45-80 degrees of nose down.

Basically, the trick to distance throwing is that once the disc passes the apex and enters the "turn" portion, the disc will be flying a diagonal left to right path with a TON of nose down. there disc is also really high and will drop rapidly as it descends from the apex... but this also accelerates the disc, you just need a ton of height for a disc to be that far nose down and falling to have room to pan and flatten. a ton of wind assistance increases the forward push of the disc (like a sail) and decreases the drop rate.

when it comes to throwing really over or understable plastic, you are looking at like 70'+ for an apex if trying to break 600'.

 

[erb]

I don't have the time right now to read this whole post, but thought I would just throw in one of my thoughts on fade/spin/shape.
I believe that much of the fade is due to the discs friction with the the air and the direction of spin on the disc. By overtaking the forward velocity (and maybe a small bit of glide) of the disc, after drag slows it down a bit, and then becoming the main force controlling the discs movement. Much like how spin affects a baseball pitches motion, and I think also bending a soccer ball kick (but I don't know that much about soccer). I think that when the disc slows down enough and the spin force is greater it fades because the nose and the front half or front semicircle of the disc start to "bite" or "grip" the air. And it rolls/moves in the direction that the spin makes it. Almost like if a disc thrown at a wall sticks then rolls left or right based on its spin. This is shown in throws with opposite spins and the direction of the discs fade (RHBH fades left, LHBH fades right). What also supports this theory is the strength of fade you see in two discs with similar glide but with different nose thickness. The thick noised disc will have a stronger fade. Dave D. knows this also, if you look at his products the Max, Firebird, Monster all have a fairly thick nose and have a strong fade. Also remember when he tried to make a more overstable Wraith (talking about the first Teerex) he just made the nose thicker, it had similar HSS but more LSS.

Thanks for contributing, erb. Many people have the same impression about fade, but it's actually not true...I'll explain:

What you speak of is called the "Magnus Force," which due to rotation causes the total aerodynamic lift force to point sideways from the velocity, making the object veer sideways. This is indeed what makes a spinning ball curve in its flight (its important in all ball sports...baseball, soccer, tennis, cricket, etc.). It is not, however, what make the disc turn or fade (see below for a possible exception). The reason why the disc is not strongly affected by the Magnus force is that the lateral surface area of the disc is very small, i.e., it has a low profile in the direction in which the force is supposed to act. (The drag force also acts on the same small profile, which is why a disc can fly far without significantly slowing down.) This is different for a ball/sphere, which shows the same cross-section area in every direction. But anyways, due to the small side profile of the disc, there is very little aerodynamic forcing generated because the area to act on is small in comparison to the area of the flight plate.

Possible exception: what Blake calls Hyper-Spin (or something similar). This is when the disc is spun ridiculously fast; where the velocity at the edge of the disc due to spin is very fast in comparison to the translational speed of the disc through the air. Then you might detect the very slightest side force. But this is not at all typical, and I personally have never seen this phenomenon unambiguously occur.

What really causes turn/fade is the lift force, and the center of lift/pressure on the disc. At slow speeds the lift torques the nose up, but due to the gyroscopic stability of the spinning disc, it rolls left (for RHBH) instead of pushing the nose up or down. This is a bit tricky, so I'll give an analogy that might help you understand how the disc responds to pitching moments...

Try to imagine a steering wheel on a car that works not by turning the wheel about its axis, but rather turns the car when you tilt the steering wheel up or down (in the same sense as the tilt position adjustment). If the car follows the same convention as that of a right-hand backhand thrower (i.e., downward angular velocity), then tilting the steering wheel forward causes the wheels to turn to the right, while tilting the wheel back makes the car steer to the left. This is the same sense as the manner in which a spinning disc turns in flight: if you try to push the nose down/lift the tail up, the disc will execute a turn that decreases the hyzer angle (right for RHBH). If you lift the nose up/push the tail down, the disc will execute a negative turn (fade) that increases the hyzer angle (left for RHBH).

More later...

Hey, thanks Blake and Jhern for the insight, yeah I can see how the disc would be different compared to a ball of some sort with the areas.

http://en.wikipedia.org/wiki/Magnus_effect Yeah, I see what you where talking about also.

Looks like I got a little bit of research/learning to get done.

 

[Muddyboots]

Okay, it seems after a thorough reading that I have my head wrapped around the idea of most of this. I have never seen a "real" distance competiton, so I may lack in that area. The Magnus Force discussion interested me greatly. A disc would have to be spun incredibly fast for the small surface area on the leading edge to impart drag against the air and turn in the opposite direction of spin, no? I think I got that part. To the uneducated hammerswinger, it would appear that the parts of flight would be easier to predict in two parts, with flat ground and negligible wind. The first part, from release to equilibrium, which I think at various points here has been referred to as apogee, cruising speed, level flight. The second part is everything after that. Basically the point where the disc is no longer making lift. I don't pretend to understand all of this, and lord knows there are what seems like an infinite number of variables (nose angle, velocity, and the like), but the way I see it, you will have to assume good form ( nose angle x to y ) and proceed from there, with the main variable being velocity. This would require the player to have a pretty good idea of their velocity in order to gain real use from the chart.
Gentleman, I applaud your efforts, this has been a great read. Please let me know if there is anything a non-physicist could do to help.

KP

 

[JHern]

1) There is actually a single cruise speed for a given disc with a given nose angle. This is the speed at which the disc can maintain level flight (it doesn't of course, because it is slowing down from drag and doesn't have a propeller or jet to balance drag). Anything faster will ascend, and anything slower will begin to descend. I know you were speaking about a range of cruise speeds before (and in your post), but in terms of my tinkering so far there is evidence that this occurs only at this exact speed, and not a range.

so cruise speed for lift/descent.

how about for turning/fading vs. straight? is that a range?

Yes, that will almost certainly be a range. I'm also fairly certain that there will be some systematic relations between these two numbers (probably arising from deep and heretofore unknown aerodynamic principles of disc flght). I'm on it.

Okay, it seems after a thorough reading that I have my head wrapped around the idea of most of this. I have never seen a "real" distance competiton, so I may lack in that area.

Me too. I have seen pros drive long shots at NT events, but I've not been around for an actual distance competition. I think for most of us, it is an extreme end-member, on the opposite end of the spectrum as throwing for catching purposes with a lid.

The Magnus Force discussion interested me greatly. A disc would have to be spun incredibly fast for the small surface area on the leading edge to impart drag against the air and turn in the opposite direction of spin, no? I think I got that part.

Cool. That about sums it up. From the scaling laws typically used for this kind of stuff, in order to be as important as the lift force (which ordinarily is responsible for disc precession and turn), the edge spin velocity would have to be higher than the velocity of the disc's motion in flight by a factor of approximately the area of the disc viewed from the top (just pi times radius squared) divided by the area of the disc when viewed edge-on (approx thickness times diameter). This ratio is then pi times the disc radius divided by twice the thickness. This is a large number for mortals (e.g., take a radius of 12 cm, and a thickness of 3 cm, and you get a factor of around 6), so the term "hyper-spin" is appropriate in cases where you can get the Magnus force working. Note that it would also be easier to get the Magnus force to work on a higher profile lid than with a sharp-rimmed driver.

To the uneducated hammerswinger, it would appear that the parts of flight would be easier to predict in two parts, with flat ground and negligible wind. The first part, from release to equilibrium, which I think at various points here has been referred to as apogee, cruising speed, level flight. The second part is everything after that. Basically the point where the disc is no longer making lift. I don't pretend to understand all of this, and lord knows there are what seems like an infinite number of variables (nose angle, velocity, and the like), but the way I see it, you will have to assume good form ( nose angle x to y ) and proceed from there, with the main variable being velocity. This would require the player to have a pretty good idea of their velocity in order to gain real use from the chart.

This is exactly the right idea, I think. I've been doing it piece-by-piece, and getting things down to the point where I can produce velocity-distance scalings, etc.. I'm still working on the lift-drag-gravity balances, and soon I will focus more intensity on the relationship between these characteristics and the turning rates/directions of the disc, which should then allow a full explication of the flight of the disc (e.g., 5-point flights, etc.).

Gentleman, I applaud your efforts, this has been a great read. Please let me know if there is anything a non-physicist could do to help.

KP

Thanks! I'll be posting a PDF in the near future for everyone to browse. It will have all the equations and stuff, since text-only typing of equations is hard to follow.

 

[mafa]

JHern,

Really can't wait for your results. I've also been thinking for some time now of putting up some sort of simulation/simulator for inspecting and understanding better how discs fly. Having a "live" disc flight chart is a great goal.

I am really interested on your thoughts on how to model the moving center of pressure. In literature pitching moment is measured to be function of AoA and v^2 (for a certain type of disc). The most intriguing question in my opinion is how this (non-linear) function could be defined as a function of (for example) semi-quantitative HSS and LSS scales. There's probably more to stability than the pitching moment alone. Another question really bothering me is how OAT (wobbly-kind) really makes discs less stable.

Matti

 

[JHern]

JHern,

Really can't wait for your results. I've also been thinking for some time now of putting up some sort of simulation/simulator for inspecting and understanding better how discs fly. Having a "live" disc flight chart is a great goal.

I am really interested on your thoughts on how to model the moving center of pressure. In literature pitching moment is measured to be function of AoA and v^2 (for a certain type of disc). The most intriguing question in my opinion is how this (non-linear) function could be defined as a function of (for example) semi-quantitative HSS and LSS scales. There's probably more to stability than the pitching moment alone. Another question really bothering me is how OAT (wobbly-kind) really makes discs less stable.

Matti

Good questions Matti. I'm still sorting out some of this myself, but so far I can tell you that...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.

The details of OAT wobble moving the center of pressure backwards is likely complicated. My guess is that vortices are generated that trail the disc and effectively makes the disc seem to have a bigger back end than it really does...hence moving the center of pressure back. But this will require some more thought.

Soon I'll be able to come up with another flight rating system that consists of real physical quantities. That will be fun. And then, of course, mapping Blake's chart into real physical numbers will be super-cool.

 

[JR]

It'll be interesting to see how the simulations compare to a video of real throw with a simulated disc. Mafa has a 250 FPS video camera so he can film my throws.

If one wanted to make ones head explode version two could contain a flight simulator based on the size and shape of the disc and inputting velocity, spin rate, angle of attack and previous vectors of force still giving momentum to the disc :-D

 

[JHern]

It'll be interesting to see how the simulations compare to a video of real throw with a simulated disc. Mafa has a 250 FPS video camera so he can film my throws.

If one wanted to make ones head explode version two could contain a flight simulator based on the size and shape of the disc and inputting velocity, spin rate, angle of attack and previous vectors of force still giving momentum to the disc :-D

If you could film a few discs, from as far away as you can (to reduce perspective distortion) and directly from the side of the throw, and throw in as straight a line as possible (e.g., flip to flat) for a few molds, then it would be possible to start extracting numbers for cruise speed and such.

Also, if you could put the disc into a downward glide and catch the angle of descent, nose angle, and glide velocity, then several other quantities could also be determined.

And the same thing for anyone else who would like to film a disc's motion. I think we can start to put some numbers to things, and this will be very cool. It would be good to also have an accurate measurement of the disc's mass. Also, to use a disc that is more common/popular. I think the Valkyrie might be a good candidate (other suggestions/additions are also welcome) for a model disc, since it is well-liked, and is more middle-of-the-road in terms of its flight characteristics. Once we have the numbers for the Valk established, then we can start to tweak parameters and capture other discs as well.

 

[JR]

It'll be interesting to see how the simulations compare to a video of real throw with a simulated disc. Mafa has a 250 FPS video camera so he can film my throws.

If one wanted to make ones head explode version two could contain a flight simulator based on the size and shape of the disc and inputting velocity, spin rate, angle of attack and previous vectors of force still giving momentum to the disc :-D

If you could film a few discs, from as far away as you can (to reduce perspective distortion) and directly from the side of the throw, and throw in as straight a line as possible (e.g., flip to flat) for a few molds, then it would be possible to start extracting numbers for cruise speed and such.

Also, if you could put the disc into a downward glide and catch the angle of descent, nose angle, and glide velocity, then several other quantities could also be determined.

And the same thing for anyone else who would like to film a disc's motion. I think we can start to put some numbers to things, and this will be very cool. It would be good to also have an accurate measurement of the disc's mass. Also, to use a disc that is more common/popular. I think the Valkyrie might be a good candidate (other suggestions/additions are also welcome) for a model disc, since it is well-liked, and is more middle-of-the-road in terms of its flight characteristics. Once we have the numbers for the Valk established, then we can start to tweak parameters and capture other discs as well.

My scale only shows full grams not decimals. A Teebird and a Roc are probably good candidates and driving with a putter gets more confusing if you ask outside of DGR. DGR choice is likely a Wizard. Perhaps a Boss to represent the fast end might be appropriate as well. I have each of these. But I lack a new Roc that doesn't slip in these temps unless my 09 USDGC Star Rancho works.

We also need to account for sea level plus a few meters at near to freezing temps we have here. I'd think that minimizing variables from disc to disc inconsistency by removing flashing should be done or rather using a new DX 175 Valk because they usually don't have flashing and mine doesn't. The trouble with videoing from the side is the low resolution of mafas camera at 250 FPS and not capturing the full flight without panning the camera which messes up the late flight information. We haven't opened up my camera to see if it could be easily fixed. If we could get my camera working or get somebody else to film the flight from in front of the tee then we might capture all the data.

Have you done your film high speed experiment yet? Can you get a great thrower to do it in front of a camera?

Cruise speed is tricky because it often starts to show only after hundreds of feet for many molds. Two hundred for ams and three+ for pros. That for us means necessarily HD resolution with much reduced frame rate and slow exposure times with blurred images and filming from far far away to catch the throw and the first two hundred feet or more. Which makes measurements very iffy. And ideally you'd want a more competent thrower than me as a test subject and especially warmer temperatures than we can get in Finland outside before late April or May. Snow is upon us very soon. No indoor hall in the closest countries allow throwing and filming from far enough. If one wants to avoid panning the camera and killing the data.

I also suggest showing some known measurement of distance as close to the tee as possible. Larger than disc width for measurement accuracy.

That's why a more professional camera with a shorter adjustable exposure time and higher resolution is needed if one wants to dabble with cruise speed. Throwing down is another challenge that we may be able to conquer by driving to the next town and using one of their sports fields that has an embankment by the field.

 

[JHern]

It'll be interesting to see how the simulations compare to a video of real throw with a simulated disc. Mafa has a 250 FPS video camera so he can film my throws.

If one wanted to make ones head explode version two could contain a flight simulator based on the size and shape of the disc and inputting velocity, spin rate, angle of attack and previous vectors of force still giving momentum to the disc :-D

If you could film a few discs, from as far away as you can (to reduce perspective distortion) and directly from the side of the throw, and throw in as straight a line as possible (e.g., flip to flat) for a few molds, then it would be possible to start extracting numbers for cruise speed and such.

Also, if you could put the disc into a downward glide and catch the angle of descent, nose angle, and glide velocity, then several other quantities could also be determined.

And the same thing for anyone else who would like to film a disc's motion. I think we can start to put some numbers to things, and this will be very cool. It would be good to also have an accurate measurement of the disc's mass. Also, to use a disc that is more common/popular. I think the Valkyrie might be a good candidate (other suggestions/additions are also welcome) for a model disc, since it is well-liked, and is more middle-of-the-road in terms of its flight characteristics. Once we have the numbers for the Valk established, then we can start to tweak parameters and capture other discs as well.

My scale only shows full grams not decimals. A Teebird and a Roc are probably good candidates and driving with a putter gets more confusing if you ask outside of DGR. DGR choice is likely a Wizard. Perhaps a Boss to represent the fast end might be appropriate as well. I have each of these. But I lack a new Roc that doesn't slip in these temps unless my 09 USDGC Star Rancho works.

We also need to account for sea level plus a few meters at near to freezing temps we have here. I'd think that minimizing variables from disc to disc inconsistency by removing flashing should be done or rather using a new DX 175 Valk because they usually don't have flashing and mine doesn't. The trouble with videoing from the side is the low resolution of mafas camera at 250 FPS and not capturing the full flight without panning the camera which messes up the late flight information. We haven't opened up my camera to see if it could be easily fixed. If we could get my camera working or get somebody else to film the flight from in front of the tee then we might capture all the data.

Have you done your film high speed experiment yet? Can you get a great thrower to do it in front of a camera?

Cruise speed is tricky because it often starts to show only after hundreds of feet for many molds. Two hundred for ams and three+ for pros. That for us means necessarily HD resolution with much reduced frame rate and slow exposure times with blurred images and filming from far far away to catch the throw and the first two hundred feet or more. Which makes measurements very iffy. And ideally you'd want a more competent thrower than me as a test subject and especially warmer temperatures than we can get in Finland outside before late April or May. Snow is upon us very soon. No indoor hall in the closest countries allow throwing and filming from far enough. If one wants to avoid panning the camera and killing the data.

I also suggest showing some known measurement of distance as close to the tee as possible. Larger than disc width for measurement accuracy.

That's why a more professional camera with a shorter adjustable exposure time and higher resolution is needed if one wants to dabble with cruise speed. Throwing down is another challenge that we may be able to conquer by driving to the next town and using one of their sports fields that has an embankment by the field.

Hi JR,

Regarding disc choice, we will indeed learn a lot more if we choose a variety of discs with very different flight characteristics. It would also be good to have stable discs in addition to discs that aren't so stable that they can't be turned over (e.g., a Roc or a Teebird) or that few players can use (e.g., the Boss). Valkyrie seems just right (plus I personally like them a lot) for a disc that lies right in the middle of all the flight characteristics, and will be very familiar to many players. It would also be nice to look at a flippable mid like a Panther, Stratus, Cobra, etc.. That being said, I would also like to do your suggestions of a stable mid (like the Roc), a stable driver (like the Teebird), and a warp speed driver (like the Boss) in order to understand exactly how their parameters vary from more middle-of-the-road discs. With putters we should also go with a stable (Wizard is cool) and turnable mold.

Regarding weight, full grams is great. That is 3 significant figures, which is as much as we can hope for (variations in runs, etc., will introduce much larger fluctuations).

Regarding air temperature and altitude, the density of air is a parameter in the model and we can use standard equations of state where this term is important to make a correction. I suppose sea level, zero humidity, and 25˚C will be the reference state. If there is any wind at all it will likely be a much larger fluctuation in the flight than the equation of state correction.

The camera technical issues you mention are going to continue to be an issue. To get a good record of the flight you need to be far away and have high frame rate...however, the dual requirements of resolution and high frame rate are expensive and uncommon.

Knowing that getting the right filming is going to be tough, I was also thinking about using our very own human disc flight recorder (aka Blake) to compare simulated flights to his knowledge of how discs will fly under various conditions, and to tune the parameters to his flight chart.

But, if we could also get some solid data to lay down a firm calibration, it would be very nice and we could then triangulate everything and nail this stuff.

 

[JR]

A lot comes down to how many data points you want per second and exposure time. 25C is too high for Finland as it may be July before we get that. We can get some data from Finnish meteorological institute for this town but that's likely to be inaccurate because we can't throw at the measuring station. And there's differences between all stations that are visible now as a test but will end in May.

IIRC the camera mafa has doesn't have a short enough exposure time for unblurred images in high speed or HD mode :-( IIRC the camera can take 50 FPS progressive scan at 1920x1080. Is that enough? Maybe the camera automatics will adjust the exposure to short enough if we film on a snowy day with sunshine because there's a lot of available light then. We haven't tested that yet so blurring may not be an issue throwing in freezing conditions. Which can be compensated for in the simulation.

We have a friend that has a Panther.

Would two different cameras filming from the side work? We could bring both cameras closer to the action if the second camera overlaps the field of view of the first one and we mark a spot on the ground that both cameras see and are at equal angles and distances apart from. The course mafa plays most has a measured 50 meter stake on the ground. And 100, 110 and 150 m. I suspect one stick is 125 m but can't be sure without measuring.

 

[JHern]

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.