How do you calculate disc weight at a certain speed

[Blobfish]

I kinda knew this was coming because I could not state the question properly because I dont know physics too well. But everyone knows a disc will feel very heavy for a split second in a good throw and objects inside the car become heavier in a crash etc. Thats the phenomena I tried to describe. Dont know what the actual name for it is.

Inertia.


Way too long answer follows:

Mass is the way we quantify inertia (for all intents and purposes, inertia and mass are synonymous).

A qualitative description of inertia is an object's resistance to a change in its state of motion. Newton's First Law of Motion (aka the Law of Inertia) is the one that says, "an object at rest stays at rest unless acted upon by an external force" or "an object at constant velocity stays at constant velocity unless acted upon by an external force".

Here, the disc starts off at rest. A good reachback isn't necessarily one where the disc gets thrust backwards; in a lot of cases, the disc stays in place relative to the ground as you move around it to set up your reachback. But still, the point is, the disc is at rest and it wants to stay at rest due to Newton's First Law.

Newton's Second Law of Motion is the one that folks remember as F=ma, but that's because a simple product is easier to remember than a fraction. However, rearranging the equation gives us a=F/m where a is acceleration, F is force that must be applied to create the acceleration, and m is mass of the object being accelerated.
Now we generally think of acceleration as "speeding up" but in fact, acceleration is the change in velocity with respect to time (where velocity is speed with a direction). As such, a positive acceleration changes velocity in the positive direction and negative acceleration changes velocity in the negative direction.
For now, let's call forward the positive direction.

So... we have a disc that is at rest. We want to get it up to 80 mph. We have the length of our reachback and pull and release to get it from 0 mph (initial velocity) to 80 mph (final velocity)
In order to get that large change in arm speed (final velocity-initial velocity) in such short real estate, the time interval has to be really small.
So remember, I said acceleration is the change in velocity with respect to time (change in velocity over change in time (dv/dt))
The smaller you make the time interval, the bigger the fraction becomes for a fixed change in velocity.
Anyway, dV/dt is the very definition of velocity.

Back to Newton's Second Law which said that a=F/m.
If we know the acceleration (change in velocity over time), then that value must equal the force needed to create that acceleration (your pull) divided by the mass of the object being accelerated (your 175 g disc)
For the same size disc, if you want to crank up the acceleration, it means you need to apply more force. This is common sense, I know, but I'm trying to put the concepts all together.
If you're really interested, the second law is actually the Impulse Momentum Theorem: Fdt=mdV because F=ma and we substituted dV/dt for a and then multiplied both sides by dt. The impulse momentum theorem says that apply a force for a given amount of time, it will change the objects momentum (mass x velocity).


Anyway, Newton had a third law of motion: We call this the law of action and reaction, but really, what it says is that forces occur in pairs and every force has an equal but opposite (in direction) reaction force. Why this is crucial is the greater the applied action force, the greater the reaction force (WHICH IS WHAT YOU FEEL)
Wait, what?
Ok, bear with me. When you are in a car and you hit the gas, you do so to make your car accelerate forwards. But it FEELS like you are thrown backwards. Really, what you are experiencing is Newton's First Law all over again. Your body wants to stay at whatever velocity (or at rest), but the car moves and so it presses into your back and you feel like you are thrown backwards. Similarly, when you stomp the brakes (negative acceleration), you feel like you are thrown forwards, because again, the law of inertia says that you want to keep going at constant velocity but the car wants to slow down, so you feel like you're thrown forwards.

The point of that example is that you FEEL a force that is in the opposite direction of the acceleration.

So when you pull on your disc with your maximum acceleration that you can muster, the disc feels the heaviest it can because of the disc's inertia.

 

[Innova63]

Or for us dumb Muricans: about 0.39 pounds(force) at 32.2 ft/s^2.

Speak for yourself only please...

 

[BogeyNoMore]

Is it OK if I just throw my disc?


Kidding aside, while I really do think it helps to understand the basic physics of disc flight, the physics pretty quickly gets more complex than your basic two semesters of Physics 101 & 102 addresses.... which is why most people won't be able to follow the complete physics of disc flight.

However, you can get a great deal of practical knowledge by accumulating a wealth of observational info. That helps build a sort of internal database, which ultimately leads to a feel for your discs, and the game.

I believe most people's best throws are about "feel" rather than about their comprehension of disc physics.

 

[ru4por]

So it's more overstable, then?

Wait...does is fly like a TeeBird?

 

[Shamis]

Uhhh...I'm getting closer to 1.72 Newtons. At least on earth's surface, with the acceleration of gravity of 9.81 m/s^2.

Or for us dumb Muricans: about 0.39 pounds(force) at 32.2 ft/s^2.

i just asked google.

 

[ThrowBot]

i just asked google.

Wolfram Alpha is better, my friend.

F=ma

F=175g * 9.81 m/s^2

Go to Wolfram, type in "175g * 9.81 m/s^2" and hit enter. It will spit out the answer in a variety of units.

 

[ejvogie]

Wait...does is fly like a TeeBird?

Yes, but longer

 

[R-Ogre]

Quick google search has a golf swing at .25 sec and a baseball swing at .15 sec. For funsies let's split the difference and call it .2 sec, and say an am can throw 80 kph (22 m/s). With a weight of 175 gm we've got all we need to ballpark it. My extremely rusty college physics and some google gives 19.25 Newtons or about 4 lbs.

I'll admit it's extremely possible that I missed a decimal place or 2 somewhere in there.

 

[R-Ogre]

And of course as pointed out you'd have to know a lot more to account for the force you put in to getting the disc spinning.

 

[ALT-J]

Inertia.


Way too long answer follows:

Thank you for your detailed answer. Really refreshed some memories from way back, especially the classic Newton laws and the delta sign that represents change in velocity and time. Good times over 15 years ago. So how do you calculate the force and mass you need to resist if you know the length of the swing, the weight of the disc and roughly the time span where the acceleration happens? How would that force translate into inertia and mass in kilograms that a thrower will feel momentarily? Dont know if these are even valid questions but lets try.

The concept of acceleration is kind of hard. In disc golf its probably easiest to see the effect in putts. The best and most consistent and repeatable putts always feel like that the time span for the actual throw is very small and compact. Yet the disc flies 60-70 feet with a very small movement. Its like going from 5 mph to probably 40 mph in a fraction of a second that makes the disc fly. Thats very confusing and counter intuitive for me for some reason.

 

[Blobfish]

F= ma = m*dV/dt
So:
F*dt = m*dV (this is the impulse momentum theorem... a fancy way to reiterate Newton's Second Law)

F*dt is the definition of impulse (applied force multiplied by the duration of time that the force is applied)
m*dV is the change in momentum (where by definition, momentum is mass * velocity)

The mass of the disc does not change, and since you are already holding it up in equilibrium against its weight to keep it on a straight line, you can ignore it's weight (which as others have said, would be 0.175*9.81=1.72N).
However, this mass is accelerating sideways in your throw.

Again, the mass does not change (it's inertia does not change), but the desired acceleration dictates how much force will be needed to be applied.

Going back to this equation:
F*dt = m*dV

You have a fixed dV (80 mph - 0 mph) and you have a fixed mass (175g) (I'm ignoring normalizing the units for now because we're not actually plugging in the numbers)
Thus, the less time you take to bring that disc up to speed (smaller dt) requires greater F. Mathematically, F and dt are inversely related by a factor of mdV

But now look at it from another perspective of work done on the disc:
The simplified physics definition of work is W=F*dx which means that the work done on an object is the product of the distance the object travels multiplied by the component of the force applied to the object that lines up with the direction of travel. I'm making the assumption that the disc is being pulled in a straight line. Therefore, the work is going to be the same force we alluded to before multiplied by the difference in distance between where you let go (final position) and the start of your reachback (initial position).

Work done on an object also directly corresponds to the change in kinetic energy of the object (0.5 m*v*v) where in this case, the "v" is the 80 mph

So W=F*dx by definition, but also W=dK which in this case because initial velocity was zero so initial K was zero, means W = final K = 0.5*m*v*v

Then, F*dx = 0.5*m*v*v

And solving for F:

F = 0.5*m*v*v/dx which translates as follows:

For a given mass (175g) and a desired final velocity (80mph), the force needed is dependent on how long the distance the force is applied. Long distance (long arms and thus long dx) means less force needed. Short distance means more force is needed to achieve the same result.

Look at sprinters and a lot of football tailbacks. They can be short with really powerful legs because they need that burst of power because their race is over in a short distance. Or if you want to think automotive, they are geared down for power and low end acceleration. On the other hand, look at longer distance runners or wideouts and you'll see longer legs because they are geared higher for maintaining top speed once they get there (Usain Bolt is an anomaly).

The concept of acceleration is kind of hard. In disc golf its probably easiest to see the effect in putts. The best and most consistent and repeatable putts always feel like that the time span for the actual throw is very small and compact. Yet the disc flies 60-70 feet with a very small movement. Its like going from 5 mph to probably 40 mph in a fraction of a second that makes the disc fly. Thats very confusing and counter intuitive for me for some reason.

This last thing you said about the compact putt isn't any different (remember, the disc is only 175 grams) but there are two things that are overlooked:
1. In the example used above, we made the assumption that you're trying to get the disc up to 80 mph. This involves getting your hand up to 80mph which means getting your arm up to speed (something less than 80 mph) to get your hand going that fast. You are now doing work to a whole lot more than 175g, as your whole body is involved. I was isolating just the point of contact of your hand providing the external force to the disc
2. Glide. Putters (unless you're throwing a RDG Scale, Kastaplast Berg, Innova Rhyno or some other brick), your putter is designed to stay aloft. A quick snap of the wrist or fingertips will have a very low dt and at the same time will have a low dx, but as you are only working on the disc itself (not trying to throw your whole arm), the force required will be small.

 

[HyzerUniBomber]

1. In the example used above, we made the assumption that you're trying to get the disc up to 80 mph. This involves getting your hand up to 80mph which means getting your arm up to speed (something less than 80 mph) to get your hand going that fast. You are now doing work to a whole lot more than 175g, as your whole body is involved. I was isolating just the point of contact of your hand providing the external force to the disc

Not quite. Your hand will be going slower than 80mph to have the disc eject @ 80mph. That's the whole point of redirecting the disc (hand on the outside), loading the wrist and using a hit. That is what accelerates the disc. I can barely move my hand and redirect the disc and get it to go much faster than my hand speed.

Yes, you could drag a disc 80mph and not redirect it, but that would be wildly inefficient.

 

[sidewinder22]

Is it OK if I just throw my disc?


Kidding aside, while I really do think it helps to understand the basic physics of disc flight, the physics pretty quickly gets more complex than your basic two semesters of Physics 101 & 102 addresses.... which is why most people won't be able to follow the complete physics of disc flight.

However, you can get a great deal of practical knowledge by accumulating a wealth of observational info. That helps build a sort of internal database, which ultimately leads to a feel for your discs, and the game.

I believe most people's best throws are about "feel" rather than about their comprehension of disc physics.

 

[Blobfish]

Not quite. Your hand will be going slower than 80mph to have the disc eject @ 80mph. That's the whole point of redirecting the disc (hand on the outside), loading the wrist and using a hit. That is what accelerates the disc. I can barely move my hand and redirect the disc and get it to go much faster than my hand speed.

Yes, you could drag a disc 80mph and not redirect it, but that would be wildly inefficient.

Yes, you're correct there. I made a lot of assumptions to simplify the problem. It's like a bendy shaft on a golf club that effectively whips the head. I tried to address the snap in a way in the second point, but yeah, good point about the hand speed.
The disc has to rotate around your last point of contact just like the tip of a bullwhip.

I was trying to focus on the "heavy" sensation that the OP mentioned when ripping a disc, but you're absolutely correct, thanks for pointing it out!

 

[Disc Golf Doctor]

I threw my Falcon (by Millenium Discs) through the entire Kessel course in 12 parsecs

a parsec is a measurement of distance

 

[ohtobediscing]

Inertia.


Way too long answer follows:

Mass is the way we quantify inertia (for all intents and purposes, inertia and mass are synonymous).

A qualitative description of inertia is an object's resistance to a change in its state of motion. Newton's....

This is why I quit teaching bio and physics and started fighting wildfires---the students didn't want that depth of focus. Well, that, and I would've been a forest ranger already, if not for Ronnie.

 

[HyzerUniBomber]

a parsec is a measurement of distance

I fail to see what the issue is with a parsec being a unit of measure of distance? He threw the disc fast enough to warp space.

 

[R-Ogre]

a parsec is a measurement of distance

Right. Han and chewie got their reputation by taking a ballsy shortcut, not just by being fast.

 

[etdefender19]

Oopsie

 

[ALT-J]

Not quite. Your hand will be going slower than 80mph to have the disc eject @ 80mph. That's the whole point of redirecting the disc (hand on the outside), loading the wrist and using a hit. That is what accelerates the disc. I can barely move my hand and redirect the disc and get it to go much faster than my hand speed.

Yes, you could drag a disc 80mph and not redirect it, but that would be wildly inefficient.

So where does the term arm speed come from? Clearly its not the thing you want to look for and so many people including me are trying too hard instead of a controlled movement that gets the job done better power and controlwise. Perhaps theres a ratio between lower arm speed and disc ejection speed that could enlighten what we need to do and look for. If we know the length of a lower arm and its speed, is it possible to know how much faster it will eject in ideal conditions?

A good example is my friend who has a good form but really tries to make his arm go fast and the disc slips. He's much more efficient and has even more power when he just focuses on a smooth throw.