1.Understand how all the forces interact with a Frisbee
2.Understand more about fluid dynamics
3.Connect the relationship between a disc and angular momentum
4.To understand the physics behind why and how good throws are good
V.R Morrison’s Experiment from the Physics Department of Mount Allison University in NB Canada:
She wanted to model the flight of a disc thrown in certain specific conditions. She also looked at the effect of lift and drag.
What she did was she wanted to simulate the flight of a disc in a program using Euler’s Method, so she didn’t actually build machine to throw a Frisbee. Euler’s method is the numerical procedure for solving ordinary differential equations with a given initial value.
Her input parameters into the program:
Initial y position = 1m
Y Velocity = 0m/s
Initial x position = 0m
X Velocity = 15mm/s
Angle of Attack = 0°- 45°
ΔTime = .001s
She also had different coefficients of lift and drag. Her Cdα (coefficient of drag) was 2.72 and her Clα (coefficient of lift) was 1.4. Also remember that α (the angle of attack), will affect the values of the coefficients.
Figure 1: Plot of height (m) vs distance (m) with initial velocity of 14m/s and an angle of attack of 5°
Figure 2: Plot of height (m) vs distance (m) with initial velocity of 14m/s and an angle of attack of 7.5°
Figure 3: Plot of height (m) vs distance (m) with initial velocity of 14m/s and an angle of attack of 10°
Results:
What she found was that in the figures above, the angle of attack surely changed the trajectory of the disc. In Figure 1 where there was the lowest AOA, there was little lift force resulting in a shorter distance traveled. Increasing the AOA allowed the disc to go further, as seen in figures 2 and 3, but it seems like the drag coefficient started to affect the flight of the disc more in figure 3 than in figure 2. My prediction is that if she did an AOA of 12.5°, it wouldn’t go that much further if any distance as the effect of lift will start to decrease.
Her study really backed up the science about the ratio between lift and drag. You don’t want to have an angle of attack that is too high because your efficiency will start to dramatically fall. The amount of lift will only decrease after a certain point. This point will be different for different objects.
Sources:
How θ and W Affects Torque & Cool Oil Flow Fluorescence Pics
Changing variables in my equation:
α = (Wf^2)/2 θ and τ=I α
I will mess around with the variables in my equation to find torque in one of my previous blog posts. I am curious to see how changing the variables will affect torque.
If the angular displacement, θ, went up, then torque would go down if the final angular momentum stayed the same.
If the angular displacement, θ, went down, then torque would go up if the final angular momentum stayed the same.
If the final angular momentum, , went up, then torque would go up if the angular displacement stayed the same.
If the final angular momentum, , went down, then torque would go down if the angular displacement stayed the same.
This is very interesting. Instead of doing a 1/8 wrist flick, but a ¼ wrist flick, it would lower my torque by half. The more I rotate my wrist, the lower torque I will get.
Also, if I launched the disc at a very high angular momentum, torque will increase. In my presentation I will include this in the “what makes a good throw a good throw” slide.
Why discs have ridges on top:
- Used to keep an airstream on top of the Frisbee, allowing it to fly farther. Without ridges, the airstream can’t stick to the surface that well. “And the tiny ridges on the Frisbee’s top surface introduce microscopic turbulence into the layer of air just above the label”
This is a picture using the method of oil flow fluorescence to simulate a disc in midflight. The technique can also be used, however, to measure velocity, temperature, and chemical concentration. The concentric rings/rim of the disc disrupts the airflow. In region B, there is a separated flow. A separated flow is key in creating lift, but it also creates drag. The airflow reattaches at C. Having the reattached airflow ensures low pressure, giving you plenty of lift and stability.
This image here also uses the oil flow fluorescence. What you are seeing is an airfoil, an object which has a respectable ratio between lift and draft, going through a simulated airstream at different angles of attack. As you can see, the different angles of attack definitely affect the flow over the top edge. This picture shows the flow visualization.
Facts/Random Notes:
- Discs will curve in the direction of the lower edge.
- When discs are thrown upside down, airstream cannot “stick” to the top surface
- The thicker the edges, the more angular momentum (aka stability) it will have.
Links:
http://www.dgcoursereview.com/forums/showpost.php?p=40186&postcount=34 http://f*ckyeahfluiddynamics.tumblr.com/ (An excellent source, but ill-chosen name for school)
The Right Hand-Rule & Center of Pressure
The Right Hand-Rule:
The torque equation is τ = r X F. This means that torque is the cross product between the moment arm (r) and the Force (F). Even though that (r) is a distance, it is also a vector. The (r) will point away from O, the pivot point. When you can do is that with your right hand, your middle finger will become the (r) vector, your point finger will be the force vector, and your thumb will be the torque vector. How you apply the force will affect the torque. For example, in the washer image, you can see that the force is going in a direction into the screen. As a result, the torque vector will point up, moving the object up the rod. If the force was going the other way, the torque vector will point down, moving the object down the rod. This also has to do with the common saying of “righty-tighty, lefty loosey”. If the force vector will be pointing to the right, then the direction of the torque vector will be pointed downwards and vice versa for if the force vector points to the left.
This is interesting because you can use this same method to figure out which way a Frisbee might veer. When you spin the disc with a clockwise rotation, the pitch down torque causes a right roll and when the disc is spun with a counter clockwise rotation, the pitch down torque causes a left roll.
Now that I mentioned “pitch”, I will explain it. The pitching moment is the torque produced by the aerodynamic forces. It is any torque acting on the pitch axis of a body. This happens on the aerodynamic center. The aerodynamic center is where the effect angle of attack is not considered, making analysis easier.
Center of Pressure:
Previously in one of my blog posts, I said that if a Frisbee doesn’t spin, it won’t go that far because the location of where the center of gravity is, is different from where the location of where the center of pressure is. I want to explain more about what is the center of pressure. It is the average location of pressure variation on an object. Two things I want you to take away is the aerodynamic forces acts through the center of pressure and the center of pressure will move accordingly to the angle of attack.
We can sort of calculate it as how we would for calculating the center of gravity. It is a bit complicated as pressure changes around the object, but we need to know the pressure distribution. If the functions are unknown, people can experiment and calculate the pressure over an x amount of distance segments and finding the average of all that. Integrating the pressure times the surface area around the body determines the aerodynamic force on the object. This force acts on one single point, which is the center of pressure.
Why is calculating this thing important? It is pertinent to the stability of bigger things such as rockets or kites.
Sources:
https://www.physics.uoguelph.ca/tutorials/torque/Q.torque.intro.html
https://www.grc.nasa.gov/www/K-12/airplane/cp.html
https://www.physicsforums.com/threads/aerodynamics-of-a-flying-disc.327993/
Example Problem: Moses
175 gram Frisbee. 24cm diameter. Half the mass is equally spread in the disc and the other half of the mass is equally spread in the rim. If Moses Rifkin throws a Frisbee at 1000rpm with a 1/8-turn of the wrist, what is…
- The total moment of inertia?
Step 1: Convert all numbers + organize information
Disk: radius = .12m – containing half mass of .0875kg
Hoop: radius = .12m – containing the other half of mass of .0875kg
Moment of Inertia disk = 1/2MR^2
Moment of Inertia hoop = MR^2
1000rpm = 104rad/sec
Step 2: Solve for I
In other words, I = Moment of Inertia disk + Moment of Inertia hoop
Total Moment of inertia = 1/2MR^2 + MR^2
= .5(.0875)(.12)^2+(.0875)(.12)^2
I = .00189 kg m 2
- The magnitude of the torque?
Step 1: Use Torque equation of τ=Iα (however I first want to derive this formula). I want to explain the connection between torque and angular acceleration.
τ = torque
I= moment of inertia
α= angular acceleration
Imagine a mass moving in a circle away from distance r with a tangential force
We know that F=ma
We can also say that a=rα
So, F=mrα
τ about the center of rotation from F: τ =Fr
Therefore τ=mr^2 α
Finally, τ=I α
Step 2: Since we already know I, solve for α
I will want to use Wf^2=Wi^2+2 α θ. This equation is parallel to the kinematics equations for linear motion. It is really cool how we can relate rotational motion and linear motion.
Wf= Angular momentum final
Wi= Angular momentum initial
Θ = angular displacement (think unit circle)
Wf=104rad/sec
Wi= 0
Θ = π/4
α = (Wf^2)/2 θ
α = 104^2 / (2(π/4))
α = 6885.6 rad/sec^2
Step 3: Plug it all back in
τ=Iα
τ = (.00189)( 6885.6)
τ=13J
Role of Angular Momentum in Frisbee
If you just apply a thrust force to a disc, it will go some distance, but not that far. However, if you apply more spin to the disc, the spin will stabilize the Frisbee, allowing it to go much farther. So how does spinning to this? Also in this blog, I will add on to my knowledge of the aerodynamic forces and its roles in angular momentum.
When a disc doesn’t spin, the aerodynamic forces are not on the center. What this means is that lift on one side of the Frisbee will be larger than the other side, creating a net torque. Torque is “a measure of how much a force acting on an object causes that object to rotate”. Once this torque is created, a stable flight is no longer possible as one side of the disc is popped up.
In this image, you can see that the center of mass is not where the center of pressure is. This will cause a torque.
Spinning gives an object angular momentum. This type of momentum is dependent on “Moment of Inertia”, I, and angular velocity, w. Therefore, L=I*W. The higher the angular momentum, the more stable the object will be.
What is moment of inertia? It is the inertia for a rotation. The moment of inertia depends on how far away mass is from the rotational axis. In other words, it depends on the distribution of mass. Also, it is the amount of resistance a body has to changing its state of rotational motion. The equation for I is MR^2. This equation is only for a solid cylinder or disc as other objects such as rods or shells will have different ones.
The faster the spin is, the more angular velocity there will be. If there is no spin, there will be no angular momentum as W=O. For example, with a motorcycle, the bike doesn’t stay upright because of the good balance of the motorist, it is from the high angular velocity from the wheels.
Since angular velocity talks about a direction as well, one can use the right hand rule to find it. Check out the next blog post to learn more about this.
Sources I used:
http://web.mit.edu/womens-ult/www/smite/frisbee_physics.pdf
https://www.grc.nasa.gov/www/K-12/airplane/cp.html
http://ffden-2.phys.uaf.edu/211_fall2013.web.dir/Matthew_Keith/Momentum.html
How a Frisbee flies is very similar to how an airplane flies. Of course, a Frisbee spins, but I will address that part in the next entry. But for now, I will talk about the aerodynamic forces, specifically Thrust, Weight, Lift, and Drag. You can find most of my findings here.
Thrust:
This is the force which move things through air. It is used to overcome the forces of drag and weight. In planes, this force is created by engines or propellers. When you throw a Frisbee, you use your arm to generate thrust. It is also a vector quantity, having a magnitude and direction. I will explain more about thrust in depth later on because it has so much to do with the fact that a Frisbee spins in flight.
Weight:
This is the force that everyone is most familiar with. Weight is caused by the gravitational attraction of Earth on the plane/Frisbee. This force is the only field force, making it fundamentally different than all of the other aerodynamic forces, which are mechanical forces. I will explain what a mechanical force is when I will talk about lift. Because of weight, the Frisbee will eventually fall back down to Earth.
Lift:
This force directly opposes weight. It is what holds the object in the air. Lift is a mechanical aerodynamic force produced by the flying motion. What this means is that this force can only be created with the interaction of a solid body with a fluid (liquid/gas). It is not a force field, where gravity and electromagnetic fields can affect objects without being in physical contact. Thus, no fluid (aka no air), no lift. For example, a space shuttle doesn’t stay in space because of the lift from its wings. Another important fact is that the force of lift acts perpendicular to its motion.
How is lift generated? Lift is made by the difference in velocity between the object and the air. I shortly talked about this in my last blog post, but I’ll rephrase my explanation here. Due to the unique shape of the airplane wing, air will travel faster on the top than the bottom. You have lift when you redirect air flow. Another thing that contributes to lift is the action-reaction dynamic. The air gets pushed down by the geometry of the wing, therefore there will be a reaction in the lift force allowing the wing to go up.
The equation for lift is L= CI * ((density*velocity^2))/2)*wing area
CI is considered the Lift Coefficient. Cl = 2*pi*a
Density deals with the density of the air
The variable “A” is the angle of attack. I will explain more about what that is more below.
This picture shows how the specific shape of the wing allows the air on top to significantly travel faster than the air on the bottom.
Drag:
You can think the force of drag as being created by the friction between the molecules of air and the surface. This force acts in the opposite direction of the motion. There are many factors that will increase or decrease the amount of drag an object will experience. One type of drag is called Form Drag. This is based on the shape. Similarly to the equation of lift, the drag equation is
Drag = Cd* ((density*velocity^2))/2)*wing area
The coefficient of drag is determined through experiments. In a wind tunnel, physicists can alter conditions such as velocity and density to figure out how much drag was produced.
Angle of Attack
Something that affects lift, thrust and even drag alike is something called the Angle of Attack. This is the angle is the difference between the Pitch Angle and the Flight Path Angle. In this picture, it is shown that the Pitch Angle is the angle between where the airplane is pointed to where the horizontal ground is. The Flight Path angle is between where the airplane is actually going (you can think of it as the trajectory vector) and to the same horizontal ground. There is a common misconception that the Angle of Attack is the Pitch Angle. This is totally false.
Why does changing the Angle of Attack affect all of these forces? As I said above, the lift coefficient is dependent on the angle of attack. The higher the angle of attack, the more lift there will be. I’m still continuing research on the importance of the Angle of Attack.
My next steps will be to look further into gyroscopic inertia.
Other Links that helped me:
Initial Research + Redefined Learning Objectives
Now that you have a much better understanding of your topic, restate your learning objectives to clarify these further and make them more specific.
- Explain the relationship between rotational inertia and a Frisbee
- Understand how all the forces interact with a Frisbee
- To understand the Bernoulli Principle
- To understand what goes into making the ideal Frisbee (one that goes farthest)
- Explain how different throws affect the path of the Frisbee
- How wind forces you to change how you throw
List the set of sources (webpages, youtube links, books, research papers, people) discovered so far and for each of the sources you have consulted, write down what you have learned so far.
- Eugene Motoyama – The Physics of Flying Discs (Research paper) csail.mit.edu/jrennie/discgolf/physics.pdf
- https://www.youtube.com/watch?v=aFO4PBolwFg (Lift correctly explained)
- https://www.mansfieldct.org/Schools/MMS/staff/hand/Flightfrisbee.htm#flightbernoulli (general info)
Summarize your PHYSICS learning with respect to your specific learning objectives and rate your progress as a percentage. 100% implies that you have completed your learning objective and are ready to explain it in detail.
Bernoulli Principle: The convex shape of the Frisbee allows it to fly when it is going through the air. This is because there is a difference in pressure on the top and bottom of the Frisbee due to the different speeds of the air.
The first way of how lift is generated is by the Coanda effect, which is the tendency of a fluid to “stick” to a nearby surface. An example of this is with a ping pong ball and a hair blower. The ball will “stick” to the lower side of the airstream, keeping it in midair. Going back to the Frisbee, when you increase the angle of attack, meaning you increase the angle to the horizontal of the Frisbee, air under the wing is deflected down and air above the wing will follow the surface and go down as well. The air under the Frisbee will be slowed and be pushed down. Because of Newton’s 3rd Law, this will cause the forces of lift and drag. However, this doesn’t mean that Bernoulli’s is wrong.
Air on the top does flow faster than air on the bottom, causing a lower pressure on top and a higher pressure on the bottom, creating lift. This only misconception was that the air reconnects at the tail end of the disc.
70%
Turbulence: Frisbee is much more susceptible to turbulent follow than an airplane wing.
I still need to learn more about angular momentum. It is still pretty confusing to me. 20%
What surprised you in your learning? Were there misconceptions (Physics related and others) you had previously which got clarified today?
I learned that the “classic” explanation of the Bernoulli principle is wrong. The “classic explanation” is that lift is created when the air travels faster than the top of the wing than the bottom of the wing because the top of the wing is longer, and that the air has to reconnect at the other end. This is completely bogus. There are two other ways to explain lift of a wing or a flying disc.
Place links to animations, videos, photos including photos/videos of your own explanations using material around your house)
Before The Journey
1) What topic did you choose and why?
I chose to talk about the physics of a Frisbee. I am curious about this topic because I play Ultimate. With the throws that I make, I would sometimes hold the disc angled in different ways so that I can throw an “inside out” or an “outside in” throw. I also learned that in windier days, I need to do certain things in order for an accurate throw. I am interested in knowing how certain positions of holding the disc can affect the flight through physics knowledge. Over my four years of playing, I have learned so many techniques without really knowing the science behind it. I want to know the science to understand why I am doing all these different throws in the different situations.
2) What are your learning objectives?
I am planning on talking about all the forces that act on the frisbee in flight, for example lift/thrust, etc. I will also want to talk about the Bernoulli principle. If anything else comes up during my research, then I will definitely include it.
1) To understand how all the forces on the frisbee allows flight.
2) To understand the Bernoulli principle.
3) Be able to relate the physics of a frisbee to other things in the universe (aka a plane)
3) How do you plan on providing evidence of your learning?
I am planning on making a powerpoint. Maybe, I will even do a short video, however I am not sure yet.
4) Place one video link and one photo related to your topic in your post.
http://www.nasa.gov/audience/foreducators/k-4/features/F_Four_Forces_of_Flight.html
5) Are you partnering with anyone? If so, put a link to their blog.
I am not.
uprepandypham15 