drag experiments in physics

February 28, 2013

Soaring Science: Test Paper Planes with Different Drag

An aerodynamic activity from Science Buddies

By Science Buddies

Key concepts Aerodynamics Planes Forces Drag Physics

Introduction Have you ever wondered what makes a paper plane fly? Some paper planes clearly fly better than others. But why is this? One factor is the kind of design used to build the plane. In this activity you'll get to build a paper plane and change its basic design to see how this affects its flight. There's a lot of cool science in this activity, such as how forces act on a plane so it can fly. So get ready to start folding!

Background The forces that allow a paper plane to fly are the same ones that apply to real airplanes. A force is something that pushes or pulls on something else. When you throw a paper plane in the air, you are giving the plane a push to move forward. That push is a type of force called thrust. While the plane is flying forward, air moving over and under the wings is providing an upward lift force on the plane. At the same time, air pushing back against the plane is slowing it down, creating a drag force. The weight of the paper plane also affects its flight, as gravity pulls it down toward Earth. All of these forces (thrust, lift, drag and gravity) affect how well a given paper plane's voyage goes. In this activity you will increase how much drag a paper plane experiences and see if this changes how far the plane flies.

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Materials • Sheet of paper • Ruler • Scissors • Large open area in which to fly a paper plane, such as a long hallway, school gym or basketball court. If you're flying your paper plane outside, such as in a field, try to do it when there isn't any wind. • Something to make at least a one-foot-long line, such as a long string, another ruler, masking tape, rocks or sticks. • Paper clips (optional)

Preparation • Make a standard, "dart" design paper airplane (for instructions, go to the Amazing Paper Airplanes Web page ). • Fold your paper into the basic dart paper plane. Fold carefully and make your folds as sharp as possible, such as by running a thumbnail or a ruler along each fold to crease it. Do not bend up the tailing edge of the wings (step 6 of the online folding instructions). • Go to a large open area and, using string, a ruler, masking tape, rocks or sticks, make a line in front of you that's at least one foot long, going from left to right. This will be the starting line from which you'll fly the paper plane.

Procedure • Place your toe on the line you prepared and throw the paper plane. Did it fly very far? • Throw the plane at least four more times. Each time before you throw the plane, make sure it is still in good condition (that the folds and points are still sharp). When you toss it, place your toe on the line and try to launch the plane with a similar amount of force, including gripping it at the same spot. Did it go about the same distance each time? • Once you have a good idea of about how far your plane typically flies, change the plane’s shape to increase how much drag it experiences. To do this, cut slits that are about one inch long right where either wing meets the middle ridge. Fold up the cut section on both wings so that each now has a one-inch-wide section at the end of the wing that is folded up, at about a 90-degree angle from the rest of the wing. • Throw your modified paper plane at least five more times, just as you did before. How far does the paper plane fly now compared with before? Why do you think this is, and what does it have to do with drag? • Extra: Make paper planes that are different sizes and compare how well they fly. Do bigger planes fly farther? • Extra: Try making paper planes out of different types of paper, such as printer paper, construction paper and newspaper. Use the same design for each. Does one type of paper seem to work best for making paper planes? Does one type work the worst? • Extra: Some people like to add paper clips to their paper planes to make them fly better. Try adding a paper clip (or multiple paper clips) to different parts of your paper plane (such as the front, back, middle or wings) and then flying it. How does this affect the plane's flight? Does adding paper clips somewhere make its flight better or much worse? Observations and results Did the original plane fly the farthest? Did the plane with increased drag fly a much shorter distance?

As a paper plane moves through the air, the air pushes against the plane, slowing it down. This force is called drag. To think about drag, imagine you are in a moving car and you put your hand out the window. The force of the air pushing your hand back as you move forward is drag, also sometimes referred to as air resistance. In this activity you increased how much drag acted on the paper plane by making a one-inch-high vertical strip on both wings. For example, this is what happens when you're in a moving car with your hand out the window and you change its position from horizontal to vertical. When your hand is held out vertically, it catches a greater amount of air and experiences a greater drag than when it is horizontal. You could probably feel this, as your hand would be more forcefully pushed back as the car moves forward. This is what happened to the modified plane—it experienced a greater amount of drag, which pushed it back more than the original plane. This experiment has clearly demonstrated that altering how just one force acts on a paper plane can dramatically change how well it flies.

Cleanup Recycle the paper plane when you are done with it.

More to explore Dynamics of Flight: Forces of Flight , from NASA What Makes Paper Airplanes Fly? , from Scholastic Forces of Flight—Drag , from The Franklin Institute How Far Will It Fly? Build and Test Various Paper Planes , from Science Buddies

This activity brought to you in partnership with  Science Buddies

Aerodynamic Drag

Pressure drag.

The force on an object that resists its motion through a fluid is called drag . When the fluid is a gas like air, it is called aerodynamic drag or air resistance . When the fluid is a liquid like water it is called hydrodynamic drag, but never "water resistance".

Fluids are characterized by their ability to flow. In somewhat technical language, a fluid is any material that can't resist a shear force for any appreciable length of time. This makes them hard to hold but easy to pour, stir, and spread. Fluids have no definite shape but take on the shape of their container. (We'll ignore surface tension for the time being. It's really only significant on the small scale — small like the size of a drop.) Fluids are polite in a sense. They yield their space relatively easily to other material things; at least when compared to solids. A fluid will get out of your way if you ask it. A solid has to be told to get out of the way with destructive force.

Fluids may not be solid, but they are most certainly material. The essential property of being material (in the classical sense) is to have both mass and volume. Material things resist changes in their velocity (this is what it means to have mass) and no two material things may occupy the same space at the same time (this is what it means to have volume). The portion of the drag force that is due to the inertia of the fluid — the resistance that it has to being pushed aside — is called the pressure drag (or form drag or profile drag ). This is usually what someone is referring to when they talk about drag.

Recall Bernoulli's equation for the pressure in a fluid…

P 1  + ρ gy 1  + ½ρ v 1 2  =  P 2  + ρ gy 2  + ½ρ v 2 2

The first term on each side of the equation is the part of the pressure that comes from outside the fluid. Typically, this refers to atmospheric pressure weighing down on the surface of a liquid (not relevant right now). The second term is the gravitational contribution to pressure. This is what causes buoyancy (also not relevant right now). The third term is the kinetic or dynamic contribution to pressure — the part related to flow (very relevant right now). This will help us understand the origin of pressure drag.

Start with the definition of pressure as force per area. Solve it for force.

Replace the generic symbol F for force with the more specific symbol R for drag. (You could also use D if you wanted to.) Drop in Bernoulli's equation for the pressure in a moving fluid…

Rearrange things a bit and here you go…

R  = ½ρ CAv 2

Wait a minute. Where'd that extra symbol come from? Who put that C in there and why?

Let's run through all the symbols one at a time, explain their meaning and how they relate to pressure drag. In essence, let's take the equation apart and put it back together again.

R  ∝ ρ

R  ∝  A

R  ∝  v 2

R  ∝  C

Combining all these factors together yields a theoretically limited (but empirically reasonable) equation. Here it is again…

Simple, compact, wonderful. A nice equation to work with — or is it?

Well, yes and no.

• Yes, but it works only as long as the range of conditions examined is "small". That is, no large variations in speed, viscosity, or crazy angles of attack. The way around this is to reduce the coefficient of drag to a variable rather than a constant. (I can live with this.) Say that C depends on some yet to be specified set of factors. It is totally acceptable to say that it varies with this that or the other quantity according to any set of rules determined by experiment.
• No, since speed is squared. [Gasp!] Recall that speed is the derivative of distance with respect to time. Have you ever tried to solve a nonlinear differential equation? No? Well, welcome to hell. Wait, let me rephrase that — Welcome to Hell! [Ca-rack! Boom!] Ah ha ha ha ha haaaa! [Rumble] You fool! Just wait till you see what's in store for you when you try to solve the differential equations. The mathematics will consume you. [Ca-rack! Boom!] Ah ha ha ha ha haaaa! [Rumble].

Whew. What the hell was that all about? I might not know how to solve every kind of differential equation off the top of my head, but so what. I can always look for the solution in a book of standard mathematical tables or an on-line equivalent. You don't scare me demonic voice in my head.

other mathematical models

The pressure drag equation derived above is to me the most reasonable mathematical model of drag — especially aerodynamic drag. But as the demonic voice in my head said, it isn't always the easiest one to work with — especially for those just learning calculus (differential equations to be more precise). Those who know a lot of calculus just deal with it. Those who don't know any calculus just ignore it.

A simplified model of drag is one that assumes that drag is directly proportional to speed. This sometimes is good enough. (Maybe we should call it the "good enough model of drag".) It is especially useful when teaching calculus students how to solve differential equations for the first time. I haven't found it to be all that applicable to real world situations, however. (We'll use b as the generic constant of proportionality from now on.)

R  = −  b v

A more general model of drag is one that is agnostic about higher powers (pun intended). This is good attitude to have when you are exploring drag experimentally. Don't assume you know anything about how drag varies with speed, just measure the two quantities and see what values work best for the power n and the constant of proportionality b .

R  = −  bv n

Possibly the most general model is one that assumes a polynomial relationship. Drag might be related to speed in a way that is partially linear, partially quadratic, partially cubic, and partially described by higher order terms.

R  = − ∑ b n v n

drag and power

If you want to go fast, you've got to work hard. That should be a statement of the obvious. But why? Well for one thing, it takes energy to get going — kinetic energy. This equation says, if you want to go twice as fast you've go to work four times harder ( K  ∝  v 2 ).

K  = ½ mv 2

While that's certainly true, it isn't of much use to us here on Earth. If we lived in the vacuum of space, all we'd ever have to worry about was the energy needed to change our state from one speed to another. Here on Earth, the atmosphere has another opinion. Whatever energy we add to a system to get it going, the atmosphere drags it away — all of it eventually. In order for a moving body to stay in motion on the Earth it not only has to get going, it has to actively work to keep going. This undeniable fact of life is why Newton's first law (the law of inertia) wasn't discovered until the 17th century.

To keep an object in motion in the presence of drag (aerodynamic or otherwise) requires an ongoing input of energy. Work must be done over some time. Power must be used. Recall the following chain of reasoning that starts from the definition of power as the rate at which work is done…

Replace the generic force variable with a generic power equation for drag…

P  = ( bv n )  v

Thus in general…

P  =  bv n  + 1

or more specifically, in the case of pressure drag…

P  = (½ρ CAv 2 )  v

P  = ½ρ CAv 3

Thus, if drag is proportional to the square of speed, then the power needed to overcome that drag is proportional to the cube of speed ( P  ∝  v 3 ). You want to ride your bicycle twice as fast, you'll have to be eight times more powerful. This is why motorcycles are so much faster than bicycles.

Power expended against drag is the biggest impediment to moving freely for both bicycles and motorcycles. Humans can do sustained physical work like cycling at the rate of about a tenth of a horsepower. Motorcycles have engines that are on the order of 100 horsepower. (Sorry for the American units.) That makes a motorcycle about one thousand times more powerful than a human on a bicycle. As a result they can go about ten times faster, since 1,000 = 10 3 . I've found through personal experience on all day bicycle rides that I typically cover ⅙ the distance that I would if I sat behind the wheel of a car all day.

Yes I realize that cars aren't motorcycles, but what we're really comparing here are wheeled vehicles powered by human muscle with those powered by internal combustion engines. Yes I realize that a 6 to 1 ratio is not exactly the same as 10 to 1, but what I'm doing here is a quick order of magnitude comparison. Your individual results may vary — but not significantly.

terminal velocity

It's much more than the name of a bad movie. It's something every student of aerodynamic drag should understand.

Imagine yourself as a parachute jumper; or better yet, imagine yourself as a BASE jumper. BASE is an acronym for b uilding, a ntenna, s pan, e scarpment. Since none of these platforms is moving horizontally, none of these jumpers has any initial horizontal velocity. Not that it matters, but this reduces some of the complexity. Step off the platform and draw your free body diagram as you fall.

You start with no initial velocity, there is no aerodynamic drag, and you are effectively in free fall with an acceleration of 9.8 m/s 2 .

Now it gets complicated. There is an initial acceleration, therefore there is an increase in speed. With an increase in speed comes an increase in drag and a decrease in net force. This decrease in net force reduces acceleration. Speed is still increasing, just not quite as fast as it was initially.

Speed continues to increase, but so too does drag. As drag increases, acceleration decreases. Eventually one can imagine a state when the drag and weight forces are equal. You are in equilibrium. You continue moving, but you cease accelerating. You have reached your terminal velocity . Given the usual posture of skydivers, the type of clothes they normally wear, and the conditions of the air near the surface of the Earth; your typical skydiver has a terminal velocity of 55 m/s (200 km/h or 125 mph). The speed that you have in this state is the one you will always acquire if you are given enough time.

That is until the parachute opens. Opening the chute significantly increases your projected area, which cranks up the aerodynamic drag proportionally. The upward drag force now exceeds the downward pull of gravity. The net force and acceleration are directed upward. Note: this does not mean the skydiver is moving upward. Acceleration does not determine the direction of motion of an object, it determines the direction of the change in motion. When a parachute is just opened, the velocity is down and the acceleration is up. Your speed decreases as a result, which is the whole point behind the parachute.

Speed decreases, so drag decreases. Drag decreases, so the net force decreases. Eventually the net force is zero, you stop accelerating, and you reach a new terminal velocity — one that makes landing more comfortable, something like 6 m/s (22 km/h or 13 mph) or less.

Note that a terminal velocity is not necessarily a maximum value. It's a limit that can be approached from either direction. An object could start off slow and speed up to a terminal velocity that's a maximum (like a skydiver stepping off a BASE) or it could start off fast and slow down to a terminal velocity that's a minimum (like a skydiver who's just opened her parachute). "Terminal" is a fancy way to say "end". A terminal velocity is one that you end up with. For falling objects, this occurs when drag equals weight.

Terminal velocity applies to situations besides skydiving. Drive your car with the accelerator in a constant position and you'll eventually reach a terminal velocity. The forward driving force of the tires on the road will eventually equal the backward drag force of the air (and the rolling resistance of the tires, which is discussed somewhere else in this book). Note how I said "eventually". Terminal velocity is a speed things approach but never quite reach. Proof of this statement requires calculus and will be discussed in the practice problems of this section.

Terminal velocity can have any value — including zero. What happens to a ship in the ocean when the propeller stops turning? The forward thrust goes away and all that's left is the backward drag. The ship goes slower and slower and slower until it stops (stops relative to any current, that is). The ship will reach a terminal velocity of zero. For large container ships this may take minutes of time and kilometers of distance, but it will eventually happen. If you don't have the time or the space and you really want to stop a large seagoing vessel, you need to run the engines in reverse. In this case it's thrust that stops the ship, not drag.

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Exploring Drag

Grade Levels

Grades K-4, Grades 5-8, Grades 9-12

Physical Science, Flight and Aeronautics

Hands-on Activities

When an airplane flies, drag is the force that pushes in the direction opposite of the airplane’s movement. Using coffee filters, try this experiment to see what affects drag.

This activity is adapted from the “ Drag and Aircraft Design” guide.

5.2 Drag Forces

Another interesting force in everyday life is the force of drag on an object when it is moving in a fluid (either a gas or a liquid). You feel the drag force when you move your hand through water. You might also feel it if you move your hand during a strong wind. The faster you move your hand, the harder it is to move. You feel a smaller drag force when you tilt your hand so only the side goes through the air—you have decreased the area of your hand that faces the direction of motion. Like friction, the drag force always opposes the motion of an object. Unlike simple friction, the drag force is proportional to some function of the velocity of the object in that fluid. This functionality is complicated and depends upon the shape of the object, its size, its velocity, and the fluid it is in. For most large objects such as bicyclists, cars, and baseballs not moving too slowly, the magnitude of the drag force F D F D size 12{F rSub { size 8{D} } } {} is found to be proportional to the square of the speed of the object. We can write this relationship mathematically as F D ∝ v 2 F D ∝ v 2 size 12{F rSub { size 8{D} } α`v rSup { size 8{2} } } {} . When taking into account other factors, this relationship becomes

where C C size 12{C} {} is the drag coefficient, A A size 12{A} {} is the area of the object facing the fluid, and ρ ρ size 12{ρ} {} is the density of the fluid. (Recall that density is mass per unit volume.) This equation can also be written in a more generalized fashion as F D = bv 2 F D = bv 2 , where b b is a constant equivalent to 0 .5 CρA 0 .5 CρA . We have set the exponent for these equations as 2 because, when an object is moving at high velocity through air, the magnitude of the drag force is proportional to the square of the speed. As we shall see in a few pages on fluid dynamics, for small particles moving at low speeds in a fluid, the exponent is equal to 1.

Drag force F D F D size 12{F rSub { size 8{D} } } {} is found to be proportional to the square of the speed of the object. Mathematically

where C C size 12{C} {} is the drag coefficient, A A size 12{A} {} is the area of the object facing the fluid, and ρ ρ size 12{ρ} {} is the density of the fluid.

Athletes as well as car designers seek to reduce the drag force to lower their race times. (See Figure 5.7 ). “Aerodynamic” shaping of an automobile can reduce the drag force and so increase a car’s gas mileage.

The value of the drag coefficient, C C size 12{C} {} , is determined empirically, usually with the use of a wind tunnel. (See Figure 5.8 ).

The drag coefficient can depend upon velocity, but we will assume that it is a constant here. Table 5.2 lists some typical drag coefficients for a variety of objects. Notice that the drag coefficient is a dimensionless quantity. At highway speeds, over 50% of the power of a car is used to overcome air drag. The most fuel-efficient cruising speed is about 70–80 km/h (about 45–50 mi/h). For this reason, during the 1970s oil crisis in the United States, maximum speeds on highways were set at about 90 km/h (55 mi/h).

Substantial research is under way in the sporting world to minimize drag. The dimples on golf balls are being redesigned as are the clothes that athletes wear. Bicycle racers and some swimmers and runners wear full bodysuits. Australian Cathy Freeman wore a full body suit in the 2000 Sydney Olympics, and won the gold medal for the 400 m race. Many swimmers in the 2008 Beijing Olympics wore (Speedo) body suits; it might have made a difference in breaking many world records (See Figure 5.9 ). Most elite swimmers (and cyclists) shave their body hair. Such innovations can have the effect of slicing away milliseconds in a race, sometimes making the difference between a gold and a silver medal. One consequence is that careful and precise guidelines must be continuously developed to maintain the integrity of the sport.

Some interesting situations connected to Newton’s second law occur when considering the effects of drag forces upon a moving object. For instance, consider a skydiver falling through air under the influence of gravity. The two forces acting on him are the force of gravity and the drag force (ignoring the buoyant force). The downward force of gravity remains constant regardless of the velocity at which the person is moving. However, as the person’s velocity increases, the magnitude of the drag force increases until the magnitude of the drag force is equal to the gravitational force, thus producing a net force of zero. A zero net force means that there is no acceleration, as given by Newton’s second law. At this point, the person’s velocity remains constant and we say that the person has reached his terminal velocity ( v t v t size 12{v rSub { size 8{t} } } {} ). Since F D F D size 12{F rSub { size 8{D} } } {} is proportional to the speed, a heavier skydiver must go faster for F D F D size 12{F rSub { size 8{D} } } {} to equal his weight. Let’s see how this works out more quantitatively.

At the terminal velocity,

Using the equation for drag force, we have

Solving for the velocity, we obtain

Assume the density of air is ρ = 1 . 21 kg /m 3 ρ = 1 . 21 kg /m 3 size 12{ρ=1 "." "21"" kg/m" rSup { size 8{3} } } {} . A 75-kg skydiver descending head first will have an area approximately A = 0 . 18 m 2 A = 0 . 18 m 2 and a drag coefficient of approximately C = 0 . 70 C = 0 . 70 size 12{C=0 "." "70"} {} . We find that

This means a skydiver with a mass of 75 kg achieves a maximum terminal velocity of about 350 km/h while traveling in a headfirst position, minimizing the area and his drag. In a spread-eagle position, that terminal velocity may decrease to about 200 km/h as the area increases. This terminal velocity becomes much smaller after the parachute opens.

Take-Home Experiment

This interesting activity examines the effect of weight upon terminal velocity. Gather together some nested coffee filters. Leaving them in their original shape, measure the time it takes for one, two, three, four, and five nested filters to fall to the floor from the same height (roughly 2 m). (Note that, due to the way the filters are nested, drag is constant and only mass varies.) They obtain terminal velocity quite quickly, so find this velocity as a function of mass. Plot the terminal velocity v v size 12{v} {} versus mass. Also plot v 2 v 2 size 12{v rSup { size 8{2} } } {} versus mass. Which of these relationships is more linear? What can you conclude from these graphs?

Example 5.2

A terminal velocity.

Find the terminal velocity of an 85-kg skydiver falling in a spread-eagle position.

At terminal velocity, F net = 0 F net = 0 size 12{F rSub { size 8{"net"} } =0} {} . Thus the drag force on the skydiver must equal the force of gravity (the person’s weight). Using the equation of drag force, we find mg = 1 2 ρCAv 2 mg = 1 2 ρCAv 2 size 12{ ital "mg"=0 "." 5ρ ital "CAv" rSup { size 8{2} } } {} .

Thus the terminal velocity v t v t size 12{v rSub { size 8{t} } } {} can be written as

All quantities are known except the person’s projected area. This is an adult (85 kg) falling spread eagle. We can estimate the frontal area as

Using our equation for v t v t size 12{v rSub { size 8{t} } } {} , we find that

This result is consistent with the value for v t v t size 12{v rSub { size 8{t} } } {} mentioned earlier. The 75-kg skydiver going feet first had a v = 98 m / s v = 98 m / s size 12{v="94"`m/s} {} . He weighed less but had a smaller frontal area and so a smaller drag due to the air.

The size of the object that is falling through air presents another interesting application of air drag. If you fall from a 5-m high branch of a tree, you will likely get hurt—possibly fracturing a bone. However, a small squirrel does this all the time, without getting hurt. You don’t reach a terminal velocity in such a short distance, but the squirrel does.

The following interesting quote on animal size and terminal velocity is from a 1928 essay by a British biologist, J.B.S. Haldane, titled “On Being the Right Size.”

To the mouse and any smaller animal, [gravity] presents practically no dangers. You can drop a mouse down a thousand-yard mine shaft; and, on arriving at the bottom, it gets a slight shock and walks away, provided that the ground is fairly soft. A rat is killed, a man is broken, and a horse splashes. For the resistance presented to movement by the air is proportional to the surface of the moving object. Divide an animal’s length, breadth, and height each by ten; its weight is reduced to a thousandth, but its surface only to a hundredth. So the resistance to falling in the case of the small animal is relatively ten times greater than the driving force.

The above quadratic dependence of air drag upon velocity does not hold if the object is very small, is going very slow, or is in a denser medium than air. Then we find that the drag force is proportional just to the velocity. This relationship is given by Stokes’ law , which states that

where r r is the radius of the object, η η is the viscosity of the fluid, and v v is the object’s velocity.

Stokes’ Law

Good examples of this law are provided by microorganisms, pollen, and dust particles. Because each of these objects is so small, we find that many of these objects travel unaided only at a constant (terminal) velocity. Terminal velocities for bacteria (size about 1 μm 1 μm ) can be about 2 μm/s 2 μm/s . To move at a greater speed, many bacteria swim using flagella (organelles shaped like little tails) that are powered by little motors embedded in the cell. Sediment in a lake can move at a greater terminal velocity (about 5 μm/s 5 μm/s ), so it can take days to reach the bottom of the lake after being deposited on the surface.

If we compare animals living on land with those in water, you can see how drag has influenced evolution. Fishes, dolphins, and even massive whales are streamlined in shape to reduce drag forces. Birds are streamlined and migratory species that fly large distances often have particular features such as long necks. Flocks of birds fly in the shape of a spear head as the flock forms a streamlined pattern (see Figure 5.10 ). In humans, one important example of streamlining is the shape of sperm, which need to be efficient in their use of energy.

Galileo’s Experiment

Galileo is said to have dropped two objects of different masses from the Tower of Pisa. He measured how long it took each to reach the ground. Since stopwatches weren’t readily available, how do you think he measured their fall time? If the objects were the same size, but with different masses, what do you think he should have observed? Would this result be different if done on the Moon?

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Physics Bootcamp

Samuel J. Ling

Section 6.12 Drag Force

Drag force is the force that a fluid applies on a moving body in the fluid. This type of friction is different from kinetic friction between solids - while the kinetic friction did not depend much on the speed of the object, the drag force depends on the speed.

Drag force occurs through two mechanisms:

• viscous drag force : due to viscous flow of the fluid around the body of the fluid.
• inertial drag force : due to pushing of the fluid out of the way from in front of the moving body.

While both of these drag forces act on a moving body, often one of them is highly dominant in a particular situation. For instance, if the body is moving very fast, the inertial drag force will be the dominant force and when the body is moving slowly in a viscous fluid, the viscous force will the dominant component. We will address both of these drag forces below.

Our treatment of drag force will give you a very simplified picture of what actually goes on when an object is moving in a fluid which is quite complicated and beyond the scope of this book. However, our treatment will give you sufficient understanding of the physics involved for you to be able to address the role of viscous forces in many practical situations. We will also study viscosity in the chapter on dynamic fluid.

Subsection 6.12.1 Viscous Drag Force

Viscous drag force occurs due to forces between the molecules of the fluid. Due to the attractive nature of these forces, molecules tend to stick to each other. When a body is moving in a fluid, the molecules next to the body will move with the velocity of the body, but molecules further away would not move much or at all. Thus, at low speeds you find layers of fluid moving past each other, causing a laminar flow .

The magnitude of the drag force is proportional to one power of speed if body is moving “slowly” so that a laminar flow of fluid around the object occurs as shown in Figure 6.12.1 . In this range of speed, the drag is dominated by viscous effects of the fluid. Sir George Stokes published in 1840s a formula for the viscous drag force on a moving sphere of radius \(R\text{.}\)

where \(v\) is the speed of sphere and \(\eta\) viscosity of the fluid. This formula is called Stoke's force , linear drag force or viscous drag force . For other shapes , you might think that the general formula may be written as

where \(k\) will be shape-dependent with dimension of length. The direction of viscous drag force is, just like the kinetic friction, in the opposite direction of the velocity of the moving object.

Subsection 6.12.2 Inertial Drag Force

If a body is moving rapidly through a fluid, the flow of the fluid around the object is no longer laminar. In these cases, the fluid becomes turbullent. This is the case, for instance, when you drop a steel ball in air. The resistive force of the fluid is mainly as a reaction to the impulse on the fluid by the moving ball, hence, it is known as inertial drag force .

Suppose a spherical ball is moving through a fluid at speed \(v \) - this would mean that from the perspective of the ball, i.e., in the ball frame, the fluid in front of the ball would be striking the ball at speed \(v \text{.}\) When the moving molecule hits the ball, it must come to rest. Net effect is the change in momentum of the fluid which is transfered to the change in momentum of the ball.

In one second, fluid will deposit a momentum equal to

where Volume is the volume in front of the ball of a cylinder of cross-section equal to the cross-section of the ball, i.e., here \(\pi R^2\text{,}\) and the height equal to \(v\text{,}\) since in one second, all the fluid up to this distance would have hit the ball.

Writing \(\rho \) for the density of the fluid, we get the rate at which momentum is deposited by the fluid on the ball in the opposite direction to the fluid flow is

We usually write a more general formula that can apply to other shapes.

where \(A \) is the frontal area of cross-section of the moving object that is blocking the fluid flow past the body, and \(C_D \) the drag coefficient . The rate of change of momentum acts as a resistive force. It is called the inertial drag force .

The drag coefficient \(C_D\) is a dimensionless number that depends on shape and speed in a complicated way, usually determined experimentally. But, for most systems, the value os between \(0.4\) and \(1.0\text{.}\) To get a sense of ballpark value of drag, you may just set it to \(1.0\text{.}\) In problems in books, \(C_D\) is normally specified with the problem or you could lok up in a table such as Table 6.12.3 , so you don't need to worry about it.

From the formula for the inertial drag in (6.12.1) , you can see that, to reduce drag, you could reduce area \(A\) in the way of the flow. This is the parameter that goes in the reduction of drag in the design of cars and airplanes. By crouching and changing shape a skiers and skydivers also manage the amount of drag on their bodies.

Subsection 6.12.3 Reynold's Number

Shoud I use \(F_{D}^{\text{viscous}}\) or \(F_{D}^{\text{inertial}} \text{?}\) Since both drags are present all the time, we need to see if we need to use both or if one of them is extremely dominant. A ratio of the inertial drag to viscous drag could be used to test how big one is compared to the other. For a spherical ball, we get

Rather than this formukla, we actually use a related dimensionless quantity, called Reynold's number , defined by

In general, we replace \(2R \) by a suitable measure of a length scale \(L \) of the moving object that is being pushed against by the fluid flow.

The rule of thumb is that if \(N_R \gt\gt 1 \text{,}\) use the inertial drag, and, if \(N_R \lt\lt 1 \) use the simpler linear drag, otherwise use the sum of the two.

Subsection 6.12.4 Terminal Speed

When an object that can present significant area \(A\) to the fluid (e.g., human falling in air) is falling the inertial drag force increases with its speed. At some point in fall, speed is such that the inertial drag force balances force of gravity and there is no further increase in speed. This speed is called terminal speed . Using Eq. (6.12.1) , we can find a general expression for terminal speed, \(v_t\text{.}\) Setting the inertial drag force for \(v=v_t\) to the weight of the body gives

For a human body, let \(C_D=0.5\text{,}\) \(m=65.0\text{ kg}\text{,}\) \(A = 1.5\text{ m} \times 0.4\text{ m} = 0.6\text{ m}^2\text{,}\) in air, \(\rho=1.225\text{ kg/m}^{3}\text{.}\) This will give terminal speed to be

With parachute, you may increase the area. Say, you make the area \(4\times\text{.}\) Then, you will cut down \(v_t\) by \(2\times\text{,}\) i.e., \(v_t\) now will be \(18.65\text{ m/s}\text{.}\)

Checkpoint 6.12.4 . Computing Viscous Drag Force Given the Speed.

An amoeba is moving in water at speed \(10\, \mu\text{m/min}\text{.}\) You can assume amoeba to be a sphere of radius \(500\, \mu\text{m}\text{.}\)

(a) What is the Reynold's number of the fluid flow at the speed of the amoeba? Decide which drag force is dominant here.

(b) Based on your decision in (a), compute the drag force on the amoeba.

(c) If the density of amoeba is that of water, how many times of the drag force is the weight?

Data: Viscosity \(\eta \) of water to be \(0.009\text{ Pa.s}\) and the density of water to be \(1000\text{ kg/m}^3\text{.}\)

Use formulas given in the definitions of drag forces.

(a) \(1.9\times 10^{-5}\text{,}\) (b) \(1.41\times 10^{-11}\text{ N} \text{,}\)(c) \(364,300\text{.}\)

(a) We use the formula for the Reynold's number to find the value. In the Reynold's number formula, we need to choose a length scale for the moving object, for which we choose the diameter of amoeba as tthe relevant length scale. We also convert all the units in the standard SI units of \(\text{m, s, kg}\text{.}\)

This says that viscous drag will be the dominant one for amoeba.

(b) We can make a drastic assumption and assume amaeba to have a spherical shape. This is just to get a ballpark answer. Using the formula for the viscous drag force for a sphere, we find

(c) To find the weight of amoeba, we need to find its mass. We will get its mass by multiplying its volume by the density.

Therefore, weight of the amoeba is

Comparing drag to weight we get.

Checkpoint 6.12.5 . Computing Inertial Drag Force.

Inertial drag force is important at high speeds. A dolphin is swimming in water at a speed of \(10 \text{ m/s}\text{.}\) Model the dolphin as a cylinder of radius \(0.5\text{ m} \) and length \(4\text{ m}\text{.}\)

(a) Find the Reynold's number for the water flow at the speed of the dolphin.

(b) Based on the Reynold's number, decide if you should omit the viscous drag and only use the inertial drag when computing the drag force, and then find the drag force on the dolphin.

(c) What will happen to the drag force, if dolphin slows down to \(5\text{ m/s}\text{?}\)

Data: Viscosity \(\eta \) of water is \(0.009\text{ Pa.s}\text{.}\) You may use the drag coefficient of dolphin to be \(C_D = 0.0036\text{.}\) Density of water = \(1000\text{ kg/m}^3\text{.}\)

(a) Use formula for Reynold's number. (b) Use formulas for \(F_D^{\text{inertial}}\text{.}\) (c) Use \(F_D^{\text{inertial}}\sim v^2\text{.}\)

(a) \(1.0 \times 10^6\) ,(b) \(141.4\text{ N}\text{,}\) (c) \(35.4\text{ N}\text{.}\)

(a) We use the formula for the Reynold's number to find the value. In the Reynold's number formula, we need to choose a length scale for the moving object, for which we choose the diameter of the cylinder modeling the dolphin since that is the size which is perpendicular to the flow.

(b) Since \(N_R \gt\gt 1 \text{,}\) the inertial drag is way more than the viscous drag. Therefore, we drop the viscous drag. Using the formula for the inertial drag force, we find

(c) Since \(F_D \sim v^2 \text{,}\) if \(v \rightarrow \dfrac{v}{2} \text{,}\) \(F_D \rightarrow \dfrac{F_D}{4} \text{.}\) That is, the drag force will become one quarter.

Checkpoint 6.12.6 . Drag Force and the Terminal Velocity.

A steel ball of radius \(2.0\text{ cm}\) is gently placed inside a tube of water and released from rest. Initially, the ball accelerates but after some time reaches a terminal velocity , i.e., velocity does not change.

Data: Viscosity \(\eta \) of water is \(0.009\text{ Pa.s}\text{.}\) You may use the drag coefficient of sphere to be, \(C_D = 0.5\text{.}\) Density of steel = \(8000\text{ kg/m}^3\text{.}\) Density of water = \(1000\text{ kg/m}^3\text{.}\)

(a) Assuming viscous drag force to be the only drag force, find the speed at which the net force on the ball is zero. This assumption turns out to be incorrect for this situation, but we will discover that in part (b) below.

(b) What is the Reynold's number of the flow at the terminal speed you found by assuming viscous drag as total drag in (a)? Decide if ignoring the inertial drag force was justified.

(c) You will find that viscous drag force is not the dominant drag force at this speed. We should be using the inertial drag force instead. Now, find the terminal velocity using the inertial drag force.

(a) Use \(F_D^{\text{viscous}}\text{.}\) (b) Use \(N_R\text{.}\) (c) Equate \(W\) to \(F_D^{\text{inertial}}\text{.}\)

(a) \(774\text{ m/s}\) ,(b) \(3,440,000\text{,}\) (c) \(2.9\text{ m/s} \text{.}\)

(a) Using the formula for the viscous drag force, we find

This must balance the weight for acceleration to be zero. We need to find the mass of the ball to find the weight. We will get that from the volume \(V \) of the ball and the density of steel.

Balancing this with the viscous drag gives

(b) We use the formula for the Reynold's number to find the value. In the Reynold's number formula, we need to choose a length scale for the moving object, for which we choose the diameter of the ball.

This is saying that at this speed, the inertial drag is 3,440,000 times more important. That means, our terminal speed calculated in (a) is wrong . We should, instead, use the inertial drag formula.

(c) Using the formula for the inertial drag force, we find

This must balance the weight for acceleration to be zero. We found weight in part (a). Now, we get the following equaiton for \(v \text{.}\)

Thus, the terminal velocity for the steel ball is \(2.9\text{ m/s}\text{.}\) This is a much more reasonable number than the wrong value of terminal speed found in (a).

Checkpoint 6.12.8 . Comparison of Inertial Drag Forces on Two Airplanes.

A commercial airliner is cruising with speed 600 mph at an altitude of 40,000 feet. When it took off, it had a speed of 150 mph. The density of air is \(1.22\text{ kg/m}^3\) near ground and \(0.385\text{ kg/m}^3\) at 40,000 ft. Compare the inertial drag force on the airplane in the two situations.

No need to convert units. Work with ratio.

Near ground : at 40,000 ft = \(0.2\text{.}\)

Let \(F_\text{d0}\) and \(F_\text{d4}\) be drag forces on ground and at 40,000 ft. Using Eq. (6.12.1) will be

We do not need to do any conversion of units since the ratio of similar quantities will cancel out the units.

Checkpoint 6.12.9 . (Calculus) Speed and Distance of a Skier with Inertial Drag Force.

A \(70\text{-kg}\) skier glides down a “frictionless” slope starting from rest on a flat incline with angle of inclination \(\theta=30^\circ\text{.}\) The motion of skier is impeded by inertial drag force from air. Suppose \(C_D=0.4\) and \(\rho_\text{air}=1.22\text{kg /m}^3\text{,}\) and the skier presents and area of \(A=1.2\text{ m}^2\text{.}\) (a) Find the terminal speed of the skier. (b) Find the expression of speed \(v\) as a function of time \(t\) with \(t=0\) at start where \(v=0\text{.}\) (c) Find the expression of distance on the slope the skier travels in time \(t\text{.}\)

(a) Set up the condition for zero acceleration. (b) Write \(F_x = m dv_x/dt\) and solve for \(v_x\text{.}\) (c) Integrate the result of (b).

(a) \(34.2\text{ m/s}\text{,}\) (b) \((34.3\text{ m/s})\; \tanh( 0.143\; t)\text{,}\) (c) \((239\text{ m}) \ln( \cosh( 0.143\; t ) )\text{.}\) You might different expressions for (b) and (c) since the integrals can be written in other forms also.

(a) Figure 6.12.10 shows three forces acting on the skier. Let \(v_x\) and \(a_x = dv_x/dt\) denote the \(x\) component of velocity and acceleration respectively. Equation of motion \(F_x = m a_x= m dv_x/dt\) will be

When speed is terminal speed \(v_t\text{,}\) then, it has zero acceleration. This gives

Putting the numerical values we get

Now, we work with the equation of motion, Eq. (6.12.4) .

Let's divide by \(m\) and replace myriad constants by symbols.

Note that \(v_t = \sqrt{a/b}\text{.}\) Rearrange Eq. (6.12.5) and integrate from \(t=0\) to \(t\text{.}\)

This gives (with \(v_t = \sqrt{a/b}\)):

Now, using the numerical values we get

Now, we integrate Eq. (6.12.6) to get the distance \(\Delta x\) on the slope.

Checkpoint 6.12.11 . (Calculus) Practice with a Friend: Accounting for Air Drag on a Bob Sled.

A bob sled with riders weighing \(500\text{ kg}\) starts at rest and comes down a straight incline of length \(100\text{ m}\) at angle \(12.5^\circ\) with the horizon. The coefficient of kinetic friction between the sled and the ground is \(0.15\text{.}\) The bob sled is also subject to inertial air drag with parameters \(C_D = 0.8\text{,}\) \(A=1.8\text{ m}^2\text{,}\) \(\rho_\text{air} = 1.22\text{ kg/m}^3\text{.}\) How long does it take the Bob sled to finish the \(100\text{ m}\) slide?

See Checkpoint 6.12.9 with \(a\) there will change to \(g\sin\theta - \mu_k g \cos\theta\text{.}\)

No solution provided.

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Let's Study Air Resistance—With Coffee Filters

In many physics problems, we simply ignore the air drag force. Why? Because of two reasons. First, the effects of air drag are often small when dealing with falling balls and rolling carts (a staple of intro physics labs). Second, calculating the motion of an object with air resistance is really difficult, because the drag force increases with velocity—it's non-constant. The normal equations in your physics course are created with the assumption of constant acceleration and constant forces.

But just because a force is difficult to model doesn't mean we should skip it. Here is a classic approach to exploring air drag.

Let's start with a model and then see if it works. Here is a common way to calculate the magnitude of the drag force on a moving object.

In this equation:

• v is the speed of the object relative to the air
• ρ is the density of air (usually around 1.2 kg/m 3 )
• A is the cross sectional area of the object
• C is the drag coefficient (a value that depends on the shape of the object)

Like I said, this is just the magnitude of the drag force. Its direction is always in the opposite direction of the velocity.

There are two things I need to do: Confirm that the model above agrees with experimental data and measure the drag coefficient for some falling object. I could estimate the other properties (density of air and cross sectional area). But if I look at something like a falling tennis ball, the drag force will just be too small to even notice. The solution is to drop something with a significant area, but low mass. Here is one of those things.

Yes. A coffee filter is perfect for exploring air drag. When you drop it, it mostly moves straight down in a stable position because of the angled sides. Also, when it is dropped from a reasonable height (like 2 meters) it will still reach terminal velocity. Finally, you can stack coffee filters and drop them. If you stack three filters, you effectively change the mass of the object but not the drag force parameters (shape and area).

But what is terminal velocity? I will answer this by considering a falling coffee filter. Suppose I let it drop from some height. Right after release, the coffee filter isn't moving. Since it has a zero velocity, the drag force is also zero. The only force on the filter is the gravitational force (which is the mass multiplied by the gravitational field g ) so that it accelerates down with an acceleration of -9.8 m 2 (like any other falling object).

However, since the filter is accelerating down, it will increase in speed. An increase in speed means that there is now a drag force pushing up (since it's moving down).

Now that there are two forces on the filter, the total force in the vertical direction is smaller than it was when it was first released. With a smaller force, it will have a smaller acceleration—but it will still accelerate. Eventually, its speed will reach a point at which the air drag force is equal in magnitude to the gravitational force.

With equal magnitude forces, the net force is zero. This means the acceleration is also zero m/s 2 . At this point the filter no longer speeds up and this is called the terminal velocity. The terminal velocity is very useful in that it can be used to find the drag coefficients. So, at terminal velocity I can write the following expression. Note that since the drag force is proportional to the velocity squared, I am just going to combine all of the other constants into one constant that I will write as K .

I can use this relationship to get some data. Here's what I will do. I will drop a coffee filter and find its terminal velocity. Then I will stack two coffee filters and drop them. With two filters, the mass and thus terminal velocity will be higher. Repeating this, I can get mass and terminal velocity data to use for a graph that will then give me the drag coefficient.

How exactly can I get the terminal velocity for a falling coffee filter? There are several methods that would probably work, but in this case I am going to use a motion detector . This device sends out a pulse of sound and measures the time for that pulse to reflect off an object and come back to the detector. It's a pretty useful device for measuring motion in one dimension. In this case, I can just put the detector on the floor (pointed up) and then drop a coffee filter on top of it. Here is the data that I get.

Notice that the filter accelerates at first, but towards the end of its motion around 2.5 to 3.0 seconds it seems to be moving at a constant velocity. By fitting a linear function to this part of the data, I can get the velocity of the filter—which would be the terminal velocity. For this particular run you can see the slope is 1.730 m/s.

Now I just need to repeat that exact same drop multiple times (I did it five times) so that I can get an average terminal velocity. But I want to plot a linear function (because linear functions are easier to deal with). If I make a plot of mass vs. velocity, it shouldn't be linear—but mass vs. velocity squared would be. Here is that graph. The error bars on the graph are the standard deviation of the five runs. Also, I'm not sure why—but this works out much better in the end if I force the fit to go through the origin (instead of letting it have a y-intercept).

The slope of this linear function is not the drag coefficient. However, we can find it from the slope. Since this is a plot of terminal velocity squared vs. mass, I could write this relationship as:

The slope of this function should be equal to g/K . If I assume g = 9.8 N/kg and the slope is 1164 m 2 /(kg*s 2 ) then the drag constant would be 0.00842 N*s 2 /m 2 .

What if I take a bunch of coffee filters and drop them from some height? Could I model the position vs. time for this falling stack? Let me start with an actual filter drop.

I can get position-time data from this video using – video analysis . Here is that data.

But how can I see if my model agrees with this data? The answer of course is to create a numerical model (I will use python because it's awesome). By using a numerical model, I can break the motion of this coffee filter into small time steps. During each of these time steps I can assume that the drag force has a constant value (which is approximately true). This takes one complicated problem and replaces it with many many simpler problems. The many problems are so simple that even a computer can solve them.

I will just jump right into the program. Here it is. Just click the "play" button to run it. Oh, and you can change parts of the code and see what will happen—you probably should.

This doesn't give exactly the same values as the data from the video, but it's pretty close. Here is a plot combining both the numerical model and the video analysis data.

From that plot you can see that the model doesn't completely agree with the data—but it's pretty close. I'm mostly happy.

Here are some extra questions for you.

• I'm not sure why my data and model don't have better agreement. Try this experiment yourself and see how well the data agrees with the model—maybe it's just me.
• In this example, I have used the air drag model that says it is proportional to the square of the velocity. Is this the best model? Would it be better to have the force proportional to just the velocity?

• What if you throw the filter up instead of dropping it? Let's say you give it an initial velocity of 3 m/s upward from a starting height of 2 meters above the ground. How long will it take to reach the ground? You will have to make a numerical model.
• Expert level question: see if you can model the motion of a ping pong ball thrown through the air. I'm probably going to do this one at some point.
• I used a drag constant K = 0.009. If you assume the density of air is 1.2 kg/m 3 , what is the drag coefficient C for a coffee filter? You will need to find the cross sectional area of a filter. You can use the picture above.

FREE K-12 standards-aligned STEM

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• What a Drag

Lesson What a Drag

Grade Level: 8 (7-9)

Time Required: 45 minutes

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Subject Areas: Physical Science, Physics

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If you take a car built before 1970 and place it next to a car built today, they look incredibly different. The older cars tend to be boxy with abrupt edges; newer cars are designed with rounded corners, edges and smooth curves. Mechanical and aerospace engineers have designed vehicles to be more aerodynamic to reduce drag force, and thus improve gas mileage.

After this lesson, students should be able to:

• Recognize the different types of friction: static friction, kinetic friction, and drag
• Understand how friction and drag work
• Learn how to calculate friction and drag
• Give examples of friction and drag

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Ask the students: "Would you slide further on a sidewalk, on the grass or on a frozen lake? Why?" (Answer: On a frozen lake, because the ice provides less friction than the sidewalk or grass.) Next, show photographs of bobsledders to the class. Point out that the sleds have a very smooth shape and that the riders tuck themselves down very low in the sled. Ask the students, "Why do the bobsledders crouch down so low?" (Answer: To reduce friction and make the sled go faster.) Explain that the scientific reason is to reduce drag, or make the sled more aerodynamic. Describe to the students that the drag force depends upon the shape of the object. Ask for some other examples of objects that are designed to move very quickly (such as, racecars, rockets, airplanes, etc). What do they have in common? (Answer: They are all shaped with smooth edges.) Explain that the position the athletes (such as, speed skaters, cyclists, ski jumpers, etc.) hold is important and determines how fast they can go. Students may be familiar with this and other examples from watching the Winter Olympics.

Friction also plays an important role in all the previous examples. Ask the students, "What would happen if they sprinkled sand on the bobsled track?" (Answer: The sleds would go much slower.) What if the tracks were made out of concrete? (Answer: The sleds would probably not slide at all, but if you pushed hard enough to move the sled, the metal skids on the sled would probably get hot.) Friction changes the energy of motion (kinetic energy) into heat. You can experience this by rubbing your hands together very quickly. Friction on ice is very low, which means that the sleds can move quickly. Many of us know that ice is very slippery, which you know if you have ever slipped and fallen on a patch of ice! In a brainstorming session, ask the students to suggest sports in which friction and drag are factors. Following the lesson have students conduct the hands-on associated activity Sliders to experimentally measure a coefficient of static friction. Refer to the associated activity Sliders (for High School)   for older ages.

Lesson Background and Concepts for Teachers

Friction is a lot like a little brother or sister that never cooperates with you. If you want to go somewhere, they want you to sit still. If you want to move forward, they are pulling you backward, and so on. There are two types of friction: static friction and kinetic friction. Static friction resists an object to start moving or sliding, which is a good thing when you start walking. If static friction didn't exist, it would be like you were constantly walking on ice! Kinetic friction resists an object that is already moving and always acts in a direction opposite of motion. Kinetic friction is the reason that anything moving or sliding will eventually come to a stop. It is important to note that static friction is always stronger than kinetic friction. For example, try sliding a heavy box across the floor. You should notice that it takes more force to start sliding the box than to keep the box sliding.

The concept of friction is an important consideration engineers must account for when designing parts that will rub against each other. The friction between two objects is primarily dependent on two things: how hard are the objects pressing against each other and the coefficient of friction (μ)(pronounced "mu") between the objects. For example, the coefficient of friction of a dry water slide is much higher than one with water on it. A measurement of the coefficient of friction is usually determined experimentally. A common equation used to determine the amount of friction an object experiences on a flat surface is:

F F = μ x W

where F F is the force of friction measured in Newtons (N) or pounds (lbs), μ is the coefficient of friction which is unit-less, and W is the weight of the object.

Drag is a special kind of friction that affects objects moving though any type of fluid. Air and water are two example fluids that vehicles move through. The amount of drag depends both on the shape and speed of an object. Drag has a greater effect on objects that move quickly. Aerodynamic shapes have smooth edges and small profiles to reduce the effects of drag. Drag and friction play an important roll in races. Professional cyclists position their bodies a certain way and wear tight clothing, racecars are made with aerodynamic shapes, and bobsledders tuck themselves into a very sleek sled, all in an effort to reduce drag.

• Sliders - Using a box, basket and weights, students collect friction data and experimentally measure a coefficient of static friction.
• Sliders (for High School) - In this hands-on activity, students learn about two types of friction — static and kinetic — and the equation that governs them. They also measure the coefficient of static friction and the coefficient of kinetic friction experimentally.

Mechanical and aerospace engineers work together when designing automobiles or airplanes. Mechanical engineers must be careful in designing engines because they have many parts that are constantly moving and rubbing against each other. If enough friction occurs, the engine could overheat and lockup or wear down and break. We add oil to engines to reduce friction and prevent such a disaster. Aerospace engineers design low-drag airplanes and cars to improve gas mileage. Drag wastes energy by making planes and cars harder to move forward. Friction and drag dissipate useful energy, forcing us to pay for more gasoline, oil and maintenance.

Friction is not always a bad thing; sometimes engineers use friction to their advantage. For example, anti-lock brakes (ABS) were designed to take advantage of static friction. Recall that static friction is always stronger than kinetic friction. ABS prevents the wheels from locking up and causing the tires to slide against the road. It keeps the tires on the brink of sliding, maximizing their static friction, and brings a car to a stop faster. Another example of engineers taking advantage of friction is in the design of parachutes. By maximizing drag, the skydiver can land on the ground safely, which is much better than the alternative of minimizing their drag.

coefficient of friction: An experimentally determined value that helps determine the amount of friction experienced between two objects.

drag: The frictional force that a fluid exerts upon an object traveling though it.

friction: The force that resists the motion of two objects pressed against each other.

kinetic friction: The resistance against an object already moving or sliding.

static friction: The resistance against an object to start moving or sliding.

Pre-Lesson Assessment

Voting: Ask the students to vote by a show of hands on the following question:

• Where would you slide further: on a sidewalk, on the grass, or on a frozen lake? (Answer: Frozen lake.)

Discussion Question: Ask the students and discuss as a class:

• Why would you slide further on a frozen lake? Explain. (Answer: You slide further on the ice because it provides less friction than the sidewalk or grass.)

Post-Introduction Assessment

Brainstorming: In small groups, have the students engage in open discussion. Remind students that no idea or suggestion is "silly." All ideas should be respectfully heard. Ask the students to:

• Name sports in which friction and drag are factors. (Possible answers: Racing — friction-tires on the road, drag-shape of car. Skiing — friction-skis on the snow, drag-position of skier.)

Lesson Summary Assessment

Numbered Heads: In teams of three to five, have the students pick numbers (or number off) so each member has a different number. Ask the students a question (give them a time frame for solving it, if desired). The members of each team should work together on the question. Everyone on the team must know the answer. Call a number at random. Students with that number should raise their hands to answer the question. If not all the students with that number raise their hands, allow the teams to work a little longer. Ask the students:

• Who would go faster? A girl on a bicycle who is not pedaling and is standing up or a girl on a bicycle who is not pedaling and is crouched over her handlebars? (Answer: Crouched down, due to less drag from the air.)
• How much frictional force is available from a bike's tires while sliding if μ = .6 and the bike weighs 150 lbs with the person riding it? Write the equation on the board. Have the students do the calculation. (Answer: F F = .6 x 150 lbs = 90 lbs.)
• What problems are most likely to occur in an engine that runs out of oil and is not properly lubricated? (Answers: The engine will heat up and possibly overheat, the heat could cause the engine to expand and lockup, the engine will wear down and eventually cause parts to break, all because of increased friction.)
• How much frictional force is available from a bike's tires when not sliding if μ = .8 and the bike weighs 150 lbs with a person riding it? What does this mean compared to the value when sliding? Have the students do the calculation. (Answer: F F = .8 x 150 lbs = 120 lbs. Compared to sliding, you have 30 lbs more frictional force to help bring the bike to a stop or keep the bike on the road.)
• If the frictional force from the bike's tires is 100 lbs, and the person on the bike weighs 140 lbs, what is the coefficient of friction? Write the equation on the board, and have the students rearrange it to solve the question. (Answer: μ = 100/150 = .714)

Open-Ended Design Question: Tell the students they have been contracted by the US Olympic Cycling Team to suggest ways to make the cyclists go faster. Aside from peddling faster, what other ways could improve the team's performance? Have the students write down their responses, draw a picture of their improved design, and turn them in. (Possible answers: Use grease or graphite lubricant to reduce friction between the wheels and axles, make the bike more aerodynamic, and make the cyclists' helmets more aerodynamic.)

Lesson Extension Activities

Assign the students the following activity as a way to verify that static friction is stronger than kinetic friction. Fill a box with books or other heavy items and have the students try to slide it across the floor. Have the students describe the amount of effort it took to move the box. To initially move the box, they will find they must gradually increase how hard they are pushing on the box until it starts sliding. Once the box is moving, the students should feel how it takes less force to keep the box sliding than to start it sliding. Have the students write a journal entry explaining which type of friction is stronger and why.

The effects of lubrication can be felt in a simple demonstration. Have the students rub their hands together quickly. They should feel heat being generated by the friction. Now give the students a small amount of hand lotion or wet their hands with water. It should be easier to rub their hands together and produce less heat (due to reduced friction).

High school students learn how engineers mathematically design roller coaster paths using the approach that a curved path can be approximated by a sequence of many short inclines. They apply basic calculus and the work-energy theorem for non-conservative forces to quantify the friction along a curve...

Students learn about two types of friction—static and kinetic—and the equation that governs them. They also measure the coefficient of static friction experimentally.

In this hands-on activity, students learn about two types of friction — static and kinetic — and the equation that governs them. They also measure the coefficient of static friction and the coefficient of kinetic friction experimentally.

On the topic of energy related to motion, this summary lesson ties together the concepts introduced in the previous four lessons and show how the concepts are interconnected in everyday applications. A hands-on activity demonstrates this idea and reinforces students' math skills in calculating energ...

Kahan, Peter. Science Explorer: Motion, Forces, and Energy. Upper Saddle River, NJ: Prentice Hall, 2000.

Contributors

Supporting program, acknowledgements.

The contents of this digital library curriculum were developed under a grant from the Fund for the Improvement of Postsecondary Education (FIPSE), U.S. Department of Education and National Science Foundation GK-12 grant no. 0338326. However, these contents do not necessarily represent the policies of the Department of Education or National Science Foundation, and you should not assume endorsement by the federal government.

Last modified: December 3, 2020

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Easy Drag Experiments: Materials and Methods for Beginners

• Thread starter jerz211
• Start date Jun 10, 2008
• Tags Drag Experiments
• Jun 10, 2008
• Higher-order topological simulation unlocks new potential in quantum computers
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wind tunnels!  

A PF Molecule

Related to easy drag experiments: materials and methods for beginners, 1. what is drag.

Drag is a force that acts on an object as it moves through a fluid, such as air or water. It is caused by the resistance of the fluid to the motion of the object.

2. How do you measure drag?

Drag can be measured using a variety of methods, including wind tunnels, force gauges, and pressure sensors. These tools allow us to measure the magnitude and direction of the force acting on an object as it moves through a fluid.

3. What factors affect drag?

The amount of drag experienced by an object depends on several factors, including the shape and size of the object, the speed at which it is moving, and the properties of the fluid it is moving through. Other factors such as surface roughness and the presence of other objects in the fluid can also affect drag.

4. How can simple drag experiments be useful?

Simple drag experiments can help us better understand the principles of fluid dynamics and how objects interact with fluids. They can also aid in the design and optimization of various structures, such as airplanes and cars, by providing insight into how to reduce drag and improve performance.

5. What are some examples of simple drag experiments?

Some examples of simple drag experiments include dropping objects of different sizes and shapes into water and observing how they fall, using wind tunnels to test the drag of different objects, and measuring the force needed to pull an object through a fluid at different speeds.

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• Physics Article

The drag force is present everywhere around us. We thrive in a ball of fluids (air and water). Drag forces appear whenever there is motion in air or water or in any other fluid.

When objects travel through fluids (a gas or a liquid), they will undoubtedly encounter resistive forces called drag forces.

The drag force always acts in the opposite direction to fluid flow. If the body’s motion exists in the fluid-like air, it is called aerodynamic drag. And, if the fluid is water, it is called hydrodynamic drag.

In order to minimise the influence of drag force, fast vehicles are created and designed, as streamlined as possible.

Examples of streamlined objects are everywhere in nature – e.g., birds and dolphins have streamlined bodies to help them move quickly through the air and water, respectively.

What is a Drag Force?

Drag is an example of mechanical force.

When a solid body interacts with a fluid (liquid or gas), a drag force is produced on the solid body.

Drag forces are not created by any force fields. In order to experience a drag force, an object has to come into physical contact with the fluid medium.

If the fluid doesn’t exist, there will be no resistance on the object’s surface; therefore, no drag will be created. A drag force is produced by the deviation or difference in velocity between the fluid and the object.

There should be movement between the fluid and the solid object. Without motion, drag is non-existent. In fact, there is no difference between whether the objects move in a static fluid or whether the fluid propagates past a stationary solid object.

As drag is a force, it’s a vector quantity with a magnitude as well as a direction. Drag is produced in an order that is polar to the object’s motion.

Drag can also be explained as friction. Drag produced in the air is called ‘aerodynamic friction’. Friction between the molecules of air and the solid surface of the moving object is one of the common sources of drag force.

As friction is between a solid and a gas, the skin friction value relies on the characteristics of both the gas and solid. In the case of a solid, a waxed or smooth surface creates less friction than a rough surface.

When we consider the case of gas, the value relies on air’s viscosity and the Reynolds number.

A video about Frictional Force

Drag Force Types

Parasite drag.

Parasite drag consists of every force that acts to slow down a vehicle’s movement.

There are a few variations of parasite drag: interference drag, skin drag force, form drag, etc.

Skin Drag Force

Skin friction drag is the air resistance generated on the aircraft due to air exposure to the craft’s outer surface.

Lift Induced Drag

Lift-induced drag is the result of the normal lift mechanism. Lift Induced drag is generated by the aircraft’s wing (vortices on the tip).

Interference Drag

Interference drag is created due to the interference of multiple airflows, which have varying speeds. The interference of various aircraft components generates this drag force. It is precisely due to non-similar airflow around the fuselage and the wing.

This unique drag force is limited to supersonic scenarios. It is a type of induced drag force produced from non-cancelling static pressure variables to either side of a shock wave striking on the outer surface of the object, from which the wave is generated.

Drag Force Discovery

Sir George Cayley is known for discovering Drag Force and all other aerodynamic forces during flight – weight, thrust and lift. He also deduced the correlation between them.

Drag Force Equation

Drag Equation is used to find the force of drag on an object due to motion through an enclosed fluid system.

F d is the drag force, ρ is the mass density of the fluid, υ is the flow velocity relative to the object, A is the reference area, C d is the drag coefficient.

Relevance of Drag Force

• Body orientation is a crucial part of skydiving because the object’s physical shape significantly affects the extent of air resistance experienced by the object. In fact, air resistance has a profound effect on terminal speed.
• Professional bike and cycle helmets are specially designed to reduce drag force.
• Swimming suits are also meticulously designed and fabricated to reduce drag force through water.
• All efficient vehicles or artificially moving objects are designed around the drag force variable. Without implementing structural designs to counter drag forces, no objects can travel smoothly through air or water. Speed and fuel efficiency will be dramatically reduced.
• Examples of vehicles or objects with extreme anti-drag properties are submarines, missiles, rockets , torpedoes, sports cars and bikes, weather balloons, bullet trains, etc.
• Fishes, birds and water mammals have various anti-drag mechanisms in their bodies. Specific examples of creatures with extreme anti-drag properties include lotus leaves, penguins, dolphins, sharks, Nepenthes pitcher plants, hawks, etc.
• Whichever the case, drag reduction is very crucial in the survival of each of these creatures.
• Humans have created efficient working models to counter drag forces in various scenarios by reverse-engineering these natural wonders.

Daily Life Examples of Drag Force

There are an infinite number of situations where the drag force shows its undeniable presence.

• Resistance on moving vehicles.
• Floating objects.
• Resistance during a storm or heavy wind.
• Resistance on gliders and parachutes.

Frequently Asked Questions – FAQs

What is a drag force.

When a solid body interacts with a fluid (liquid or gas), a drag force is produced on the solid body. Drag forces are not created by any force fields. In order to experience a drag force, an object has to come into physical contact with the fluid medium.

What is aerodynamic drag?

If the body’s motion is through fluid-like air, it is called aerodynamic drag.

What is hydrodynamic drag?

If the body’s motion is through fluid-like water, it is called hydrodynamic drag.

What does drag force depend on?

Drag relies on the square of the velocity, compressibility, air density, viscosity, size and structure of the body, etc.

Is drag a contact or non-contact force?

Drag forces are not created by any force fields. In order to experience a drag force, the object has to come into physical contact with the fluid medium.

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• Published: 23 June 2021

Fizeau drag in graphene plasmonics

• Y. Dong 1 , 2   na1 ,
• L. Xiong 1   na1 ,
• I. Y. Phinney 3 ,
• Z. Sun   ORCID: orcid.org/0000-0002-0342-6248 1 ,
• R. Jing   ORCID: orcid.org/0000-0002-0358-6831 1 ,
• A. S. McLeod   ORCID: orcid.org/0000-0002-5232-634X 1 ,
• S. Zhang 1 ,
• S. Liu   ORCID: orcid.org/0000-0002-3046-3335 4 ,
• F. L. Ruta   ORCID: orcid.org/0000-0002-8746-9420 1 , 2 ,
• Z. Dong 3 ,
• J. H. Edgar   ORCID: orcid.org/0000-0003-0918-5964 4 ,
• P. Jarillo-Herrero   ORCID: orcid.org/0000-0001-8217-8213 3 ,
• L. S. Levitov 3 ,
• A. J. Millis 1 ,
• M. M. Fogler 5 ,
• D. A. Bandurin 3 &
• D. N. Basov   ORCID: orcid.org/0000-0001-9785-5387 1  

Nature volume  594 ,  pages 513–516 ( 2021 ) Cite this article

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• Electronic devices
• Electronics, photonics and device physics
• Optical properties and devices
• Surfaces, interfaces and thin films

Dragging of light by moving media was predicted by Fresnel 1 and verified by Fizeau’s celebrated experiments 2 with flowing water. This momentous discovery is among the experimental cornerstones of Einstein’s special relativity theory and is well understood 3 , 4 in the context of relativistic kinematics. By contrast, experiments on dragging photons by an electron flow in solids are riddled with inconsistencies and have so far eluded agreement with the theory 5 , 6 , 7 . Here we report on the electron flow dragging surface plasmon polaritons 8 , 9 (SPPs): hybrid quasiparticles of infrared photons and electrons in graphene. The drag is visualized directly through infrared nano-imaging of propagating plasmonic waves in the presence of a high-density current. The polaritons in graphene shorten their wavelength when propagating against the drifting carriers. Unlike the Fizeau effect for light, the SPP drag by electrical currents defies explanation by simple kinematics and is linked to the nonlinear electrodynamics of Dirac electrons in graphene. The observed plasmonic Fizeau drag enables breaking of time-reversal symmetry and reciprocity 10 at infrared frequencies without resorting to magnetic fields 11 , 12 or chiral optical pumping 13 , 14 . The Fizeau drag also provides a tool with which to study interactions and nonequilibrium effects in electron liquids.

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Data availability.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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The code used to analyse data are available from the corresponding author upon reasonable request.

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Acknowledgements

Research on the physics and imaging of the plasmonic Fizeau effect at Columbia was supported by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under award no. DE-SC0018426. D.A.B. acknowledges the support from MIT Pappalardo Fellowship. M.M.F. is supported by the Office of Naval Research under grant ONR-N000014-18-1-2722. Work in the P.J.-H. group was supported by AFOSR grant FA9550-16-1-0382, the Gordon and Betty Moore Foundation’s EPiQS Initiative through grant GBMF9643, and Fundacion Ramon Areces. The development of new nanofabrication and characterization techniques enabling this work has been supported by the US DOE Office of Science, BES, under award DE-SC0019300. The development of the universal cryogenic platform used for scanning probe measurements is supported as part of the Energy Frontier Research Center on Programmable Quantum Materials funded by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under award no. DE-SC0019443. The development of infrared nano-optics is supported by Vannevar Bush Faculty Fellowship to D.N.B., ONR-VB: N00014-19-1-2630. D.N.B. is Moore Investigator in Quantum Materials EPIQS #9455. This work also made use of the Materials Research Science and Engineering Center Shared Experimental Facilities supported by the National Science Foundation (NSF) (grant no. DMR-0819762). Support from the Materials Engineering and Processing programme of the National Science Foundation, award number CMMI 1538127 for hBN crystal growth is also greatly appreciated.

Author information

These authors contributed equally: Y. Dong, L. Xiong

Authors and Affiliations

Department of Physics, Columbia University, New York, NY, USA

Y. Dong, L. Xiong, Z. Sun, R. Jing, A. S. McLeod, S. Zhang, F. L. Ruta, R. Pan, A. J. Millis & D. N. Basov

Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY, USA

Y. Dong & F. L. Ruta

Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA

I. Y. Phinney, H. Gao, Z. Dong, P. Jarillo-Herrero, L. S. Levitov & D. A. Bandurin

The Tim Taylor Department of Chemical Engineering, Kansas State University, Manhattan, KS, USA

S. Liu & J. H. Edgar

Department of Physics, University of California San Diego, La Jolla, CA, USA

M. M. Fogler

You can also search for this author in PubMed   Google Scholar

Contributions

D.A.B. and D.N.B. conceived and supervised the project. Y.D., L.X., S.Z., D.A.B. and D.N.B. designed the experiments. I.Y.P. and D.A.B. fabricated the devices. S.L. and J.H.E. provided the isotopic hBN crystals. Y.D., L.X., A.S.M. and R.P. performed the experimental measurements. Y.D., L.X., R.J., F.L.R., D.A.B. and D.N.B. analysed the experimental data. Z.S., M.M.F., A.J.M. and L.S.L. developed the theoretical analysis of the experimental data with input from P.J.-H., H.G. and Z.D. Y.D., L.X., Z.S., M.M.F., D.A.B. and D.N.B. co-wrote the manuscript with input from all co-authors.

Corresponding authors

Correspondence to D. A. Bandurin or D. N. Basov .

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Competing interests.

The authors declare no competing interests.

Additional information

Peer review information Nature thanks Joel Cox, Jiahua Duan and Hugen Yan for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended data fig. 1 gate-dependent transport of a typical device..

Two-terminal resistance R 2pt of a typical device as a function of the back-gate voltage V g at T  = 170 K. Inset shows the transport measurement configuration, where a source meter (Keithley 2450) was used to source gate voltage, and a lock-in amplifier (SR 830) was used to measure the resistance of the entire device.

Extended Data Fig. 2 Experimental configuration for measuring current-gating effects.

Voltage is applied across the source/drain electrode and SPP imaging is performed close to the drain. The black streamlines symbolize the d.c. current. The voltmeter measures the electrostatic potential of the SPP launcher as a function of the biasing current.

Extended Data Fig. 3 Current–voltage characteristics of a typical device.

The black symbols represent the source–drain voltage while sourcing current through the device. The blue symbols represent the simultaneously measured voltage on the SPP launcher, representing the current-gating effect induced by the biasing current. Inset shows a magnified view of the low-voltage region.

Extended Data Fig. 4 Characteristic real-space nano-infrared and topography images.

a , Near-field image taken in the vicinity of a gold launcher at T  = 170 K and V g  = 50 V. Gold-launched λ p fringes and tip-launched λ p /2 fringes near the graphene edge are clearly visible. Dashed rectangles mark the regions magnified in c and d . b , AFM topography image taken simultaneously with the near-field image in a . The graphene region is uniform with minimal topographic variations. c , d , Magnified near-field images near graphene edges, showing the tip-launched and edge-reflected SPP fringes with λ p /2 periodicity.

Extended Data Fig. 5 Real-space nano-infrared and topography line profiles under current.

a – d , Representative results for simultaneously taken topography ( a , b ) and near-field ( c , d ) data as a function of current density at T  = 170 K and V g  = −50 V. a , AFM topography collected in the vicinity of a gold launcher on the left of the field of view. The 2D plot is assembled from AFM line profiles measured at different current densities while scanning along the same line in real space. Red and black arrows and dashed lines indicate positions where the averaged line profiles in b are acquired. b , Averaged line profiles of AFM topography for current densities of ±0.75 mA μm −1 , whose topography signals are essentially the same. One of the line profiles is shifted vertically for clarity. c , Near-field data, taken simultaneously with a . A standard one-dimensional Fourier filter was applied here to reduce noise. d , Averaged line profiles of the near-field signal in c for the same current densities as the topography data in b . A Fizeau shift is clearly visible.

Extended Data Fig. 6 Uncertainty analysis for fitted SPP wavelength.

a , Distribution of the least-squares estimate of the SPP wavelength in equation ( 7 ) generated by Monte Carlo simulation. b , Examples of typical simulated SPP line profiles used for analysis in a . c , I: Dependence of variance (bright and dark red lines) and bias (blue line) of wavelength estimate on spatial resolution (SR). Bright red line corresponds to zero signal noise ( σ y / A  = 0). Dark red and blue lines correspond to σ y / A  = 10%; II: Dependence of bias and variance in wavelength estimate on pixel size in units of wavelength. The pixel size has minimal effect on σ λ as long as one samples above the Nyquist rate, as indicated by the vertical green dashed line. d , I: Strong dependence of error in wavelength estimate on signal noise σ y . The variance of the wavelength estimate (bright red, dark red and green lines) will increase roughly linearly with σ y until about 25%, and the bias (bright and dark blue lines) is less than 1 nm for SR = 20 nm; II: Dependence of error in wavelength estimate on SPP propagation length 1/ q 2 . Both the variance (bright and dark red lines) and the bias (blue line) of the wavelength estimate improve with 1/ q 2 , even more so when there is positioning noise σ x (dark red line). e , Assessing the statistical significance of the Fizeau shift using an F  test. Solid red and purple lines represent the dependence of F statistics on the sample wavelength-shift standard deviation s Δ λ . Purple line assumes α  = 0 and red line assumes α is finite (see text). Cyan shaded region corresponds to F statistics that reject the null hypothesis of no Fizeau shift ( F  >  F crit  = 2.65). Vertical dashed line corresponds to wavelength-shift standard deviation s Δ λ estimated from data in Fig. 3a, b .

Extended Data Fig. 7 Additional datasets revealing plasmonic Fizeau drag in graphene.

Other representative data when scanning along the same line at different d.c. currents (averaged ±25 μA μm −1 for each profile) for different gate voltages, temperatures and devices. Within a set of polariton line profiles, the first polariton fringes are aligned to enable better visual inspection of Fizeau shifts. Line profiles are shifted vertically for clarity. Within each panel, the fitted line profiles of the smallest and largest current densities are shown in the lower panel for visual comparison. The images of the devices are near-field scattering amplitude measured at 170 K without gating. a , Device 1, T  = 170 K, V g  = −47 V; b , Device 1, T  = 170 K, V g  = +47 V; c , Device 1, T  = 170 K, V g  = −60 V; d , Device 1, T  = 60 K, V g  = +60 V; e , Device 2, T  = 170 K, V g  = +50 V; f , Device 3, T  = 60 K, V g  = +60 V.

Supplementary information

Supplementary information.

This file contains a list of the notations, details regarding the theory of Fizeau plasmon drag in graphene (this section includes Supplementary Figures 1-4), Supplementary Table 1 and the Supplementary References.

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Dong, Y., Xiong, L., Phinney, I.Y. et al. Fizeau drag in graphene plasmonics. Nature 594 , 513–516 (2021). https://doi.org/10.1038/s41586-021-03640-x

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Thrust/drag for an experiment.

i’m not very advanced in physics, so this might seem like a stupid question. basically as a final project i had to design an experiment, and it could basically be as basic as i wanted so i made it super easy. essentially there’s a cart traveling on a track, and a fan is blowing behind the cart to made it move forward so that velocity and position can be tracked (the cart has bluetooth connected to a computer). the actual experiment is that i put “sails” on the cart, and the only thing that is different about the sails is the shape (surface area is all the same). my question is: when looking at the velocity vs position graph for each different shape sail, would a greater thrust be the thing contributing to greater velocities? at first i thought it had something to do with drag, but now i’m thinking that it wouldn’t really make sense to mention drag because the control group (no sail) had the lowest velocity. i assume i am looking at which shape contributed to the least amount of drag and the greatest amount of thrust, but please correct me if i’m wrong. sorry if that did not make sense at all 🙏🏻

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Mayo is weirdly great for understanding nuclear fusion experiments.

A schmear campaign aims to understand how materials transition from elastic to plastic behavior 

Connoisseurs call it “creamy,” haters call it “slimy,” and mechanical engineers call it a “soft solid.” Mayonnaise could help scientists better design nuclear fusion experiments.

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Mayonnaise’s texture inspires love and loathing. Either way, it’s perfect for physics experiments. 

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LZ Experiment Sets New Record in Search for Dark Matter

New results leave fewer places for elusive dark matter particles to hide.

• by Lauren Biron
• August 26, 2024

Figuring out the nature of dark matter, the invisible substance that makes up most of the mass in our universe, is one of the greatest puzzles in physics. New results from the world’s most sensitive dark matter detector,  LUX-ZEPLIN (LZ), have narrowed down possibilities for one of the leading dark matter candidates: weakly interacting massive particles, or WIMPs.

LZ, led by the Department of Energy’s Lawrence Berkeley National Laboratory (Berkeley Lab), hunts for  dark matter from a cavern nearly one mile underground at the Sanford Underground Research Facility in South Dakota. Mani Tripathi, Distinguished Professor in the UC Davis Department of Physics and Astronomy, is a member of the LZ project team. 

The experiment’s new results explore weaker dark matter interactions than ever searched before and further limit what WIMPs could be.

“These are new world-leading constraints by a sizable margin on dark matter and WIMPs,” said Chamkaur Ghag, spokesperson for LZ and a professor at University College London (UCL). He noted that the detector and analysis techniques are performing even better than the collaboration expected. “If WIMPs had been within the region we searched, we’d have been able to robustly say something about them. We know we have the sensitivity and tools to see whether they’re there as we search lower energies and accrue the bulk of this experiment’s lifetime.”

Fewer places for WIMPs to hide

The collaboration found no evidence of WIMPs above a mass of 9 gigaelectronvolts/c 2 (GeV/c 2 ). (For comparison, the mass of a proton is slightly less than 1 GeV/c 2 .) The experiment's sensitivity to faint interactions helps researchers reject potential WIMP dark matter models that don't fit the data, leaving significantly fewer places for WIMPs to hide. The new results were presented at two physics conferences on August 26: TeV Particle Astrophysics 2024 in Chicago, Illinois, and LIDINE 2024 in São Paulo, Brazil. A scientific paper will be published in the coming weeks.

The results analyze 280 days’ worth of data: a new set of 220 days (collected between March 2023 and April 2024) combined with 60 earlier days from LZ’s first run. The experiment plans to collect 1,000 days’ worth of data before it ends in 2028. 

“If you think of the search for dark matter like looking for buried treasure, we’ve dug almost five times deeper than anyone else has in the past,” said Scott Kravitz, LZ’s deputy physics coordinator and a professor at the University of Texas at Austin. “That’s something you don’t do with a million shovels – you do it by inventing a new tool.”

LZ’s sensitivity comes from the myriad ways the detector can reduce backgrounds, the false signals that can impersonate or hide a dark matter interaction. Deep underground, the detector is shielded from cosmic rays coming from space. To reduce natural radiation from everyday objects, LZ was built from thousands of ultraclean, low-radiation parts. The detector is built like an onion, with each layer either blocking outside radiation or tracking particle interactions to rule out dark matter mimics. And sophisticated new analysis techniques help rule out background interactions, particularly those from the most common culprit: radon.

This result is also the first time that LZ has applied “salting”– a technique that adds fake WIMP signals during data collection. By camouflaging the real data until “unsalting” at the very end, researchers can avoid unconscious bias and keep from overly interpreting or changing their analysis.

“We’re pushing the boundary into a regime where people have not looked for dark matter before,” said Scott Haselschwardt, the LZ physics coordinator and a recent Chamberlain Fellow at Berkeley Lab who is now an assistant professor at the University of Michigan. “There’s a human tendency to want to see patterns in data, so it’s really important when you enter this new regime that no bias wanders in. If you make a discovery, you want to get it right.”

The invisible 85 percent

Dark matter, so named because it does not emit, reflect, or absorb light, is estimated to make up 85% of the mass in the universe but has never been directly detected, though it has left its fingerprints on multiple astronomical observations. We wouldn’t exist without this mysterious yet fundamental piece of the universe; dark matter’s mass contributes to the gravitational attraction that helps galaxies form and stay together.

LZ uses 10 tonnes of liquid xenon to provide a dense, transparent material for dark matter particles to potentially bump into. The hope is for a WIMP to knock into a xenon nucleus, causing it to move, much like a hit from a cue ball in a game of pool. By collecting the light and electrons emitted during interactions, LZ captures potential WIMP signals alongside other data. 

“We’ve demonstrated how strong we are as a WIMP search machine, and we’re going to keep running and getting even better – but there’s lots of other things we can do with this detector,” said Amy Cottle, lead on the WIMP search effort and an assistant professor at UCL. “The next stage is using these data to look at other interesting and rare physics processes, like rare decays of xenon atoms, neutrinoless double beta decay, boron-8 neutrinos from the sun, and other beyond-the-Standard-Model physics. And this is in addition to probing some of the most interesting and previously inaccessible dark matter models from the last 20 years.”

LZ is a collaboration of roughly 250 scientists from 38 institutions in the United States, United Kingdom, Portugal, Switzerland, South Korea, and Australia; much of the work building, operating, and analyzing the record-setting experiment is done by early career researchers. The collaboration is already looking forward to analyzing the next data set and using new analysis tricks to look for even lower-mass dark matter. Scientists are also thinking through potential upgrades to further improve LZ, and planning for a next-generation dark matter detector called XLZD.

“Our ability to search for dark matter is improving at a rate faster than Moore’s Law,” Kravitz said. “If you look at an exponential curve, everything before now is nothing. Just wait until you see what comes next.”

LZ is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics and the National Energy Research Scientific Computing Center, a DOE Office of Science user facility. LZ is also supported by the Science & Technology Facilities Council of the United Kingdom; the Portuguese Foundation for Science and Technology; the Swiss National Science Foundation, and the Institute for Basic Science, Korea. Over 38 institutions of higher education and advanced research provided support to LZ. The LZ collaboration acknowledges the assistance of the Sanford Underground Research Facility.

Media Resources

News release from Lawrence Berkeley Lab

LUX-ZEPLIN Dark Matter Detector Starts Up (2022)

Media Contacts

• Mani Tripathi, Physics and Astronomy, [email protected]
• Andy Fell, UC Davis News and Media Relations, 530-304-8888, [email protected]

Lauren Biron is a science writer at the Lawrence Berkeley Laboratory. 

LZ experiment sets new record in search for elusive dark matter

Dr Theresa Fruth, from the School of Physics, prepares to descend a mile underground at the LZ experiment facility in South Dakota, USA.

Figuring out the nature of dark matter, the invisible substance that makes up most of the mass in our universe, is one of the greatest unsolved puzzles in modern physics. New results from the world’s most sensitive dark matter detector, LUX-ZEPLIN (LZ), have narrowed down possibilities for one of the leading dark matter candidates: weakly interacting massive particles, or WIMPs.

LZ, led by the United States Department of Energy’s Lawrence Berkeley National Laboratory (Berkeley Lab), hunts for dark matter from a cavern nearly one mile underground at the Sanford Underground Research Facility in South Dakota. The experiment’s new results have set further limits on what WIMPs could be.

Dr Theresa Fruth from the School of Physics at the University of Sydney was instrumental in commissioning the LZ detector in South Dakota and is an active participant in the hunt for dark matter at the LZ experiment. She has worked on the project for nine years, including during her time at the University of Oxford and University College London.

“This detector is the best asset we have anywhere in the world in our hunt for WIMP dark matter over coming years. This result shows how sensitive the detector is and how useful it will be in helping us to solve this most intriguing of scientific puzzles,” she said.

LZ’s central detector in a surface lab clean room before delivery underground. Photo: Matthew Kapust/Sanford Underground Research Facility

Dark matter, so named because it does not emit, reflect, or absorb light, is estimated to make up 85 percent of the mass in the universe but has never been directly detected, though it has left its fingerprints on multiple astronomical observations.

Dr Fruth said: “We wouldn’t exist without this mysterious yet fundamental piece of the universe; dark matter’s mass contributes to the gravitational attraction that helps galaxies form.”

In the new result, the team found no evidence of WIMPs above 9 giga-electronvolts/c2 (GeV/c2), which is 1.6 x 10-26 kilograms, about ten times the mass of a proton.

“While finding ‘nothing’ doesn’t sound like much of a result, this is hugely important in narrowing down where we could find direct evidence of dark matter,” Dr Fruth said.

“Will dark matter fit snugly into the Standard Model of particle physics, or will its discovery need us to rewrite our theoretical models? We simply don’t know yet.”

The important new data has been presented today at physics conferences in Chicago, USA, and São Paulo, Brazil. A paper will be prepared for peer-review in coming weeks.

“If you think of the search for dark matter like looking for buried treasure, we’ve dug almost five times deeper than anyone else has in the past,” said Professor Scott Kravitz, LZ’s deputy physics coordinator and a professor at the University of Texas at Austin. “That’s something you don’t do with a million shovels, you do it by inventing a new tool.”

Researchers sit between two outer layers of LZ during construction. Photo: Matthew Kapust/Sanford Underground Research Facility

Professor Chamkaur Ghag, LZ spokesperson and professor University College London said: “These are new world-leading constraints by a sizable margin on dark matter and WIMPs. We know we have the sensitivity and tools to see whether they’re there as we search lower energies and accrue the bulk of this experiment’s lifetime.”

The experiment’s sensitivity to faint interactions helps researchers reject potential WIMP dark matter models that don’t fit the data, leaving fewer places for WIMPs to hide.

This result is also the first time that LZ has applied “salting”– a technique that adds fake WIMP signals during data collection. By camouflaging the real data until “unsalting” at the very end, researchers can avoid unconscious bias and keep from overly interpreting or changing their analysis.

“We’re pushing the boundary into a regime where people have not looked for dark matter before,” said Scott Haselschwardt, the LZ physics coordinator and a recent Chamberlain Fellow at Berkeley Lab who is now an assistant professor at the University of Michigan. “There’s a human tendency to want to see patterns in data, so it’s really important when you enter this new regime that no bias wanders in. If you make a discovery, you want to get it right.”

LZ uses 10 tonnes of liquid xenon at 175 Kelvin (minus 98.15 degrees) to provide a dense, transparent material for dark matter particles to potentially bump into. The hope is for a WIMP to knock into a xenon nucleus, causing it to move, much like a hit from a cue ball in a game of pool. By collecting the light emitted during such interactions by the detector’s 494 light sensors, LZ could capture WIMP signals with other rare events.

LZ is a collaboration of about 250 scientists from 38 institutions in the United States, United Kingdom, Portugal, Switzerland, South Korea, and Australia.

Dr Fruth leads the only Australian-based research group working on LZ. She is also a collaborator at the  Australian dark matter detector  (SABRE South) being built in an active gold mine in Stawell, Victoria.

LZ Completes TPC Assembly from Sanford Lab on Vimeo .

Declaration

LZ is supported by the US Department of Energy, Office of Science, Office of High Energy Physics and the National Energy Research Scientific Computing Center, a DOE Office of Science user facility. LZ is also supported by the Science & Technology Facilities Council of the United Kingdom; the Portuguese Foundation for Science and Technology; the Swiss National Science Foundation, and the Institute for Basic Science, Korea. More than 38 institutions of higher education and advanced research provided support to LZ. The LZ collaboration acknowledges the assistance of the Sanford Underground Research Facility.

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• [email protected]

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