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Geometry and Algebra - Glow With the Flow - Contenido educativo
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NASA Connect Video containing six segments as described below. NASA Connect Segment explaining air flow. The video describes how drag, lift, and thrust work. NASA Connect Segment exploring drag and agebraic relationships. The video explains flow visualization and air flow and how engineers use algebra in their work. NASA Connect Segment explaining the new concept aircraft in development known as the blended wing body. The video explains how engineers and scientists uses geometry to help with development. NASA Connect Segment involving students in a classroom activity called What A Drag. The video explores how shape affects drag. NASA Connect Segment involving students in a classroom activity. The video explores how surface area affects drag. NASA Connect Segment exploring computer simulation tools for research on drag. The video features the Mars Airbourne Explorer simulation computer program.
Hi, welcome to NASA Connect, the show that connects you to the world of math, science,
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technology and NASA.
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I'm Jennifer Pulley and this is Van Hughes.
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Jennifer, what is up with the blindfold?
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Just one second.
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We always start each NASA Connect episode with a celebrity who introduces the show and
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today I thought I'd surprise Van.
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Is it Norbert?
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No, Van, it's definitely not Norbert.
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However, every time Norbert appears with questions, have your cue cards from the lesson guide
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ready to answer the questions he gives you.
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And teachers, every time Norbert appears with a remote, that's your cue to pause the videotape
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and discuss the cue card questions.
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And teachers, don't forget, the lesson guide can be downloaded from our NASA Connect website.
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Okay, now that you have all that important information out of the way, what about my
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surprise?
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Okay, follow me.
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Jen?
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Jen?
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Just kidding, just kidding.
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Come on.
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Are you ready?
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Stand right there.
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Okay.
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Hang tight, one second.
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No way!
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Jackie Chan, you're here!
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I'm here!
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I'm here!
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I'm here!
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I'm here!
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I'm here!
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I'm here!
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I'm here!
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I'm here!
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I'm here!
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I'm here!
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I'm here!
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I'm here!
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I'm here!
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Jackie Chan, you are a celebrity?
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I've seen all your movies.
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I've seen Shanghai Noon, Rush Hour, Rumble in the Bronx.
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I can't believe you're here at NASA Langley Research Center in Hampton, Virginia.
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Van, hang on.
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We need to really let Jackie introduce the show.
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Oh, okay.
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Sorry.
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It's okay, Van.
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You know, during my visit here at NASA Langley, I've learned that this center is one of the
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largest collections of wind tunnels in the world.
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In fact, I filmed a movie in a wind tunnel once.
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Wow, the wind is so strong.
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On today's NASA Connect, you learn how NASA engineers and researchers use geometry and
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algebra every day in their work.
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You test shapes for drafts just like NASA researchers.
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You get connected to a really cool web activity and take a sneak peek at a new airplane.
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Is it a bird or a plane?
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So get ready, get set, and glow with the flow.
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Here on NASA Connect.
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Okay, here's the deal.
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Van and I are going to conduct a little experiment about drag using go-karts.
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Van and I are riding in the same kind of go-kart with the same amount of fuel.
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These are constants.
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However, Van is taller and heavier than I am.
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These two variables, height and weight, might affect the race.
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And hopefully, I'll cross the finish line first.
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I am the superior driver.
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I can't change my weight, but if I change the variable of being taller and crouch down
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and become more streamlined, I might have a chance.
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Ha!
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No way!
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How did you win?
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Let me explain, Jennifer.
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I changed my shape, which allowed the air to flow more smoothly around me.
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Your shape interrupted the airflow and caused drag.
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This slowed you down and allowed me to win.
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So what is drag?
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Drag is the force that opposes or resists motion.
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The interruption or resistance to airflow causes drag.
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You've probably experienced drag when you've ever stuck your hand out the window of a moving car.
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When you extend your arm like this, with your palm forward, the force of drag pushes your hand back.
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But when you tilt your hand like this, it creates lift and lifts your hand upward.
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Lift and drag are a few of the aerodynamic forces that act on an airplane when it flies.
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How do airplanes fly?
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Well, to understand flight, you must first understand air.
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We are surrounded by air all the time, but we can't feel it
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because the air pressure is equal on all sides of our body.
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But what if we change the air pressure on one side of an object?
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Check out this cool experiment.
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Hey, why did the paper lift up when I blew across the top?
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Well, when the paper is resting against my chin like this,
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the air pressure on top is equal to the air pressure on the bottom.
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But when I blow, I change the air pressure on the top.
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The shape of the paper in its original position is kind of like an airplane's wing.
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It is curved on the top.
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Because of this shape, air molecules move faster across the wing's top than across its bottom.
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Swiss mathematician Daniel Bernoulli discovered that faster-moving fluids, such as air,
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exert less pressure than slower-moving fluids.
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Because of its shape, the air over the top of the wing moves more quickly and exerts less pressure.
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When the pressure on top of the wing is less than the pressure under the wing,
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lift is produced and the airplane flies.
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What does all this have to do with algebra and geometry?
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Everything! Geometry is the study of shape and size.
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Geometry was probably first developed to help measure the Earth and its objects.
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Knowledge of geometry helps you better understand things like engineering and science.
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Algebra is a mathematical tool for solving problems.
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Learning algebra is a bit like learning to read and write.
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Knowledge of algebra can give you more power to solve problems and accomplish what you want in life.
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At NASA, engineers use algebra and geometry when they measure and design models to be tested in wind tunnels.
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Like today's NASA engineers, Orville and Wilbur Wright used algebra and geometry.
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By blowing a certain amount of air over models in a wind tunnel,
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the Wright brothers tested and compared different wing shapes, rudder shapes, and propeller shapes.
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Hey, let's conduct an experiment very similar to the Wright brothers and test different shapes for drag.
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Good idea, Van, but first, teachers, make sure you check out the NASA Connect website
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and download the lesson guide for today's program.
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In it, you'll find step-by-step instructions and analysis questions for today's classroom activity. Van?
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In honor of the Wright brothers, NASA Connect traveled south to Kill Devil Hills, North Carolina
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to conduct today's classroom activity.
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Hi, we're from First White Middle School in Kill Devil Hills, North Carolina.
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NASA Connect asked us to show you how to do this show's classroom activity.
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It's called...
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What a Drag!
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This activity has three parts.
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In part one, you'll learn how shape affects drag.
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In part two, you'll learn how surface area affects drag.
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And in part three, you'll apply what you've learned from parts one and two
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to determine the object with the least amount of drag.
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Make sure your teacher has a lesson guide for this program.
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All the steps and materials are in it.
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Before starting the experiment, construct your drag apparatus.
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Then discuss these questions.
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What is drag?
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How would shape affect drag?
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What are some direct and indirect negative effects of drag on a vehicle?
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Now, let's test these four shapes for drag.
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First, verify that each of the shapes has the same amount of frontal surface area
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and record your information in the data sheet.
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Next, place two shapes on the drag apparatus like this.
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Turn the fan on low.
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Which shape moves closer to the fan?
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That's the one with the least amount of drag.
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Record your observations and repeat these steps using different combinations of the shapes.
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Look at your data.
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Which shape had the least amount of drag?
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Does shape affect drag?
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Why or why not?
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What other variables could have affected the outcome of the experiment?
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Thanks, Debbie. Nice job, guys.
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Take five, because we'll be back a little later to continue this activity.
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But first, let's head to NASA Langley to see how engineers there are using algebra to solve problems with drag.
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They use a wind tunnel instead of a box fan to test models with different shapes.
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Why are patterns important in determining drag?
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What algebraic relationship shows that a car has drag?
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Explain the relationship between pressure and glow.
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This is one of NASA Langley's many wind tunnels.
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It's called the Basic Aerodynamics Research Tunnel, or BART for short.
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Engineers like me use the BART and a technique called flow visualization to try to understand how the air flows around aircraft.
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By looking at or visualizing the airflow, we can help aircraft designers create new shapes that are more aerodynamic and produce less drag.
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Drag slows down a vehicle or an object, as you observed in the activity you just conducted.
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Recently, NASA Langley used its experience in testing and simulating aircraft
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to help a car manufacturer visualize and describe the airflow over one of its automobiles.
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What we as engineers would really like to see is the air flowing continuously from the front of the car to the back of the car,
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like the flow over this cylinder.
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There is no interruption in the airflow and there is no drag.
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Unfortunately, this is not how things work in real life, so we have to make airplanes and cars streamlined.
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This particular automobile is streamlined, which means it was designed to offer minimal resistance to airflow.
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Because of its shape, this car has little drag.
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You know, that sounds like our activity.
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The tetrahedron had the lowest drag because of its shape.
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That's right. The shape of airplanes and cars is mainly determined by aerodynamics and safety.
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However, a car has additional factors that may affect its shape.
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The vehicle must look good for people to buy it, the passengers must be comfortable,
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and the vehicle must be able to transport people, cargo, or both.
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With this in mind, automotive engineers use geometry to design cars with one of three shapes,
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a hatchback, a squareback, or a notchback.
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Which of the three shapes do you think would have the highest drag?
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Looks like the notchback has the most drag.
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You're right. After deciding on the shape to test, we created a scale model of a typical passenger vehicle with a notchback design.
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To visualize and measure the airflow around this model, we used the BART,
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and materials like kerosene and titanium dioxide, a white powdery substance used in paint.
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Visualizing the airflow provides a picture of how the air moves around the vehicle.
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Okay, so how do you visualize airflow?
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You can't really see air, can you?
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No, you can, and that's a good question.
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Without special materials, you really can't see air flowing.
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So we mixed titanium dioxide and kerosene together and applied it to the surface of the model.
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We turned on the wind tunnel, and as air flowed over the model, the kerosene evaporated or turned into a gas.
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The titanium dioxide left on the surface shows us an airflow pattern.
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This pattern tells us how the air is moving close to the surface.
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The measurements we collect allow us to describe the air's properties in motion with numbers.
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Luther, that looks really cool, you know, but what does this pattern say about the shape of the car and the drag it produces?
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Well, this pattern tells us that the air is actually traveling in the same direction as the car, or in other words, towards the back window.
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This is called reverse flow.
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Reverse flow creates low pressures on the back of the vehicle, which increases drag.
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Remember this drawing?
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See how the air flows smoothly over the cylinder and comes together again in the back?
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Although this isn't how things work in the real world, the air pressure in the front, P-F, is the same or equal to the pressure in the back, P-B.
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When the pressure in the front is equal to the pressure in the back, then there is no drag.
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However, look at our notchback model.
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See how the air flow separates at the back of the vehicle and the air actually begins to flow in the reverse direction?
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This is reverse flow, and the pressure in the front of the model is greater than the pressure in the back.
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When the pressure in the front is greater than the pressure in the back, you have drag.
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Flow visualization helps us understand how the air flows over the model, but in order to measure the pressures on the surface, we had to use additional techniques.
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The most exciting is probably pressure-sensitive paint.
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In addition to NASA Langley, NASA Glenn Research Center in Ohio and NASA Ames Research Center in California use pressure-sensitive paint in their wind tunnel tests.
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Pressure-sensitive paint, or PSP, is a special paint that glows when exposed to blue light.
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The glow is really due to special molecules embedded in the paint called luminophores.
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Luminophores. Sounds like a word that comes from illuminate.
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That's right. These luminophores are excited or given excess energy by the blue light.
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The luminophores don't like to have excess energy, so they get rid of it by either glowing or by bumping into nearby oxygen molecules.
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The behavior of the luminophores allows us to see a relationship between the brightness of their glow and the pressure on the surface.
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Hmm. A relationship. Sounds like algebra.
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That's right. I use algebra in my work every day. Let me show you.
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Remember when I said that the behavior of the luminophores allows us to relate the brightness of the glow to the pressure on the surface?
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This is done using a graph like this.
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The curve on the graph shows an inverse relationship between pressure and glow.
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When glow increases, we know the pressure has decreased.
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But when glow decreases, we know the pressure has increased.
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This inverse relationship can be represented with the following algebraic equation.
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Pressure equals quantity glow minus one divided by the slope of the curve.
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Using the graph in this algebraic equation, we solve for pressure.
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The pressures we calculate can be displayed using different colors like this.
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The red regions show where the pressures are high, and the blue regions show where the pressures are low.
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As you can see, the pressures in the front of the car are higher than the pressures in the back.
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As we calculated earlier, this difference determines the vehicle's drag.
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This information is used by car designers to decide if the shape or geometry of a car needs to be changed.
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If I were a car designer, I'd change the notchback shape of the car. It creates too much drag.
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Well, Van, the research conducted here at the NASA Langley Research Center can be used by automotive engineers and designers
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to create new designs and shapes with reduced drag and better fuel efficiency.
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This allows drivers like us to save money and protect the environment.
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Okay, we've seen how different shapes affect drag.
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Now, let's head back to First Flight Middle School and see what would happen if we changed the frontal surface area of an object.
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Are you ready, guys?
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Ready, Jennifer. Now let's find out how surface area affects drag.
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Your teacher will give each group a copy of the disc patterns.
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From the lesson guide, select and construct five discs.
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Look at one of the discs. What do you think the area is?
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Make a prediction and write it down.
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Now, calculate the actual area.
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What is the difference between your prediction and the actual area?
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Are you close?
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Repeat these steps for each disc.
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Before beginning the experiment, construct the test track.
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Choose any disc and place it on the front of the test vehicle like this.
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Place the vehicles on the start line.
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Make sure the string is nice and tight.
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Predict the distance that the test vehicle will travel when the fan is turned on and write it down.
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I predict it will travel about 42 centimeters.
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I predict it will travel 50 centimeters.
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Turn the fan on high for approximately 10 seconds.
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This is only a suggested time.
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Your time will depend on the fan speed and test vehicles.
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Now, measure the distance that the test vehicle moves backward and record it on the data sheet.
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Calculate the difference between the predicted distance and the actual distance and record your answer.
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How did you do?
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Now, test the other discs.
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Now that we've gathered our data, let's create a graph that shows the relationship between frontal surface area and distance.
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Could I have one member of each group to come up and graph their data?
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Great job, guys. Let's look at the graph and answer some questions.
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What kind of graph is it?
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Do you see a correlation?
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If so, what kind is it?
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Which surface area produced the least amount of drag?
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Now let's put it all together.
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Look at the data from the first experiment you did.
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Which shape had the least amount of drag?
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Tetrahedron.
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This shape?
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Now look at your data from the second experiment we did on surface area.
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What did you find out about the surface area and drag?
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Based on your results, which of these four tetrahedrons should have the least amount of drag?
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How can we test your predictions?
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Let's put the shapes on the drag stand and see what happens.
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Great, let's do it.
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We'd like to thank the AIAA student mentors from North Carolina State University.
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Good job, guys.
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Well, thus far, you've seen these students use some of the tools for research.
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That being design, construction, testing, and analysis of an experiment.
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But you know what? NASA uses some other tools for research.
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Computer simulations.
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And with a little help from our friend Norbert here,
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we're going to transport you to the Fernbank Science Center in Atlanta, Georgia.
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Fernbank Science Center is a science resource center for DeKalb County School System.
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It has had a relationship with NASA since the early Apollo missions
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and recently installed the NASA Aeronautics Education Laboratory to use in its education programs.
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Waiting for you at Fernbank are students from McNair Middle School
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who will introduce you to the program's featured web simulation, MAX, or Mars Airborne Explorer.
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Made especially for NASA Connect by Space.com.
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From Norbert's lab, click the activity button.
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You'll get to create a Mars exploration aircraft and fly it over a simulated Martian terrain.
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You'll be able to see the relationships between thrust, drag, and lift.
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Your mission is to pilot the Mars aircraft and release a number of probes
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that must land on designated targets.
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The right combination and balance will lead to a successful flight.
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ePALS Classroom Exchange brings to teachers and students the opportunity
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to collaborate with peers, experts, and others using ePALS' free telecommunications
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and collaborative tools.
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And teachers, be sure to visit Norbert's lab and browse a section called Manager,
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a special section to help guide teachers in using activities
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that have educational technology interwoven.
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A special thanks to another NASA Connect online partner, Space.com.
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Devoted to space news, it offers special portals to kids and teachers
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at SpaceKids.com and TeachSpace.com.
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And a final thanks to our AIAA student mentors from Georgia Tech.
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Well, I think that's a wrap from my end, bringing you the power of digital learning.
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I'm Shelley Canright for NASA Connect Online.
00:19:32
Okay, let's review.
00:19:35
So far, we've learned how NASA engineers use geometry and algebra,
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flow visualization, and glowing paints to help them create more aerodynamic vehicles,
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and how shape and surface area affect drag.
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We've also learned how computer technology can help you solve problems that are out of this world.
00:19:49
Now, let's learn how NASA engineers are using geometry
00:19:53
to create a concept airplane that looks a lot like a flying wing.
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Describe the differences between the blended wing body and today's commercial airplanes.
00:20:05
How do NASA engineers use geometry to estimate frontal surface area?
00:20:10
What design features would increase the drag on a low-speed vehicle?
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How could engineers compensate for that drag?
00:20:18
The blended wing body, or BWB as we call it for short,
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is an advanced concept passenger airplane.
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That means that we're still in the process of deciding and testing what will be the best design.
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So far, early studies estimate the blended wing body
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to accommodate 1,500 passengers, have a wingspan of 247 feet,
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a length of 160 feet, and be more than 40 feet or four stories high.
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It kind of resembles a flying wing.
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Engineers believe the BWB has potential to perform better than traditional tube-with-wings airplanes,
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like the Boeing 747.
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Some estimates predict that this new airplane will reduce operating costs
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and the amount of fuel the airplane uses.
00:21:02
So, Wendy, what makes the blended wing body so special?
00:21:06
It's shape.
00:21:10
Since we've been discussing shape and geometry in today's program,
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let me show you what makes the BWB different from other airplanes today.
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If you look down on the top of the plane, you can see that its fuselage,
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that's the part that people ride in, and the wing are blended together.
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That's how it got its name, the blended wing body.
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If we look over the frontal view, we can see that there's a smooth transition
00:21:34
from the fuselage to the wings.
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This shape allows more people to sit in the fuselage and even out into the wings.
00:21:42
Remember the picture of the streamlined car Luther showed you?
00:21:46
Just like a car, when an airplane has a smooth shape, it can help reduce drag.
00:21:50
Do you see anything else that makes the BWB different from other airplanes?
00:21:54
Hmm.
00:21:58
Well, like other airplanes.
00:22:02
Right. Just like blending the wing and fuselage together helps to reduce drag,
00:22:06
taking off both the horizontal and vertical tails also helps reduce drag.
00:22:10
Drag, which you learned about earlier, resists thrust.
00:22:14
Thrust, the force that propels the airplane, is usually provided by jet engine.
00:22:18
If an airplane has too much drag, it will need more thrust or engine power.
00:22:22
However, when the airplane is designed for less drag, like the BWB,
00:22:26
less thrust is needed. So, what does this all mean?
00:22:30
Less thrust means less fuel is needed.
00:22:34
And less fuel means less money to buy a ticket.
00:22:38
You got it. Now, Wendy, you said earlier that the BWB is just a concept airplane,
00:22:42
so I guess that means it hasn't been built yet.
00:22:46
Right. It would be too expensive to build the full-size BWB.
00:22:50
NASA and Boeing engineers come together and design some scale models.
00:22:54
Does that mean there's going to be more than one model of the BWB?
00:22:58
Absolutely. If we only built one model, we couldn't collect enough information.
00:23:02
So, we've built a model that's approximately 1% the size of the BWB.
00:23:06
Hey, let's do the math.
00:23:10
What would a 1% model of the BWB look like?
00:23:14
Would it fit in your classroom or in a shoebox?
00:23:18
I know. Let's figure it out.
00:23:22
The BWB will be 247 feet wide,
00:23:26
160 feet long, and 40 feet tall.
00:23:30
Using middle math, let's take 1% of each of those measurements.
00:23:34
Okay. 1% of 247 is 2.47,
00:23:38
or about 2.5 feet wide.
00:23:42
1% of 160 is 1.6, or about 1.5 feet long.
00:23:46
1% of 40 is .4,
00:23:50
or about a half foot tall.
00:23:54
So, yeah.
00:23:58
1% model of the BWB should definitely fit in your classroom. Right, Wendy?
00:24:02
That's right. And here it is.
00:24:06
As I said earlier, building just one scale model like this didn't give us all the information we needed.
00:24:10
So, we built a 2%, 3%, and a 4% model.
00:24:14
They'll all be tested here at NASA Langley in the wind tunnels to determine performance and stability.
00:24:18
Because we can't always predict how the BWB will perform,
00:24:22
it can't tell us how a real pilot will be able to control it in the air.
00:24:26
So, NASA Langley is building another subscale model called the Low-Speed Vehicle,
00:24:30
or LSV, and it will actually fly.
00:24:34
We will take our LSV wind tunnel predictions and compare them to actual flight test data.
00:24:38
The flight test will take place at NASA Dryden Flight Research Center in California.
00:24:42
Engineers want to learn how to control and stabilize this new concept airplane
00:24:46
safely. In a wind tunnel, you just can't simulate that.
00:24:50
The LSV is about 14% the size of a full-size BWB.
00:24:54
14% model of the BWB is about 35 feet wide,
00:24:58
22 feet long, and 6 feet high.
00:25:02
Remember in the classroom activity when you determined that a greater frontal surface area
00:25:06
produced greater drag? Let's look at the frontal view of the
00:25:10
14% BWB model. To estimate the frontal surface area,
00:25:14
all we need is the width, the height, and a little geometry.
00:25:18
First, we take the frontal view and divide it into parts using geometric shapes
00:25:22
like this. Then, we estimate the area of each geometric
00:25:26
shape and add them together to get the total frontal surface area.
00:25:30
Next, we combine the total frontal surface area with all the flight test
00:25:34
data we've collected and calculate the drag force for this particular model.
00:25:38
We know that to fly, we need a certain amount of thrust to overcome the drag force.
00:25:42
Okay, so figuring out the frontal surface area of the 14% model
00:25:46
helps you calculate drag, which then determines how much thrust is needed.
00:25:50
Right. But this is just a concept airplane, right? I mean,
00:25:54
what if you wanted to add something, maybe like an observation deck on top?
00:25:58
An observation deck would definitely increase the frontal surface
00:26:02
area, Van, which would then increase drag. In order to overcome that amount
00:26:06
of drag, we need to increase thrust by adding more powerful engines.
00:26:10
You know what? That applies to the go-kart race I had with Van.
00:26:14
My frontal surface area was greater than his because
00:26:18
I didn't crouch down into an aerodynamic shape. This greater frontal
00:26:22
surface area created more drag, and I lost. However,
00:26:26
if I had more thrust, I could have easily overcome the drag
00:26:30
and left Van in the dust. Well, you know what?
00:26:34
That's all we have time for today. Yep. We hope you've all made the connection
00:26:38
between the aeronautical research conducted here at NASA and the math, science, and technology
00:26:42
that you do in your classrooms every day. Jennifer and I would love to hear from you
00:26:46
with your questions, comments, or suggestions, so write us at
00:26:50
NASAConnect, NASA Langley Research Center, Mail Stop 400, Hampton, Virginia
00:26:54
23681, or send us an email at connect
00:26:58
at edu.larc.nasa.gov.
00:27:02
Hey, teachers, if you would like a videotape of this program and the accompanying
00:27:06
guide, check out the NASA Connect website. From our site, you can link to
00:27:10
CORE, the NASA Central Operation of Resources for Educators,
00:27:14
or link to the NASA Educator Resource Center Network.
00:27:18
We'd like to thank everyone who helped make this episode of NASA Connect possible,
00:27:22
especially Jackie Chan. No, I thank you, you, and thank you,
00:27:26
Van, and thank you, NASA, for inviting me. I learned a lot of things
00:27:30
because when I was young, the only thing I knew was martial arts.
00:27:34
Kicking, punching, all kinds of things.
00:27:38
I never knew education was important. Whenever I go,
00:27:42
I always support the children because education is very important, remember.
00:27:46
You heard it right from Jackie Chan. We'll see you next time.
00:27:50
Well, to understand flight, you must first under...
00:27:54
That's right, the aerodynamics of...
00:27:58
Now, let's learn
00:28:02
Let's learn how NASA researchers, or NASA engineers, are using
00:28:06
geometry as they... Remember the pictures,
00:28:10
they're a little... We'd like the tank.
00:28:14
So get ready, get set, and flow,
00:28:18
and go, and flow.
00:28:22
...
00:28:26
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- Fecha:
- 28 de mayo de 2007 - 16:51
- Visibilidad:
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- Enlace Relacionado:
- NASAs center for distance learning
- Duración:
- 28′ 31″
- Relación de aspecto:
- 4:3 Hasta 2009 fue el estándar utilizado en la televisión PAL; muchas pantallas de ordenador y televisores usan este estándar, erróneamente llamado cuadrado, cuando en la realidad es rectangular o wide.
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