SOLAR IMPULSE - LAB WORK - BALANCE (ENG)

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BALANCE IN FLIGHTAerial acrobatics!

This worksheet introduces a range of phenomena that help understand how a plane stays balanced when in flight, and what the pilot has to do to steer it.

Covered topics include the center of gravity, first for surfaces, then for three-dimensional objects.

It also proposes a number of activities that will help students become familiar with the notion of acceleration and the gyroscopic effect. At the same time, students will be able to understand the physics behind the forces that a pilot is exposed to during a flight.

This worksheet also includes exercises that involve spatial awareness.

Project: EPFL | dgeo | Solar Impulse

Writing: Angélique Durussel

Graphic design: Anne-Sylvie Borter, Repro – EPFL Print Center

Project follow-up: Yolande Berga

Concepts coveredMathematics:

• Unit transformations

• Proportionality

• Representations in space

Physics:

• Center of gravity, Support polygon

• Speed, acceleration

• Introduction to the gyroscopic effect

Duration of the activitiesIntroduction and discussion: 2 periodsChallenges: 4 periodsExercises: 2 periods

BALANCE IN FLIGHT - GUIDE 3/9

THE CENTER OF GRAVITY

You can remind your students that the center of gravity of a triangle is located at the intersection of its medians. If the students are not familiar with this, you can ask them to verify it for themselves on any triangle by first finding the intersection of its medians and then balancing it on the tip of a compass needle at that spot. If necessary, remind the students that the balancing point is also called the center of gravity.

Can you make a random cardboard shape balance on the tip of your compass?

Most students will test convex shapes.There are concave shapes that are impossible to balance on the tip of a compass needle because their center of gravity lies outside the outline of the shape. If you have enough time, let the students figure this out themselves.

To save time you can provide the shapes: a simple convex shape, a concave shape that can be balanced, and a concave shape that is impossible to balance (for example shaped like a horseshoe).

If you have access to an equipped science room, you might want to use a stand to simplify the experiment. To do so, use the stand to fix the metal rod from which you can hang the cardboard shapes and the plumb line.

The two experiments below will let the students feel for themselves how the size of their support polygon and the height of their center of gravity influence their balance:1) Working in pairs, one student can try to push the other, who is standing first on one

foot, then on both feet, first close to each other, then further apart. As the size of their support polygon increases, it becomes more and more difficult to make them lose their balance.

2) Students can try to push classmates who are standing on both feet spread apart, but this time, crouched lower and lower down. Crouching down lowers their center of gravity, making it more difficult to make them lose their balance.

The plumb line method can also be used for 3D objects, as long as the objects can be crossed by the string. One possible object is a colander. Attach the plumb line to one of the holes of the colander. Hang it along two different axes and mark the point where the lines intersect. This point is the center of gravity.

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Quiz

Draw a vertical line from the center of gravity and see whether or not it crosses the support polygon.

The man will tip forward because the vertical line crosses the ground in front of the support polygon.

The horse is in an unstable equilib-rium because its support polygon is very small. The slightest movement will make it lose its balance.

The bottle holder is stable.

The tractor is in balance, but if the slope gets any steeper, it will topple over backwards.

FUN ACTIVITIES

Cool potato!The balance achieved in this experiment is sur-prising, as the support polygon, located beneath the contact point, is very small. With a toothpickThere is the same surprise factor as in the previ-ous experiment.Burning the inside end of the toothpick has no effect on the stability of the setup because the mass of half a toothpick is negligible compared to the other elements. A video of this experiment can be seen here: youtube.com/watch?v=sgp3vxmh3cU Youtube, un incroyable équilibre!, roidubuzz


Rock towers You can take your students to a beach or a river to find large stones. Start with “easy” towers and then try using less stable rocks. Work in teams to make towers, always looking for the center of gravity and compensating for uneven rocks.

Science classes in the 2nd and 3rd “cycles” include activities that help understand how to balance mass-es in a system involving levers. A plane can be considered a type of lever. Its “hinge” is its center of gravity.

INSTRUMENTS THAT ASSIST THE PILOT: ACCELEROMETERS

Geologists also use accelerometers, which they place on the ground to collect information on the move-ments of the ground during earth-quakes.

Some anecdotes about g –forces The average acceleration of a proton in the Large Hadron Collider (LHC) is 190,000,000 g!

Accelerations that drive blood into a pilot’s feet are measured as “positive g,” while those that force blood upwards to the head are measured as “negative g.”

This video shows the effect of an increasing g-force on the body. youtube.com/watch?v=Yjg6mRFzZzE Youtube, Hilarious G-Force training, shondon

Accelerometers calculate linear accelerations along three or-thogonal axes. axis 2

axis 1

axis 3


TECHNOLOGY: A HOMEMADE ACCELEROMETER

The faster an accelerometer reacts, the better the effect of acceleration becomes visible. If you test the device you put together in class, you will see this: youtube.com/watch?v=_J5zE-LuAzc Youtube, Un accéléromètre, Unisciel

The cork that is attached to the string moves forward if the car accelerates in a straight line, and to-wards the inside of a curve if the car takes a roundabout.

Quiz

A plane taking off A B C D E

A car breaking * A B C D E

A rocket taking off vertically A B C D E

A train at 100 km/h A B C D E

A train at 0 km/h A B C D E

A box falling vertically A B C D E

* You can chose A or B, because we do not know whether the car is going from left to right (A) or from right to left (B).

A B C D E

This video provides an explanation to how the accelerometers that are used in iPhones work and how they are made: youtube.com/watch?v=FnQ43TJtE54 Youtube, Fonctionnement et fabrication de l’accéléromètre d’un smartphone, Moroccan Engineer


INSTRUMENTS THAT ASSIST THE PILOT: GYROSCOPES

To see examples of gyroscopes in action: youtube.com/watch?v=--vZiFmuuUA Youtube, Gyroscope, Christian Piard

Who can make his top spin longest?

When the top spins slowly, its precession (the circle made by the summit of the vertical axis) is larger than when it spins quickly. You can change the size of the disk and its position on the vertical axis, and observe the effects on the precession.

Funny tops!

At first, the rattleback or anagyre’s rotational kinetic energy makes it rotate around its vertical axis. But because of its asymmetry, the slightest irregularity it encounters on the surface on which it is spinning will lead to an oscillation that absorbs all of this energy. Because of the way it is shaped, these oscillations give rise to friction against the surface, which in turn generates a lateral force that makes it rotate in the opposite direction. To see an anagyre in action: youtube.com/watch?v=zH3k2oiPJhE Youtube, Anagyre, Expériences EPFL

HOW A PLANE GENERATES LIFT AND TURNS IN FLIGHT

Do it yourself

You have to hold the sheet and blow across its top surface. The half that is curved upwards is driven down, while the half that is curved downwards goes up (often to the great surprise of the class). The students’ intuition would have them blow below the sheet for it to rise! When the students blow below the sheet, the half that rose before is drawn downwards and vice versa!

To see a piece of paper rise when a student blows across its top surface: phymain.unisciel.fr/vive-le-vent Physique à main levée , Vive le vent

For more information and exercises on lift, you may refer to the NIGHT FLIGHT worksheet.

youtube.com/watch?v=bnvbnUrv5pUYoutube, L’effet gyroscopique, 1001experiences

without blowing

with blowing


ALL OF THIS IN NUMBERS…

Exercise 1

Exercise 2 The closer the center of gravity is to the ground, the larger the angle α becomes. As a result, the center of gravity has more “freedom to move” above the support polygon.

Exercise 3

a) We know that 1 g = 9.81 m/s 2, so 3 g = 29.43 m/s 2

b) We know that 1 g = 9.81 m/s 2, so 46 g = 451.26 m/s 2

c) 100 km/h = 27.8 m/s. The initial acceleration is therefore: 27.8 / 2.4 ≈ 11.58 m/s 2

Considering that 1 g = 9.81 m/s 2, 11.58 m/s 2 = 1.18 g

Exercise 4

a) 4 g = 39.24 m/s 2. The speed before the deceleration is: 39.24 ∙ 0.2 ≈ 7.85 m/s ≈ 28.25 km/h

b) Using the formula:

Therefore the pilot turns at a speed of : acceleration ∙ radius = 6 ∙ 9.81 ∙ 4.5 ≈ 16.27 m/s ≈ 58.6 km/h

The centrifuge spins at: 16.27 / (2π ∙ 4.5) ≈ 0.58 revolutions per second

acceleration [m/s 2] = speed ∙ speed [m2/s2]radius [m]

α

α

Using the picture you can show that the wheels are located beneath the outer mo-tors, below the tail and the cockpit.


Exercise 7

a) Step 1 : The pilot pulls back on the yoke to rotate the pitch axis by 90°. Step 2 : The pilot uses the pedals to rotate the yaw axis by 180°. Step 3 : The pilot pulls back on the yoke to rotate the pitch axis by 90°. A comment for die-hard fans of aerobatics competitions: you can also observe a rotation of the roll

axis in step 2. The gyroscopic effect of the motor forces the plane into a rotation to the left around the roll axis. If the pilot did not push the yoke to the right (or even pump the yoke) during the rotation along the yaw axis to the left, the plane would do a stall turn that would not be very flat (on the virtual surface that it rotates on) and it would not have the same angle of descent as it did on its way up.

b) The pilot has to push the yoke forward.

a)

c)

e)

b)

d)

f)

The rectangular surface is parallel to

axis 1 axis 2 axis 3











Exercise 5

Exercise 6

a) b)

c) d)

The plane turned around the

pitch axis roll axis yaw axis







SOLAR IMPULSE - LAB WORK - BALANCE (ENG)

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