SOLAR IMPULSE - LESSON - BALANCE (ENG)

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BALANCE IN FLIGHTAerial acrobatics!

Imagine everything that is involved in flying a plane and keeping it perfectly under control!

This worksheet proposes a series of activities that will help you understand how a plane keeps itself balanced and what the pilot has to do to steer it. You will also get a better understanding of the physical forces that a pilot is exposed to and feels during a flight.

Project: EPFL | dgeo | Solar Impulse

Writing: Angélique Durussel

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

Project follow-up: Yolande Berga

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THE CENTER OF GRAVITY

When a plane is airborne, it has to be perfectly in balance. Before we set out to determine the rules that govern balance, let’s take a look at the various components that make up an airplane:

• The airframe, which includes the fuselage, the wings, the empennage (horizontal stabilizers and vertical rudder), the landing gear, the elevators, (and the equipment).

• The engines, which either drive the propellers or provide the thrust to propel the plane forward.

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

Material

• cardboard

• a pair of scissors

• a compass

The weight of the engines, which are the heaviest part of the plane, has to be counterbalanced by the empennage, the horizontal stabilizers and the wings for the plane to stay horizontal when flying.

The balance point of an object is called its center of gravity. We can consider that gravity acts on that point only.

fuselagetailplane

horizontal stabilizer

vertical rudder

engineselevators

wings

landing gear

Try out different shapes.

BALANCE IN FLIGHT 3/16

You may have found the balance point of your shape, or its center of gravity, through trial and error. There is also a more systematic way to find it. In addition to the cardboard, the scissors, and the point of your compass, you will need a thin metal rod, some string, a small weight, and a hole puncher.

Instructions 1) Cut out several irregularly shaped pieces of cardboard (including at least one concave one). 2) Using the hole puncher, punch three small holes into the outer part of each cardboard shape. Make

sure that they are regularly spaced. 3) Make a plumb line by attaching a small heavy object to the end of a piece of string. 4) Stick the metal rod through one of the holes of the cardboard shape and hang the string with the

weight from the rod.5) Once the string stops swinging, mark the point that the string crosses on the opposite end of the

cardboard with a cross. 6) Remove the metal rod and use a pencil and a ruler to draw a line connecting the hole and the cross.

7) Repeat the same procedure for the remaining holes.8) You can test to see if you found the center of gravity by balancing the shape on the tip of your com-

pass where the three lines intersect!

You can use the same method to determine the center of gravity of a three dimensional object. When the object is supported at its center of gravity, or in the axis of its center of gravity, it stays in balance. It is stable if it is supported above its center of gravity and unstable if it is supported below it.

A three-dimensional object that is placed on the ground is in balance if its center of gravity is above the surface that carries it. This surface is also referred to as its support polygon.

The support polygon is the surface that is defined by the contact points between the object and the ground. As an example, consider a person standing upright. In this case, the support polygon is de-fined by the shape of the person’s footprint on the ground. If the person is standing on both feet, the support polygon includes both footprints and the space between them.

To stay in balance, the person’s center of gravity has to be located somewhere vertically above the polygon.

metal rod

plumb line

metal rod


The support polygons for the silhouettes shown below are indicated in blue. The center of gravity of each figure is represented by a red dot, and the arrow indicates that the center of gravity is located vertically above the support polygon.

The dancer’s support polygon (under her toes) is very small, making her balance very delicate.

The man is standing in a more stable po-sition, because his support polygon in-cludes the entire surface between his feet.

The dog is even more stable. His support polygon (between his four paws) is the largest. On top of that, the fact that his center of gravity is closer to the ground further stabilizes his position.

Quiz

Who is in balance?The red dots represent the center of gravity of each shape.

pictograms of a person, dog & tractor designed by freepik.com

bottle holder


When Solar Impulse is in the air, it does not have a support polygon. Instead, it has to be well balanced around its center of gravity, and that in three dimensions.

Cool potato!Cut a slice of potato and stick a pencil through its center. Next, poke a fork into the side of the slice as shown in the picture. Now try to balance the pencil on its tip on the edge of a table.

FUN ACTIVITIES

With a toothpickConnect a fork and a spoon and insert a toothpick into the tines of the fork as shown in the image. Try to balance the whole thing on the edge of a glass. Now, burn the end of the toothpick that is inside the glass and watch what happens. Can you explain what you observe?

Rock towers Begin with relatively flat rocks. Next, try using pointy, asymmetrical rocks, etc.

Just like any object, Solar Impulse has a cen-ter of gravity. But for the plane to fly, you also have to find its neutral point, or its aerodynam-ic center.Solar Impulse’s center of gravity is located close to its nose, while its aerodynamic center is always situated further back. Having the aerodynamic center located behind the center of gravity stabilizes the plane and makes it possible for it to fly. If the two points were at the same place, the plane would not even be able to take off. To calculate the location of the aerodynamic center, you need to know the position and the area of the wings and the hor-izontal stabilizer. The center of gravity depends on the weight of the components and their positions. Engineers study this process even before they start to build the plane. The weight of each element that is produced has to be carefully controlled to make sure that the proper-ties of the plane, once built, correspond to those used in the design process.

When a plane is built, its mass has to be spread out evenly for it to stay in balance. In the same way, when objects are loaded onto a plane, they also have to be distributed evenly.


INSTRUMENTS THAT ASSIST PILOTS: THE ACCELEROMETER

When in flight, especially in the absence of visible landmarks, it is extremely difficult to stabilize the plane, keep it horizontal, and make sure that it stays on course. That is why pilots are assisted by in-struments that provide information on the plane’s position and state. Here we will focus on two import-ant instruments: the accelerometer and the gyroscope.

An object’s speed is given by the ratio between the distance it covers and the time required:

An object’s acceleration is the change in speed per unit of time:

This change in speed can be either an increase (acceleration) or a decrease (deceleration).

A plane’s acceleration has to be measured constantly. Acceleration in mea-sured in g, which corresponds to the acceleration that an object experience due to its weight on the surface of the earth. For reference: 1 g = 9,81 m/s 2.

Our bodies are not affected by the speed at which we travel. They are, however, affected by changes in speed, whether in size (breaking or accelerating) or in direction (turning).

Astronauts or military pilots use centrifuges in their training.

speed [m/s] =

acceleration [m/s 2] =

distance [m]

speed [m/s]

time [s]

temps [s]

Using centrifuges, their resistance to acceleration can be tested and increased. To do so, the pilot enters a box that is attached to the extremity of a beam and is spun in circles, as the centrifuge spins rapidly around its axis.


Accelerations at constant speed can be measured using the following formula:

First, lets take a look at the effect of positive g forces have on your body. At 2 g, it would become difficult for you to stand up. At 3 g, you would have a hard time moving your legs, and at 6 g, it would almost be impossible to move your arms. At the same time, the pressure of the blood flowing towards your head would decrease, leading to a lack of blood in your brain and eyes. Your peripheral vision would be affected first, and if the acceleration were to continue to increase, you could black out com-pletely.

Blackouts are a physiological phenomenon that pilots are particularly exposed to when they fly in ex-treme conditions (for example aerobatics). The brain no longer receives enough blood, leading to a loss of vision, and at about 5 g, a loss of consciousness.

If, during an acrobatic maneuver, the plane abruptly stops climbing, the pilot is exposed to a negative g force: the blood flow towards the pilot’s head increases, which is very dangerous. Our bodies cannot handle negative g forces well (they can cause the blood vessels in the eyes to pop).

Some examplesA trip in the Silverstar (Europapark) 4 gA parachutist in free fall 0 to 0,95 gUn ascenseur en démarrage ou en freinage between 0,9 g and 1,1 g

An accelerometer is a device that measures the linear acceleration of the object to which it is attached. Here is a small project that will help you understand how an accelerometer works.

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


TECHNOLOGY: A HOME MADE ACCELEROMETER

Materials

• a mason jar with a lid

• a cork

• a plastic document wallet (for binders)

• a piece of string

Instruction1) Cut the cork into three pieces. You will only need one for the accelerometer. Cut out a plastic disk from the document wallet with a diameter that is slightly smaller that that of

your jar.2) Poke a hole into the plastic disk and make the string go through it. Attach it to the disk by tying a

knot that is bigger than the hole. 3) Tie the cork to the other end of the string. Remember that the string will be stretched in the jar, so

make sure you adapt the length of the string to the size of your jar. 4) Fill the jar with water and add the disk with the string and the cork so that you get the setup shown

above when you flip over the closed mason jar. There you go, you just made an accelerometer!

Hold it horizontally and observe how it reacts when you spin around, move forward, stop, etc.

Today, accelerometers are very common, even in devices made for the general public. They are made of silicon and integrated into electronic chips. They can be tiny, just a few millimeters across, and you can find them in a number of everyday objects, such as:

• running shoes (to measure speed, step rate and the distance covered)

• laptop computers (to protect the hard drive in

• case it falls)

• cars (to trigger the airbag)

• video game controllers (for example the WII)

• cellphones

• … and of course in planes!

QuizHere are five accelerometers. For each case, circle the corresponding accelerometer, as seen from the side.

water

cork

attached with the string

to the plastic (which the water pressure keeps in place against the jar lid)

An airplane taking off A B C D EA breaking car A B C D EA rocket taking off vertically A B C D E

A train at 100 km/h A B C D EA train at 0 km/h A B C D EA box falling vertically A B C D E

A B C D E


INSTRUMENTS THAT ASSIST PILOTS: THE GYROSCOPE

A gyroscope, Greek for “one that observes ro-tation,” is a device that measures and allows to control an object’s orientation in space.

The most important part of the device is a wheel (or any other well-balanced object that spins around an axis), which, once it is set into motion, resists any change in its orientation. A spinning gyroscope will stay balanced on a string, but will fall over when it stops.

Gyroscopes appear to defy gravity!

Let’s try to get an intuitive understanding of how a gyroscope works, as the physical and mathematical explanations of the phenomenon are very complicated. Imagine you are riding a bike.

When you are not moving, you have to put down a foot to increase the area of your support polygon, which will stabilize your position. But once you are riding fast enough, you can put your feet on the pedals. Despite the small support polygon between the wheels, you will not fall. You’ve achieved equilibrium through mo-tion.

It is as though, as long as the wheels are spinning, invisible forces were helping you to stay in balance. These forces are represented by green arrows, which line up with the axes of the bicycle’s wheels.

The same phenome-non can be observed on a top. The faster the top spins, the more stable its balance. A gyroscope works in the same way.

You can find gyroscopes in smartphones, tablets, remote controlled drones, etc. Gyroscopes are ap-plied in games and applications that use the movements of the device held by the player.

gravity

speed speed

silhouettes : Artem, vectorartbox.com


Who can spin a top the longest?

Materials

• a toothpick

• a paper or cardboard disk

You can fine tune the balance of your disk using masking tape.

Observe the motion of the axis of the top when it spins quickly and when it spins slowly. What do you notice? Try to change the height of the disk on the toothpick, its size, its mass, etc. Try to make it work on an inclined plane.

Quirky tops!

Anagyres are ellipsoidal objects that spin very quickly when spun in one direction, but when they are spun the other way, they stop almost immediately only to change direction and continue spinning the same way as before.

Their asymmetry can be visible or it can be hidden in the way their mass is distributed (non-homogenous density). Anagyres can be hollow and non-homogenous, which caus-es them to behave asymmetrically, even if they appear to be symmetrical.

Because they resist to changes in their orientation, gyroscopes can be used in aviation to monitor and preserve the orientation of the aircraft. Gyroscopes are placed into boxes that are at-tached to the plane.

Gyroscopes resist changes in their orientation and do not move. At the same time, their box, which is attached to the plane, moves, following the plane’s motion. Contact points in-form the pilot of the plane’s orientation.

The sensitivity of the device can be set by changing the po-sition of the contact points. For Solar Impulse, the tolerance threshold is very low. Given its low weight and wide wingspan, small inclinations can have large consequences, which is why the alarm is set to go off early.

Contact

Casing attached to the plane

Gyroscope


Instruments in the cockpit constantly inform the pilot about the orientation of the aircraft as it moves in three-dimensional space. Its position can be defined by referring to three perpendicular axes that cross at the plane’s center of gravity.

The vertical axis is called the yaw axis. There are two horizon-tal axes, the pitch axis (parallel to the wings) and the roll axis (parallel to the fuselage).

The pilot can use his controls to change the orientation of the plane according to these three axes. To do so, the pilot chang-es the inclination of the rudders (R, T, and L) shown in the figure below.

HOW A PLANE GENERATES LIFT AND TURNS IN FLIGHT

Now, lets try to understand how the position of the rudders can change the orientation of the airplane.

Piotr Jaworski & A. Nordmann (CC-BY-SA)

The rudders are movable surfaces that are attached to flat surfaces (wings, horizontal stabilizers, and tail).

The figure below shows in detail how the rudders along the pitch axis can be moved.

L

R

T

TR

Pitch axisYaw axis

Roll axis

Do it yourself

Start with a piece of aluminum foil (29 x 20 cm). Fold in half and then in half again so that you end up with a sheet that is about 7 x 20 cm. Now, fold it in half in the other direction so that you end up with an 8-layered piece that is about 7 x 10 cm large. Cut about 6 cm into this sheet, perpendicular to the last fold, in the middle. Then, slightly curl one half of the aluminum foil upward, and the other half downward, as shown in the picture on the right.

Blow above the aluminum foil in the direction of the arrow. What do you notice?And what happens when you blow under the sheet?

downward curl

upward curl


You just demonstrated that the position of the rudders influence the plane’s lift. Lift is covered in more detail in the worksheet NIGHT FLIGHT.

The yoke, or the control column, allows the pilot to change the pitch axis or the roll axis:

• If the pilot pushes or pulls on the yoke, the T rudders move, changing the pitch axis.

• If the pilot turns the yoke to the left or the right, it moves the R rudders (one upwards, the other downwards, at the same time), changing the roll axis.

The rudder pedals, controlled by the pilot’s feet, move the L rudder, modifying the yaw axis. A plane changes direction or sticks to its course when it encounters turbulence using a combination of modifications to these three axes.

When the pilot wants the plane to dive, he has to turn it by 90° along the pitch axis. To do so, he has to push the yoke forwards. Once the plane is diving, he has to straighten the yoke again.

To do a loop, which corresponds to a 360° rotation along the pitch axis, the pilot has to pull on the yoke until the plane is horizontal again.

For a barrel role, the pilot has to make the plane ro-tate along the roll axis. This involves turning the yoke to the left or to the right, depending on which way he wants to roll.

To do a stall turn, the yaw axis has to be modified. For this, the pilot uses the rudder pedals so that the plane turns before the dive.

When performing these maneuvers, the pilot has to constantly check all three axes of the plane, and other factors, such as the movement of the air. This involves continuously using the rudders.

It takes many hours to translate designs laid out on blueprints into the plane’s final composite structure, the skeleton that gives the plane it’s shape and ri-gidity at the lowest possible weight. This meticulous task requires craftsmen like Sylvie.

SYLVIE CAVANNAZ, DRAPING PROCESSOR PORTRAIT

Sylvie is a draping processor at Décision SA, a company that specializes in composite materials and that produced the majority of the pieces that make up Solar Impulse. Draping processing is a little known profession that plays an important role in the production of composite materials.


AND ALL OF THIS IN NUMBERS…

Exercise 1

On the pictures below, the wheels on which the plane rests (and lands) have been circled.

Draw the support polygon of the plane on the image below.

The craftsman is responsible for putting together the layers of fiber that go into the final component, and the physical properties of the component, once completed, depend on the craftsman’s dexterity and precision. In projects that are as complex as Solar Impulse, even a tiny imperfection could make a completed component fail the final quality control.How did Sylvie find her way into this field? Through a huge coincidence! After having completed a de-gree in sales, she found a temporary job at a shipyard with the help of a job placement agency. There she learned the skills of the trade, and thanks to her knack for handiwork, she soon felt drawn to the challenge of learning more about materials to produce a palette of final components. She’s been on the job for the past 14 years, and has thoroughly enjoyed it. So what is it that Sylvie is passionate about? The job is extremely diverse, and each new piece she has to build brings a new challenge to find the optimal way to translate a plan into a final component. Based on the plan, the first step is to define the steps she will have to take to make the piece. Then comes the preparation of the various components – cutting inserts out of foam, honeycomb structures, or textiles. Next, she has to adjust the pieces, lay them out, and bake them so that they solidify, forming the final piece. To get the job done, she works closely with her colleagues on the construction site to draw on their expertise. And after achieving a task, it is always satisfactory to see the pieces she helped produce put to use.


Exercise 3

a) Calculate the acceleration that a pilot is subject to when he is under 3 g.

Exercise 4

a) Upon landing, a 70-kg parachutist undergoes an acceleration of 4 g. How fast was he flying before he landed if you consider that it took him two tenths of a second to come to a halt?

b) Earlier in the worksheet we talked about the centrifuges that are used to train astronauts and army pilots. How fast does a NASA centrifuge have to rotate for the pilot in training to experience 6 g? The seat is 4.5 m from the axis of rotation.

Exercise 2

Why is an object more stable when its center of gravity is close to the ground?

What acceleration does this correspond to (in m/s2) ?

c) How many g does the driver of a Bugatti Veyron experience when accelerating from 0 to 100 km/h in 2.4 s?

b) It’s a record! John Stapp en-dured 46 g for 1.1 seconds in 1954. You can see the effect of the increasing g-force on his face.


axis 1

axis 2

axis 3

Exercise 5

In the orthonormal systems shown below, which axis are the rectangular surfaces parallel to.

a)

c)

e)

b)

d)

f)

The rectangular surface is parallel to

axis 1 axis 2 axis 3











axis 1

axis 2

axis 3

axis 1

axe 2

axis 3

axis 1

axe 2

axis 3

axis 1

axe 2

axis 3

axis 1

axe 2

axe 3


Exercise 6

Which axis did these planes turn around if they started in a horizontal position?

a)

Exercise 7

a) The pilot wants to perform a stall turn. Does he have to use the yoke or the pedals?

Help him through the three key steps of his maneuver by indicating along which axis he has to turn.

b) A plane is flying upside down. What does the pilot have to do to fly an upward loop?

b)

c) d)

Concorde par Aero Icarus (CC-BY-SA)

The plane turned around the

pitch axis roll axis yaw axis







1

3

2

Technology

SOLAR IMPULSE - LESSON - BALANCE (ENG)