This document introduces concepts related to how planes maintain balance in flight. It covers topics like center of gravity, forces that affect balance like acceleration and gyroscopic effects, and the role of instruments like accelerometers and gyroscopes. Activities are proposed to help students understand these concepts physically through challenges that explore balance and spatial reasoning. Formulas are provided for calculating values like g-forces. Diagrams demonstrate how control surfaces and the position of the center of gravity impact balance.

1. 1/9
BALANCE IN FLIGHT
Aerial 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

2. Concepts covered
Mathematics:
• Unit transformations
• Proportionality
• Representations in space
Physics:
• Center of gravity, Support polygon
• Speed, acceleration
• Introduction to the gyroscopic effect
Duration of the activities
Introduction and discussion: 2 periods
Challenges: 4 periods
Exercises: 2 periods

3. 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.

4. 4/9 BALANCE IN FLIGHT - GUIDE
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 toothpick
There 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

5. BALANCE IN FLIGHT - GUIDE 5/9
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

6. 6/9 BALANCE IN FLIGHT - GUIDE
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

7. BALANCE IN FLIGHT - GUIDE 7/9
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=bnvbnUrv5pU
Youtube, L’effet gyroscopique, 1001experiences
without blowing
with blowing

8. 8/9 BALANCE IN FLIGHT - GUIDE
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.

9. BALANCE IN FLIGHT - GUIDE 9/9
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
The rectangular surface is parallel to
axis 1 axis 2 axis 3
The rectangular surface is parallel to
axis 1 axis 2 axis 3
The rectangular surface is parallel to
axis 1 axis 2 axis 3
The rectangular surface is parallel to
axis 1 axis 2 axis 3
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
The plane turned around the
pitch axis roll axis yaw axis
The plane turned around the
pitch axis roll axis yaw axis
The plane turned around the
pitch axis roll axis yaw axis