Why Planes Fly
Using Bernoulli’s Equation to Understand Lift


OBJECTIVES
Students will learn how pressure
differentials create lift.
Students will gain an understanding
of how planes fly.
CORE LEARNING GOALS
1.1.3 The student will apply addition,
subtraction, multiplication and/or division
of algebraic expressions to mathematical
and real-world problems.
1.2.5 The student will apply formulas
and/or use matrices (arrays of numbers) to
solve real-world problems.
MATERIALS

Copies of Vocabulary and
Mathematical Glossary
 Several balloons
 Drinking straw and partially filled
glass of water
 For hair dryer demonstration: hair
dryer, piece of oak tag or light
cardboard, thumbtack, piece of

paper.
 For the airfoil demonstration:
electric fan, piece of Styrofoam
about 6” long and at least 1 ½”
thick, two 12” lengths of wire coat
hanger, 18” length of dowel about
¼” in diameter, glue.
ACTIVITIES
1. Demonstration #1
2. Demonstration #2

CALCULATOR SKILLS
Simple calculations using order of
operations.
EQUATIONS
1
p 1
 v12  gh1  2  v 22  gh2
1 2
2 2
p1
ADDITIONAL RESOURCES
See the related Engineering Topic on Bernoulli’s Principle.
www.engineerinyou.com
www.asee.org
www.asme.org/education/precollege
www.aiaa.org/education/index.hfm?edu=2
www.howstuffworks.com
www.algebra.com
http://connect.larc.nasa.gov/
www.engineergirl.org
www.eweek.org
Why Planes Fly
Using Bernoulli’s Equation to Understand Lift
TEACHER GUIDE
Lesson/Background:
The first concept introduced is the idea of pressure differentials (the results of a high
pressure and a low pressure acting upon a solid) and how they account for the lift of an
airplane. The Bernoulli equation is used to introduce this concept. Since the equation
can be solved using algebra, the students can see for themselves how pressure and
velocity are interrelated. Once the students understand this concept, they can learn why
an airfoil (wing) of a correct shape will create lift.
Through the lesson, you will perform various demonstrations to clarify the main
concepts. The visualization helps reinforce the understanding of the physical phenomena
that make flight possible.
Activities:
Procedure:
1. Provide motivation for the lesson plan by throwing a Frisbee or glider around the
room.
2. Ask students why they think planes are able to fly.
3. Remind students about the previous lessons on pressure.
4. Use the hair dryer experiment (demonstration #1) to reinforce Bernoulli’s equation.
5. Show the airfoil cutout or draw a copy on the chalkboard. Use the picture to explain
why air must travel faster on the top than on the bottom of the airfoil (wing), as a result
of the airfoil’s shape.
6. Do demonstration #2 and relate it to the preceding student problem. Ask students to
explain how the relatively faster velocity of the air above the airfoil affects the pressure
on the top and bottom of the airfoil. Ask how the power pressure on the top of the airfoil
affects the flight of the airplane.
7. Introduce the concept of thrust. Tell the students that thrust is what causes the plane
to move upward.
8. Blow up a balloon, but do not tie the end. Explain that the air pressure inside the
balloon is higher than the pressure outside. Release the balloon and watch it fly all over
the room. Point out that the air is under high pressure inside the balloon and as it escapes
through the nozzle it pushes the balloon forward. Relate this to the thrust of an airplane
engine.
Demonstration #1:
1. Cut the cardboard into a disk about 8” in diameter. Cut a round opening in the center
that will allow the disk to fit tightly around the nozzle of the hair dryer. (The cardboard
is used to create extra surface area and doesn’t affect the principles being demonstrated.)
2. Stick a thumbtack through the center of a piece of paper with the point facing up.
(The tack is used to keep the paper under the flow of the hair dryer and is otherwise
unrelated to the experiment.) Lay the paper on a desk. With the cardboard in place, turn
on the hair dryer and direct the flow of air straight down on the paper. The increase in
the velocity of air above the paper will cause a lower pressure on top of the paper than
on the bottom. The air flow should pull the piece of paper up onto the hair dryer rather
than blow it away. (NOTE: Experiment with this procedure before demonstrating it to
the class.)
Demonstration #2:
1. Cut out the airfoil pattern and place it on the edge of a piece of Styrofoam. The
Styrofoam should be thick enough to trace the pattern onto and about 4” to 6” long. If
your school has a science lab, ask the teacher in charge there to place the Styrofoam on
its end and cut it out for you on the band saw. Otherwise, use a serrated bread knife.
After cutting out the shape, sand the surface until it is smooth. (Making airfoils that will
fly is an excellent homework assignment for students – see Enrichment Activities.)
2. Take two 12” lengths of wire coat hangar and bend the end of each into a circle that
fits around a dowel stick (at least ¼” diameter). The dowel should be approximately 18”
long.
3. Dip the ends of the wire into glue and insert them into the edge of the wing to a depth
of 1”.
4. As shown in the illustration, insert the dowel into the two circles you formed in the
wires. (Tape a small wooden block onto the dowel so that the rear wire loop cannot be
blown back along the dowel when the fan is turned on.)
5. Hold the dowel in your hand so that it is horizontal and the airfoil is hanging down in
front of the fan and facing it head on. Have someone turn the fan on. The airfoil will
create lift from the flow of the oncoming air because of the pressure differential caused
by the airfoil’s shape. Once you have the airfoil lifted by the wind from the fan (that is,
when the wing is flying) and you tilt the dowel upward enough, the angle of attack will
become too steep and the wing will start dropping down because of the turbulence
formed on its top surface.
Additional Resources:
www.engineerinyou.com
An engineering degree can take you anywhere that you want to go!
www.asee.org
The “engineering resources” section of the American Society for Engineering
Education website offers information on engineering careers.
www.asme.org/education/precollege
ASME Pre-College education services include workshops, teaching materials and
partnership opportunities to help teachers and engineers to strengthen the math, science,
engineering, and technology skills of young people and to assist them in becoming more
aware of the role of engineering in their lives.
www.aiaa.org/education/index.hfm?edu=2
The American Institute of Aeronautics and Astronautics realizes that learning
starts with a teacher, a curious student, and fun in the classroom.
www.howstuffworks.com
Learn about how things work – from helicopters to computers and more.
www.algebra.com
Fun with algebra. Get help with your algebra homework online.
http://connect.larc.nasa.gov/
NASA Connect – the show that connects you to math, science, technology, and
NASA.
www.engineergirl.org
Turn imagination into reality with a future in engineering.
www.eweek.org
Learn about the new faces of engineering as we recognize the new generation of
engineers who are turning ideas into reality.
Why Planes Fly
Using Bernoulli’s Equation to Understand Lift
Student Worksheet
Vocabulary
Airfoil
A suitably curved sheet of material (such as a wing of an airplane) which, because of its
shape, creates lift when air flows over it.
Angle of attack
The angle at which an airfoil is moved forward into the air. Up to a point, the steeper the
angle of attack, the more lift is created. However, too steep an angle of attack will cause
the air on the upper surface to become turbulent, thus slowing it down instead of speeding
it up, thereby creating a cessation in lift, which will cause the aircraft to fall.
Drag
The resistance of the surface of the airplane fuselage to the forward motion of the aircraft.
Fuselage
The body of an airplane.
Pressure
The force of the air as it pushes on a surface. It is measured either in pascals or in pounds
per square inch.
Pressure differential
The difference between the pressures on opposite sides of an airfoil, which creates the lift
for the airfoil.
Thrust
The force that causes a forward motion in an aircraft; it may be provided by jet engines
or propellers.
Wind tunnel
A small tunnel designed for use in a laboratory in which a stream of air can be blown on
an airfoil. Because the tunnel is closed on its sides, the stream of air can be delivered
forcefully and without interference from drafts.
Mathematical Glossary:
Constant
A measured quantity that does not change, or that stays the same under particular
conditions. A constant is often entered in equations as a letter symbol for convenience.
The acceleration of gravity near the earth’s surface is a constant; it is always equal to
32.2 feet per second. Another very familiar constant is the number p (pi), which is the
ratio between the circumference and the diameter of a circle.
Cross multiplication
A method of simplifying an equation in order to solve it for a particular variable or
unknown, or in order to show it in a form having fewer fractions. If you multiply (or
divide) both sides of an equation by the same amount, the result will still be a correct
equation – that is, the two sides will still be equal. Suppose you know the formula
x w

y z
and you also know values for w, y, and z. If you multiply both sides by y, you will have

x  y
w
z
You can then find x by substituting the three known values. You can also express the
original equation without fractions, by multiplying both sides by y and then by z:

x w

y z
x  y

w
z
x z  y w
 multiplication was used to change the appearance of the
In each of these examples, cross
equation.

Equation
A statement written in numbers and symbols and having the two sides connected by an
equal sign. The equal sign tells you that the amount represented by all the numbers and
symbols on the left is the same as the amount represented by those on the right. For
example,
y = 2x + 3
is an equation that tells you how to find the value of y whenever you know the value of x.
Exponent
A small number placed to the right of and slightly above a number or a letter symbol to
show how many times the quantity should be multiplied by itself. Compare square.
Factor
A single quantity among a group of quantities which when multiplied together will form
a given product. The number 6 has the factors 2 and 3. In the expression
2x + 2y
the two terms 2x and 2y each have the factor 2. They are thus said to have a common
factor of 2.
Factoring
Separating a product into the different factors that it is composed of. This procedure is
very useful in solving equations for unknowns. You can factor the expression 2x + 2y to
get 2(x + y).
Ratio
A comparison of two numbers, expressed as the quotient you get by dividing the first by
the second. Ratios work the same way as fractions. The ratio of 8 to 2 (also written 8:2)
is the same as the ratio of 4 to 1, or simply 4.
Square
The product you get when you multiply any quantity by itself. Squares are indicated by
the exponent 2. For example,
42 = 4 x 4 = 16
and V2, where V = 60 meters per second (m/s), is
V x V = (60 m/s)2) = 3600 m2/s2
We read 22 as “two squared” and V2 as “V squared.”
Square Root
A number which when squared will give the desired number. Square roots are shown by
a “radical” sign. The square root of 16, is 4 and appears as follows:
16  4
The square root of any number x2 is x. The square root of 2 is not a whole number but is
approximately 1.414.

Actually, each of these has both a positive and a negative square root, as you will learn
later. Thus the square root of any number x2 is +x, and so the square root of 16 is +4.
Subscript
A small letter or number written or printed to the right of and slightly below a letter
symbol. Subscripts may be used, for instance, to identify different variables that are
similar enough to each other to have the same main letter.
Unknown
A quantity whose actual value is not known. An unknown, like a variable, is symbolized
in mathematics by a letter.
Variable
A measurable quantity (such as distance, speed, weight, or temperature) that does not
need to have a subscript
d = diameter of circle 1
d = diameter of circle 2