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Engineering Education
for today’s classroom.
Rocketry: Achieving Liftoff
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Engineering Education
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Outline
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Forces on a Rocket
Newton’s 1st and 2nd Laws of Motion
Newton’s 3rd Law
Combustion and Chemical Rockets
Understanding Rocket Trajectories
The Acceleration Phase
The Descent Phase
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1.1 Forces on a Rocket
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Did you Know?
In order to reach orbit,
NASA’s space shuttle must
attain a speed of 7,847
meters per second (about
17,500 miles per hour).
How do rocket engines
launch objects into space?
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Forces
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Rocket engines are
able to move rockets at
high speed because
they apply a large
amount of force to the
rocket.
Forces are quantities
known as vectors
because they have
both a magnitude and a
direction.
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Vectors are often drawn as arrows whose
lengths indicate the magnitudes of the
forces.
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Forces on Rockets
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Thrust is the force created by the combustion of fuel that
propels the rocket upward.
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Drag is a force that results from the rocket pushing on
the surrounding molecules of air. Drag is friction that acts
in the direction opposite the motion of the rocket.
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Weight is caused by gravity and pulls the rocket toward
the ground.
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Mass and Weight
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Mass and weight are not one and the same. Mass
measures the amount of matter in an object and does not
vary from place to place. Weight measures the force of
gravity on an object and varies depending on the strength
of the gravity.
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Weight can be represented as W = mg, where m is the
mass of the object, and g is the acceleration due to
gravity.
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Powered Ascent
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There are three main phases of
rocket flight for rockets that do not
enter orbit—powered ascent,
coasting ascent, and descent.
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Powered ascent occurs while the
engine is producing thrust.
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During powered ascent, T > W + D.
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Coasting Ascent
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Coasting ascent happens after the
engine has stopped producing
thrust.
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During this phase, drag is very
small compared to weight, so the
force acting on the rocket is
roughly equal to the weight.
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The force of the weight causes the
rocket to decelerate until its
velocity reaches zero.
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T=0
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Descent
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Descent occurs after the velocity of
the rocket reaches zero, at which
point the rocket begins to
accelerate toward the ground.
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Most rockets have a parachute or
other recovery system to increase
drag until it balances the weight.
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Increased drag slows the rocket
down during descent.
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Rocket Components
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A rocket consists of the rocket body,
the payload, the recovery system, and
the engine, which includes the fuel.
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The engine provides thrust and the
recovery system increases drag.
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The payloads of real rockets can
include satellites, equipment, or
people.
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Example 1
The mass of a model rocket body, payload, and recovery
system is 34.0 g. The mass of the engine is 16.0 g. What is the
weight of the rocket?
First, we have to find the total mass of the rocket.
m = 34.0 g+16.0 g = 50.0 g
Next, we should convert the mass to kilograms, so that our solution for
weight works out to be newtons.
m = 50.0 g×
1kg
= 0.05 kg
1,000 g
Finally, we multiply the acceleration due to gravity (g) by mass to get weight.
W = 0.05 kg×9.81m / s2 = 0.491kg×m / s2 = 0.491N
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1.2 Newton’s 1st and 2nd
Laws
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Newton’s 1st Law & Inertia
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Newton’s first law of motion states that an
object’s speed and direction of motion will
remain unchanged unless an outside force
acts on the object.
The tendency to resist changes in motion is a
property of matter called inertia.
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Newton’s 2nd Law & Acceleration
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When a net force acts on an
object and causes it to
change its speed or its
direction of motion, the
object is said to be
accelerated.
Newton’s 2nd law of motion
states that to accelerate an
object, we need to apply a
force to the object.
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Fnet = ma
Fnet = net force
m = mass
a = acceleration
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Calculating Acceleration
Acceleration is the
change in speed of
an object per unit of
time, or the rate of
change of an
object’s speed.
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change in speed v1 - v 0
a=
=
time
t1 - t0
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Newton’s 2nd Law
For any two objects with the same net force, Fnet,
Newton’s 2nd Law requires that a1 m2 .
=
a2 m1
In other words, if you apply the same net force to two
objects, and one of the objects has twice the mass of
the other, the more massive object will accelerate
only half as quickly as the less massive object.
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Exercise 1.3: Mass, Force, and Acceleration
Suppose you are performing acceleration experiments on two objects that
have equal mass—a pillow and a shoe.
If you accelerate the shoe twice as quickly as the pillow, how much more force do
you need to apply to the shoe?
SOLUTION
Newton’s 2nd law of motion states that if the masses of two objects are the same,
then the rate at which each object is accelerated is proportional to the net force. If
the shoe is accelerated twice as quickly as the pillow, then the net force on the shoe
is twice as large.
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Rocket Motion
According to Newton’s 2nd law, accelerating a rocket upward, or in a
positive direction, requires a net upward force. The net forces acting on
the rocket throughout its three phases of flight are as follows:
Launch and Powered Ascent: Fnet = T - W
Coasting Ascent:
Fnet = - W
Descent: Fnet = D - W
*Notice that we always subtract W because it is always acting downward,
or in a negative direction. Also, it is assumed that D  0 during ascent.
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Example 4
If a rocket has a mass of 50 g and the engine produces a thrust of 8 N
at launch, what will be the initial acceleration of the rocket?
Step 1: Solve for
a by dividing
both sides by m
Step 2: Find
value of W
Fnet
Fnet ma
a
=
=
= a; therefore,
m
m
m
 1kg 
2
W = mg = 50 g× 
 ×9.81m / s
 1,000 g 
= 0.491kg× m / s2 = 0.491N
Step 3: Plug in
numbers to find Fnet
Fnet =T -W = 8.0N- 0.491N = 7.51N
Step 4: Simplify and
convert to SI units
Fnet 7.51N 7.51kg×m / s2 7.51kg× m / s2
a=
=
=
=
=150.2 m / s2
1kg
m
50 g
0.05 kg
50 g×
1,000 g
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Engineering Education
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Activity 1.6: Testing Newton’s 2nd Law with a Rocket Car
Objective:
You will conduct several trials to determine the effect of mass
on the time it takes your rocket car to travel a certain distance.
In each trial, the net force applied to the car should be
approximately the same.
Analysis:
The travel time increases as mass is added to the car.
According to Newton’s 2nd law of motion, the more massive
an object is, the more net force is required to accelerate it at a
given rate.
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2.1 Newton’s 3rd Law
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Rocket Power
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How do rocket engines propel aircraft?
Or launch missiles from beneath the sea?
Or launch spacecraft into orbit?
Like all propulsion systems, rocket engines
generate thrust.
Thrust can be generated according to Newton’s
3rd law of motion.
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Engineering Education
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Newton’s 3rd Law
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Any force is always
accompanied by a
force of equal
magnitude that acts in
the opposite direction
In other words, the
“action-reaction”
principle
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If you were standing on a skateboard and
threw a ball, the ball would move forward
and you would move backward.
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Conservation of
Momentum
The final momentum
of the system equals
the initial momentum
of the system, so
the momentum of
the system is
conserved.
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momentum = mass x velocity
MV = -mv
MV
= momentum of person
mv
= momentum of the ball
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Putting it All Together
• Rocket engines and a person throwing a ball
while standing on a skateboard generate thrust
in a similar way.
• In rockets, the engine creates thrust by forcing
propellant away from the rocket at high speed.
• This causes a reaction force (thrust) that pushes
the rocket in the opposite direction.
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Activity 2.4
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Build a slingshot “car” that will demonstrate Newton’s 3rd law of
motion.
Explain how Newton’s 3rd law relates to the behavior of your
slingshot car. How are the number of rubber bands and the amount
of weight in the film canister related to the distance traveled by the
car?
Answer: Even though the mass in the canister and the number of
rubber bands varied, the action of launching the canister always
occurred with the equal reaction of moving the car. When more
rubber bands were added, the thrust force of the slingshot increased.
When more mass was added to the film canister, the same amount
of thrust would move the car farther.
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2.2 Combustion and
Chemical Rockets
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Combustion
How does a rocket
engine move the
propellant away from
the rocket at a high
velocity?
Answer: A chemical
reaction known as
combustion
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Fuel + Oxidizer → Products + Energy
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Did you Know?
The Saturn V rocket
that launched the
Apollo missions to
the moon used liquid
oxygen (LOX) as an
oxidizer and a form
of kerosene for fuel.
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Energy for Propulsion
This figure illustrates the
results of burning paper
in a box. In the case of a
rocket engine,
combustion of
the fuel and the oxidizer
results in an extremely
high gas pressure in the
combustion chamber.
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A Rocket Engine
In real rocket engines, the “box” where combustion
takes place is called the combustion chamber.
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A Model Rocket Engine
Model rocket engines (also called “motors”) are chemical
rockets that use black powder as a propellant.
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Engineering Education
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Activity 2.6
Objective
Discover how Newton’s laws of motion determine the performance of
a chemical rocket.
Materials
several sheets of construction paper, clear tape, scissors, paper
towels, several effervescing antacid tablets, water, plastic 35 mm film
canister, safety goggles, lab apron, paper towels for cleanup
Procedure
Record any observations you have on the performance of your
rocket. Include an estimate of how high your rocket flew.
Repeat the experiment several times, each time changing one of the
parameters of your rocket.
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3.1 Understanding Rocket
Trajectories
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Three Phases
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The path that a
rocket takes while in
flight is called a
trajectory.
If the rocket doesn’t
go into orbit, it
completes three
phases.
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1. Powered ascent
2. Coasting ascent
3. Descent
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Graph of a Rocket Trajectory
h
H
tb
t
Powered Ascent
Coasting Ascent
In a graph of
height vs. time,
constant
acceleration is
shown as a
curved path
called a parabola
and constant
velocity is shown
as a straight line.
Descent
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3.2 The Acceleration
Phase
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Predicting How Fast
and How High
Maximum Velocity
Vb 
I
 gtb
M avg
Vb = velocity at burnout
I = impulse
Mavg = average rocket mass
g = acceleration caused by gravity
tb = engine burn time
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Maximum Height
1  I
H
2 g  M avg




2
H = maximum height
g = acceleration caused by gravity
I = impulse
Mavg = average rocket mass
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Putting it All Together
The key factors that determine the maximum
height and speed of a rocket are the engine
impulse, the average mass of the rocket, and
the engine burn time. Higher altitudes can be
achieved by increasing the rocket’s impulse,
by decreasing the burn time, or by decreasing
the rocket’s average mass.
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3.3 The Descent Phase
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Importance of Drag
Unless a large drag is
present during the
descent phase, the
rocket will fall at a high
rate of speed and crash
into the ground.
Parachutes and other
types of recovery
systems increase drag.
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Drag Force
1
D  C D dAVD2
2
D = drag force
CD = drag coefficient
d = density of air
A = area of recovery system
VD = descent speed
Objects like race cars and
airplanes have low drag
coefficients.
CD for a parachute = 1.4
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Drag and a Parachute’s Radius
For a parachute, A is
the area seen
when looking
straight up.
We can calculate area
using A=πr2
The drag developed
by the recovery
system is
determined by the
shape of the
recovery system
(CD), its size (A),
and the descent
speed of the entire
system.
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Example 1
After an Alpha III rocket with a B6-4 engine reaches a maximum
altitude of 378 m at burnout, its parachute, with a diameter of 0.305
m, is deployed. The mass of the rocket, including its engine, is 53.1
g, and the mass of the propellant is 5.6 g. Assuming that the drag
coefficient is 1.4 and the density of air is 1.20 kg/m3, how long will it
take the rocket to reach the ground after the parachute is deployed?
Solution: First, calculate area of the parachute. Next, calculate the
velocity, and finally, solve for the descent time. td = 2 min 15 sec
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