Water-Bottle Rockets: Design Brief
Several groups of engineers (including your group) have been asked by
NASA to develop a water-bottle rocket capable of reaching a launch
height of 200 - 300 ft. In addition, the following are desired outcomes:
 Groups should work cooperatively with each other.
 Groups must be able to accurately collect and organize data and perform
the calculations necessary to engineer this project.
 Groups should use creativity and problem-solving skills to design
solutions to given problems.
 Groups should be able to use simulation software to accurately predict
rocket flight prior to building their solutions.
 Groups should use graphs and tables along with collected data to
extrapolate and determine additional information.
Design Brief - Continued
Specifically, the job of the engineering groups is to design a rocket so that it flies
vertically a minimum of 200 ft high (61 meters) and lands at least within a 75 foot
radius. In addition, the rocket must be recoverable and reusable so that it can be used
for multiple flights. In order to do this there are several design specifications to
consider. For example:
 What is the maximum safe pressure by which to launch the rocket?
 Since water can also be used in the launching process, what is the optimum
amount of water by which to launch the rocket?
 What designs (i.e., fin, nosecone, body length) might need to be incorporated
in order to increase aerodynamics, decrease drag and increase flight height and
stability?
 What type of parachute or other device might be used to make the rocket
recoverable?
 To aid in the design and development of the rockets, this water-rocket design
presentation along with an online water-bottle rocket simulation
program have been provided.
 Finally, your group will be provided with experimental launch period during
which groups can launch their rockets and collect flight data on water volume
used, launch pressures, and rocket design and then optimize the different
variables to obtain a best flight.
Steps to Complete the Assignment:
1. Meet with your team and review the section is this presentation “Water
2.
3.
4.
5.
6.
Rocket Design Considerations”
Complete and submit the worksheet section at the end of this document.
Use the internet to do a search on water-bottle rockets. Research what others
have done and come up with some initial sketches for your rocket (at least
three different designs).
Choose one of your designs and build a prototype of a rocket.
Make a cardboard cutout of your rocket that shows the center of mass and
center of pressure.
Given the dimensions for your rocket, use one of the following simulation
programs to conduct an analysis of how high your rocket should be able to fly.
http://www.et.byu.edu/~wheeler/benchtop/sim.php
2. http://www.grc.nasa.gov/WWW/K-12/rocket/rktsim.html
1.
Steps to Complete the Assignment
(continued)
7. As part of this analysis make a graph on MS Excel to plot rocket flight
height against some independent variable that you can manipulate.
8. During the experimental launch period collect data on your rocket
flights. Note: you must have at least four lines of data to turn in.
9. Turn in your Launch Portfolio
 Water Rocket Worksheet
 Initial design sketches
 Cardboard Cutout (silhouette) showing the Center of Mass and
Center of Pressure
 Graphed from simulation
 Data from experimental launch / best launch
 Rocket (or what’s left of it)
Sample of Graphed Data
Sample Sketches
Water-Bottle Rocket Grade Form: Evaluation
Worksheet
Sketches
Silhouette (cardboard cutout with CM & CP)
Graphed Data (from simulation)
Experimental Launch Sheet (Data for all launches)
Launch Accuracy
Launch Height
Points for Launch
> 9.0 s = 110 pts
8.7s – 9.0s = 100 pts
8.5s – 8.69s = 95 pts
8s – 8.49s=90 pts
7.5s – 7.99s = 85 pts
7s – 7.49s = 80pts
< 7s = 75 pts
Possible
Received
40 points
10 points
20 points
20 points
30 points
30 points
100 points
________
________
________
________
________
________
________
Accuracy
25ft radius = 30 pts
50ft radius = 26 pts
75 ft radius = 22 pts
Exceeds 75 ft radius= 20pts
Closest = 5 bonus points
Legend
7s = 60m=197ft
7.5s = 69m = 226 ft
8.0s = 78m = 257ft
8.5s = 89m = 290ft
9.0s = 99m = 326ft
9.25s = 105m = 344 ft
9.5s = 111m = 363 ft
9.75s = 116m = 382 ft
10s = 123m = 400ft
Equipment
 Launcher
 High Volume Pump - an air compressor or scuba tank
might also be used.
 A graduated beaker - To measure fluid added to the
rocket
 Scientific Calculator
 Altitude Guns - Can also use a protractor with a string
and weight.
 Scales - To determine the mass of the rockets
 Stopwatch
Basic Supplies
 Assortment of 2-liter bottles
 Foam board - for fins
 Oak Tag Board - Poster Board (If a paper type nose cone is made)
 PL Premium Construction Adhesive - Best adhesive for attaching fins
 Caulk gun
 Modeling clay - excellent for adding weight to the rocket
 Hot Glue Gun (Do not use for the fins)
 X-acto Knives / Cutting boards
 Plastic and String (If students decide to use a parachute design)
 Duct Tape - just in case
 To help in the design, students are encouraged to bring in many
assorted items from home (Paper Tubes, tennis balls, Nerf balls,
racquet balls).
Experimental Launch Data Sheet
Before Simulation
T eam or
Person
Dry
Mass of
Rocket
(grams)
Freddie Mercury
245
Fluid
Percentage
Height
added to T otal (%) of water Launch
T otal
from
the
Mass of mass to total Pressure T ime in
Chart
rocket
Rocket
mass of
(psi)
Air
(meters)
(in ml)
rocket
700
945
Actual Launch Data and Calculations
Height Formulas
Average Angle Formula
Littlewood's
Simulation
Angle
#1
(Deg)
Angle #2
(Deg)
58
62
700/945 = 74% 95 psi
Best Launch
Enter Data From Simulation Results Enter Data Collected From Launches
Average Calculate T otal Height
Angle d Height T ime in
in
(Deg)
(feet)
Air
Meters
60.0
260
7.96
78
Height
in Feet
Distance
From
Launch Pad
255
22ft
These slides are provided to help in the design of
your water-bottle rocket. Complete this
presentation and answer the questions at the
end BEFORE designing and building your rocket
Newton’s First Law: Objects at rest will stay at rest, or objects in
motion will stay in motion unless acted upon by an unbalanced force.
When the rocket is sitting on the launcher, the forces are balanced because the
surface of the launcher is pushing up the rocket up while gravity pulls it down.
Newton’s Third Law: For every action there is always an
opposite and equal reaction (if you push something it pushes back).
When we pressurize the fluid inside the rocket and release the locking
clamps the forces become unbalanced. A small opening in the bottom
of the rocket will allow fluid to escape in one direction and in doing so
provides thrust (force) in the opposite direction allowing the rocket to
propel skyward.
Up
Bottle and Remaining
Water Mass
Down
Ejected Water Mass
This force continues until the pressure forces the last of the fluid to
leave the rocket.
Newton’s Second Law: The acceleration of an object is directly related
to the force exerted on the object and inversely related to the mass of that
object.
• If the thrust continues until all the water is expelled then more water
(mass) should be better right?? Not necessarily!!!
• Acceleration= Force / Mass
• For example: If you use the same amount of force, you can throw a baseball
faster that a basketball because the baseball has less mass.
Smaller Mass (water)
Larger Mass (water)
Larger Acceleration
Smaller Acceleration
Shorter Duration of Thrust Longer Duration of Thrust
• Note: The thrust of the rocket is due to the pressure of the fluid and
the acceleration of the fluid as it leaves the bottle.
Aerodynamics: Drag
 As a rocket moves through the air, friction between the
rocket surface and the air (air drag) will slow it down. At
the high velocities these rockets achieve, air drag becomes
a very significant force.
 To reduce air drag, the rocket should be designed so that air
passing over the surfaces of the rocket flows in smooth
lines (streamlining) thus reducing eddy currents and thus
drag.
Eddy
Currents
Airflow
Aerodynamics: Nosecone
High Drag
Low Drag
Popular Nose Cone
Configurations
A Nerf or tennis ball helps
add mass to the nosecone (CM)
and helps keep the rocket from
being destroyed when it lands
Aerodynamics: Drag
(Continued)
 It turns out that the drag is more effected by the tail
shape than it is by the nosecone shape. For a
particular soda bottle it is hard to change the shape of
the tail, however. The shape of 2L bottles is pretty
standardized, but for smaller bottles there are more
choices. A quick trip to the grocery store shows there
are some so-called "designer" water bottles with quite
aerodynamic shapes (Dean Wheeler).
Stability of Rocket Flight: Center of
Mass and Center of Pressure
• Clip from October Sky:
• http://www.youtube.com/watch?v=cP_OM5VVcSo
• If you launch a plain 2-liter bottle it will quickly lose
stability and turn end-over-end as soon as the water is
expelled, leading to greatly increased air drag.
• In order for your rocket to reach heights of 200-300
feet, the rocket must be aerodynamically stable during
flight.
• To increase the stability of the rocket you need to
understand the principles of Center of Mass and
Center of Pressure
Center of Mass (CM)
 The CM of the rocket is easy
to find: it is the point at
which the rocket balances. If
you were to tie a string
around the rocket at its CM,
it would balance from the
string horizontally.
Center of Pressure (CP)
 The CP is more difficult to determine. The CP exists only
when air is flowing past the moving rocket. The CP is defined
as the point along the rocket where, if you were to attach a
pivot and then hold the rocket crossways into the wind by that
pivot, the wind forces on either side of the CP are equal.
 This principle is similar to that of a weather vane. When wind
blows on a weathervane the arrow points into the wind
because the tail of the weathervane has a surface area much
greater than the arrowhead. The flowing air imparts a greater
force on the tail and therefore the tail is pushed away.
Relationship of CM to CP
 In order for a rocket to fly in a stable fashion the center
of mass (CM) of the rocket must be forward of the
center of pressure (CP).
Center of Mass =
Center of Pressure =
Stable Rocket
Unstable Rocket
Stability: Moving the CM Forward
 Adding weight to the nose cone section will help move the
CM toward the nose of the rocket. Experiment with your
rocket by adding amounts of modeling clay to the
nosecone section of the rocket and then launching it to
check stability and height.
 Tradeoff: Be careful not to add too much mass as this will
decrease acceleration (Acceleration= Force / Mass).
 Diminishing returns
Center of Mass =
Stability and adding mass
 There is another reason to add mass (in addition to
stability) and that is to add momentum that allows the
rocket to overcome air drag during the flight. As an
example, if you throw a golf ball and a table-tennis ball
at the same time, the golf ball will go much further
because its greater mass allows it to resist air drag to a
greater degree than the table-tennis ball.
Stability: Moving the CP to the Back
 Adding fins to a rocket increases the surface area of the tail section. The wind
forces will thus increase in the tail section which in turn will move the CP
toward the fins. In fact, that is the main function of fins. The larger the fins,
the further back the CP will be.
 Tradeoff: larger fins move the CP back but they also add mass to your rocket
 In addition, The fins add surface area to the rocket, which increases the "skin
friction" on the rocket. Once stability is reached, continuing to add fin area
will actually increase overall drag on the rocket.
 Diminishing returns
Center of Pressure =
Rocket Fins and Center of Pressure
 Rounded edges on a fin produce less drag than square edges
 Check large swept fins to insure they can be mounted on the
launcher.
 You might also “feather” your fins so that they can easily slice
through the air (less drag)
 3 fins vs 4 fins
 Popular fin configurations
• One method of approximating the CP of a rocket is to
make a cardboard cutout shaped like the silhouette of
the rocket, and then find the balance point of the
cutout. This point provides an approximation of the
CP of the rocket.
Sample Silhouettes with CM and CP marked
Stability: Length of Rocket
• Typically, the longer the rocket, the more stable the
rocket’s flight will be.
• Tradeoff: The longer the rocket, typically the more massive
the rocket will be. This means that you need to increase the
thrust to compensate for the extra mass.
Less Stable
Less Mass
More Stable
More Mass
• Essentially, you need to minimize the rockets mass without
compromising stability.
Fill Ratio of Water in Rocket
 A rocket with water will fly much higher than a rocket filled only
with air.
 When water is added to the rocket, the effect of mass is
demonstrated. As the pressurized air leaves the rocket the water is
expelled which results in thrust. Because water has a much
greater mass than air, it contributes to a much greater thrust
(Newton’s 2nd Law).
 The thrust of the rocket is dependent on the mass being expelled
and the speed of expulsion.
 The best way to determine the fill ratio is to launch 4-5 test flights
using differing amounts of fluid and graph the height of rocket
flight for each.
400 ml
800 ml
1200 ml
Pressure of Fluid
 A high pressure bicycle pump or air compressor can be used to
pressurize the air inside the rocket and thus increase the thrust
available to the rocket for lift off.
 The rocket launchers you will use for this activity have been regulated
to a maximum launch pressure of 100 psi (constraint).
 Tradeoffs: The higher the pressure the greater the initial thrust.
However, high thrust also means an increase in drag forces. Does your
rocket have sufficient aerodynamics to minimize this increase in drag
forces??? Rockets with poor aerodynamics have been ripped apart at
launch because of high drag forces
To get your water bottle rockets to fly to great
heights you will need to evaluate trade-offs
• Minimize the rocket’s mass while maximizing the amount of
•
•
•
•
force.
Be careful when minimizing the rocket’s mass. If the rocket is
too light it will lose stability as soon as the water is expelled
and turn end over end.
The greater the mass of the fluid expelled from the rocket, and
the faster the fluid can be expelled from the rocket, the greater
the thrust (force) of the rocket.
Increasing the pressure inside the bottle rocket produces
greater thrust. This is because a greater mass of air inside the
bottle escapes with a higher acceleration.
Energy is stored in pressurized air. So even though you need
to have water (mass) to eject to get thrust if you have too much
water and not enough energy (pressurized air) you won’t get a
good thrust
Height Calculations
• There are many ways to calculate the height of the water
bottle rockets in this class.
• The first method would be to use right-angle trigonometry.
However, in order to use this method the rockets would
need to always travel straight in the air (90° to the earth)
and as you will soon learn, this isn’t always the case.
• Another way would be to use the trigonometric method
know as the Law of Sines.
• A third method that is easy to use and provides a close
approximation to the height of the rocket flight is known
as the average angle method. Since the average angle
method is the easiest and most commonly used, it will be
the first method we will use for this activity.
Average Angle Method
Note: This method makes an approximation of rocket height rather than an exact calculation.
However, considering human error and the crude measuring instruments used in this activity,
this method is fairly accurate in calculating rocket height.
Step #1:Measure two locations 150 feet on either side of and in a direct line with
the launch pad. Place a person at each of these locations with an altitude gun
(see figure).
Step #2: Assume that your team has launched a rocket and Person A measures
45° and Person B measures 30° (See figure).
Step #3: Use the average angle formula to calculate the height of the rocket.
Average Angle formula: a = b(tan A)
a= height of rocket flight
b= distance from the launch pad (150 feet)
A = the average of the two angles
Practice Example:
• (Given Angle 1 = 45°, and Angle 2 = 30°, A= 37.5°)
• Using the formula a = 150 (tan 37.5), the height of this
rocket flight would be 115 feet (a = 115 ft).
Calculation Helps:
• Make sure your calculator is in degrees mode and not
in radians mode!!!!!!!
• On most calculators you will need to
• 1) Enter in the average angle (in this case 37.5),
• 2) Hit the tangent button, and then
• 3) Multiply this value by 150.
Littlewood’s Law: Calculating Rocket Height
• J.E. Littlewood a British Mathematician who performed
calculations for the British military during World War 1
developed a formula for ballistic flights.
• Note: In order for a flight to be considered ballistic the rocket
cannot use a parachute or have the ability to change it’s
coefficient of drag during the flight.
• Because the water and pressurized air used to launch our rockets
is usually expelled about 0.15 seconds into the flight our rocket
launches can be considered largely ballistic.
• Using the following formula, Littlewood calculated the heights
of ballistic launches: hap = g/8 (tend)2
where:
hap = height at apogee
g = gravity = 9.8 m/sec2
tend = total flight time
Note: This information has been adapted from Dr. Dean Wheeler’s
website: www.et.byu.edu/~wheeler/benchtop/flight.php
Littlewoods Law: Sample Problem
 Assume that the time for rocket flight was 7.96
seconds (tend = 7.96 seconds).
 Using Littlewood’s formula we calculate a height
of:
hap = 9.8/8 (7.96)2 = 77.6 meters
Questions:
1.
2.
(Newton’s 1st law) How long does the thrust force last
when a rocket is launched?
(Newton’s 2nd Law) If you want to increase the
acceleration of your rocket you need to: (Choose one
of the following statements)
(A)Decrease the thrust force and increase the mass of
the rocket.
(B)Decrease the thrust force and decrease the mass of
the rocket.
(C)Increase the thrust force and decrease the mass of
the rocket.
(D) Increase the thrust force and increase the mass of
the rocket.
3.
Describe how can you determine where the
center of mass (CM) is on your rocket?
4.
Describe how can you determine the center of
pressure (CP) for your rocket?
5. If you want your rocket to have stable flight which of the
following is true? (Choose one)
(A)
The center of mass (CM) and the center of pressure
(CP) should be at the same point on the rocket.
(B) The center of mass (CM) should be towards the tail of the
rocket and the center of pressure (CP) should towards the
nose of the rocket.
(C) The center of mass (CM) should be towards the nose of
the
rocket and the center of pressure (CP) should towards
the
tail of the rocket.
6.
What modification(s) can you make to your rocket to
change the position of the center of mass (CM)?
7.
What modification(s) can you make to your rocket to
change the position of the center of pressure (CP)
8.
True or False: A longer rocket is typically
more stable in flight than a short rocket?
9.
Why does a rocket with water fly higher than
a rocket with no water? (Be Specific!)
10.
What is air drag?
11.
List three things you can do to your rocket to
decrease the air drag.
1.
2.
3.
12.
What is the purpose of fins on a rocket?
13.
1)
2)
List two purposes of a nose cone on a rocket?
14.When you launch your rocket, two persons from
your group will use altimeter guns to measure the
angle of the rocket flight and thus determine the
flight height.
If these persons measured angles of 55° and 49°
respectively, use the average angle formula to
determine the height of the rocket flight. Assume
that each of the persons are 150 feet from the
launch site.
Formula: Height = 150 (Tan A)
Note: A= average of the two angles
Height of rocket flight =
Ft
15. If you launched a second rocket and these persons measured angles
of 55°and 61° respectively, what is the height of the rocket flight?
Height =
16. Rocket Height Problem using Littlewood’s Law
If you launched a rocket and the total flight time (tend) = 9.23 seconds,
how high (hap) did your rocket fly?
hap= ___________ meters
hap= ___________ feet
17. Using Littlewood’s Law, how many seconds would the total flight
time (tend) of your rocket need to be to have a flight height (hap) of
300 ft ? (Don’t forget ft to m conversion!)
Time: ____________