Transcript 2. - the School District of Palm Beach County

1
Revised 07/10/06
What is the mission? The mission is to design a Water Rocket
Vehicle capable of accurately targeting a specified bullseye.
While promoting Space Propulsion Awareness, the Water Bottle
Rocket Competition serves to familiarize students with the basic
principles of rocketry, design engineering, manufacturing
engineering, and presentation skills.
Students will design and manufacture a water rocket using a 2-Liter
bottle as the pressure vessel. The rocket must be capable of
accurately targeting a specified bullseye launching from the UTC
Rocket Launcher. The design must be supported by technical
documentation and presentation outlining all mathematical and
scientific principles used. Additionally, each team will develop a
patch design, used to symbolically commemorate the objectives of
each team. The team’s complete success will not solely be judged on
rocket performance, but the combined effort of the team.
...……………………………......GOOD LUCK and Safe Flying !!
*** Remember you will never be a winner unless you try and if
you try your best, you have already made it to the bullseye :-) ***
(Refer to Rules & Guidelines and “How to Build Rockets” manual for detailed information.)
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Rules and Guidelines
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Keys for Safe & Enjoyable Launch Activities:
•Extreme caution should be used at ALL times during launch
activity.
•The Water Rocket Launcher and Water Rockets are NOT toys;
thorough understanding of their function is required prior to
conducting ANY launch activities.
•Safety Goggles/Glasses shall be worn during all launch
activities.
•NEVER stand directly in front of launcher at ANY time.
•NEVER approach a rocket that is under pressure.
•No running, horseplay, etc. around launch area/ during launch
activities. Be attentive at ALL times.
•Use Only single CLEAR 2L bottles for rocket pressure vessel
(Bottles should be in good condition without kinks, cracks or
dents).
•Always use a CLEAR audible countdown (5!... 4!... 3!... 2!... 1!)
before EACH launch.
•All Rockets should be thoroughly inspected prior to launch.
•Do NOT over-pressurize rockets 80psi MAX.
•Use ONLY Large open fields for Launch…..250m or MORE of
down range distance is preferred.
•Rope-off or clearly mark Launch Area/Field.
•Always conduct a trial launch at low air pressure (e.g. 35-40psi)
to get an idea of how far your rockets will travel with respect to a
given launch area.
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1. Maximum number of 6 students and a minimum of 4 students per team are allowed.
2. Each team is required to submit a completed technical paper, rocket design,
technical drawing and patch design to qualify for the awards. Note: Awards will be
presented at the annual FACTRAC banquet.
3. On the day of competition, (but prior to launch) an actual operating rocket with its
launching requirements [1. volume of water in milliliters and liters, 2. air pressure in
psi (min 30 psi & max 80 psi), 3. Dry Weight in grams, and 4. Nozzel Exit Radius in
inches, and 5. Calculated Final Range in meters and feet], corresponding technical
drawing, and patch design must be submitted in order to compete in the
competition.(Ref. Required note card detailed in Technical Drawing Section, page 12)
Note:
1) At this time each entry must pass a visual inspection and weight requirement
in order to be eligible to compete. Entries that fail inspection will be given ONE
opportunity to make modifications to pass inspection, prior to the beginning of
the water rocket launching competition.
2) Technical paper must be submitted on _____________________________
4. An overall winner will be judged upon the following criteria detailed on page 17.
5. The objective of the contest is for each team to construct a rocket propelled by
water and air which will be launched at a 45 degree angle to hit a target that will be
positioned 61 meters away (distance from HP Rocket Launcher to red bull’s eye;
~200ft), in the target area zone, see Diagram 1a. The target area zone is a 45 degree
zone (25 degrees from each side of the target area centerline) if your rocket lands
outside of this zone 50 points will be deducted from the accuracy of trajectory score,
see Diagram 1b.
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NOTE: Launch accuracy will be scored using the distance and angle from the target
the rockets hits in the target area. The scoring equations is as follows:
1875 *
1 + 1
r+30 C+50
Where r = radial distance of rocket from target
C = distance of rocket centerline to
launch target area centerline
(see Example below)
Example:
Lets imagine five rockets, Rocket A, Rocket B, Rocket D, Rocket E and Rocket F,
have launched and this is where they landed ( see Diagram 1b). Rocket D wins
First Place for the accuracy of trajectory. Who wins Second Place? Third Place?
If rB= rA, Rocket B would win second place for this scenario, as it is closer to the
trajectory path. This is because the trajectory path deviation factor “C” . C A is
greater than CB, therefore Rocket B wins Second Place in lieu of rB= rA. and Rocket A
wins Third Place for accuracy of trajectory , for this scenario. Also Rocket E and
Rocket F will have a 50 point deduction for landing outside the target area zone.
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Diagram 1a
HP Rocket Launcher
Launch Command
Launch Controller
Launch Operator
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GENERAL AUDIENCE
** Note: Field markings in FEET.
Diagram 1b
Scoring Example Scenario
F
r
A
D
CA
B
CB
E
Launch Target
Centerline
Target Area
Zone
HP Rocket Launcher
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1. The pressure vessel must be ONE clear 2 liter bottle, see Diagram 2.
2. Water and air pressure will be the sole source of propellant. Before launching
rocket, water volume (liters) and air pressure (psi) must be given.
NOTE: The air pressure minimum is 30 psi and maximum is 80 psi.
3. Do not use metal, glass, or spikes to construct the rocket. *Use of these
materials will automatically disqualify the team from the competition.*
4. On the bottom of the rocket, leave 7.5 cm from the throat of the exit plane clear of
any coverings (paint, markings, drawings, etc.), see Diagram 2.
5. Maximum total height of rocket is 76.0 cm, see Diagram 2.
6. Nose-cone tip must have a minimum radius of 1.5 cm, see Diagram 3.
7. No forward swept type of fins are allowed to be used on the rocket.
8. The maximum fin width distance from the bottle is 10.0 cm
(or 16.5 cm from center of bottle axis).
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Diagram 2
Rocket Identification
Nose Cone
Bottle Height
(max. 76.0 cm)
Pressure Vessel
(Clear 2 Liter Bottle)
Fin
Rocket Clear of Any
Coverings (min. 7.5 cm)
Fin
Bottle Throat
Throat
Exit Plane
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Diagram 3
Nose Cone Diagram
Min Cone Radius = 1.5 cm
Cone Tip
R
Diagram 4
Fin Diagram
max 16.5 cm
max 10.0 cm
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As part of the competition, the team is required to prepare a scaled drawing depicting the
rocket that they have designed and built.
1. The Water Rocket Drawing entry is required to illustrate the actual rocket built by the
team (photographs will NOT be allowed).
2. The size of the engineering paper is required to be the standard 18” X 24”
(Allowing for the 1” margin, the actual drawing is to cover an exposed area of
16” X 22” of the paper).
NO MOUNTING, NO FRAMES ALLOWED
3. All dimensions are required to be illustrated on the drawing.
4. The scale and the units are required to be indicated on the drawing.
5. The team’s Water Rocket Drawing is required to show a side and top (or bottom) view.
6. All parts of the rocket are required to be named.
7. A 4” X 5” title card with the following information is required:
 Team name and number
 Team members’ names and discipline
 Rocket Name (if applicable)
 Launch Requirements & Specs (Air Pressure (psi), Water Volume (mL
and L) Dry Weight (grams) and Calculated Final Range (m and ft)
 Picture of Rocket
 Date
AT COMPETITIONS, THE WATER ROCKET DRAWING WILL BE JUDGED ON:
RESEMBLANCE (Between the actual rocket and the drawing)
SCALE
NAMING/LABELING (Of all the parts used)
APPEARANCE/NEATNESS
25
25
25
25
100
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What is a “Patch”?
It is a creative display that reflects the dedication and mission of the team.
This symbolic picture must comply with the following rules:






Each entry is to be prepared and submitted by the teams who will be participating in the
Water Rocket Design Competition.
Patch designs must be submitted on 8.5”x11” paper.
All entries must contain the team name as well as a detailed explanation of the patch design
All teams participating in the Water Rocket Competition must be prepared to display their
patch at the Mini-Design Review.
Patches must be hand-made original work.
Ink pens, pencils, markers or paint may be used.
AT THE COMPETITION, THE PATCH DESIGN WILL BE JUDGED ON:
•
•
•
•
ORIGINALITY - Innovativeness of the design.
CREATIVITY - Uniqueness of the information depicted
APPEARANCE - The attractiveness and neatness of the presentation
CONTENT - Design representation of the Team’s name and SECME theme
30
30
20
20
100
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“Here is an Example...”
Explanation of Patch
The propelled rocket represents the school system, supported by the educators and students,
following a path towards excellence. The radiant five 4-point stars symbolize the five
colleges of Tuskegee University. Where as, the seven 8-point stars represent for the seven
business units of United Technologies. The three distinct contrails steaming behind the
rocket, symbolize the support offered through Students, Tuskegee University, and UTC. The
ring before the rocket depicts the student’s path through the FASTREC program, returning
full circle to support the efforts of the program. As we approach the new millennium, the sun
over the horizon symbolizes of the induction of the new Water Rocket Design Competition
into the FASTREC program. Accuracy, the focus of the contest, is represented by the target
created by the outer ring, deep space, and the earth. The border is supported on either side
by the chemical symbols respectively, for water and compressed air, which are used to
propel the rockets.
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As a part of the Water Rocket Competition, the team is required to write a Technical Report describing the
design, construction and operation of the Water Rocket. Reference numbers 1, 2, 3, 4 and 6 are required to be
presented together within a maximum of 7 pages. Add pages as appropriate for number 5. Drawings, sketches,
and tables may be included in an appendix (optional).
1. COVER PAGE (Required to contain):
Title of Technical Report
The team’s name
Names and disciplines of team members
Date
2. ABSTRACT (One half to one page summary of the Technical Report)
3. INTRODUCTION
4. DESIGN BACKGROUND
5. CALCULATIONS : Table of equations and constants
Assumptions
Mass flow rate calculations
Drag calculated assumptions
Trajectory calculations
- location of bottle when all of its water is expelled
- final destination point of bottle (Hint: diagram of time vs. distance traveled)
{Calculations will be scored on units, assumptions, accuracy, etc..}
6. CONCLUSIONS/RECOMMENDATIONS
AT THE COMPETITION, THE WATER ROCKET DESIGN TECHNICAL REPORT WILL BE
JUDGED ON:
 ABSTRACT
 DESIGN BACKGROUND
 PAPER STRUCTURE
 CALCULATIONS
 CONCLUSION/RECOMMENDATIONS
 GRAMMAR
10
10
5
40
20
15
100 points
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 Overall Winner
 Best Technical Paper
 Accuracy of Trajectory
 Best Technical Drawing
 Best Patch
 Best Design Review Presentation
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Overall Winner:
Accuracy of Trajectory
25
Technical Paper
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Technical Drawing
15
Patch Design
10
Design Review Presentation 10
Innovative Design
5
100
Points:
Best Patch:
Originality
Creativity
Appearance
Content
Best Technical Drawing:
(30)
(30)
(20)
(20)
Accuracy of Trajectory:
Target Position
(100)
Best Technical Paper:
Abstract
Design Background
Paper Structure
Calculations
Conclusions
Grammar
(10)
(10)
(5)
(40)
(20 )
(15 )
Resemblance
Scale
Name/Labeling
Appearance/Neatness
Best Presentation:
Effectiveness
Creativity
Content/Communication
Appearance
(25)
(25)
(25)
(25)
(40)
(10)
(25)
(25)
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Calculations
Manual
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Although you may be anxious to begin building your
rocket, some important decisions need to be made
about launch conditions that can help ensure a more
accurate launch. Remember: the goal of the
competition is to launch the rocket a specific distance. Your
task is to ensure your rocket meets that requirement. The
following calculations will help you determine what choices to
make to predict how far your rocket will go!
These calculations are what is known as an iterative
(repeated) process. First, choose the amount of air
pressure and water to add to the rocket. Then calculate
approximately how far your rocket is predicted to fly. If the resultant
distance is not what you desire, choose another value for air pressure
or water and re-calculate until you reach the answer you want.
Note: How your rocket really flies will not be exactly what is predicted here. The
actual launch will vary due to real world elements such as wind changes, drag and
differences in your rocket’s physical design that will not be accounted for now. These
factors are left out to simplify calculations. But the following pages will give you a
general starting point for choosing water and air pressure values and will show you their
effect on your rocket’s flight.

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Assume:
Air pressure of the bottle rocket (from 30 to 80 psi) This is the
amount of pressure that will be pumped into your rocket at the time of
launch.
 Choose the mass of water you will use to fuel your rocket.
Remember mass= density x Volume. So, for example, if you plan to
add 1Liter (volume, about the amount in a sports drink bottle) of water:
Vol= 1Liter= 1000mL= 1000cm3 or 0.001m3
 = Density of water= 998 (kg/m3)( a constant)
mH2O =  x Vol (in kg)
Find:
The Average Mass Flow Rate, m , of the water. This is the amount of

water
(mass) that flows out of the “rocket nozzle”, or throat of the bottle over
a period of time ( in a second).

.
m  A  cd  2    P (kg/sec)
Where A= Area of nozzle (m ) =  x r (r is half the diameter of
the 2 liter bottle’s throat)
cd= Discharge Coefficient= 0.98 (a dimensionless constant
based on nozzle shape and flow conditions)
= Density of water=998 (kg/m ) ( a constant)
P= (1+(Vi/Vf)(Pi)/2. (N/m )
 Pi = Initial Air Pressure of bottle (N/m )
 Ref: Atmospheric Pressure= 14.7(psi) (or 101,353.56 N/m )
2
2
3
2
2
2
(a constant)
•Final air vol = Vf = 2L
•Initial air vol = Vi = 2L – initial water volume
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Find:
Use your result from m

to find the Exit Velocity, V, (velocity at the bottle
exit), of the water. (m/sec)

m
V 
   A
Find:
Find the Thrust, f , of the Rocket. This is the amount of force that pushes
t
the rocket in a forward direction. ( in Newtons)

f t  m V
Find:
Thrust isn’t the only force acting on your rocket. There are also forces
acting against the rocket’s motion. The weight (mavex g) of the rocket
acts against its attempts to move forward. Drag (fd), (the force of wind
acting against the surface of the rocket) also acts on the rocket, but for
these calculations, drag will be neglected. (in Newtons)
NetForce  f  f t  f d  mave  g 
f = 0 since the rocket is very small.
M = ave. mass of the rocket= [M
+ M )/2
g = gravitational acceleration constant= 9.8 m/sec
d
ave
empty rocket
h2o
2
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Scholar’s note: You may be beginning to see how the amount of water you
add affects thrust. The Range equation (equation 8) shows that the higher the
water mass, the longer time the rocket will be propelled, therefore seeming to
increase the Range. So why not just fill the bottle up with water and make it
soar? Well, keep equations 6 and 7 in mind. The mass of the water, has two
functions. It not only increases the time the rocket is propelled, but it also
adds to the force acting against the motion of the rocket (weight), decreasing
acceleration. Too little weight can also be harmful; it can make the rocket
easily affected by the ‘neglected’ elements discussed earlier, like wind
changes. A balance must be achieved.
Find:
Find the Acceleration, a (m/s ), of the rocket. Use the equation:
2
f  mave  a (force in Newtons: N)
Now find the Range, R, or distance the Rocket will travel, for the water and
air pressure conditions you have chosen.
Range  R 
V 2 bottle  sin 2q
g
Where V
:
t mm
H 2O
&
bottle
(in meters)
 at
 Time when all of the water is expelled from the Rocket.
q angle Rocket is being launched = 45
o
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There are two remaining factors that will help better determine the
actual range of your vehicle. Up until this point we have not taken
Drag into consideration for purposes of simplification. It is necessary
to account for Drag to predict your rocket’s Final Range (RF).
Recall, Drag is the resistance produced on bodies as they move
through air. The effects of drag increase with respect to increases in
velocity.
Determining a Drag Factor
To account for the Drag force on your vehicle use the following
formula:
D = 1 – (Dc)
where Dc : Drag coefficient
and D : Drag Factor
Select a value for Dc based your nose cone design. See Chart A and
calculate D. Note: lower velocities results in lower Dc, (i.e. .15.)
CHART A
Dc = .21
Dc = .20
Dc = .19
Dc = .23
RF = R x D
Now, multiply your Range (R) times the Drag Factor following the
Requation
final distance calculation.
F is your below:

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The effects that the changing water volume and related
pressurized air volume will have on your rocket’s
performance was accounted for in the initial mass flow rate
and acceleration equations.
Why???
Well there are two major reasons to address the
changing pressure in the bottle:
1. Actually, the bottle’s internal pressure drops extremely
fast as the water is being expelled and the air volume
inside the bottle expands.
Take a moment and think of a balloon that is full and one
that is only half full, the air pressure in the half-full balloon is
LESS than that in the full balloon.
2. Another important concept to understand is Gas
Compression and Expansion (For our case the gas is
Air). Compressed gases within a pressure vessel WILL
EXPAND (increase in volume) once the vessel is opened
to the atmosphere.
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In your water rocket problem, the air in your bottle expands
as it pushes the water out. Keep in mind that your bottle has
a fixed volume (2L), therefore, as you INCREASE the
VOLUME of WATER, the VOLUME of AIR inside your bottle
DECREASES.
Take note:
LARGER VOLUMES of GAS will expand
MORE than SMALLER VOLUMES of GAS at
the SAME PRESSURE.
Think of the 2L bottles filled with soda you open during a
pizza party: Even though the internal pressure of the bottles
may reach as high as 40-50psi, the bottle WILL NOT fly
wildly out of your hand because the air volume inside,
though under significant pressure, is VERY SMALL.
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So, you’ve calculated the Range, or distance the rocket is
predicted to travel, would the rocket reach the target? Would
the rocket fly too far? Vary the values for water mass and air
pressure. How does the Range Change?
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How To Build A Water Rocket
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FUNDAMENTAL PRINCIPLES OF ROCKET SCIENCE
Newton’s First Law: The Law of Inertia
The Law of Inertia says, “A body in motion remains in motion, a body at rest
remains at rest, until acted upon by an outside force.”
Inertia is the tendency to resist any change in motion. It is associated with an
object’s mass.
Desired Path of Motion

(Trajectory)
Wind
Direction
HEAVIER rockets
have MORE Inertia,
because they have
MORE mass. MORE
Inertia will offer
GREATER resistance
to a change in direction.
Therefore the wind will
have LESS effect on a
bottle with MORE
INERTIA.

A LIGHTER bottle
rocket has LESS
inertia,because it has
LESS mass. LESS
inertia means the
rocket will have LESS
resistance to change
in direction. As a result,
the wind has a GREATER
effect on the rocket’s path
of motion.
At rest: Forces are balanced. The force of gravity on the rocket balances
with the force of the launch pad holding it up.
In Motion: Thrust from the rocket unbalances those forces. The rocket
travels upward until it runs out of fuel.
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Newton’s Second Law: Force
depends upon Mass and Acceleration
Newton’s second law says: Force = (Mass)(Acceleration)
F = ma
The pressure created inside the rocket is the force (thrust). Mass represents
the mass of the rocket and its fuel supply, which in this case is water.
Therefore, the mass of the rocket changes during flight. As the fuel is used
and expelled, the rocket weighs less and acceleration increases. Thrust
continues until the water is completely expelled.
Acceleration
Force
F = ma implies that if the
forces are the same,
then the bigger the mass
the smaller the
acceleration. The
smaller the mass, the
larger the acceleration.
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Newton’s Third Law: Action and Reaction
Newton’s third law says, “For every action, there is an equal and opposite reaction.”
A rocket takes off when it expels liquid. Action: The rocket pushes liquid
outward. Reaction: The liquid exiting the bottle causes the rocket to move in
the opposite direction. The Action (Thrust) has to be greater than the weight
of the rocket for the Reaction (Liftoff) to happen.
UP
(Bottle + Water Mass) x
(Bottle velocity)
EQUALS
(Ejected Water Mass) x
(Ejected Water velocity)
DOWN
Essentially, the faster the fluid is ejected, and the more mass that is
ejected, the greater the reaction force on the bottle.
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Drag Equivalent to Air Resistance
Air Resistance causes Friction which will slow down the rocket.
Air Friction
(DRAG)
UP
MOTION
MASS
EXITING
DOWN
How to reduce DRAG?
A more pointed nose cone will decrease the air resistance at the
front of the rocket, but keep in mind that the minimum nose cone
radius is 1/2 inch.
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Balance: Center of Mass and Center of Pressure
The center of mass (CM) is the point at which all of the mass of an object
is perfectly balanced. Around this point is where an unstable rocket
tumbles.
The center of pressure (CP) exists only when air is flowing past the
moving rocket. Flowing air rubbing and pushing against the rocket can
cause it to move around on one of its three axes. It is extremely important
that the CP of the rocket is located toward the tail and the CM is located
toward the nose.
When the CP and CM are located in the correct place, the rocket will tend
to have more stability.
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DESIGN AND DEVELOPMENT
Brainstorm
The first step in the design of a water bottle rocket is brainstorming.
Brainstorming is a problem-solving technique that involves the
spontaneous contribution of ideas from all members of the group.
Design Possibilities
The following are illustrations of possible designs for the fins. Any
variation of these suggested designs may be used and found to
perform better than another when combined with various bottle
designs.
!Stop! All fins must be at least 4” from the throat
exit plane of the bottle (see page 21). This
schematic is provided solely to give examples of
fin design. We encourage you to be creative.
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Choose best design
Square fins create more stability, but also produce greater drag.
Triangular fins introduce less drag, but yield less stability. Taking into
consideration the principles of projectile motion, choose the proposed
design which best satisfies the objective of the competition.
Design Tips:
Lengthening the rocket makes it more stable by moving
the center of mass of the rocket closer to the nose.
Adding fins to the rocket makes it more stable by moving the
location where drag forces act on the rocket further to the
rear.
Adding mass near the tip of the nose cone makes the rocket
more stable by moving the center of mass closer to the nose
of the rocket.
Heavier rockets have more inertia; therefore they have
more stability. However, remember not too heavy, because
the rocket needs to liftoff.
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MATERIALS AND CONSTRUCTION
Off-limit Materials
The following list of materials should NOT be used in any
form in the construction of the water rocket. They are
dangerous and could cause harm to the operator and those
in the presence of the water rocket launch.
Metal
Glass
Spikes and Antennas of any kind.
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Material and Tools Needed
Pressure Vessel (Clear 2-Liter Bottle)
Note: Be certain that your clear, 2-liter bottle is free of
scratches, nicks, dents, and discoloration.
Adhesive
Foam mounting tape (approximately 1/16 thick,
2-sided adhesive)
Carpet tape (thin 2-sided adhesive)
Clear packing tape or Strapping Tape
Use adhesive to bond fins, nose cone, and other allowed
materials onto the water rocket
Cutting utensils (Scissors, Hacksaw Blade,
Utility Knife, etc.)
Safety First: Children should be supervised at all times
while constructing their Water Rockets
For Fin Construction:
Balsa and Bass Wood, Cardboard,
Plastic, Foam Board, 1/4” to 1/2”
thick Styrofoam & Etha Foam,
Plastic Plates, and PE (2L) Bottle
Material
36
BUILDING YOUR WATER ROCKET
Fin Design & Construction
Determine a fin pattern from your analytic design
or trial and error.
Use the recommended materials, however we encourage
you to be creative. Keep in mind not to use the off-limit
materials.
Cut fins out of the material you choose.
You can use as many fins as you feel are needed.
Attach the fins to the lower section of the rocket using
glue, Velcro, tape, or other adhesives.
Tip: It is easier to attach fins to a bottle that is slightly
pressurized. You can pressurize the bottle by placing the
bottle with its top off in a freezer for 2-3 hours. Next, take
it out of the freezer and put the top on very tight,
eventually, the air inside warms and the bottle will
become slightly pressurized.
Tip: Using a Low melt glue gun is an excellent way to
quickly bond fins. First clearly mark desired locations on
the bottle prior to bonding. Try applying glue to a fin; then
apply the fin to one of the marked locations on your bottle.
This technique will aid in preventing your pressure vessel
(ie. bottle) from deforming due to the ‘initially’ very warm
temperature of the glue.
37
Typical Fin Patterns
THIS ATTACHED SIDE
WILL HAVE THE SAME
PROFILE OF THE SIDE
OF 2-LITER BOTTLE
38
Fin Patterns
THIS ATTACHED SIDE
WILL HAVE THE SAME
PROFILE OF THE SIDE
OF 2-LITER BOTTLE
39
More Fin Patterns
THIS ATTACHED SIDE
WILL HAVE THE SAME
PROFILE OF THE SIDE
OF 2-LITER BOTTLE
40
Nose Cone Design & Construction:
Determine what material you want to use.
Pattern the nose cone and cut it out.
Attach the nose cone to the top of the rocket
by using some recommended adhesives.
Note: Remember use only the material
recommended and maintain a nose radius
of 0.5 inch or greater.
Tip: Add ballast (weight) to nose cone (e.g.
Styrofoam-peanuts, shredded paper, etc.) to
shift the water rocket’s center of mass forward
and increase its flight stability. Smaller
amounts of more dense materials such as clay,
sand, water, etc. may also be used as ballast.
Remember not to use the Off-Limit materials.
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Preferred Nose Cone ConstructionWater Rocket Assembly Method
Step 1: Cut the bottom
off of a 2L Bottle
(discard bottom).
Step 2: Carefully align
top portion of bottle on
the 2L bottle to be used
for the pressure vessel.
Step 3: Rotate and observe
your water rocket from several
angles to ensure good
alignment.
Step 4: Tape/secure the joint
between the nose cone stage
and the pressure vessel.
Tips: - Remember to add ballast to your nose cone stage.
- The pressure vessel should be in good condition free42of
scratches and dents)
Option 1: A) The neck can be cut off of
the top of the nose cone as shown in
Step 4; this will slightly improve the
aerodynamics of the rocket. B) The
resulting hole can simply be covered
with tape. (Use a hack saw blade for
cutting through the thicker material
at the neck of bottle. Utility and other
knives are NOT recommended for this
process).
Option 2: Ballast can be added
before or after you permanently
affix the nose cone to the
pressure vessel.
BEFORE
AFTER
43
Option 3: The length of the Rocket
can be increased by adding another
bottle between the nose cone stage
and the pressure vessel. Remember
to stay within the dimensional limits
for the competition.
Note: Taller rockets will not
necessarily perform better than
shorter ones. Try to keep your
construction/assembly process as
simple as possible.
44
Alternative Example of Nose
Cone Construction
Step 1: Cut a Circle
out of thick stock paper
or thin poster material
(Using 16” or larger
diameter).
Step 3: Rotate the paper
into a cone. Next Tape or Glue
the seam to maintain the cone’s
shape. You can adjust angle of
the cone with more rotation.
(Keep mind that the base of your
cone needs to be large enough
to fit around the top of the
pressure vessel).
Step 2: Cut a line
along the radius
as shown.
Uniform Fit AllAround Here
Step 4: If needed trim the
base of cone as required so
that it has a uniform fit with
the diameter of a 2L bottle.
45
Step 6: Uniformly trim top
of paper nose cone to accept a
craft foam or styrofoam ball or
cone.
Step 7: Add the foam ball or
cone to create a 0.5” or larger
nose cone radius.
Step 8: Secure the resulting
nose cone to the pressure
vessel using an adhesive
like tape, glue, velcro etc...
Be certain to use some form of ballast
(weight) to shift your rocket’s center of
mass forward.
46
Other Tips
More on Water Rocket Construction:
Pressure
Vessel
A
B
C
A) For lengthened rockets (Option 3 Page 20) A piece of
1/2” PVC Pipe can be used to align the nose cone
to a second bottle prior to assembly with the main
pressure vessel bottle.
B) Join the bottles together on the PVC shaft and tape
the joint between bottles securely. (Make certain tape
lays flat on the bottle’s surface).
C) Now, remove the PVC shaft and join upper nose cone
stage to the pressure vessel. Carefully align the
the stages.
(Note: you will NOT be able to use the PVC shaft to
align the nose cone and attached bottle to the pressure 47
vessel).
FINS: Whether your fins are wide or thin the primary
‘assembly’ objectives/considerations should be:
1) Make certain fins are aligned with center axis of rocket.
2) Be sure fins are well affixed to bottle to prevent
separation or deflection/movement during flight.
3) Wider fins (1/4”-1/2” thick) provide a larger attachment/
contact surface. They can be securely attached using tape
only and are useful for quick assembly & especially when
working with young children due to ease of assembly.
4)Thinner fins (3/16” or less) are excellent for reducing the
effects of drag, however, more effort is usually involved
with securely attaching them to your water rocket. Thin
fins must be very stiff once mounted to prevent
movement during flight.
48
5) A minimum of three fins are recommend for stable
flight (4 fins are a good choice as well)
6) All fins should be spaced equally apart regardless
of the number (e.g. 3 fins-120o apart, 4 fins-90o
apart, and so on).
Note: Aligned fins are recommended, particularly when
competing. Tilting fins will cause rockets to spin. This
action may slightly increase flight stability but will likely
make it more difficult to ‘calculate’ how far the rocket will
travel. In case fins are tilted to cause ‘spin’:
• They must ALL be tilted in the same direction.
• They should only be tilted slightly (e.g. 2o to 10o).
• The fins should be equally spaced.
• It is strongly suggested that you try the aligned fin
approach first!!!
49
Examples Section
50
Mass Flow Rate
Mass Flow rate is a measure of the amount of mass (Fluid) passing through
a given area with respect to time. Some every day examples of mass flow
rate are water traveling through a fireman’s hose, soda flowing from a
fountain into a cup, and propellant being rapidly expelled from a rocket’s
engines. The mass flow rate of a given fluid can be determined with the
following equation:
.

m  A  cd  2    P
Example 1
A mother needs to fill a bathtub half full so that her young daughter can take a bath. The
tub has a total capacity of 80 liters. If water flows through the nozzle into the tub at flow
rate of .20kg/sec how long will it take to fill the tub half way?
Step 1
Determine half the tub’s volume capacity. Total capacity = 80L,
so the half capacity = 40L.
Step 2
Next we must calculate mass for 40L of water. Convert the water volume
to mass by multiplying the volume of water required by the density of
water . (is pronounced ‘rho’).
 = 998kg/m3
1L =.001m 3
We know that
40L = .04m 3
therefore,
now multiply,
Step 3
.04m3 x 998kg/m3 = 39.92kg
Now that we know the mass of water required we can determine the
amount of time (t) required to fill the tub half full based on the defined
mass flow rate of .20kg/sec, that is for every second that passes .20kg of
water will flow into the tub.
mH 2O ( kg)
t=
t=

m( kg / sec)
39.92(kg)
.20(kg / sec)
t = 199.6 sec or 3 min 19.6sec
Challenge: If the mass flow rate for the above example equals .20kg/sec,
what is the volume flow rate equal to?
51
Example 2
A gardener must water his garden daily due to a severe drought. It is important that his small
crop of vegetables get at least 200L of water each day. He uses a nozzle attached to a hose
that supplies water at a pressure of 25psi. Considering the nozzle has an exit diameter of 2cm,
determine the mass flow rate.
Comprehension:
It is critical to understand exactly what is occurring during this process. While the water is being
supplied at a pressure (Ps) of 25 psi, it is being expelled into a pressurized environment ‘Our
Atmosphere’. While atmospheric pressure varies, it is safe to assume that atmospheric pressure
Patm equals 14.7 psi for this sea level application. This pressure will offer resistance to the water
being ejected from the nozzle and therefore must be accounted for. Hence, the pressure
difference or P (pronounced ‘delta’ P) is derived by subtracting the atmospheric pressure Patm
or (14.7psi) from the supply pressure Ps (25psi). We will useP for the mass flow rate
calculation.
Likewise, it is necessary to calculate P for your rocket’s mass flow rate equation
based on its initial ‘vessel’ or internal pressure and Patm
Step 1


Given supply pressure (Ps) and atmospheric pressure (Patm) calculate P:
Ps = 25psi
Patm = 14.7psi
P = Ps - Patm
P = 10.3psi
For this metric calculation, psi (pounds square inch) must be converted to
N/m2 (Newton per square meter) so multiply 10.3 psi by 6.8948 x 103 or 6894.8,

P = 71016.4 N/m2
Step 2
We know the density of water H2O is 998 kg/m3 at room temperature
Step 3
Calculate the ‘effective flow area’ for your nozzle. First, determine the area for a
gardener’s nozzle having a 2cm exit diameter. Multiply the result by .98, the
discharge coefficient or cd.
About Discharge Coefficients: Discharge Coefficients are used to account for flow losses
caused by non-uniform flow paths. Since a gardener’s nozzle converges down to 2cm
from 4cm it is reasonable to assume that the flow rate will be reduced by a dimensionless
factor of .98 or 2 percent due to the change in flow area.
You will be required to apply a discharge coefficient during the mass flow rate
calculation for your rocket, due to the converging nozzle of your 2L bottle.
52
Example 2 Continued…………….
(A) = r2
Area for a circle
 = 3.14
where
and
d=2cm or .02m
r = d/2 = 1cm
and
1cm = .01m
A = x .(01m)2
A = 3.14 x .1000m2
A = .000314m2
thus,
Acd = .000314m2 x .98
Acd = .000308m2
Step 4
Now calculate the mass flow rate given:
P = .01 N/m2
H2O = 998 kg/m3
Acd = .000308m2
.

m  A  cd  2    P

m = .000308m2 x
Keep in mind that
1N = 1
2 x 998
kg
N
x 71016.4 2
m3
m
kg  m
sec2
That is one Newton equals the acceleration of 1 m/sec 2 to a one kilogram mass.
kg  m

m = .000308m2 x 2 x 998 kg x 71016.4 sec 2
m3
m2
Now pay close attention to what happens to the units……

m = .000308m2 x 14.17 x 107
kg 2
m  sec 2
4

m = .000308m2 x 11905.8 2 kg
m  sec

m

m
kg
= .000308m2 x 11905.8 m 2  sec
kg
= 3.67sec
53
Thrust
Jet and rocket engines create thrust by accelerating propellants (usually hot gases) to high
speeds. Other objects can create forces in similar ways, though. As Newton’s Third Law states,
all action forces create an equal and opposite reaction force. Thus any object that causes mass
to accelerate in one direction will experience a ‘thrust’ force (ft) in the opposite direction. The
amount of force is described by the thrust equation:

ft = m  V

where m is the mass flow rate (in kilograms/second) of the propellants out of the object and V is
the velocity (in meters/second) that it exits. Note that if the exiting propellants are high-pressure
fluids exiting into the air, thrust will be somewhat higher. Most of the time, though, we can
assume that a jet of propellants exits at atmospheric pressure and use the above equation.
Example 3
Firefighters often need to spray large amounts of water to great heights. To do so, they
use high-power pumps and heavy-duty hoses that accelerate the water to high speeds.
This spraying creates a reaction force on the hose that could cause it to move
backwards violently. Two or more firefighters thus often hold a firehose steady to
counteract this thrust.
Consider one such firehose attached to a truck that pumps water at a mass flow rate of
80 kg/s. The diameter (d) of the nozzle is .1 meters. Find the thrust force on the hose
created by the spraying of water (density = 998 kg/m 3). You may assume that the water
exits the hose at atmospheric pressure.
Solution
The equation for thrust is:

ft = m  V

where m is the mass flow rate and V is the velocity of the water exiting the nozzle.
Though we are only given the value of mdot, we can find V from the equation:

m
V=
(   A)
where  is the density of the water. To find V we must first determine the exit area of the
nozzle. Since we know that area =   R2 where R is half the nozzle diameter, we have:
A =   r2
A =   (d / 2)2
A =   (.1 m / 2)2
A = .008 m2
54
Example 3 Continued……………….
Now we can find the exit velocity:

m
V=
(   A)
V = 80 kg/s / (998 kg/m3  .008 m2)
V = 10.0 m/sec
Now we know mass flow rate and velocity so we can find thrust:

ft = m  V
ft = 80 kg/s  10.0 m/sec
ft = 801 N
Thus the firefighters have to put almost 200 lbs of force on the hose to keep it from
accelerating backwards!
Now take a moment to apply the above theory to your water rocket:
Gravity acts on the mass of your rocket and keeps at rest on the launcher,
at least until another force acts on the rocket. In order for the rocket to
move, the other force acting on it MUST be GREATER than earth’s
gravitational pull. In Example 3 think of the force the firemen apply to the
hose as gravity or a ‘holding force’. Unlike the firemen’s success with
keeping the hose in position, the thrust force produced by the water rapidly
exiting from your bottle will overcome the effects of gravity on the total
mass of the rocket…………at least temporarily. Since the thrust force (ft)
is applied only for a short time, gravity will eventually win causing the
rocket to return to earth.
55
Force & Acceleration
Newton’s First Law of motion tells us that an object will only accelerate when a
force is applied to it. Be careful, though! Often times, forces will cancel each
other by acting in opposite directions. For example, your weight is a force that is
pulling you toward the center of the earth. The chair you are sitting in, however,
is exerting an upward support force that is exactly equal to your weight. Thus
the net force is zero and you do not experience an acceleration.
When the net force on an object is not zero—i.e. when unbalanced forces exist—
the object will accelerate. Newton’s Second Law states this acceleration by the
following equation:
F = ma
Solving for acceleration,
a=F/m
Where F is the net force in Newtons, m is the mass in kilograms, and a is the
acceleration in meters/second2. Note that a and F will always act in the same
direction.
Example 4
Rocket engines create thrust through the principle of
reaction forces. In the previous example, the firemen
applied a reaction force equal to the thrust force
generated by the rapid mass flow rate of water being
expelled.
In this case, rocket engines accelerate
propellants (usually hot gases) downwards to create an
upward reaction force.
Consider the Space Shuttle, which weighs approximately
2,700,000 kg as it sits on the launch pad. Once the main
engines and solid-rocket boosters have started and
reached full power, they produce a total of 34,400,000N of
thrust. The shuttle does not move upward, however, until
explosive bolts release the boosters. Recalling that
acceleration is a result of the net force acting on an
object, calculate the instantaneous upward acceleration of
the shuttle when the bolts release.
Solution:
The two forces acting on the shuttle are its weight and the thrust of the engines.
The weight force W is simply the mass times the acceleration of gravity:
W = -mg
W = -(2,700,000 kg)(9.8 m/s2)
W = -26,460,000 N (downwards)
56
Example 4 Continued……………
Again,
Fnet = Ft + W
Fnet = 34,400,000 N + (-26,460,000 N)
therefore,
Fnet = 7,940,000 N
From the Second Law, we can thus find the initial acceleration:
Fnet = F
F = ma
a=F/m
a = 7,940,000 N / 2,700,000 kg
a = 2.94 m/s2
Note that the mass of the shuttle is actually constantly changing: propellants are being
expelled from the engines at high speed. Thus the acceleration will continue to increase
dramatically as the shuttle lifts off.
57
Acceleration and Velocity
We have just seen how Newton’s laws help describe the relationship between
an object’s acceleration and the forces acting on it. This is important because
we hope to predict the motion of our rocket and find its range. But how does
knowing the acceleration help us? Remember that acceleration is simply how
fast an object’s velocity is changing at that moment. If we can assume that
acceleration is constant during a time period t, then we can find the change in
an object’s velocity (v - vo ):
v - vo = a t
(3)
change in velocity = acceleration  time
or we can rewrite the equation:
v = a t + vo
(4)
final velocity = acceleration  time + initial velocity
This shows us that we only need to know the initial velocity and acceleration to
find the final velocity after time t.
Example 5
A sports car is traveling forward at 62 ft/s when
the driver lightly applies the brakes. The brakes
cause a constant deceleration of 6 ft/s2. How
much time will it take the car to come to a
stop?
Solution:
The time t can be found by rearranging equation (4) and substituting v = 0
(because the car will be stopped after time (t). The acceleration a = -6 m/s2 is
negative because it is in the direction opposite of the car’s velocity:
v = a t + vo
t = (v - vo)/a
t = -62 ft/s / -6 ft/s
t = 10.3 seconds
58
Range
Range is the distance an object will travel depending on its velocity and angle of
trajectory (q). Thus two objects having the same mass will travel the same distance
unless acted upon by outside forces such air resistance (drag); this fact explains why it
is difficult to toss a balloon filled with air, but rather easy to toss a balloon partially filled
with water. Keep in mind that more force is required to accelerate a heavier mass to the
same velocity as that of a lighter mass.
The dry mass of your rocket is critical for stability and for overcoming drag, but
excluding drag rockets having the same velocity (speed) would travel the same
distance. Air resistance will have a greater effect on the range of lighter masses
than larger masses moving at the same velocity.
Example 6
A women playing centerfield must quickly throw a softball to second base during a
game to prevent a player on the opposing team from advancing from first base. If she
releases the ball from her hand at an angle of 30 o, at what velocity must the ball be
thrown in order to reach second base which is 50m away?
Note: For simplicity we will ignore the drag force of ‘air’ in this example, however, drag
has a significant effect with many trajectory applications, including the trajectory
calculation for your rocket.
Using the Range Equation
V
R=
where,
2
x sin q
g
R : Range = 50m
V : Velocity = ? (m/sec)
T : Release or ‘Trajectory’ Angle = 30 o
G : Gravitational Acceleration = 9.81m/sec 2
Determine Velocity:
First we must rearrange the range equation as shown:
R x g
V2 = sin 2q
V=
R x g
sin 2q
59
Example 6 Continued……………
50m x 9.81
m
sec 2
sin 2 x 30o 
V=
m2
sec 2
.8660
490.5
V=
m2
V = 566.4
sec 2
therefore,
V = 23.8
m
sec
Wow that’s neat but I relate better to miles per hour (mph)……………..
Okay, to convert meters per second to miles per hour use the following relationship:
1m/sec = 2.2369 mph
So we multiply the result by 2.2369
23.8m/sec x 2.2369 = 53.2 mph!
Example 7
A high school quarterback passes a football at velocity of 20m/sec to a receiver
running down field directly in front of him. If the quarterback releases the football at an
angle (q) of 45o, what distance must the receiver reach to catch the ball? (Assume that
the receiver will catch the ball at the same height that it was thrown from.)
Again:
R=
V
2
x sin 2q
g
60
Example 7 Continued…………………
quickly,
V= 30m/sec
q= 45o
g = 9.81 m/sec2
2
m 

 20
 x sin 2q
sec 

R=
m
9.81 2
sec
400
R=
m2
x sin 90 o
2
sec
m
9.81 2
sec
m2
sec 2
R=
m
9.81 2
sec
R = 40.8m
400
Considering sin90o = 1,
Great, but I want to know the equivalent of 40.8m in feet (ft).
Well we know
1m = 3.2808 ft
so simply multiply
40m x 3.2808
We have
R= 133.8ft
Congratulations on reading through this brief Appendix. These examples
are intended to help you better understand how many of the physical
principles of Rocketry relate to everyday applications. We encourage you
to create and work through problems of your own to further stimulate your
understanding of the concepts of Mass Flow, Thrust, The Laws of Motion,
and Trajectory Calculation. More in depth equations and examples will
follow in future editions of this manual. Good Luck Rockeeters as you aim
for the Stars!
Note: A useful conversion table is provided on the following page.
61
Conversion Table
Multiply
centimeter (cm)
cubic centimeter (cm3)
cubic foot (ft3)
cubic inch (in3)
cubic meter (m3)
foot (ft)
foot/second (fps)
inch (in)
kilogram (kg)
kilogram/square meter
(kg/m2)
liter (l)
meter (m)
meter/second (m/sec)
mile/hour
newton (N)
By
3.2808 x 10-2
3.9370 x 10-1
1.0000 x 10-2
6.1024 x 10-2
1.0000 x 10-6
2.8317 x 104
1.7280 x 103
2.8317 x 10-2
5.7870 x 10-4
1.6387 x 10-5
1.0000 x 106
3.5315 x 10
6.1024 x 104
3.0480 x 10
3.0480 x 10-1
1.0973
3.0480 x 10-1
6.8182 x 10-1
2.5400
2.54 x 10-2
1.0000 x 103
3.5274 x 10
2.2046
9.8067
To obtain
feet
inches
meters
cubic inches
cubic meters
cubic centimeters
cubic inches
cubic meters
cubic feet
cubic meters
cubic centimeters
cubic feet
cubic inches
centimeters
meters
kilometers/hour
meter/second
miles/hour
centimeters
meters
grams
ounces
pounds
newtons
9.8067
3.5315 x 10-2
2.6417 x 10-1
1.0000 x 10-3
1.0000 x 102
3.2808
3.2808
3.6000
2.2369
1.4667
1.6093
4.4704 x 10-1
1.0197 x 102
1.0197 x 10-1
2.2481 x 10-1
newtons/square meter
cubic feet
gallons (U.S. Liquid)
cubic meters
centimeters
feet
feet/second
kilometers/hour
miles/hour
feet/second
kilometers/hour
meters/second
grams
kilograms
pounds
Please Note: The above Conversion Table is provided as an aid. Use of the all of conversion
factors is not required for the trajectory calculations. Be careful! Pay attention to units and
62
exponents. Make sure you use only those conversions which are needed for your calculations.
newton/square meter
newton/square meter
(pascal (Pa)) (N/m2)
ounce (oz)
pound (mass) (lb)
pound (force) (lbf)
pound/square inch (psi)
square foot (ft2)
1.0197 x 10-1
2.0885 x 10-2
1.4504 x 10-4
2.8349 x 10
2.8349 x 10-2
6.2500 x 10-2
4.5359 x 102
4.5359 x 10-1
1.6000 x 10
4.4482
4.4482
7.0307 x 102
6.8948 x 103
1.4400 x 102
1.4400 x 102
9.2903 x 10-2
kilograms/square meter
pounds/square foot
pounds/square inch
grams
kilograms
pounds
grams
kilograms
ounces
newtons
kilonewtons
kilograms/square meter
newtons/square meter
pounds/square foot
square inches
square meters
Please Note: The above Conversion Table is provided as an aid. Use of the all of conversion
factors is not required for the trajectory calculations. Be careful! Pay attention to units and
exponents. Make sure you use only those conversions which are needed for your calculations.
63
Construction Help
64
Building Fins From 2-Liter Bottles
1. Cut Top and Bottom Off
2. Flatten and Cut
3. Reverse the Fold and Recrease
Note: The method of design and construction shown here
is only an example. Use your imagination to create new
designs using the recommended materials.
65
An Example Only:
Building Fins From 2-Liter Bottles
4. Add Double Side Tape
Thin Carpet Tape
(Trailing Edge)
Thick Mounting
Tape Center Spar
5. Trim to Desire Sweep, Add Clear Packing
Tape Over Trailing Edge.
Note: Adding clear packing tape keeps the leading edge from curling
up and mounting tape add strength and stiffness to the fin.
Tip: Add a smooth fillet of glue around the base of each fin.
66
Diagram 1
Rocket Identification
Min Cone Radius = 0.5 inches
Ballast Added to the
Nose Cone (e.g.
Styrofoam-peanuts,
shredded paper, etc.)
Nose Cone
Bottle Height
(max. 30 inches)
Pressure Vessel
(Clear 2 Liter Bottle)
Fin
Rocket Clear of Any
Coverings (min. 3 inches)
Fin
Bottle Throat
Fins Start
(min. 4 inches)
Throat
Exit Plane
67
Diagram 2
Nose Cone Diagram
Min Cone Radius = 0.5 inches
Cone Tip
R
Note: Make certain
to construct the tip
of the nose cone
per the minimum
cone radius
(0.5 inches) for safe
operation.
Diagram 3
Fin Diagram
max 16.5 cm
max 10.2 cm
68