Water-Bottle Rockets: Design BriefSeveral 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 - ContinuedSpecifically, 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 Rocket Design Considerations”2. Complete and submit the worksheet section at the end of this

document. 3. 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).

4. Choose one of your designs and build a prototype of a rocket.5. Make a cardboard cutout of your rocket that shows the center of

mass and center of pressure.6. 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. 1. http://www.et.byu.edu/~wheeler/benchtop/sim.php2. http://www.grc.nasa.gov/WWW/K-12/rocket/rktsim.html

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 PortfolioWater Rocket Worksheet Initial design sketchesCardboard Cutout (silhouette) showing the Center of Mass

and Center of PressureGraphed from simulationData from experimental launch / best launchRocket (or what’s left of it)

Steps to Complete the Assignment (continued)

Sample of Graphed Data

Sample Sketches

Water-Bottle Rocket Grade Form: Evaluation 

Possible Received Worksheet 40 points ________Sketches 10 points ________Silhouette (cardboard cutout with CM & CP) 20 points ________Graphed Data (from simulation) 20 points ________Experimental Launch Sheet (Data for all launches) 30 points ________Launch Accuracy 30 points ________Launch Height 100 points ________ 

Points for Launch Accuracy Legend> 9.0 s = 110 pts 25ft radius = 30 pts 7s = 60m=197ft8.7s – 9.0s = 100 pts 50ft radius = 26 pts 7.5s = 69m = 226 ft8.5s – 8.69s = 95 pts 75 ft radius = 22 pts 8.0s = 78m = 257ft8s – 8.49s=90 pts Exceeds 75 ft radius= 20pts 8.5s = 89m = 290ft7.5s – 7.99s = 85 pts Closest = 5 bonus points 9.0s = 99m = 326ft7s – 7.49s = 80pts 9.25s = 105m = 344 ft< 7s = 75 pts 9.5s = 111m = 363 ft

9.75s = 116m = 382 ft

10s = 123m = 400ft

EquipmentLauncherHigh Volume Pump - an air compressor or

scuba tank might also be used.A graduated beaker - To measure fluid added

to the rocketScientific CalculatorAltitude Guns - Can also use a protractor with

a string and weight.Scales - To determine the mass of the rocketsStopwatch

Basic SuppliesAssortment of 2-liter bottlesFoam board - for finsOak Tag Board - Poster Board (If a paper type nose cone is

made)PL Premium Construction Adhesive - Best adhesive for

attaching finsCaulk gunModeling clay - excellent for adding weight to the rocketHot Glue Gun (Do not use for the fins)X-acto Knives / Cutting boardsPlastic and String (If students decide to use a parachute

design)Duct Tape - just in caseTo help in the design, students are encouraged to bring in

many assorted items from home (Paper Tubes, tennis balls, Nerf balls, racquet balls).

Team or Person

Dry Mass of Rocket (grams)

Fluid added to

the rocket (in ml)

Total Mass of Rocket

Percentage (%) of water mass to total

mass of rocket

Launch Pressure

(psi)

Total T ime in

Air

Height from Chart

(meters)

Angle #1

(Deg)

Angle #2 (Deg)

Average Angle (Deg)

Calculated Height

(feet)

Total T ime in

Air

Height in

Meters

Height in Feet

Distance From

Launch Pad

Freddie Mercury 245 700 945 700/945 = 74% 95 psi 58 62 60.0 260 7.96 78 255 22ft

Best Launch

Enter Data From Simulation ResultsEnter Data Collected From Launches

Before Simulation Simulation Actual Launch Data and CalculationsHeight Formulas

Average Angle Formula Littlewood's

Experimental Launch Data Sheet

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.

This force continues until the pressure forces the last of the fluid to leave the rocket.

UpBottle and Remaining

Water Mass

DownEjected Water Mass

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 AccelerationShorter 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: DragAs 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.

Airflow

Eddy Currents

Aerodynamics: Nosecone

High Drag Low Drag

Popular Nose ConeConfigurations

A Nerf or tennis ball helpsadd mass to the nosecone (CM)and helps keep the rocket frombeing 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 CPIn 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).

Unstable Rocket

Stable Rocket

Center of Mass = Center of Pressure =

Stability: Moving the CM ForwardAdding 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 massThere 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 BackAdding 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 PressureRounded edges on a fin produce less drag than

square edgesCheck 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 finsPopular 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.

• Essentially, you need to minimize the rockets mass without compromising stability.

More StableMore Mass

Less StableLess Mass

Fill Ratio of Water in RocketA 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 FluidA 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 MethodNote: 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 flightb= 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 apogeeg = 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 ProblemAssume 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

1. (Newton’s 1st law) How long does the thrust force last when a rocket is launched?2. (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.

Questions:

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. List two purposes of a nose cone on a rocket? 1) 2)

 

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: ____________