Water Rocket ModelingWater Rocket Modeling

Sean MunsonSean Munson

Ben DonaldsonBen Donaldson Alex DillonAlex Dillon

Design GoalsDesign Goals

• RangeRange

• AccuracyAccuracy

• AestheticsAesthetics

These tell us little about how to build a rocket!These tell us little about how to build a rocket!

The ModelThe Model

What happens to the rocket?What happens to the rocket?

Boost PhaseBoost Phase

Water leaving rocket under pressureWater leaving rocket under pressure

Air Thrust PhaseAir Thrust Phaseremaining air pressure leaves rocketremaining air pressure leaves rocket

Coast PhaseCoast PhaseGravity, drag act on rocket Gravity, drag act on rocket until it smashes to the grounduntil it smashes to the ground

Boost PhaseBoost Phase

Boost Phase: ThrustBoost Phase: Thrust

exhaustThrust mF

2surface

2nozzle

A

A - 1

a)h(t)+(g2+2P(t)

exhaustexhaustThrust mvF

nozzleexhaustexhaust Avm

Coast PhaseCoast Phase

Coast Phase: DragCoast Phase: Drag

2

2

1vACF airDDrag

maF

““Whoa, what about the Air Phase?”Whoa, what about the Air Phase?”

Us:Us: “We neglected it, sort of.” “We neglected it, sort of.”

You:You: “You can’t just do that…” “You can’t just do that…”

Us:Us: “Well, actually, since we made some other “Well, actually, since we made some other assumptions…”assumptions…”

What’s Important?What’s Important?

• Cross Sectional Area (Nozzle, bottle)Cross Sectional Area (Nozzle, bottle)

• Coefficient of Drag (CCoefficient of Drag (CDD, Surface area), Surface area)

• Mass of RocketMass of Rocket• PressurePressure• Volume of WaterVolume of Water

Validation of the ModelValidation of the Model& Experiments& Experiments

A PrefaceA Preface• Rocket for tests was constructed in ~20Rocket for tests was constructed in ~20

minutes, with cardboard finsminutes, with cardboard fins

• Launchers don’t workLaunchers don’t workmost launches required a kickmost launches required a kickto free the rocket, making itto free the rocket, making itdifficult to measure the angledifficult to measure the angle

Mass vs. RangeMass vs. Range

0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.1685

86

87

88

89

90

91

92

93

Mass (kg)

Ran

ge (

m)

• Pressure: 70 psig

• Volume H20: 0.7 liters

• Angle: 35°

Observations:

• Launch without ballast (rocket mass: 70 grams) highly erratic

• Stability problems above or below 0.11 kg

•Determined CD to be 1.8

Volume HVolume H22O vs. RangeO vs. Range

0.2 0.4 0.6 0.8 1 1.2 1.4 1.630

40

50

60

70

80

90

Volume (l)

Ran

ge (

m)

•Mass: 0.150 kilograms

•Pressure: 70 psig

•Angle: 30°

Pressure vs. RangePressure vs. Range

50 55 60 65 70 75 80 85 9040

50

60

70

80

90

100

110

Pressure (psig)

Ran

ge (

m)

•Mass: 0.186 kilograms

•Volume H20: 0.8 liters

•Angle 30°

Observations:

• Last set of tests. Fins mush Data unreliable

• Clearly, more pressure is good so long as you do not exceed safety margins

What the #&$% ?

The stout kick requiredlikely changed the angleto 20° or 25°.

What the #&$% ?

The stout kick requiredlikely changed the angleto 20° or 25°.

Design Goals:Design Goals:

• Low CLow CDD, A, A– Parabolic, smooth noseParabolic, smooth nose– Experiment with multiple 1L bottlesExperiment with multiple 1L bottles

• Mass: ~115 gramsMass: ~115 grams

• Experimentation with nozzle area?Experimentation with nozzle area?– Difficult with these launchersDifficult with these launchers

• Tight but loose fit on launcher?Tight but loose fit on launcher?

Questions?Questions?