Aerodynamics of a RocketAerodynamics of a Rocket

Mentor: A/P Andrew WeeMentor: A/P Andrew WeeGroup Members:Group Members:

• Darwin GosalDarwin Gosal• Martin LeeMartin Lee• Tan Hai SiongTan Hai Siong• Tan Kim SengTan Kim Seng

OutlineOutline IntroductionIntroduction Theoretical BackgroundTheoretical Background Procedure / Set UpProcedure / Set Up Results and AnalysisResults and Analysis ConclusionConclusion ImprovementsImprovements Further ExperimentFurther Experiment

IntroductioIntroductionn

These fin shapes with angle These fin shapes with angle varying from 45º to varying from 45º to 90º90º (in increasing steps of 5º) (in increasing steps of 5º) will be inserted onto will be inserted onto the rocket body shaft during the experiment. A wind the rocket body shaft during the experiment. A wind tunnel will be used to channel moving air currents tunnel will be used to channel moving air currents upward towards the rocket body. An empirical upward towards the rocket body. An empirical relation between the resulting drag force and the relation between the resulting drag force and the angle angle would be obtained from the experimental would be obtained from the experimental results. The interdependence between the wind results. The interdependence between the wind speed with these two variables was investigated.speed with these two variables was investigated.

IntroductioIntroductionn

ROCKET BODY

Viscous DragViscous Drag :- :- drag due to skin drag due to skin frictionfriction

Form DragForm Drag :- :- drag due to the drag due to the separation of the flow from the body separation of the flow from the body which results in the alteration of which results in the alteration of pressure distribution.pressure distribution.

Theoretical Theoretical BackgroundBackground

The expressions for the coefficient of The expressions for the coefficient of viscosity viscosity and the shearing stress and the shearing stress in in terms of the properties of the fluid & of the terms of the properties of the fluid & of the flow are:flow are:

= 1/3 = 1/3 c L c L

= = u / u / yy

Theoretical Theoretical BackgroundBackground

The concept of a shearing stress is:The concept of a shearing stress is:Rate of transfer of downstream Rate of transfer of downstream momentum in a direction lateral to momentum in a direction lateral to the flow.the flow.

The shearing stress at the surface : The shearing stress at the surface : = = u / u / yy is the skin friction is the skin friction ((Force per unit areaForce per unit area.).)

This is exerted by the fluid on the This is exerted by the fluid on the surface in the tangential direction.surface in the tangential direction.

Theoretical Theoretical BackgroundBackground

1. Euler’s Equation may be written as:

2. After summing up the pressure and shear forces on an element in a boundary layer : -

3. We thus obtain the boundary layer equation of motion:

Theoretical Theoretical BackgroundBackground

4. The continuity equation for incompressible flow :-

5. The boundary layer equation of motion and the continuity equation are the equations available for the solution of our aerodynamic problem.

Theoretical Theoretical BackgroundBackground

Figure 3.3: - Boundary Layer on a flat plate

y

Ue

y= 1. For the steady flow of the incompressible viscous fluid along a flat plate:

2. Upon solving these differential equations, we obtained an expression for the drag force:

drag per unit area = where ue is the speed of wind of the wind tunnel as measured by the anemometer.

2/1

241

vxu

uA ee

Theoretical Theoretical BackgroundBackground

Procedure / Set Procedure / Set UpUp

F2 F3

Wind Tunnel

F1

Rocket Body with Fins

Balance Pan with StandardWeights

Voltmeter

ForceTransducer

Lever

pivot

Pulley

ConnectingWires

Anemometer

Results & Results & AnalysisAnalysis

F1 vs wind speed

0.0025

0.003

0.0035

0.004

0.0045

0.005

0.0055

0.006

0.0065

0.007

7 7.5 8 8.5 9 9.5 10 10.5 11

Wind speed (m/s)

F1 (N

)

45

50

55

60

65

70

75

80

85

90

Results & Results & AnalysisAnalysis

Graphs

Velocity of wind(m/s)

Total increase (10-4N)

Gradient of Regression line (10-5 N degree-1)

A 7 3.72780 1.390

B 8 5.54694 1.909

C 9 8.91686 2.736

D 10 10.1992 3.029

E 11 20.8160 4.718

Results & Results & AnalysisAnalysis

Graph A : V=7m/s

y = 0.0000139x + 0.0025471

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

0.0045

40 45 50 55 60 65 70 75 80 85 90 95

Angle

F1

Results & Results & AnalysisAnalysis

Graph B : V=8m/s

y = 0.00001909x + 0.00252356

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

0.0045

40 45 50 55 60 65 70 75 80 85 90 95

Angle

F1

Results & Results & AnalysisAnalysis

Graph C : V=9m/s

y = 0.0000273592x + 0.0023886791

0

0.001

0.002

0.003

0.004

0.005

0.006

40 45 50 55 60 65 70 75 80 85 90 95

Angle

F1

Results & Results & AnalysisAnalysis

Graph D : V=10m/s

y = 0.00003029x + 0.00267907

0

0.001

0.002

0.003

0.004

0.005

0.006

40 45 50 55 60 65 70 75 80 85 90 95

Angle

F1

Results & Results & AnalysisAnalysis

Graph E (V=11m/s)

y = 0.00004718x + 0.00221553

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

40 45 50 55 60 65 70 75 80 85 90 95

Angle

F1

Results & Results & AnalysisAnalysis

Graph Angle (degrees) Gradient of Regression Line (N m-1 s)

F 45 0.000326G 50 0.000270H 55 0.000500I 60 0.000429J 65 0.000310K 70 0.000515L 75 0.000577M 80 0.000516N 85 0.000584O 90 0.000715

Conclusion Conclusion ….….

There is a clear, direct relationship There is a clear, direct relationship between resistive force and the between resistive force and the variables and furthermore more that it variables and furthermore more that it is an increasing function of both of is an increasing function of both of them.them.

It has also been observed that with It has also been observed that with higher wind speed, the resistive force higher wind speed, the resistive force increases more quickly with increasing increases more quickly with increasing angles.angles.

Problems & Problems & ImprovementsImprovements

Problems & Problems & ImprovementsImprovements

Problems & Problems & ImprovementsImprovements

Problems & Problems & ImprovementsImprovements

Problems & Problems & ImprovementsImprovements

Further Further ExperimentExperiment

P

Rocket

Fishing lines connected to the 4 corners of the frame.

Frame to be secured to retort stand.

Wind Tunnel

PART A

PulleyFishing Line

Force Transducer

Voltmeter

Further Further ExperimentExperiment

Slack String

Original Position

Force F acting on string

To Force transducer

Note that because of 4 taut strings holding the rocket to the frame, the rocket can only turn in the frame but cannot move up or down in the frame.

Further Further ExperimentExperiment

Upward force acting on the force transducer’s rod.

Force transducer

Further Further ExperimentExperiment

THE END

Weight BalanceWeight Balance

PulleyPulley

AnemometerAnemometer

Rocket BodyRocket Body

Force TransducerForce Transducer

Wind TunnelWind Tunnel

PivotPivot