Aerodynamics and Trajectory

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Indian Institute of Space Science and Technology

Aerodynamics and

Trajectory design of

Sounding Rocket Preliminary Design Report

Vijith Mukundan, Pulkit Goyal, Jyothish R Pillai

5/24/2010



1. Objectives

1. To design a sounding rocket that is stable throughout its flight.

2. To minimize drag and maximize the performance of the sounding rocket.

3. To predict the trajectory and various parameters related to trajectory based on the

Thrust-time profile and the Aerodynamic design.

2. Progress achieved till now

1) A trajectory (and trajectory parameters) has been generated using drag data of

RH200 sounding rocket.

2) Heat flux on the nose cone has been roughly estimated using an empirical relation.

3) Methodology for design of fins and nose cone (and their analysis for obtaining refined

trajectories) has been worked out.

3. Parts to be designed and their design methodology

3.1. Nose cone

The nose cone design is of great significance for any flying vehicle. As for a rocket, the

nose cone is the part that first interacts with the flow. It diverts the flow coming at the

rocket and thus determines the drag forces on the rocket. It protects the payload and

dissipates the heat produced by drag, efficiently.

Generally, a nose cone of a particular profile is efficient only at some range of velocities.

Thus, knowledge of velocity variation during flight is essential for designing a good nose

cone.

Various nose cone profiles are used in sounding rockets. Some of them are: Conical,

Tangent Ogive, Secant Ogive, Von-Karman nose, Elliptical, Parabolic.

In our project we have chosen to have conical nose due to its ease of analysis and

fabrication.

3.1.1. Design methodology for nose cone

Design of an optimum nose is a trade off between nose tip heat flux and drag coefficient.

Bluntness is provided at the tip to reduce heat flux. Bluntness, on the other hand,

increases drag coefficient of the nose.

Similarly, nose cone angle is decided to minimize nose tip heat flux, drag coefficient and

normal force. A large nose cone angle will give low heat flux but will have large drag

coefficient. On the other hand, a small cone angle will decrease drag but will have high

heat flux.

As the rocket diameter has been fixed, a small nose cone angle means a long nose and

hence larger normal force.



Considering the above conditions, a nose cone has to be designed based on the

constraints given by the Thermal Protection and Trajectory.

3.2. Fins

Fins are essential to keep the Center of pressure X cp of the rocket behind the Center of gravity X cg and thus maintaining a positive Static margin. Static Margin= (Xcp Xcg )/ D .

This plays a key role in stabilizing the rocket during its flight.

The fins of the rocket are meant to produce a negative, or stabilizing, pitching moment if

the rocket encounters a positive angle of attack.This has to be achieved keeping its C d

low.

There are many fin configurations like rectangular, delta, clipped delta, trapezoidal,

elliptical. We have chosen rectangular fins because of ease of analysis.

3.2.1. Design methodology for fins

Based on the variation of CG of the rocket during the flight and the moment on the

rocket, a fin has to be designed to generate sufficient force to balance the moment on

the rocket.

The fin dimensions then has to be optimized to minimize drag and vortex formation.

3.3. Body

The body of the rocket has been finalized to be a cylinder of 200mm diameter and a

specified length owing to manufacturing considerations, and hence no change can be

made to this.

3.4 Overall design process

On every design of nose and fins, the drag coefficient of the entire rocket changes and

this affects the trajectory of the rocket. With this, some trajectory parameters which

have been used to design nose and fins also change. Thus we have to perform a few

iterations until we reach an optimum and stable design.

The design calculations related to the nose cone and fins will initially be done using

empirical relations and will then be validated using CFD simulation.



4. Trajectory calculation methodology

4.1. Assumptions

1. The Flat earth gravity model is used.

2. It is assumed that the angle of attack is always zero.3. For drag, the fore body drag data of RH200 has been used because of its similarity to

the dimensions of our rocket.

4. The exponential model of density variation and standard atmospheric model of

temperature variation in atmosphere has been used.

5. It is assumed that the initial velocity as 0.1 m/s in x direction and 1.14 m/s in y

direction, due to difficulty in giving initial condition owing to the zero angle of attack

scenario.

6. Reference area is cross-sectional area of cylinder.

7. An empirical relation is used for heat flux calculation around nose (Drag variation

with nose radius not considered)

q=1.83 X 10 -4 X

X (V) 3 X

q=heat flux; Rn=Nose radius; V= velocity; hw= enthalpy at wall; hw is taken

corresponding to constant 300K surface temperature.

4.2. Formulation



The governing equations are:

��

��

Splitting these equations by the substitution,

We have,

��

��

, obtained as input from the propulsion team

��

, where Re=6378km

��)

, where R=287 m/sK and =1.4



Drag data of RH200 is given below:

Mach no. M CD

0 0

0.4 0.2609

0.6 0.28420.8 0.2861

0.9 0.3289

0.94 0.3787

1.05 0.5159

1.1 0.5122

1.2 0.5011

1.6 0.4179

2.0 0.3738

2.5 0.3315

3.0 0.2908

3.5 0.2627

3.8 0.2429

These values have been fitted using parabolic interpolation. After mach no. 3.8, a

constant CD=0.2429 has been used.

The atmospheric temperature model used in the calculations is given below:



4.3. Solution of the governing equations

The governing equations are then numerically solved with the following initial

conditions:

The initial conditions of velocities in x and y directions give the launch angle of 87 o. We

have obtained the trajectories for different initial masses corresponding to different

options of materials used.

The thrust-time data is provided by the propulsion team, which completes the

requirements for generating the solution. This is given below:

Burn time=14.87s



4.4. Trajectory results

4.4.1. Variation of trajectory with mass

Initial mass

(kg)

Max.

Altitude(km)

Max.

Acceleration(in gs)

Max. Mach

no.

Max.

Velocity(km/s)

Dynamic

pressure(kPa)

54 48.9665 96.66 8.5329 2.5474 930.659

56 55.1672 71.08 7.9 2.3756 860.016

58 58.0289 56.14 7.3731 2.2317 810.163

60 58.6206 50.21 6.923 2.1079 767.635

62 57.7601 45.55 6.5315 1.9996 730.4296

64 55.9914 41.78 6.1859 1.9033 697.2402

66 53.6669 38.67 5.8774 1.8169 667.2285





4.4.2. Trajectory parameters for two specific initial masses

Initial mass 54kg 66kg

Max. altitude(km) 48.9665 53.6669

Max. mach number 8.5329 5.8774

Max. acceleration (in gs) 96.66 38.67

Max. dynamic pressure

(kPa)

920.659 667.2285



4.4.3. Trajectory plots for initial mass of 54kg







4.4.4. Plots for initial mass of 66kg





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Aerodynamics and Trajectory