presentation

Engineering MechanicsEngineering Mechanics

Presented by- Ashruth Vallabdhas

Chandan Kumar Sinha Prathamesh Deshmukh

Vineeth Bodapati Chandan Yadav

Term Project Semester II2014

Structural and Force Analysis of RocketStructural and Force Analysis of Rocket

Force AnalysisForce Analysis Basic Forces Basic Forces

● Weight Gravitational forces acting on various parts of rocket.

● Thrust Due to exhaust of gases making rocket a variable mass system.

● Drag and Lift – Aerodynamic forces due to relative movement between fluid and solid body. (Acts on Centre of Pressure of which 'drag' and 'lift' are the components along and perpendicular to flight movement respectively)

Source- http://exploration.grc.nasa.gov/educationTrivia- For rocket aligned with flight path, lift

force is zero.

Weight & Centre of GravityWeight & Centre of Gravity

● The weight of the system keeps on changing due to exhaust of gases.

● As the consequence, the centre of gravity keeps shifting.

● Internal arrangement of rocket is kept such that the centre of gravity is as close to the nose as possible.

Source- nasa.gov/force.model.rocket.pdf

Rocket Equation- Rocket Equation- A variable mass systemA variable mass system

Source- http://www.real-world-physics-problems.com

=Tangential component of external forces (gravity+drag)

= Relative velocity of exhaust wrt. rocket (const. at any time t)

(1)

● Thrust force acts in the opposite direction when the mass is leaving the system.

If the gravity & drag is neglected, then

In that case-

Aerodynamic aspectsAerodynamic aspects ● Lift and Drag forces are net forces normal and

parallel to air flow respectively.

Rocket Drag equationDynamic pressure

CD : Drag coefficient. Contains all complex dependencies like air compressibility, viscosity body shape and angle-of-attack.

A : Reference area, typically the base diameter of the nose. Different A, affect the value of CD.

: Density of the atmosphere of consideration (typically.23kg/m3 for air at sea-level).

The Force Factor-The Force Factor-(A comparison between airplane and rocket)(A comparison between airplane and rocket)

Well, when we look into these two modern technologies- airplane & rocket, a novice thought is all they do is just flying in sky consisting of almost similar forces, but there are some significant differences in the application of forces:

Aspects AeroplaneAeroplane RocketRocket

Lift forces Used to overcome the weight.Lift is used to stabilize and control the direction of flight. Thrust is used in opposition to weight.

Aerodynamic Forces

Generated by wings and tail surfaces.

generated by the fins, nose cone, and body tube.

Lift to drag ratio

High Low, drag is usually much greater than the lift.

Acting Forces Magnitude and direction remains fairly constant.

Changes dramatically during a typical flight.

Center of Pressure (CCenter of Pressure (Cpp)-)-

Source- tir-33.pdf by centuri

● Its the point where all the air pressure acting on rocket seem to be concentrated. Air pressure force distributed on the rocket ahead of Cp is same as there behind it.

● Normal air pressure force mainly determines the Cp while axial forces contributes to aerodynamic drag, important for calculating altitude performance of rocket.

No role in determining stability.

Center of Pressure Center of Pressure (Theoretical calculation)(Theoretical calculation)Assumptions-

● Rocket align itself parallely to the air flow (angle of attack 0)

● Speed is low as compared to speed of sound ( mach number<0.6)

● The structure is ideal (thin compared to length, tip-pointed nose, axial symmetry, flat plates fins).

Normal force acting on rocket

= Coefficient of normal force accounting for shape of rocket.

= Refrence area indicating size. Generally equals cross sectional area at the base of nose.

= Angle of attack

● In general,the normal force on the nose is identical for all shapes while location on nose varies with each different nose shape.


Stability Criteria-Stability Criteria-

● As told earlier, the lift force is zero when rocket is aligned along flight path.

● But what if it isn't?

● Now the 'angle of attack' comes into role affecting the size and shape of the normal force distribution.

● The consequent normal force developed acting on centre of pressure produces a torque about centre of gravity in order to decrease .

● The distance between and is called 'static margin'. It should be larger in order to bring to zero proportionally faster.

Stabil i ty Criteria Stabil i ty Criteria.-cont.-cont

● The important conclusion drawn from it Centre of pressure should be behind the Center of gravity.

● As rocket's angle of attack increases, the moves forward, simultaneously causing unstability in the rocket.

● But why the produced torque act about Centre of gravity only?

● In free flight, any body rotates about its centre of gravity.


Source- https://encrypted-tbn3.gstatic.com/images

More about structural analysisMore about structural analysis (Fuselage structural strength) (Fuselage structural strength)● Why do the shape of fuselage cylindrical mainly?

– High strength of thin-walled aluminium cylinder loaded primarily in axial compression.

– structurally efficient, carrying the applied load in such a manner that the load is evenly distributed, resulting in an even stress level throughout the wall.

– The applied stress in cylinder walls is given by-

P=applied load (lbs), D=avg. Fuselage diameter, t=wall thickness.

– With L/D ratio > 15, bukling failure occurs.

Source-http://www.nakka-rocketry.net/fusestru.html

An Example An Example

http://www.nakka-rocketry.net/fusestru.html

So, if we take a model rocket with specifications- L= 20 inch, wall thickness t = 0.016 inch, the average diameter D = 2.234 inch

● Fuselage strength- If the fuselage is made up of aluminium, then compressive yield strength is about 15000psi.So max. allowable axial load that can be handled-

● Fuselage loading- 1.Calculating the aerodynamic force using earlier formula-

2.Additionally, inertial force acts here with m=2.0lbs & g

max=50 g's

Total compressive force,

Which is much less than previously allowable Which is much less than previously allowable compressive foce, thus having wide margin of safety.compressive foce, thus having wide margin of safety.