ENGG952 - Engineering Computing - Report Writing Assignment Help

ENGG952 - Engineering Computing - Report Writing Assignment Help

Task:

Question 1: Rocket Flight - ENGG952
The flight of a test rocket weighing 25 metric tonnes can be modelled as follows. At time t = 0, the rockets engines generate exactly the right amount of upward thrust to maintain the rocket against gravity. From t = 0 to 10s, the thrust increases linearly to a maximum of 50000 kgf (kilogram-force). The engines then shut down and the rocket moves only under the force of gravity. After it reaches the apex the rocket starts to fall back down. When the magnitude of the downwards velocity reaches v = 30 m/s, a parachute opens and the rocket continues to move down at a constant speed of chute v = 20 m/s until it hits the ground (assume parachute deployment and change in velocity are instant).

Write a MATLAB program that calculates and plots the speed and altitude of the rocket as a function of time during the flight.
Tips for analysis of the problem
• The force of gravity, g = 9.81 m/s2
• The rocket may be assumed to be a particle that moves along a straight line in the vertical plane.
• Make sure all your values are converted to consistent SI units
A. Stage 1: The first 10s when the rocket engine is on. During this period, the rocket moves up with an acceleration determined by,

m
F mg a − =

where, F is the instantaneous thrust of the engines. The velocity and height as a function of time are: v(t) = at and 2
2
1 h(t) = at

where, the initial velocity and initial position are both zero. The time, velocity, and height at the end of this stage are t1, v1, and h1

B. Stage 2: The motion from when the engine stops until the parachute opens. In this stage the rocket moves with a constant deceleration, g. The speed and height of the rocket as a function of time are given by:

( ) ( ) 1 1 v t = v − g t − t 2
1 1 1 1 ( ) 2
1 h(t) = h + v (t − t ) − g t − t

The time and height at the end of this stage are t2, and h2
C. Stage 3: The motion from when the parachute opens until the rocket hits the ground. In this stage the rocket moves with constant velocity (zero acceleration). The height as a function of time is given by:

( ) ( ) 2 2 h t h v t t = − chute −
where, chute v is the constant velocity after the parachute opens.
D. Does the rocket reach a height of 1km measured from its starting position? If yes, what is the overshoot? If not, then what maximum thrust is required to achieve this height?

Question 2: Solution of equation - ENGG952
Mechanical engineers, as well as most other engineers, use thermodynamics extensively in
their work. The following polynomial can be used to relate the zero-pressure specific heat of
dry air, ccpp kJ/(kg K), to temperature (K):

ccpp = 0.99403 + 1.671 × 10−4TT + 9.7215 × 10−8TT2
−9.5838 × 10−11TT3 + 1.952 × 10−14TT4

Question 3: Cable tension analysis - ENGG952
An object of mass M kg is hung from the end of a rigid 2.5m long horizontal pole of negligible weight. The pole is attached to the wall by a pivot and is supported by a 2.2m cable that is attached to the wall at a higher point as shown in the figure below. The tension in the cable can be calculated as,

TT = 9.81 ∗ MM ∗ llcc ∗ llpp
dd?llcc
2 − dd2

Where, TT is the tension in the cable (N), M is the mass of the object (kg), llcc is the length of the cable (m), llpp is the length of the pole (m) and dd is the distance between the wall and the attachment point of the cable to the pole (m). Set M as the sum of the ages of all team members in your team.

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