Rocket Propulsion:

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Theory:

·         Rocket motion is based on Newton’s second law of motion (𝐹 = 𝑚𝑎).

·         Rocket motion is a variable mass problem i.e rocket mass changes as the propellant is used up.

·         Air density varies with altitude.

·         In flight, a rocket is subjected to four forces: thrust, lift, drag, and weight.


Governing equations:

1. Drag equation

𝐷𝑟𝑎𝑔 𝑓𝑜𝑟𝑐𝑒 = 𝐶𝑑 ∗𝜌𝐴𝑣/2

Where:

a)      Cd=drag co-efficient (obtained from the NASA’s Glenn Research Centre website)

b)      Ρ=air density (I used the ISA model because using the standard ideal value of 1.2kg/m3 would not reflect the practical air density conditions encountered during rocket flight)

c)      A= rocket area (frontal) N/B: the area used i.e whether surface or frontal affects the drug force

d)     V= rocket velocity

2. Weight

𝑤 = 𝑚 ∗ 𝑔


MATLAB Simulation Model



About the Model:

·         Thrust is imported from excel file into a work space variable. It is set to zero at the end of burn time since in the practical sense, we do not expect thrust generation after all the fuel has been used up.

·         The rocket simulation is a non-linear simulation with mass varying over time. This is also expected during a practical rocket flight. After all the fuel has undergone combustion, the mass of the rocket is constant for the rest of the flight.

·         The thrust, motor impulse, propellant mass, rocket mass rocket diameter and area can all be changed.

Simplified assumptions:

·         Initial launch angle is 0 ͦ

·         The rocket is a single stage rocket

·         Initial velocity of the rocket is zero

·         Lift force is zero


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