For this assignment, we will analyze performance characteristics of the Merlin 1D, determine key factors in maintaining consistent performance, and identify methods of improving performance over the baseline design. Your computations must be performed in MATLAB. When presenting data, round your result (at the end!) to three decimal places.

It is up to you to determine how best to present your results (tables, plots, equations, etc.) and

demonstrate your mastery of these topics. Make it easy to follow your thinking and verify your

work (which includes commenting your code)

ANSWER PART 3 based on Part 1 dont solve part 1 only part 3 and the extra credit

Part 3: Merlin Vacuum I The Merlin variant used on the Falcon 9's second stage has essentially the same combustion chamber and pressurization systems as the booster version, but with a significantly extended engine bell to allow for greater expansion. This substantially improves the upper stage's massto-orbit performance at the expense of slightly increase engine mass. To prevent the engine from overstressing the payload, the rocket also throttles down throughout the burn to maintain a constant acceleration. Modify your calculations for the values given in Part 1 to use an expansion ratio of 160:1. Repeat the computations to find specific impulse, exhaust equivalent velocity, and vacuum thrust of the new configuration at full throttle. Continue to assume the vehicle is operating in a vacuum, so that no other quantities need to change (exit Mach, combustion temperature, A, etc.), and the flow remains choked. If the ending thrust is 60% of the full throttle value, estimate the throttled mass flow rate. Extra Credit: Reserve Propellant Running the propellant turbopumps without any propellant flowing through them is an extremely dangerous situation (they can easily overspeed and explode), so the tank is always filled with more than enough propellant to guarantee the delta-V requirement for the launch is met without running dry. While this incurs a performance penalty (extra propellant mass that cannot be burned is carried to orbit), it is necessary to maintain the safety of the rocket and its payload. With the Merlin 1D vacuum engine running in the conditions found in Part 3, how much extra propellant mass is required to provide a five second margin of propellant at burnout, and what is the total impulse of that propellant mass in vacuum? Part 1: Thrust Generation and Analysis As of its 2013 design cycle, each Merlin 1D engine produces a thrust of 850kN in vacuum, with an expansion ratio of 16:1, a mixture ratio of 2.35, and a vacuum specific impulse of 285s. Using the equations provided in class and your knowledge of rocket components, supersonic flow, chemistry, and so on, find the following: - The stoichiometric equation for the reaction (using standard atomic weights from NIST" and taking the definition of RP-1 as CH1.945 ). Use the smallest possible integer coefficients for both propellants. Let oxygen be the limiting reactant, which is completely consumed. - Consider only RP-1 and LOX as propellants, and consider water, carbon dioxide, and residual RP-1 as the only products. Hint: you should solve for the stoichiometric coefficients in Matlab for the first part, but you are free to set up the equation by hand before putting the relationships into the script. - Equivalent velocity, mass flow rate, exit Mach, and exhaust velocity in vacuum, given =1.3, a chamber pressure of 9.65MPa, and an exit area of 0.95 square meters. (Hint: the chamber pressure can be considered stagnation pressure of the flow, and you can ignore pressure losses across the shock at the throat.). - Thrust, specific impulse, equivalent velocity, exit Mach, and exhaust velocity at sea level, if the mass flow rate and mixture ratio remain the same. This is partially a trick question. - The amount of each propellant required to operate the engine at sea level for five minutes. This is partially a trick