The newly designed Raptor Rocket Engine by SpaceX utilizes liquid methane (CH.(1)) as the propellant and...

 

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The newly designed Raptor Rocket Engine by "SpaceX" utilizes liquid methane (CH.(1)) as the propellant and liquid oxygen (O(1)) as the oxidizer. The thrust produced by the Raptor is related to the flow rate of the propellant and the oxidizer. An experimental observation is carried out by taking different mixtures of the propellant (P) and oxidizer (X) and the Net Thrust (T) is recorded for different settings. The observed data is as follows: Propellant Flow Rate Oxidizer Flow Rate (P, kg/sec) (X, kg/sec) 100 110 120 130 140 150 160 170 180 190 550 570 590 610 630 650 670 690 710 730 Net Thrust (T, KN) 1650 1810 1975 2140 2305 2470 2635 2800 2970 3140 (a) As an Engineer tasked to do the calculations, establish a relationship between the net thrust (T) and the propellant/oxidizer (P and X) flow rates using a proper numerical method from the above data. Estimate the standard error of your model to verify that your relationship is optimal. [Hints: The relationship might be either Linear i.e., have the form: y = ao+a11 +0222 or the relationship might have an exponential form: y = ao or might have the quadratic form: y = ao + aiz+axx + 3x (b) The existing turbo pumps at SpaceX can hypothetically produce a maximum O(1) flow rate of 900 kg/sec and CH4 (1) flow rate of 250 kg/sec. Without going on to the test bench again, can you utilize your obtained relationships in the previous step to predict the Net Thrust at the Maximum Settings of the turbo pumps? (c) Model the system using another mathematical model you have not used in (a). Repeat (b) for the new model and report the percent deviation of the result. calculations should be done using minimum 3 digits of significance. The newly designed Raptor Rocket Engine by "SpaceX" utilizes liquid methane (CH.(1)) as the propellant and liquid oxygen (O(1)) as the oxidizer. The thrust produced by the Raptor is related to the flow rate of the propellant and the oxidizer. An experimental observation is carried out by taking different mixtures of the propellant (P) and oxidizer (X) and the Net Thrust (T) is recorded for different settings. The observed data is as follows: Propellant Flow Rate Oxidizer Flow Rate (P, kg/sec) (X, kg/sec) 100 110 120 130 140 150 160 170 180 190 550 570 590 610 630 650 670 690 710 730 Net Thrust (T, KN) 1650 1810 1975 2140 2305 2470 2635 2800 2970 3140 (a) As an Engineer tasked to do the calculations, establish a relationship between the net thrust (T) and the propellant/oxidizer (P and X) flow rates using a proper numerical method from the above data. Estimate the standard error of your model to verify that your relationship is optimal. [Hints: The relationship might be either Linear i.e., have the form: y = ao+a11 +0222 or the relationship might have an exponential form: y = ao or might have the quadratic form: y = ao + aiz+axx + 3x (b) The existing turbo pumps at SpaceX can hypothetically produce a maximum O(1) flow rate of 900 kg/sec and CH4 (1) flow rate of 250 kg/sec. Without going on to the test bench again, can you utilize your obtained relationships in the previous step to predict the Net Thrust at the Maximum Settings of the turbo pumps? (c) Model the system using another mathematical model you have not used in (a). Repeat (b) for the new model and report the percent deviation of the result. calculations should be done using minimum 3 digits of significance.