2. (25 points) The following describes a tiny part of the airplane design process - Choosing the engine size needed to meet a take-off distance requirement (STO). Sto is the distance an airplane will roll on the runway before it is able to lift off into the air. Calculating Sro is performed using a sequence of five equations shown below. Those equations require seven parameters that control takeoff performance. The engine thrust parameter is a major factor in determining take-off distance. The graph shows how take-off distance gets shorter as engine thrust is increased. Weight -tho-S-Clmax Thrust - 13000 Weight = 56000 $ - 1000 CLmax = 2.4 CD - 0.0279 tho - 0.002377 ge - 322 "To - 1.2 Vstall 6000 4000F B. weight 3 tho-s(Cp)] Sto(trust) 2000F dV 10000 - 30000 20000 thrust 4- 12 Write a Python program that includes and calls the following three functions: def STO(thrust): Thrust: the value of the engine thrust. Important, this is the only argument to be passed to this function. All of the other required airplane parameters may be assumed constant. Local variables for those parameters may be defined and assigned values inside the STO function. Use the airplane parameter values given in the figure above. The function calculates and returns: the airplane take-off distance, calculated using the five equations given above. The first four of those equations calculate the value of three constants to be used in the fifth equation (VTO, A and B). That fifth equation requires the use of numerical integration. Use your Simpson function to perform the integration, b) def ThrustNeededForTakeoff(distance): distance: the required take-off distance. Important, this is the only argument to be passed to this function. All of the other required airplane parameters may be assumed constant. Local variables for those parameters may be defined and assigned values inside the ThrustNeeded For Takeoff function. Use the airplane parameter values given in the figure on the previous page. The function calculates and returns: the engine thrust needed to allow the airplane to take-off in the specified distance. Hint: The ThrustNeeded ForTakeoff function behaves as the inverse of the STO function. Therefore it must use a root-finding method to find the value of thrust that causes: STO(thrust) - distance = 0 Use your Secant function so solve for this value of thrust. c) def main(): main() has no arguments and no return value. main() does the following: a) calls STO (13000) to calculate the take-off distance for an engine thrust of 13000 pounds. Print the answer with one decimal place, using a nice text label. The nice text label should include the thrust value of 13000 pounds. b) calls ThrustNeeded For Takeoff(1500) to calculate the thrust needed to allow takeoff in 1500 feet. Print the answer with two decimal places, using a nice text label. The nice text label should include the takeoff distance of 1500 feet. c) calls ThrustNeeded For Takeoff(1000) to calculate the thrust needed to allow takeoff in 1000 feet. Print the answer with two decimal places, using a nice text label. The nice text label should include the takeoff distance of 1000 feet 2. (25 points) The following describes a tiny part of the airplane design process - Choosing the engine size needed to meet a take-off distance requirement (STO). Sto is the distance an airplane will roll on the runway before it is able to lift off into the air. Calculating Sro is performed using a sequence of five equations shown below. Those equations require seven parameters that control takeoff performance. The engine thrust parameter is a major factor in determining take-off distance. The graph shows how take-off distance gets shorter as engine thrust is increased. Weight -tho-S-Clmax Thrust - 13000 Weight = 56000 $ - 1000 CLmax = 2.4 CD - 0.0279 tho - 0.002377 ge - 322 "To - 1.2 Vstall 6000 4000F B. weight 3 tho-s(Cp)] Sto(trust) 2000F dV 10000 - 30000 20000 thrust 4- 12 Write a Python program that includes and calls the following three functions: def STO(thrust): Thrust: the value of the engine thrust. Important, this is the only argument to be passed to this function. All of the other required airplane parameters may be assumed constant. Local variables for those parameters may be defined and assigned values inside the STO function. Use the airplane parameter values given in the figure above. The function calculates and returns: the airplane take-off distance, calculated using the five equations given above. The first four of those equations calculate the value of three constants to be used in the fifth equation (VTO, A and B). That fifth equation requires the use of numerical integration. Use your Simpson function to perform the integration, b) def ThrustNeededForTakeoff(distance): distance: the required take-off distance. Important, this is the only argument to be passed to this function. All of the other required airplane parameters may be assumed constant. Local variables for those parameters may be defined and assigned values inside the ThrustNeeded For Takeoff function. Use the airplane parameter values given in the figure on the previous page. The function calculates and returns: the engine thrust needed to allow the airplane to take-off in the specified distance. Hint: The ThrustNeeded ForTakeoff function behaves as the inverse of the STO function. Therefore it must use a root-finding method to find the value of thrust that causes: STO(thrust) - distance = 0 Use your Secant function so solve for this value of thrust. c) def main(): main() has no arguments and no return value. main() does the following: a) calls STO (13000) to calculate the take-off distance for an engine thrust of 13000 pounds. Print the answer with one decimal place, using a nice text label. The nice text label should include the thrust value of 13000 pounds. b) calls ThrustNeeded For Takeoff(1500) to calculate the thrust needed to allow takeoff in 1500 feet. Print the answer with two decimal places, using a nice text label. The nice text label should include the takeoff distance of 1500 feet. c) calls ThrustNeeded For Takeoff(1000) to calculate the thrust needed to allow takeoff in 1000 feet. Print the answer with two decimal places, using a nice text label. The nice text label should include the takeoff distance of 1000 feet