Fall_2023_AAE251_HW2
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Purdue University *
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251
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Industrial Engineering
Date
Feb 20, 2024
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7
Uploaded by ElderRock8381
1 Name Team Number AAE 251: Introduction to Aerospace Design Homework 2
—
Space Environment and Aircraft Sizing Due Tuesday September 12
th
, 11:59 PM ET on Gradescope Instructions This homework is a short homework with only two questions to give you time to complete the Individual Self-Assessment as well. For question 1, you must download the space hazards worksheet, fill it in, and attach it to this HW. For question 2, refer to Raymer Chapter 3, and Raymer Box 3.1 posted on Brightspace. You can add more boxes for space as needed. There are multiple steps involved to complete your submission on Gradescope. You can follow the step-by-step guide posted on Brightspace. Select the relevant pages of your final answer for each question in your Gradescope submission. Check your submission thoroughly after submitting on Gradescope to make sure there is nothing missing. Note: You must submit ONE PDF on Gradescope.
2 Question 1 [30 points]: Download the fillable space hazards worksheet from Brightspace. Complete the worksheet and attach it with your homework.
3 Question 2 [20 points]:
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4 Chapter 3 in Raymer (download from BS) concludes with trade studies for calculating the takeoff weights of an aircraft for ranges of 1000, 1500, and 2000 nautical miles (see Boxes 3.1, 3.2, and 3.3, which summarize the lessons of the entire chapter). a)
Write a well commented MATLAB algorithm that estimates the takeoff weight based on the information from the chapter for a jet transport aircraft performing a typical commercial transport mission (see Fig. 3.2). Your inputs will be range, payload weight, engine type (see Tables 3.3
–
4), unit type (metric, English), as well as any other inputs you deem necessary. Paste your code in the answer box. b)
Using the Boeing 747-400 aircraft and the information in Boxes 1, 2 and 3 as a reference for your sizing code (make sure to adapt the mission to a jet transport mission with 7 crew members –
consider that each crew member weights 200 lb, 45 min per loiter, cruise altitude of 35000 ft, and a divert distance of 200 nmi), report the converged calculated gross vehicle take-off weight (
𝑊
𝑔?𝑜??
) for a range (obs: the range excludes the divert segment distance it only considers the cruise phase traveled distance) requirement of: i)
5750 nmi and a payload of 125,000 lb., Mach = 0.85 ii)
6400 nmi and a payload of 80,000 lb., Mach = 0.80 Aircraft design teams will be using this code in their designs. And all of you will use it again in subsequent homework assignments, so make sure your code is well commented!
5 Answer 2a: % AAE 251 Fall 2023 % Homework 2 % Gross Takeoff Weight % Author: Arya Patel % Input Parameters weight_payload = 125000; % lb weight_crew = 1400; % lb range1 = 5750; % Nautical Mile range2 = range1 - 200; % Nautical Mile cruise_speed_Mach = 0.85; % Cruise speed weight_estimate = 60000; % Initial Weight Estimate (lb) weight_estimate2 = weight_estimate; current_weight_lbs = 0; weight_tolerance_lbs = 2; % Weight tolerance (lb) count = 0; % Iteration Counter % Performance Factors climb_W = 0.97; % Climb cruise_W = 0.985; % Cruise endurance1 = 2700; % s endurance2 = 1200; % s takeoff_W = 0.995; % Calculate GTOW % Constants conversion = 6076; % Nautical miles to feet conversion C1 = 0.00013891; % 1/s C2 = 0.0001111; % 1/s velocity = 0.85 * 1125; % ft/s % Performance Parameters distance1_ft = range1 * conversion; % ft distance2_ft = range2 * conversion; % ft lift_R1 = 13.9; lift_R2 = 17; % Calculate Weight Ratios loiter_W1 = exp(-distance1_ft * C1/ (velocity * lift_R1)); % Loiter cruise_W2 = exp(-endurance1 * C2 / (lift_R2)); % Cruise loiter_W2 = exp(-distance2_ft * C1 / (velocity * lift_R1)); % Loiter land_W = exp(-endurance2 * C2 / (lift_R2)); % Land % Calculate Initial Weight Ratio Wf = takeoff_W * land_W * loiter_W2 * cruise_W2 * loiter_W1 * cruise_W * climb_W; %final weight ratio % Weight Estimation Iteration while abs(weight_estimate - current_weight_lbs) >= weight_tolerance_lbs weight_estimate = weight_estimate2; fuel_weight_ratio = 1.06 * (1 - Wf); empty_weight_ratio = 1.51 * weight_estimate ^ -0.07; empty_weight_lbs = empty_weight_ratio * weight_estimate;
6 current_weight_lbs = (weight_payload + weight_crew) / (1 - fuel_weight_ratio - empty_weight_ratio); weight_estimate2 = current_weight_lbs; count = count + 1; end % Display Results disp([
'Payload Weight: '
, num2str(weight_payload)]) disp([
'Crew Weight: '
, num2str(weight_crew)]) disp([
'Estimated Current Weight: '
, num2str(current_weight_lbs)])
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7 Answer 2b: i)
940752.5901 lb ii)
1,340,642.8334 lb