AAE251 HW 2
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Purdue University *
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Dec 6, 2023
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1 Name Team Number Andrea Goh A202 AAE 251: Introduction to Aerospace Design Homework 2
—
Space Environment and Aircraft Sizing Due Tuesday February 1
st
, 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]:
3 Question 2 [20 points]: Chapter 3 in Raymer (download from Brightspace) 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. 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 antisubmarine warfare aircraft example for other parameters and the information in Boxes 1, 2 and 3 as a test case for your sizing code, report the converged calculated gross vehicle take-off weight (
𝑊
𝑔?𝑜??
) for a range requirement of: i)
2000 n mi and a payload of 11,000 lb., Mach = 0.7 ii)
3250 n mi and a payload of 8,000 lb., Mach = 0.6 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!
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4 Answer 2a: %User Inputs range = input(
'Input range of cruise in nautical miles: '
); range_ft = range * 6076; %convert range from nautical miles to ft payload_weight = input(
'Input payload weight in pounds: '
); engine_type = menu(
"Choose an engine type:"
, [
"Pure turbojet" "Low-bypass turbofan" "High-
bypass turbofan" "Piston-prop(fixed pitch)" "Piston-prop (variable pitch)" "Turboprop"
]); unit_type = menu(
"Choose a unit type:"
, [
"metric" "English"
]); %Assumed variables mach = 0.6; velocity = mach * 994.8; %ft/s LDmax = 16; loiter_time1 = 10800; %s loiter_time2 = 1200; %s crew_weight = 800; %lb %Other known variables SFC_cruise = [0.9,0.8,0.5,0.4,0.4,0.5] ./ (60*60); %1/s SFC_loiter = [0.8,0.7,0.4,0.5,0.5,0.6] ./ (60*60); %1/s A = 0.93;
5 C = -0.07; %Known weight fractions fraction_WT = 0.97; fraction_C = 0.985; fraction_L = 0.995; %Calculated weight fractions if engine_type <= 3 %if engine is a jet fraction32 = exp(-(range_ft * SFC_cruise(engine_type))/(velocity * LDmax * 0.866)); fraction43 = exp(-(loiter_time1 * SFC_loiter(engine_type)) / LDmax); fraction65 = exp(-(loiter_time2 * SFC_loiter(engine_type)) / LDmax); else %engine is a propeller fraction32 = exp(-(range_ft * SFC_cruise(engine_type))/(velocity * LDmax)); fraction43 = exp(-(loiter_time1 * SFC_loiter(engine_type)) / LDmax * 0.866); fraction65 = exp(-(loiter_time2 * SFC_loiter(engine_type)) / LDmax * 0.866); end %Total weight fractions fraction_total = fraction_WT * fraction_C * fraction32 * fraction43 * fraction65 * fraction32 * fraction_L;
6 fuel_fraction = 1.06 * (1 - fraction_total); %First guess guess_weight = 30000; empty_fraction = A * power(guess_weight, C); calculated_weight = (payload_weight + crew_weight) / (1 - fuel_fraction - empty_fraction); %Iterate guesses until the guess weight equals the calculated weight while guess_weight < abs(calculated_weight) guess_weight = guess_weight + 1; empty_fraction = A * power(guess_weight, C); calculated_weight = (payload_weight + crew_weight) / (1 - fuel_fraction - empty_fraction); end %Convert output to the desired unit that the user wants if unit_type == 1 calculated_weight = calculated_weight / 2.205; fprintf(
'Takeoff weight is %d kg.'
, calculated_weight) else fprintf(
'Takeoff weight is %d lb'
, calculated_weight)
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7 end
8 Answer 2b: i)
70369 lb ii)
281518 lb