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Developing a Weight and Balance Calculator for Aircraft Safety

School
Iowa State U College of Vet Med**We aren't endorsed by this school
Course
AERO 2
Subject
Industrial Engineering
Date
Dec 11, 2024
Pages
19
Uploaded by caros192004
Joseph Bermudez MedinaIowa State UniversityProject report Aero 161010/17/2024
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Table of ContentsProblem 1Problem Statement .............................................................................page no #3.Theory .................................................................................................page no #3-4.Solution ...............................................................................................page no #5-6.Discussion ..........................................................................................page no #7.Problem 2Problem Statement .............................................................................page no #8.Theory .................................................................................................page no#9-10.Solution ...............................................................................................page no#11.Discussion ..........................................................................................page no#12.Appendix #13
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Problem 1Problem statementThe problem I solved involves creating a weight and balance calculator for the 1965 Piper Cherokee PA-28-180 aircraft, which is essential for safe flight operations. Proper weight and balance calculations are crucial, as incorrect loading can lead to instability and potentially cause accidents. To address this issue, I developed a program that collects the users input regarding fuel amount and the weights of the pilot, co-pilot, and passengers while validating the fuel to ensure it does not exceed the aircraft's maximum capacity of 50 gallons. The program calculates the total weight of the aircraft (ramp weight) by summing the empty weight, fuel weight, and occupant weights. It then computes the moments for different sections of the aircraft to determine the Center of Gravity (CG) and checks if this CG falls within safe limits. If its within safe limits the code will give you the green light to fly.
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Theory1. Weight CalculationRampWeight=𝑊?????+ 𝑊????+ 𝑊?𝑖???+ 𝑊??−?𝑖???+ 𝑊???????? 1+ 𝑊????????? 2Gives us the full weight of the airplane •Variables:o𝑊?????=Empty weight of the aircraft (1471 lbs)o𝑊????=Weight of the fuel calculated as Fuel(gallons)o𝑊?𝑖???= Weight of the piloto𝑊??−?𝑖???= Weight of the co-piloto𝑊???????? 1= Weight of the first passengero𝑊????????? 2= Weight of the second passenger2. Moment CalculationMoment= W x drelates to how weight affects the aircraft's balance based on its distance from a reference point.•Variables:oW=Empty weight of the aircraft (1471 lbs)od: Moment arm, which is the distance from the reference point (inches) for that section
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3. Total Moment Calculation Total Moment=𝑀?????+ 𝑀????+ 𝑀?????_????+ 𝑀???? ????aggregates the moments from various sections of the aircraft, which is crucial for determining stability•Variables:o𝑀?????= Moment due to empty weigho𝑀????= Moment due to fuel, calculatedo𝑀?????_????= Moment due to front seatso𝑀???? ????= Moment due to rear seats4. Center of Gravity Calculation?𝐺 =𝑡?𝑡𝑎? ???𝑒?𝑡𝑟𝑎?? 𝑤𝑒𝑖𝑔ℎ𝑡helps assess whether the aircraft is balanced; a CG within specified limits ensures safe flight operations.•Variables:oCG= center of gravity
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SolutionTo solve the weight and balance problem for the 1965 Piper Cherokee PA-28-180 in MATLAB, I systematically developed a program that collects user inputs for fuel and occupant weights, while ensuring the fuel does not exceed 50 gallons. The program calculates the total ramp weight by summing the empty weight, fuel weight, and the weights of the pilot, co-pilot, and passengers. It then computes the moments for various sections of the aircraft, including the empty weight and fuel, and calculates the Center of Gravity (CG) by dividing the total moment by the ramp weight. The final output displays the ramp weight and CG, confirming whether the aircraft is within the specified weight and balance limits. For testing, I used inputs of 40 gallons of fuel, and weights of 200 lbs for the pilot, 170 lbs for the co-pilot, and 150 lbs for passenger one, resulting in a ramp weight of 2241 lbs and a CG of 93.75 inches, both within acceptable limits. This structured approach effectively ensures safe flight operations by validating the aircraft's weight and balance.
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DiscussionTo solve the weight and balance problem for the 1965 Piper Cherokee PA-28-180 in MATLAB, I developed a program that collects user inputs for fuel and occupant weights, ensuring that the fuel does not exceed 50 gallons. The program calculates the total ramp weight by summing the empty weight, fuel weight, and the weights of the pilot, co-pilot, and passengers. It then computes the moments for various sections of the aircraft and determines the Center of Gravity (CG) by dividing the total moment by the ramp weight. The output displays the ramp weight and CG, confirming whether the aircraft is within the specified weight and balance limits. In my test scenario, I inputted 40 gallons of fuel, with weights of 200 lbs for the pilot, 170 lbs for the co-pilot, and 150 lbs for passenger one, resulting in a ramp weight of 2241 lbs and a CG of 93.75 inches, both of which were within acceptable limits. Therefore, the aircraft is able to fly safely, as it met the criteria for weight and balance.Weight and balance are crucial in aviation because they directly affect the aircraft's performance, stability, and control. An improperly balanced aircraft can lead to difficulties in maneuvering, increased risk of stalling, or even crashes. Throughout the project, I faced challenges in calculations and validating user inputs. To address these issues, I implemented clear input prompts and validation checks within the MATLAB program to guide the user and prevent errors. This structured approach not only helped in maintaining accuracy but also made the program user-friendly, ensuring a reliable analysis of the aircraft's weight and balance. Overall, the project reinforced the importance of weight and balance calculations in aviation safety and operational efficiency.
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Problem 2Problem statementIn this project, I focused on developing a MATLAB program to calculate density altitude, an essential metric for pilots that reflects how air density affects aircraft performance based on real-time weather data. Density altitude takes into account variables such as temperature, humidity, and pressure, which can significantly influence lift and engine efficiency. By utilizing the OpenWeatherMap API, I retrieved current weather information, allowing the program to dynamically calculate density altitude.This project not only deepened my understanding of the factors affecting flight performance but also highlighted the importance of accurate data analysis in aviation safety. Through this process, I aimed to provide a tool that aids in evaluating whether an aircraft can safely operate under given conditions, emphasizing the critical relationship between weather variables and flight capability.
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Theory1.Dewpoint Calculation:𝑻?= 𝑻?-???−??𝒎????𝒚𝟓I converted temperature from Kelvin to Celsius and calculated the dewpoint temperature using the given formula.•Variables:o𝑻?=Dewpoint temperature in Celsiuso𝑻?=Temperature in Celsius2.Vapor Pressure:e=6.11×10(7.5𝑥𝑇?237.7+𝑇⬚)I calculated the vapor pressure and subsequently the virtual temperature based on the weather data.•Variables:oe: Vapor pressure in millibar3.Virtual Temperature:𝑇?=𝑇𝑣1−(?𝑝𝑚𝑏)?(1−0.622)•Variables:o𝑇?=Virtual temperature in Kelvino𝑃??=Pressure in millibar (from API)
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4.Pressure Conversion𝑃𝑖???=𝑃??x 0.02953Using the calculated values, I determined the density altitude•Variables:o𝑃𝑖???=Pressure in inches of mercury5.Density Altitude Calculation:????=FieldElevation+(145366×(1−(17.326×𝑃𝑖???/𝑇?)^0.235))Using the calculated values, I determined the density altitude.•Variables:o????=Density altitudeoFieldElevation= Field elevation (955.6 feet for Ames Airport)
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SolutionTo tackle the density altitude calculation project, I began by retrieving real-time weather data from the OpenWeatherMap API, focusing on extracting key variables such as temperature, pressure, and humidity. Since the API provided temperature in Kelvin, I created a function to convert it to Celsius, which was essential for calculating dew point and vapor pressure. This led to the computation of virtual temperature, which accounts for humidity's effects on air density.The calculated density altitude was approximately 1,481.84 feet, with additional results showing a virtual temperature of 293.2708 K (or 527.9074 Rankine), a pressure of 30.0025 inHg, and a dew point temperature of 5.51°C. This information is crucial in aviation, as it indicates the altitude at which an aircraft feels it is flying under current atmospheric conditions. Higher density altitudes can impair engine performance and lift, making takeoffs and landings more challenging. Understanding density altitude helps pilots assess their aircraft's capabilities and ensure safe operations.Throughout the project, I faced challenges in interpreting the API data and ensuring accurate calculations. I overcame these hurdles by consulting API documentation and debugging my code step by step, which clarified the data structure and reinforced my understanding of how weather variables impact aviation performance. Overall, this project not only improved my programming skills but also highlighted the importance of precise calculations in flight planning.
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DiscussionIn this project, I calculated the density altitude to better understand how weather conditions affect aircraft performance. The density altitude I determined was approximately 1,481.84 feet. This value indicates how high the aircraft feels it is flying, which can significantly influence its lift and engine performance. In aviation, understanding density altitude is crucial; higher density altitudes can lead to reduced engine efficiency and longer takeoff distances, potentially compromising safety.Weight and balance are fundamental aspects of aviation because they directly affect the aircraft's stability and control during flight. An improperly balanced aircraft can lead to difficulty in handling, increased risk of stalling, or even structural damage. Ensuring that the weight is within the aircraft's limits and that the center of gravity falls within specified bounds is essential for safe flight operations.Throughout this project, I faced challenges, particularly in retrieving and interpreting data from the OpenWeatherMap API. Initially, the data structure seemed complex, but by carefully analyzing the returned JSON format and using MATLAB's built-in functions, I was able to extract the necessary values. Debugging my calculations also proved crucial, as ensuring accurate conversions and calculations for vapor pressure, virtual temperature, and ultimately density altitude required attention to detail. This iterative process not only enhanced my technical skills but also deepened my understanding of how various atmospheric conditions impact aviation safety and performance.
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AppendixP1-clear, clc,% Aero 1610, Joseph Bermudezfprintf('Welcome to the Weight and Balance Calculator of the Piper Cherokee PA-28-180!\n');while true% Variables with their respective values and unitsEmpty_Weight = 1471; % lbsCenter_Gravity_empty = 85.9; % inchesFront_Seats = 85.5; % inchesFuel_Tanks_Moment_Arm = 95; % inchesRear_Seats_Moment_Arm = 118.1; % inchesMaximum_ramp_weight = 2400; % lbs% Get user input by calling the function[Fuel, p_weight, co_weight, one_passenger, two_passenger] = getUserInput();% Calculate the weight of the fuel (1 gallon = 6 lbs)F_weight = Fuel * 6;% Calculate the total weight
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Ramp = F_weight + one_passenger + two_passenger + co_weight + p_weight + Empty_Weight;% Print the total weightfprintf('The total weight is: %d lbs.\n', Ramp);% Check if the ramp is over the maximum weightif Ramp > Maximum_ramp_weightfprintf('It''s too heavy to fly.\n');elsefprintf('The weight is within limits, ready to fly!\n');end% Calculate moments for each areaEmpty_Moment = Empty_Weight * Center_Gravity_empty;Pilot_Moment = p_weight * Front_Seats;CoPilot_Moment = co_weight * Front_Seats;Passenger1_Moment = one_passenger * Rear_Seats_Moment_Arm;Passenger2_Moment = two_passenger * Rear_Seats_Moment_Arm;Fuel_Moment = F_weight * Fuel_Tanks_Moment_Arm;% Total momentTotal_Moment = Empty_Moment + Pilot_Moment + CoPilot_Moment + Passenger1_Moment + Passenger2_Moment + Fuel_Moment;% Calculate Center of Gravity (CG)CG_aircraft = Total_Moment / Ramp;% Print CG
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fprintf('Calculated Center of Gravity (CG): %.2f inches\n', CG_aircraft);% Check if CG is within acceptable limitsif CG_aircraft >= 86.8 && CG_aircraft <= 95.8fprintf('The aircraft is within weight and balance limits.\n');elsefprintf('The aircraft is NOT within weight and balance limits and should not be flown.\n');end% Ask the user if they want to run the program againrepeat = input('Press 1 to exit or any other key to continue: ');if repeat == 1break;endendfprintf('Thank you for using the Weight and Balance Calculator! Goodbye!\n');P1,function-function [Fuel, p_weight, co_weight, one_passenger, two_passenger] = getUserInput()% Function to get user inputs for weight and fuelMaximum_Fuel = 50; % gallons% User input for flight information
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Fuel = input('How much fuel is on board? (in US Gallons): ');% Verify that the amount of fuel does not exceed the maximum capacitywhile Fuel > Maximum_Fuelfprintf('You cannot add more than 50 gallons.\n');Fuel = input('Please enter a valid amount of fuel (in US Gallons): ');endp_weight = input('What is the weight of the pilot (in lbs)?: ');co_weight = input('What is the weight of the co-pilot (in lbs)?: ');one_passenger = input('What is the weight of passenger one? (if no passenger enter 0): ');two_passenger = input('What is the weight of passenger two? (if no passenger enter 0): ');endP2-clear, clc%aero 1610, % Define API key,options and url for weather datakey = '7cab1fcaf444883263bc48dd983e6018';options = weboptions('ContentType', 'json');url = ['https://api.openweathermap.org/data/2.5/weather?q=', 'Ames', '&APPID=', key];%data from the API
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CurrentData = webread(url, options);% Extract temperature in Kelvin, pressure, and humiditytemp_K = CurrentData.main.temp; % Temperature in Kelvinpressure = CurrentData.main.pressure; humidity = CurrentData.main.humidity; % Convert temperature from Kelvin to CelsiustempC = kelvinToCelsius(temp_K); % Calculate air density using the ideal gas law% Specific gas constant for dry air in J/(kg*K)R = 287.05; % Density in kg/m^3density = pressure / (R * temp_K); % Assume elevation (replace with actual value if different)% Elevation in metersH = 300; % Standard pressure in hPaP0 = 1013.25; % Calculate density altitudeDA = H + ((P0 - pressure) * 0.12); % Convert hPa to feet% Calculate dewpoint temperature
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dewpoint = tempC - ((100 - humidity) / 5);% Calculate vapor pressurevaporpressure = 6.11 * 10^((7.5*dewpoint)/(237.7+dewpoint));% Assuming temp_K, pressure, and vaporpressure are already defined% Calculate Virtual Temperature (Tv)Tv = temp_K * (1 - (vaporpressure / pressure) * (1 - 0.622));% Convert Virtual Temperature to Rankine (Tvr)virtualtempR = (9/5 * (Tv - 273.15) + 32) + 459.69;% Convert Pressure from Millibar to Inches of Mercury (PinHG)pressure_HG = pressure * 0.02953;% Define field elevation in feetfieldelv = 955.6;% Calculate Density Altitude (Dalt)density_al = fieldelv + (145366 * (1 - (17.326 * (pressure_HG / virtualtempR))^0.235));% Display resultsdisp(['Virtual Temperature (K): ', num2str(Tv)]);disp(['Virtual Temperature (Rankine): ', num2str(virtualtempR)]);disp(['Pressure (inHg): ', num2str(pressure_HG), ' inHg']);disp(['Dew Point Temperature (C): ', num2str(dewpoint)]);disp(['Density Altitude (feet): ', num2str(density_al), ' feet']);
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P2,Function-function tempC = kelvinToCelsius(temp_K)% Converts temperature from Kelvin to CelsiustempC = temp_K - 273.15;end
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