Added scripts to calculate M.O.I.

MATLAB/momentOfInertia/getAverageMomentOfInertia.m

+function averageMOI = ...
+    getAverageMomentOfInertia( directoryLocation, massUsed_grams_array )
+    %Given a directory of data labeled "Test_1", "Test_2", etc, will find
+    %the moment of inertia for each data set, using the mass used in grams
+    %at the corresponding index of the massUsed_grams_array. And from
+    %finding all of the moments of inertia, in this way, this function will
+    %return the average.
+    
+    %First find the number of tests we need to run (will be equal to the
+    %length of the massUsed_grams_array)
+    numRuns = length(massUsed_grams_array);
+    
+    %Create a sum variable, to which we will add our calculated MOI values:
+    sumOfMOIs = 0;
+    
+    %For each of the runs, calculate the moment of inertia
+    for i = 1:numRuns
+    
+        %Create the file name for the current run, in string:
+        currFileName = ['Test_', num2str(i), '.csv'];
+        
+        %Create the full file path for the current run:
+        currFullFilePath = [directoryLocation, '\', currFileName];
+        
+        %Get the current mass used in grams
+        massUsed_grams = massUsed_grams_array(i);
+        
+        %Get the moment of inertia for this run
+        curr_MOI = getMomentOfInertia(currFullFilePath, massUsed_grams);
+        
+        %Add this run's moment of inertia value calculated to the sum
+        sumOfMOIs = sumOfMOIs + curr_MOI;
+        
+    end %for i = 1:numRuns
+    
+    %Get the average moment of inertia value, by dividing by the total
+    %number of runs
+    averageMOI = sumOfMOIs / numRuns;
+
+end

MATLAB/momentOfInertia/getMomentOfInertia.m

+function momentOfInertia = getMomentOfInertia( fullFilePath, massUsed_grams )
+%This function will calculate a single moment of inertia value, given a
+%file location to a csv file, along with the mass value used on the mass
+%handle as a torque. (Note, there's no need to have to consider the mass of
+%the handle, which is 5.0 grams, since this function takes care of that)
+
+    %fileLocation = 'C:\Users\Tara\Desktop\Project Documents\Current Project Documents\EE 491\Data\Physics Department Measurements\Test\';
+    %fileName = 'Test_1.csv';
+
+    %Mass used in grams
+    %mass_grams = 200.1;
+    massHandle_grams = 5.0;
+    totalMass_grams = massUsed_grams + massHandle_grams;
+    totalMass_kg = totalMass_grams / 1000.0;
+
+    %Define a cut-off start angle in radians
+    angleStart_cutoff = 0.1;
+
+    %Radius of the knob where the string was pulling from (in meters)
+    radius = 0.04445;   %(4.445 centimeters - or 1.75 inches)
+
+    %Acceleration constant due to gravity (in meters per second squared)
+    g = 9.80665;
+
+    %Define a cut-off "padding" to stop taking data before reaching the end of
+    %the data recorded in the file
+    %For example, if dataEndPadding is 10, we will "cut-off" our data when we
+    %get to 10 data points from the very end of the data run
+    dataEndPadding = 5;
+
+    %Define columns of the table
+    timeCol = 1;
+    angleCol = 2;
+    angularVelCol = 3;
+    %angularAccelCol = 4;
+
+    %Create full file path
+    %fullFilePath = [fileLocation, fileName];
+
+    %Bring in Data
+    dataTable = readtable(fullFilePath);
+
+    %Extract the time, angle (in radians), and angular velocity (in radians per
+    %second) arrays from the data table
+    timeArray = dataTable{:, timeCol};
+    angleArray = dataTable{:, angleCol};
+    angularVelArray = dataTable{:, angularVelCol};
+
+    %Find the first positive angle value
+    i_start = find(angleArray > angleStart_cutoff, 1);
+
+    %Get the start time and start angular position, based on this start index
+    time_start = timeArray(i_start);
+    angle_start = angleArray(i_start);
+
+    %Find the initial angular velocity, which is the corresponding angular 
+    %velocity value at this start index (in radians per second)
+    w_o = angularVelArray(i_start);
+
+    %Determine the end time of our data collection, so first get the length of
+    %the time array
+    timeArray_len = length(timeArray);
+
+    %Get the last index based on the length of the data and the "padding"
+    %amount defined at the beginning
+    i_end = timeArray_len - dataEndPadding;
+
+    %Get the end time and end angular position in radians
+    time_end = timeArray(i_end);
+    angle_end = angleArray(i_end);
+
+    %Get the difference in time and angular position (in radians)
+    angle_diff = angle_end - angle_start;
+    time_diff = time_end - time_start;
+
+    %Using this expression, where alpha is the constant angular acceleration:
+    %   theta_diff = w_o*t_diff + (1/2)*alpha*(t_diff^2)
+    %We can solve for alpha to get
+    %   (theta_diff - w_o*t_diff) = (1/2)*alpha*(t_diff^2)
+    %   2*(theta_diff - w_o*t_diff) / (t_diff^2) = alpha
+
+    %Thus the angular acceleration in radians per second-squared, denoted by 
+    %alpha can be found like this:
+    angularAccel = 2*(angle_diff - w_o*time_diff) / (time_diff * time_diff);
+
+    %This constant angular acceleration should be due to the torque caused by
+    %the gravitational force caused by our falling mass (m*g*r)
+    torque_gravity = totalMass_kg * g * radius;
+
+    %The moment of inertia would be this torque divided by the constant angular
+    %acceleration value (in kilograms meters-squared)
+    momentOfInertia = torque_gravity / angularAccel;
+
+
+end
+

MATLAB/momentOfInertia/getMomentOfInertiaFinalData.m

+%Create the massesUsed_grams_array, which represents the masses we used for
+%each run, which we keep the same for the runs done for each of the
+%testing (yaw, pitch, roll, and their calibration tests as well)
+massesUsed_grams = [200.1, 300.1, 100.1];
+numTrialsPerMass = 5;
+massUsed_grams_array = [ ones(1, numTrialsPerMass) * massesUsed_grams(1), ...
+                         ones(1, numTrialsPerMass) * massesUsed_grams(2), ...
+                         ones(1, numTrialsPerMass) * massesUsed_grams(3)];
+
+%Set the directory locations for the pitch, roll, and yaw data and their
+%calibration runs
+topLevelDir = 'C:\Users\Tara\Desktop\Project Documents\Current Project Documents\EE 491\Data\Physics Department Measurements\Moment of Inertia Data';
+directoryLocation_yawCalib = [topLevelDir , '\Calibration Testing Yaw'];
+directoryLocation_pitchCalib = [topLevelDir, '\Calibration Testing Pitch and Roll'];
+directoryLocation_rollCalib = [topLevelDir, '\Calibration Testing Pitch and Roll'];
+directoryLocation_yawData = [topLevelDir, '\Yaw Data'];
+directoryLocation_pitchData = [topLevelDir, '\Pitch Data'];
+directoryLocation_rollData = [topLevelDir, '\Roll Data'];
+                     
+%Get the average moment of inertia values for the pitch, roll, and yaw data
+%as well as their calibration funs
+averageMOI_yawCalib = getAverageMomentOfInertia( ...
+    directoryLocation_yawCalib, massUsed_grams_array );
+
+averageMOI_pitchCalib = getAverageMomentOfInertia( ...
+    directoryLocation_pitchCalib, massUsed_grams_array );
+
+averageMOI_rollCalib = getAverageMomentOfInertia( ...
+    directoryLocation_rollCalib, massUsed_grams_array );
+
+averageMOI_yawData = getAverageMomentOfInertia( ...
+    directoryLocation_yawData, massUsed_grams_array );
+
+averageMOI_pitchData = getAverageMomentOfInertia( ...
+    directoryLocation_pitchData, massUsed_grams_array );
+
+averageMOI_rollData = getAverageMomentOfInertia( ...
+    directoryLocation_rollData, massUsed_grams_array );
+
+%Now determine the quadcopter's average moment of inertia about the pitch,
+%roll, and yaw axes of rotation
+quadYaw = averageMOI_yawData - averageMOI_yawCalib
+quadPitch = averageMOI_pitchData - averageMOI_pitchCalib
+quadRoll = averageMOI_rollData - averageMOI_rollCalib
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