Representing the aircraft solid and its weight force vector¶

The plan:

• Read a struct variable representing the aircraft external surface.Use the provided function loadAircraftMAT.
• Plot the faceted shape of the aircraft in a 3D space with the function patch and display the two reference frames ${\mathcal{F}}_{{\mathrm{E}}}$ and ${\mathcal{F}}_{{\mathrm{B}}}$ .
• Plot the weight force vector and its components along the body axes, ${\mathcal{F}}_{{\mathrm{B}}}$ .

Initialize MATLAB¶

In [1]:

clearvars; close all; clc

% make the functions in this work directory available to matlab
% current_dir = pwd;
% addpath(genpath(current_dir));

% Set all interpreters to latex
list_factory = fieldnames(get(groot,'factory'));
index_interpreter = find(contains(list_factory,'Interpreter'));
for i = 1:length(index_interpreter)
    default_name = strrep(list_factory{index_interpreter(i)},'factory','default');
    set(groot, default_name,'latex');
end

clearvars; close all; clc % make the functions in this work directory available to matlab % current_dir = pwd; % addpath(genpath(current_dir)); % Set all interpreters to latex list_factory = fieldnames(get(groot,'factory')); index_interpreter = find(contains(list_factory,'Interpreter')); for i = 1:length(index_interpreter) default_name = strrep(list_factory{index_interpreter(i)},'factory','default'); set(groot, default_name,'latex'); end

Load the 3D model¶

In [2]:

%% Load aircraft shape
shapeScaleFactor = 1.0;
shape = loadAircraftMAT('aircraft_pa24-250.mat', shapeScaleFactor);

%% Load aircraft shape shapeScaleFactor = 1.0; shape = loadAircraftMAT('aircraft_pa24-250.mat', shapeScaleFactor);

Draw the shapes¶

See:

• function plotBodyE.m
• function plotEarthAxes.m
• function plotPoint3DHelperLines.m

In [3]:

%% Setup the figure/scene
h_fig1 = figure(1);

grid on;
hold on;
light('Position',[1 0 -2],'Style','local');
% Trick to have Ze pointing downward and correct visualization
set(gca,'XDir','reverse');
set(gca,'ZDir','reverse');

%% Set the aircraft in place
% Posision in Earth axes
vXYZe = [1,1,-2];
% psi, theta, phi -> 'ZYX'
vEulerAngles = convang([20,10,0],'deg','rad');
% Observer point-of-view
theView = [105 15];
% body axes settings
bodyAxesOptions.show = true;
bodyAxesOptions.magX = 1.5;
bodyAxesOptions.magY = 2.0;
bodyAxesOptions.magZ = 2.0;
bodyAxesOptions.lineWidth = 2.5;
plotBodyE(h_fig1, shape, vXYZe, vEulerAngles, bodyAxesOptions, theView);

%% Plot Earth axes
hold on;
xMax = 2; % max([abs(vXYZe(1)),5]);
yMax = 2; % max([abs(vXYZe(2)),5]);
zMax = 0.2*xMax; % max([abs(max(vXYZe(1))),0.18*xMax]);
vXYZ0 = [0,0,0];
vExtent = [xMax,yMax,zMax];
plotEarthAxes(h_fig1, vXYZ0, vExtent);

%% draw CoG coordinate helper lines
hold on;
helperLinesOptions.lineColor = 'k';
helperLinesOptions.lineWidth = 1.5;
helperLinesOptions.lineStyle = ':';
plotPoint3DHelperLines(h_fig1, vXYZe, helperLinesOptions);

%% Mass data
mass = 1200.0; % kg
g = 9.81; % m/s^2

%% Euler angles
psi   = vEulerAngles(1);
theta = vEulerAngles(2);
phi   = vEulerAngles(3);

%% DCM
% Transf. matrix from Earth- to body-axes
Tbe = angle2dcm(psi, theta, phi, 'ZYX')

%% Setup the figure/scene h_fig1 = figure(1); grid on; hold on; light('Position',[1 0 -2],'Style','local'); % Trick to have Ze pointing downward and correct visualization set(gca,'XDir','reverse'); set(gca,'ZDir','reverse'); %% Set the aircraft in place % Posision in Earth axes vXYZe = [1,1,-2]; % psi, theta, phi -> 'ZYX' vEulerAngles = convang([20,10,0],'deg','rad'); % Observer point-of-view theView = [105 15]; % body axes settings bodyAxesOptions.show = true; bodyAxesOptions.magX = 1.5; bodyAxesOptions.magY = 2.0; bodyAxesOptions.magZ = 2.0; bodyAxesOptions.lineWidth = 2.5; plotBodyE(h_fig1, shape, vXYZe, vEulerAngles, bodyAxesOptions, theView); %% Plot Earth axes hold on; xMax = 2; % max([abs(vXYZe(1)),5]); yMax = 2; % max([abs(vXYZe(2)),5]); zMax = 0.2*xMax; % max([abs(max(vXYZe(1))),0.18*xMax]); vXYZ0 = [0,0,0]; vExtent = [xMax,yMax,zMax]; plotEarthAxes(h_fig1, vXYZ0, vExtent); %% draw CoG coordinate helper lines hold on; helperLinesOptions.lineColor = 'k'; helperLinesOptions.lineWidth = 1.5; helperLinesOptions.lineStyle = ':'; plotPoint3DHelperLines(h_fig1, vXYZe, helperLinesOptions); %% Mass data mass = 1200.0; % kg g = 9.81; % m/s^2 %% Euler angles psi = vEulerAngles(1); theta = vEulerAngles(2); phi = vEulerAngles(3); %% DCM % Transf. matrix from Earth- to body-axes Tbe = angle2dcm(psi, theta, phi, 'ZYX')

Out[3]:

Tbe = 3x3    
    0.9254    0.3368   -0.1736
   -0.3420    0.9397         0
    0.1632    0.0594    0.9848

In [4]:

Teb = Tbe';
vWeight_E = [0;0;mass*g] % N

Teb = Tbe'; vWeight_E = [0;0;mass*g] % N

Out[4]:

vWeight_E = 3x1    
           0
           0
       11772

In [5]:

vWeight_B = Tbe*vWeight_E

vWeight_B = Tbe*vWeight_E

Out[5]:

vWeight_B = 3x1    
1.0e+04 *
   -0.2044
         0
1.1593

In [6]:

%% Draw Weight pointing downward
hold on
scale_weight = 0.0001;
weightVecMag = scale_weight*mass*g;
qW = quiver3( ...
    vXYZe(1),vXYZe(2),vXYZe(3), ...
    0, 0, weightVecMag, ...
    'AutoScale', 'off', 'Color', [1 0 1], ... % weight vector in magenta
    'LineWidth', 2.5 ...
    );

text(vXYZe(1),vXYZe(2)-0.2,vXYZe(3)+1, ...
    ' !!!EQ_4!!! ' ...
    )

%% Vector W_XB * i_B
% application point along z_B
pWZB_B = scale_weight.*[0;0;vWeight_B(3)];
pWZB_E = vXYZe' + Teb*pWZB_B;
% Vector W_XB * i_B (body-components)
vWeight_XB_B = scale_weight.*[vWeight_B(1);0;0];
% Vector W_XB * i_B (Earth-components)
vWeight_XB_E = Teb*vWeight_XB_B;
quiver3( ...
    pWZB_E(1), pWZB_E(2), pWZB_E(3), ...
    vWeight_XB_E(1), vWeight_XB_E(2), vWeight_XB_E(3), ...
    'AutoScale', 'off', 'Color', [0 1 1], ... % vector W_XB*i_B in cyan
    'LineWidth', 2.0, ...
    'MaxHeadSize', 4.0 ...
    );
xlabel(' !!!EQ_5!!! '); ylabel(' !!!EQ_6!!! '); zlabel(' !!!EQ_7!!! ');

%% Draw Weight pointing downward hold on scale_weight = 0.0001; weightVecMag = scale_weight*mass*g; qW = quiver3( ... vXYZe(1),vXYZe(2),vXYZe(3), ... 0, 0, weightVecMag, ... 'AutoScale', 'off', 'Color', [1 0 1], ... % weight vector in magenta 'LineWidth', 2.5 ... ); text(vXYZe(1),vXYZe(2)-0.2,vXYZe(3)+1, ... ' !!!EQ_4!!! ' ... ) %% Vector W_XB * i_B % application point along z_B pWZB_B = scale_weight.*[0;0;vWeight_B(3)]; pWZB_E = vXYZe' + Teb*pWZB_B; % Vector W_XB * i_B (body-components) vWeight_XB_B = scale_weight.*[vWeight_B(1);0;0]; % Vector W_XB * i_B (Earth-components) vWeight_XB_E = Teb*vWeight_XB_B; quiver3( ... pWZB_E(1), pWZB_E(2), pWZB_E(3), ... vWeight_XB_E(1), vWeight_XB_E(2), vWeight_XB_E(3), ... 'AutoScale', 'off', 'Color', [0 1 1], ... % vector W_XB*i_B in cyan 'LineWidth', 2.0, ... 'MaxHeadSize', 4.0 ... ); xlabel(' !!!EQ_5!!! '); ylabel(' !!!EQ_6!!! '); zlabel(' !!!EQ_7!!! ');

Out[6]: