From 4fbe70cf817d2e31cbae5aae264d0ef1a3821afc Mon Sep 17 00:00:00 2001
From: blendoit <blendoit@gmail.com>
Date: Mon, 30 Sep 2019 18:47:15 -0700
Subject: Delete MATLAB scripts

---
 README.org                          |   6 +-
 wing_scripts/eye_beam_example.m     |  70 -----
 wing_scripts/get_dp.m               |   4 -
 wing_scripts/get_ds.m               |  20 --
 wing_scripts/get_int.m              |  35 ---
 wing_scripts/get_z.m                |  34 ---
 wing_scripts/my_progress.m          | 459 ----------------------------
 wing_scripts/stringersBeamExample.m |  47 ---
 wing_scripts/wingAnalysis_190422.m  | 579 ------------------------------------
 9 files changed, 4 insertions(+), 1250 deletions(-)
 delete mode 100644 wing_scripts/eye_beam_example.m
 delete mode 100644 wing_scripts/get_dp.m
 delete mode 100644 wing_scripts/get_ds.m
 delete mode 100644 wing_scripts/get_int.m
 delete mode 100644 wing_scripts/get_z.m
 delete mode 100644 wing_scripts/my_progress.m
 delete mode 100644 wing_scripts/stringersBeamExample.m
 delete mode 100644 wing_scripts/wingAnalysis_190422.m

diff --git a/README.org b/README.org
index caa04a9..a2cb900 100644
--- a/README.org
+++ b/README.org
@@ -1,7 +1,9 @@
-#+TITLE: UCLA MAE 154B
-#+SUBTITLE: Spring 2019 Final Project
+#+TITLE: Aircraft Studio
+#+AUTHOR: Marius Peter
 
 This program enables the creation of NACA airfoils;
 the analysis of the airfoil's structural properties;
 the optimization via genetic algorithm of a population of airfoils;
 With the final objective of designing a lightweight FAR 23 compliant airfoil.
+
+I adapted it from my own code for the UCLA MAE 154B final project (Spring 2019).
diff --git a/wing_scripts/eye_beam_example.m b/wing_scripts/eye_beam_example.m
deleted file mode 100644
index 70b4d92..0000000
--- a/wing_scripts/eye_beam_example.m
+++ /dev/null
@@ -1,70 +0,0 @@
-% Bending/Shear stress example
-close all; 
-
-length = 20; % in
-force = 10000; %lbs
-
-%eye-beam dimensions
-
-max_width = 4; % in
-min_width = 1; % in
-y_max = 4; % in
-center_y = 2; % in
-
-
-%max bending moment at the root...
-
-M = force*length;
-
-I = min_width*(2*center_y)^3/12 + 2*( max_width*(y_max-center_y)^3/12 + ...
-    max_width*(y_max-center_y)*((y_max+center_y)/2)^2);
-
-sigma_max = M * y_max / I;
-
-
-% solve for shear stress distribution
-% V / (I * t) * int(y*da)
-
-% Point 1: evaluated at location just before thickness changes from 4 to 1 in
-tempCoeff = force / (I * max_width);
-int_y_da = ((y_max+center_y)/2) * max_width*(y_max-center_y);
-shear_1 = tempCoeff*int_y_da;
-
-% Point 2: evaluated at location just after thickness changes from 4 to 1 in
-tempCoeff = force / (I * min_width);
-shear_2 = tempCoeff*int_y_da;
-
-
-% Point 3: evaluated at center of beam
-tempCoeff = force / (I * min_width);
-int_y_da = (center_y/2) * min_width*center_y;
-shear_3 = shear_2+tempCoeff*int_y_da;
-
-%evaluating continous integral for width of 4..
-int_y_da_4 = force / (I * max_width)*4*(y_max^2/2 - (center_y:.1:y_max).^2/2);
-
-%evaluating continous integral for width of 1..
-int_y_da_1 = shear_2 + force / (I * min_width)*1*(center_y^2/2 - (0:.1:center_y).^2/2);
-
-figure; grid on; hold on;set(gcf,'color',[1 1 1]);
-plot(int_y_da_4,center_y:.1:y_max,'linewidth',2)
-plot(int_y_da_1,0:.1:center_y,'linewidth',2)
-plot(int_y_da_1,0:-.1:-center_y,'linewidth',2)
-plot(int_y_da_4,-center_y:-.1:-y_max,'linewidth',2)
-plot([shear_1 shear_2],[center_y center_y],'linewidth',2)
-plot([shear_1 shear_2],[-center_y -center_y],'linewidth',2)
-
-plot(shear_1,center_y,'o')
-plot(shear_2,center_y,'o')
-plot(shear_3,0,'o')
-plot(shear_2,-center_y,'o')
-plot(shear_1,-center_y,'o')
-
-xlabel('shear stress (lb/in^2)','fontsize',16,'fontweight','bold');ylabel('Distance from Center (in)','fontsize',16,'fontweight','bold')
-set(gca,'FontSize',16,'fontweight','bold');
-
-
-figure; grid on; hold on;set(gcf,'color',[1 1 1]);
-plot([0 4 4 2.5 2.5 4 4 0 0 1.5 1.5 0 0],[4 4 2 2 -2 -2 -4 -4 -2 -2 2 2 4],'linewidth',2)
-
-
diff --git a/wing_scripts/get_dp.m b/wing_scripts/get_dp.m
deleted file mode 100644
index 2a3281d..0000000
--- a/wing_scripts/get_dp.m
+++ /dev/null
@@ -1,4 +0,0 @@
-function z = get_dp(xDist,zDist,Vx,Vz,Ix,Iz,Ixz,A)
-
-denom = (Ix*Iz-Ixz^2);
-z = -A*xDist*(Ix*Vx-Ixz*Vz)/denom - A*zDist*(Iz*Vz-Ixz*Vx)/denom;
diff --git a/wing_scripts/get_ds.m b/wing_scripts/get_ds.m
deleted file mode 100644
index 2f0eb9d..0000000
--- a/wing_scripts/get_ds.m
+++ /dev/null
@@ -1,20 +0,0 @@
-function ds = get_ds(xi,xf,u)
-
-dist = 0;
-numSteps = 10;
-dx = (xf-xi)/numSteps;
-z0 = get_z(xi,u);
-x0 = xi;
-for i=1:10
-    tempX = x0+dx;
-    if tempX > 0
-        tempZ = get_z(tempX,u);
-    else 
-        tempZ = 0;
-    end
-    dist = dist + (dx^2+(tempZ-z0)^2)^.5;
-    z0 = tempZ;
-    x0 = tempX;
-end
-
-ds =dist;
\ No newline at end of file
diff --git a/wing_scripts/get_int.m b/wing_scripts/get_int.m
deleted file mode 100644
index edbfda3..0000000
--- a/wing_scripts/get_int.m
+++ /dev/null
@@ -1,35 +0,0 @@
-function z = get_int(xi,xf,u)
-
-M = 0.02;
-P = 0.4;
-T = 0.12;
-a0 = 0.2969;
-a1 = -0.126;
-a2 = -0.3516;
-a3 = 0.2843;
-a4 = -0.1015;
-
-
-%evaluate the integral of camber line, depending on xi and xf related to P
-
-if xf <P
-    intCamb =  M/P^2*(2*P*xf^2/2 - xf^3/3) - M/P^2*(2*P*xi^2/2 - xi^3/3);   
-elseif xi<P
-    intCamb = (M/(1-P)^2)*((1 - 2*P)*xf +2*P*xf^2/2 - xf^3/3) - (M/(1-P)^2)*((1 - 2*P)*P +2*P*P^2/2 - P^3/3);
-    intCamb = intCamb + M/P^2*(2*P*P^2/2 - P^3/3) - M/P^2*(2*P*xi^2/2 - xi^3/3);
-else
-    intCamb = (M/(1-P)^2)*((1 - 2*P)*xf +2*P*xf^2/2 - xf^3/3) - (M/(1-P)^2)*((1 - 2*P)*xi +2*P*xi^2/2 - xi^3/3);
-end
-
-% do integral on thickness line
-%z_thickness = (T/0.2)*(a0*x^.5+a1*x+a2*x^2+a3*x^3+a4*x^4);
-
-intThickness = (T/0.2)*(a0*xf^1.5/1.5 + a1*xf^2/2 + a2*xf^3/3 + a3*xf^4/4 +a4*xf^5/5);
-intThickness = intThickness - (T/0.2)*(a0*xi^1.5/1.5 + a1*xi^2/2 + a2*xi^3/3 + a3*xi^4/4 +a4*xi^5/5);
-
-% combine both integral results to get total integral
-if u == 1
-   z = intCamb + intThickness; 
-else
-   z = abs(intCamb - intThickness);
-end
\ No newline at end of file
diff --git a/wing_scripts/get_z.m b/wing_scripts/get_z.m
deleted file mode 100644
index 5387b52..0000000
--- a/wing_scripts/get_z.m
+++ /dev/null
@@ -1,34 +0,0 @@
-function z = get_z(x,u)
-
-
-
-if (x < 0 )
-    disp('invalid X')
-end
-
-M = 0.02;
-P = 0.4;
-T = 0.12;
-a0 = 0.2969;
-a1 = -0.126;
-a2 = -0.3516;
-a3 = 0.2843;
-a4 = -0.1015;
-
-if x <P
-    z_camber = M/P^2*(2*P*x - x^2);
-else
-    z_camber = (M/(1-P)^2)*(1 - 2*P +2*P*x - x^2);
-end
-
-%z_camber = M/P^2*(2*P*x - x^2);
-z_thickness = (T/0.2)*(a0*x^.5+a1*x+a2*x^2+a3*x^3+a4*x^4);
-
-if u==1
-    z = z_camber + z_thickness;
-else
-    z = z_camber - z_thickness;
-end
-
-
-
diff --git a/wing_scripts/my_progress.m b/wing_scripts/my_progress.m
deleted file mode 100644
index e87ef23..0000000
--- a/wing_scripts/my_progress.m
+++ /dev/null
@@ -1,459 +0,0 @@
-%wing shear flow
-clear all;
-close all;
-
-Vx = 1; Vz = 1; My = 1;  %test loads will be applied individually
-
-
-%Ixz = -Ixz;
-
-%define webs
-
-%% web cell 1
-
-%upper webs
-numStringers = numTopStringers;
-stringerGap = upperStringerGap;
-webThickness = t_upper;
-tempStringers = topStringers;
-
-for i=1:(numStringers+1)
-    web(i).xStart = sparCaps(1).posX + stringerGap*(i-1);
-    web(i).xEnd = sparCaps(1).posX + stringerGap*(i);
-    web(i).thickness = webThickness;
-    web(i).zStart = get_z(web(i).xStart/chord,1)*chord;
-    web(i).zEnd = get_z(web(i).xEnd/chord,1)*chord;
-    if i==1
-        web(i).dp_area = sparCaps(1).area;
-        web(i).dP_X = 0;
-        web(i).dP_Z = 0;
-        web(i).qPrime_X = 0;
-        web(i).qPrime_Z = 0;
-    else
-        web(i).dp_area = tempStringers(i-1).area;
-        dx = web(i).xStart-centroid.posX; dz = web(i).zStart-centroid.posZ;
-        web(i).dP_X = get_dp(dx,dz,Vx,0,Ix,Iz,Ixz,web(i).dp_area);  %just Vx
-        web(i).dP_Z = get_dp(dx,dz,0,Vz,Ix,Iz,Ixz,web(i).dp_area);  %just Vz
-        web(i).qPrime_X = web(i-1).qPrime_X - web(i).dP_X;
-        web(i).qPrime_Z = web(i-1).qPrime_Z - web(i).dP_Z;
-    end
-    tempInt = get_int(web(i).xStart/chord,web(i).xEnd/chord,1)*chord^2;  %integral of airfoil function
-    triangle1 = abs( (web(i).xStart - sparCaps(1).posX)*web(i).zStart/2);
-    triangle2 = abs((web(i).xEnd - sparCaps(1).posX)*web(i).zEnd/2);
-    web(i).Area = tempInt + triangle1 - triangle2;
-    web(i).ds = get_ds(web(i).xStart/chord,web(i).xEnd/chord,1)*chord;
-    web(i).dS_over_t = web(i).ds / web(i).thickness;
-
-    web(i).q_dS_over_t_X = web(i).qPrime_X * web(i).dS_over_t;
-    web(i).q_dS_over_t_Z = web(i).qPrime_Z * web(i).dS_over_t;
-    web(i).two_A_qprime_X = 2*web(i).Area*web(i).qPrime_X;
-    web(i).two_A_qprime_Z = 2*web(i).Area*web(i).qPrime_Z;
-    web(i).qp_dx_X = web(i).qPrime_X *(web(i).xEnd-web(i).xStart);
-    web(i).qp_dx_Z = web(i).qPrime_Z *(web(i).xEnd-web(i).xStart);
-    web(i).qp_dz_X = web(i).qPrime_X *(web(i).zEnd-web(i).zStart);
-    web(i).qp_dz_Z = web(i).qPrime_Z *(web(i).zEnd-web(i).zStart);
-end
-webTop = web;
-web = [];
-
-%rear spar
-i=1;
-web(i).xStart = sparCaps(3).posX;
-web(i).xEnd = sparCaps(4).posX;
-web(i).thickness = t_rearSpar;
-web(i).zStart = sparCaps(3).posZ;
-web(i).zEnd = sparCaps(4).posZ;
-web(i).dp_area = sparCaps(3).area;
-dx = web(i).xStart-centroid.posX; dz = web(i).zStart-centroid.posZ;
-web(i).dP_X = get_dp(dx,dz,Vx,0,Ix,Iz,Ixz,web(i).dp_area);
-web(i).dP_Z = get_dp(dx,dz,0,Vz,Ix,Iz,Ixz,web(i).dp_area);
-web(i).qPrime_X = webTop(numTopStringers+1).qPrime_X - web(i).dP_X;
-web(i).qPrime_Z = webTop(numTopStringers+1).qPrime_Z - web(i).dP_Z;
-
-web(i).Area = (sparCaps(3).posX-sparCaps(1).posX)*sparCaps(3).posZ/2 + ...
-    abs((sparCaps(3).posX-sparCaps(1).posX)*sparCaps(4).posZ/2);
-web(i).ds = abs(sparCaps(3).posZ - sparCaps(4).posZ);
-web(i).dS_over_t = web(i).ds / web(i).thickness;
-
-web(i).q_dS_over_t_X = web(i).qPrime_X * web(i).dS_over_t;
-web(i).q_dS_over_t_Z = web(i).qPrime_Z * web(i).dS_over_t;
-web(i).two_A_qprime_X = 2*web(i).Area*web(i).qPrime_X;
-web(i).two_A_qprime_Z = 2*web(i).Area*web(i).qPrime_Z;
-web(i).qp_dx_X = web(i).qPrime_X *(web(i).xEnd-web(i).xStart);
-web(i).qp_dx_Z = web(i).qPrime_Z *(web(i).xEnd-web(i).xStart);
-web(i).qp_dz_X = web(i).qPrime_X *(web(i).zEnd-web(i).zStart);
-web(i).qp_dz_Z = web(i).qPrime_Z *(web(i).zEnd-web(i).zStart);
-
-webRearSpar = web;
-web = [];
-
-
-%lower webs
-numStringers = numBottomStringers;
-stringerGap = lowerStringerGap;
-webThickness = t_lower;
-tempStringers = bottomStringers;
-
-for i=1:(numStringers+1)
-    web(i).xStart = sparCaps(4).posX - stringerGap*(i-1);
-    web(i).xEnd = sparCaps(4).posX - stringerGap*(i);
-    web(i).thickness = webThickness;
-    web(i).zStart = get_z(web(i).xStart/chord,0)*chord;
-    web(i).zEnd = get_z(web(i).xEnd/chord,0)*chord;
-    dx = web(i).xStart-centroid.posX; dz = web(i).zStart-centroid.posZ;
-    if i==1
-        web(i).dp_area = sparCaps(4).area;
-        web(i).dP_X = get_dp(dx,dz,Vx,0,Ix,Iz,Ixz,web(i).dp_area);
-        web(i).dP_Z = get_dp(dx,dz,0,Vz,Ix,Iz,Ixz,web(i).dp_area);
-        web(i).qPrime_X = webRearSpar.qPrime_X - web(i).dP_X;
-        web(i).qPrime_Z = webRearSpar.qPrime_Z - web(i).dP_Z;
-    else
-        web(i).dp_area = tempStringers(i-1).area;
-        web(i).dP_X = get_dp(dx,dz, Vx,0,Ix,Iz,Ixz,web(i).dp_area);
-        web(i).dP_Z = get_dp(dx,dz, 0,Vz,Ix,Iz,Ixz,web(i).dp_area);
-        web(i).qPrime_X = web(i-1).qPrime_X - web(i).dP_X;
-        web(i).qPrime_Z = web(i-1).qPrime_Z - web(i).dP_Z;
-    end
-
-    tempInt = get_int(web(i).xEnd/chord,web(i).xStart/chord,0)*chord^2;  %integral of airfoil function
-    triangle2 = abs((web(i).xStart - sparCaps(1).posX)*web(i).zStart/2);
-    triangle1 = abs((web(i).xEnd - sparCaps(1).posX)*web(i).zEnd/2);
-    web(i).Area = tempInt + triangle1 - triangle2;
-    web(i).ds = get_ds(web(i).xStart/chord,web(i).xEnd/chord,0)*chord;
-    web(i).dS_over_t = web(i).ds / web(i).thickness;
-
-    web(i).q_dS_over_t_X = web(i).qPrime_X * web(i).dS_over_t;
-    web(i).q_dS_over_t_Z = web(i).qPrime_Z * web(i).dS_over_t;
-    web(i).two_A_qprime_X = 2*web(i).Area*web(i).qPrime_X;
-    web(i).two_A_qprime_Z = 2*web(i).Area*web(i).qPrime_Z;
-    web(i).qp_dx_X = web(i).qPrime_X*(web(i).xEnd-web(i).xStart);
-    web(i).qp_dx_Z = web(i).qPrime_Z*(web(i).xEnd-web(i).xStart);
-    web(i).qp_dz_X = web(i).qPrime_X*(web(i).zEnd-web(i).zStart);
-    web(i).qp_dz_Z = web(i).qPrime_Z*(web(i).zEnd-web(i).zStart);
-
-    %web(i).radCurv = ...   Example:  get_curve(web(i).xStart,web(i).xEnd,1)
-end
-webBottom = web;
-web = [];
-
-%front Spar
-i=1;
-web(i).xStart = sparCaps(2).posX;
-web(i).xEnd = sparCaps(1).posX;
-web(i).thickness = t_frontSpar;
-web(i).zStart = sparCaps(2).posZ;
-web(i).zEnd = sparCaps(1).posZ;
-web(i).dp_area = sparCaps(2).area;
-dx = web(i).xStart-centroid.posX; dz = web(i).zStart-centroid.posZ;
-web(i).dP_X = get_dp(dx,dz,Vx,0,Ix,Iz,Ixz,web(i).dp_area);
-web(i).dP_Z = get_dp(dx,dz,0,Vz,Ix,Iz,Ixz,web(i).dp_area);
-web(i).qPrime_X = webBottom(numBottomStringers+1).qPrime_X - web(i).dP_X;
-web(i).qPrime_Z = webBottom(numBottomStringers+1).qPrime_Z - web(i).dP_Z;
-web(i).Area = 0;
-web(i).ds = abs(sparCaps(2).posZ - sparCaps(1).posZ);
-web(i).dS_over_t = web(i).ds / web(i).thickness;
-
-web(i).q_dS_over_t_X = web(i).qPrime_X * web(i).dS_over_t;
-web(i).q_dS_over_t_Z = web(i).qPrime_Z * web(i).dS_over_t;
-web(i).two_A_qprime_X = 2*web(i).Area*web(i).qPrime_X;
-web(i).two_A_qprime_Z = 2*web(i).Area*web(i).qPrime_Z;
-web(i).qp_dx_X = web(i).qPrime_X *(web(i).xEnd-web(i).xStart);
-web(i).qp_dx_Z = web(i).qPrime_Z *(web(i).xEnd-web(i).xStart);
-web(i).qp_dz_X = web(i).qPrime_X *(web(i).zEnd-web(i).zStart);
-web(i).qp_dz_Z = web(i).qPrime_Z *(web(i).zEnd-web(i).zStart);
-
-webFrontSpar = web;
-web = [];
-
-
-
-
-%% web cell 2
-
-%lower nose webs
-numStringers = numNoseBottomStringers;
-stringerGap = lowerNoseStringerGap;
-webThickness = t_lower_front;
-tempStringers = noseBottomStringers;
-
-for i=1:(numStringers+1)
-    web(i).xStart = sparCaps(2).posX - stringerGap*(i-1);
-    web(i).xEnd = sparCaps(2).posX - stringerGap*(i);
-    web(i).thickness = webThickness;
-    web(i).zStart = get_z(web(i).xStart/chord,0)*chord;
-    web(i).zEnd = get_z(web(i).xEnd/chord,0)*chord;
-    dx = web(i).xStart-centroid.posX; dz = web(i).zStart-centroid.posZ;
-
-    if i==1
-        web(i).dp_area = sparCaps(2).area;
-        web(i).dP_X = 0;
-        web(i).dP_Z = 0;
-        web(i).qPrime_X = 0;
-        web(i).qPrime_Z = 0;
-    else
-        web(i).dp_area = tempStringers(i-1).area;
-        web(i).dP_X = get_dp(dx,dz,Vx,0,Ix,Iz,Ixz,web(i).dp_area);
-        web(i).dP_Z = get_dp(dx,dz,0,Vz,Ix,Iz,Ixz,web(i).dp_area);
-        web(i).qPrime_X = web(i-1).qPrime_X - web(i).dP_X;
-        web(i).qPrime_Z = web(i-1).qPrime_Z - web(i).dP_Z;
-    end
-    tempInt = get_int(web(i).xEnd/chord,web(i).xStart/chord,0)*chord^2;  %integral of airfoil function
-    triangle1 = abs((web(i).xStart - sparCaps(2).posX)*web(i).zStart/2);
-    triangle2 = abs((web(i).xEnd - sparCaps(2).posX)*web(i).zEnd/2);
-    web(i).Area = tempInt + triangle1 - triangle2;
-    web(i).ds = get_ds(web(i).xStart/chord,web(i).xEnd/chord,0)*chord;
-    web(i).dS_over_t = web(i).ds / web(i).thickness;
-
-    web(i).q_dS_over_t_X = web(i).qPrime_X * web(i).dS_over_t;
-    web(i).q_dS_over_t_Z = web(i).qPrime_Z * web(i).dS_over_t;
-    web(i).two_A_qprime_X = 2*web(i).Area*web(i).qPrime_X;
-    web(i).two_A_qprime_Z = 2*web(i).Area*web(i).qPrime_Z;
-    web(i).qp_dx_X = web(i).qPrime_X *(web(i).xEnd-web(i).xStart);
-    web(i).qp_dx_Z = web(i).qPrime_Z *(web(i).xEnd-web(i).xStart);
-    web(i).qp_dz_X = web(i).qPrime_X *(web(i).zEnd-web(i).zStart);
-    web(i).qp_dz_Z = web(i).qPrime_Z *(web(i).zEnd-web(i).zStart);
-
-    %web(i).radCurv = ...   Example:  get_curve(web(i).xStart,web(i).xEnd,1)
-end
-webLowerNose = web;
-web = [];
-
-%upper nose webs
-numStringers = numNoseTopStringers;
-stringerGap = upperNoseStringerGap;
-webThickness = t_upper_front;
-tempStringers = noseTopStringers;
-
-for i=1:(numStringers+1)
-    web(i).xStart = stringerGap*(i-1);
-    web(i).xEnd = stringerGap*(i);
-    web(i).thickness = webThickness;
-    web(i).zStart = get_z(web(i).xStart/chord,1)*chord;
-    web(i).zEnd = get_z(web(i).xEnd/chord,1)*chord;
-    dx = web(i).xStart-centroid.posX; dz = web(i).zStart-centroid.posZ;
-    if i==1
-        web(i).dp_area = 0;
-        web(i).dP_X = 0;
-        web(i).dP_Z = 0;
-        web(i).qPrime_X = webLowerNose(numNoseBottomStringers+1).qPrime_X - web(i).dP_X;
-        web(i).qPrime_Z = webLowerNose(numNoseBottomStringers+1).qPrime_Z - web(i).dP_Z;
-    else
-        web(i).dp_area = tempStringers(i-1).area;
-        web(i).dP_X = get_dp(dx,dz,Vx,0,Ix,Iz,Ixz,web(i).dp_area);
-        web(i).dP_Z = get_dp(dx,dz,0,Vz,Ix,Iz,Ixz,web(i).dp_area);
-        web(i).qPrime_X = web(i-1).qPrime_X - web(i).dP_X;
-        web(i).qPrime_Z = web(i-1).qPrime_Z - web(i).dP_Z;
-    end
-    tempInt = get_int(web(i).xStart/chord,web(i).xEnd/chord,1)*chord^2;  %integral of airfoil function
-    triangle2 = abs((web(i).xStart - sparCaps(2).posX)*web(i).zStart/2);
-    triangle1 = abs((web(i).xEnd - sparCaps(2).posX)*web(i).zEnd/2);
-    web(i).Area = tempInt + triangle1 - triangle2;
-    web(i).ds = get_ds(web(i).xStart/chord,web(i).xEnd/chord,1)*chord;
-    web(i).dS_over_t = web(i).ds / web(i).thickness;
-
-    web(i).q_dS_over_t_X = web(i).qPrime_X * web(i).dS_over_t;
-    web(i).q_dS_over_t_Z = web(i).qPrime_Z * web(i).dS_over_t;
-    web(i).two_A_qprime_X = 2*web(i).Area*web(i).qPrime_X;
-    web(i).two_A_qprime_Z = 2*web(i).Area*web(i).qPrime_Z;
-    web(i).qp_dx_X = web(i).qPrime_X *(web(i).xEnd-web(i).xStart);
-    web(i).qp_dx_Z = web(i).qPrime_Z *(web(i).xEnd-web(i).xStart);
-    web(i).qp_dz_X = web(i).qPrime_X *(web(i).zEnd-web(i).zStart);
-    web(i).qp_dz_Z = web(i).qPrime_Z *(web(i).zEnd-web(i).zStart);
-
-end
-webUpperNose = web;
-web = [];
-
-
-%front Spar
-i=1;
-web(i).xStart = sparCaps(1).posX;
-web(i).xEnd = sparCaps(2).posX;
-web(i).thickness = t_frontSpar;
-web(i).zStart = sparCaps(1).posZ;
-web(i).zEnd = sparCaps(2).posZ;
-web(i).dp_area = sparCaps(1).area;
-dx = web(i).xStart-centroid.posX; dz = web(i).zStart-centroid.posZ;
-
-web(i).dP_X = get_dp(dx,dz,Vx,0,Ix,Iz,Ixz,web(i).dp_area);
-web(i).dP_Z = get_dp(dx,dz,0,Vz,Ix,Iz,Ixz,web(i).dp_area);
-web(i).qPrime_X = webUpperNose(numNoseTopStringers+1).qPrime_X - web(i).dP_X;
-web(i).qPrime_Z = webUpperNose(numNoseTopStringers+1).qPrime_Z - web(i).dP_Z;
-web(i).Area = 0;
-web(i).ds = abs(sparCaps(1).posZ - sparCaps(2).posZ);
-web(i).dS_over_t = web(i).ds / web(i).thickness;
-web(i).q_dS_over_t_X = web(i).qPrime_X * web(i).dS_over_t;
-web(i).q_dS_over_t_Z = web(i).qPrime_Z * web(i).dS_over_t;
-web(i).two_A_qprime_X = 2*web(i).Area*web(i).qPrime_X;
-web(i).two_A_qprime_Z = 2*web(i).Area*web(i).qPrime_Z;
-web(i).qp_dx_X = web(i).qPrime_X *(web(i).xEnd-web(i).xStart);
-web(i).qp_dx_Z = web(i).qPrime_Z *(web(i).xEnd-web(i).xStart);
-web(i).qp_dz_X = web(i).qPrime_X *(web(i).zEnd-web(i).zStart);
-web(i).qp_dz_Z = web(i).qPrime_Z *(web(i).zEnd-web(i).zStart);
-
-webFrontSparCell2 = web;
-web = [];
-
-
-%check that q'*dx sums up to Vx
-
-Fx = sum([webTop.qp_dx_X])+webRearSpar.qp_dx_X+ sum([webBottom.qp_dx_X])+webFrontSpar.qp_dx_X;  %cell 1
-Fx = Fx + sum([webLowerNose.qp_dx_X])+ sum([webUpperNose.qp_dx_X]);  %cell 2
-Fx
-Fz = sum([webTop.qp_dz_X])+webRearSpar.qp_dz_X+ sum([webBottom.qp_dz_X])+webFrontSpar.qp_dz_X;  %cell 1
-Fz = Fz + sum([webLowerNose.qp_dz_X])+ sum([webUpperNose.qp_dz_X]);  %cell 2
-Fz
-
-%check that q'*dz sums up to Vz
-
-
-Fx = sum([webTop.qp_dx_Z])+webRearSpar.qp_dx_Z+ sum([webBottom.qp_dx_Z])+webFrontSpar.qp_dx_Z;  %cell 1
-Fx = Fx + sum([webLowerNose.qp_dx_Z])+ sum([webUpperNose.qp_dx_Z]);  %cell 2
-Fx
-Fz = sum([webTop.qp_dz_Z])+webRearSpar.qp_dz_Z+ sum([webBottom.qp_dz_Z])+webFrontSpar.qp_dz_Z;  %cell 1
-Fz = Fz + sum([webLowerNose.qp_dz_Z])+ sum([webUpperNose.qp_dz_Z]);  %cell 2
-Fz
-
-%%
-
-% sum up the ds/t and  q*ds/t to solve 2 equations, 2 unknowns
-
-% [A]*[q1s q2s] = B
-
-A11 = sum([webTop.dS_over_t])+webRearSpar.dS_over_t+ sum([webBottom.dS_over_t])+webFrontSpar.dS_over_t;
-A22 = sum([webLowerNose.dS_over_t])+ sum([webUpperNose.dS_over_t])+webFrontSparCell2.dS_over_t;
-A12 = -webFrontSpar.dS_over_t;
-A21 = -webFrontSparCell2.dS_over_t;
-
-B1_X = sum([webTop.q_dS_over_t_X])+webRearSpar.q_dS_over_t_X+ sum([webBottom.q_dS_over_t_X])+webFrontSpar.q_dS_over_t_X;
-B2_X = sum([webLowerNose.q_dS_over_t_X])+ sum([webUpperNose.q_dS_over_t_X])+webFrontSparCell2.q_dS_over_t_X;
-B1_Z = sum([webTop.q_dS_over_t_Z])+webRearSpar.q_dS_over_t_Z+ sum([webBottom.q_dS_over_t_Z])+webFrontSpar.q_dS_over_t_Z;
-B2_Z = sum([webLowerNose.q_dS_over_t_Z])+ sum([webUpperNose.q_dS_over_t_Z])+webFrontSparCell2.q_dS_over_t_Z;
-
-Amat = [A11 A12; A21 A22];
-Bmat_X = -[B1_X;B2_X];
-Bmat_Z = -[B1_Z;B2_Z];
-
-qs_X = inv(Amat)*Bmat_X;
-qs_Z = inv(Amat)*Bmat_Z;
-
-
-
-sum_2_a_q_X = sum([webTop.two_A_qprime_X])+webRearSpar.two_A_qprime_X+ sum([webBottom.two_A_qprime_X]);  %cell 1 qprimes
-sum_2_a_q_X = sum_2_a_q_X + sum([webLowerNose.two_A_qprime_X])+ sum([webUpperNose.two_A_qprime_X]);   %cell 2 qprimes
-sum_2_a_q_X = sum_2_a_q_X +  2*qs_X(1)*(sum([webTop.Area])+webRearSpar.Area+ sum([webBottom.Area]));
-sum_2_a_q_X = sum_2_a_q_X +  2*qs_X(2)*(sum([webLowerNose.Area])+ sum([webUpperNose.Area]));
-
-sum_2_a_q_Z = sum([webTop.two_A_qprime_Z])+webRearSpar.two_A_qprime_Z+ sum([webBottom.two_A_qprime_Z]);  %cell 1 qprimes
-sum_2_a_q_Z = sum_2_a_q_Z + sum([webLowerNose.two_A_qprime_Z])+ sum([webUpperNose.two_A_qprime_Z]);   %cell 2 qprimes
-sum_2_a_q_Z = sum_2_a_q_Z +  2*qs_Z(1)*(sum([webTop.Area])+webRearSpar.Area+ sum([webBottom.Area]));
-sum_2_a_q_Z = sum_2_a_q_Z +  2*qs_Z(2)*(sum([webLowerNose.Area])+ sum([webUpperNose.Area]));
-
-%shear center
-sc.posX =  sum_2_a_q_Z / Vz + frontSpar*chord;
-sc.posZ = - sum_2_a_q_X / Vx;
-
-
-% now consider the torque representing shifting the load from the quarter
-% chord to the SC  (need to check signs on these moments)
-
-torque_Z = Vz*(sc.posX - 0.25*chord);
-torque_X = -Vx*sc.posZ;
-
-
-Area1 = sum([webTop.Area]) + webRearSpar.Area + sum([webBottom.Area]);
-%check area
-Area1_check = get_int(frontSpar,backSpar,1)*chord^2 + get_int(frontSpar,backSpar,0)*chord^2;
-
-Area2 = sum([webLowerNose.Area]) + sum([webUpperNose.Area]);
-Area2_check = get_int(0,frontSpar,1)*chord^2 + get_int(0,frontSpar,0)*chord^2;
-
-
-%for twist equation  (see excel spreadsheet example)
-
-q1t_over_q2t = (A22/Area2 + webFrontSpar.dS_over_t/Area1)/(A11/Area1 + webFrontSpar.dS_over_t/Area2);
-
-q2t = torque_X/(2*Area1*q1t_over_q2t + 2*Area2);
-q1t = q2t*q1t_over_q2t;
-qt_X = [q1t;q2t];
-
-q2t = torque_Z/(2*Area1*q1t_over_q2t + 2*Area2);
-q1t = q2t*q1t_over_q2t;
-qt_Z = [q1t;q2t];
-
-
-
-% --- - add up all shear flows:  qtot = (qPrime + qs) + qt
-
-
-
-
-%--- insert force balance to check total shear flows ---
-
-% --- --
-
-
-%end
-
-sc
-
-
-%plotting airfoil cross-section
-
-xChord = 0:.01:1;
-xChord = xChord*chord;
-upperSurface = zeros(1,length(xChord));
-lowerSurface = zeros(1,length(xChord));
-
-for i=1:length(xChord)
-    upperSurface(i) = get_z(xChord(i)/chord,1)*chord;
-    lowerSurface(i) = get_z(xChord(i)/chord,0)*chord;
-end
-
-figure; hold on; axis equal; grid on;
-%plot(xChord,z_camber,'-')
-plot(xChord,upperSurface,'-k','linewidth',2)
-plot(xChord,lowerSurface,'-k','linewidth',2)
-plot([0 1],[0 0],'--k','linewidth',1)
-
-
-for i = 1:length(webTop)
-   vecX = [frontSpar*chord webTop(i).xStart webTop(i).xEnd];
-   vecZ = [0 webTop(i).zStart webTop(i).zEnd];
-   fill(vecX,vecZ,[0.9 0.9 0.9])
-end
-
-for i = 1:length(webBottom)
-   vecX = [frontSpar*chord webBottom(i).xStart webBottom(i).xEnd];
-   vecZ = [0 webBottom(i).zStart webBottom(i).zEnd];
-   fill(vecX,vecZ,[0.9 0.9 0.9])
-end
-
-for i = 1:length(webUpperNose)
-   vecX = [frontSpar*chord webUpperNose(i).xStart webUpperNose(i).xEnd];
-   vecZ = [0 webUpperNose(i).zStart webUpperNose(i).zEnd];
-   fill(vecX,vecZ,[0.7 0.9 1.0])
-end
-
-for i = 1:length(webLowerNose)
-   vecX = [frontSpar*chord webLowerNose(i).xStart webLowerNose(i).xEnd];
-   vecZ = [0 webLowerNose(i).zStart webLowerNose(i).zEnd];
-   fill(vecX,vecZ,[0.7 0.9 1.0])
-end
-
-   vecX = [frontSpar*chord sparCaps(3).posX sparCaps(4).posX];
-   vecZ = [0 sparCaps(3).posZ sparCaps(4).posZ];
-   fill(vecX,vecZ,[0.9 0.9 0.9])
-
-
-sparCapSize = 18;
-stringerSize = 18;
-plot([sparCaps(1).posX sparCaps(2).posX],[sparCaps(1).posZ sparCaps(2).posZ],'-k','linewidth',2)
-plot([sparCaps(3).posX sparCaps(4).posX],[sparCaps(3).posZ sparCaps(4).posZ],'-k','linewidth',2)
-plot([sparCaps.posX],[sparCaps.posZ],'.b','markersize',sparCapSize)
-plot([topStringers.posX],[topStringers.posZ],'.r','markersize',stringerSize)
-plot([bottomStringers.posX],[bottomStringers.posZ],'.r','markersize',stringerSize)
-plot([noseTopStringers.posX],[noseTopStringers.posZ],'.r','markersize',stringerSize)
-plot([noseBottomStringers.posX],[noseBottomStringers.posZ],'.r','markersize',stringerSize)
-plot(centroid.posX,centroid.posZ,'.k','markerSize',18)
-plot(sc.posX,sc.posZ,'.g','markersize',18)
diff --git a/wing_scripts/stringersBeamExample.m b/wing_scripts/stringersBeamExample.m
deleted file mode 100644
index cd3bcb6..0000000
--- a/wing_scripts/stringersBeamExample.m
+++ /dev/null
@@ -1,47 +0,0 @@
-close all; 
-force = 8000; % lbs
-stringer_A = 0.5; % in^2
-thickness = 0.04; % in
-
-top_stringers_y = 6; % in
-middle_stringers_y = 2; % in
-
-I = 2*stringer_A*top_stringers_y^2 + 2*stringer_A*middle_stringers_y^2;
-
-% solve for shear stress distribution.  this calc ignores the thickness of
-% the web between teh stringers (assumes bending taken by stringers)
-% V / (I * t) * int(y*da)
-
-shear_top_web = force / (I*thickness) * top_stringers_y * stringer_A;
-shear_middle_web = shear_top_web + (force / (I*thickness) * middle_stringers_y * stringer_A);
-
-figure; grid on; hold on;set(gcf,'color',[1 1 1]);
-
-
-plot([shear_top_web shear_top_web],[middle_stringers_y top_stringers_y],'linewidth',2);
-plot([shear_middle_web shear_middle_web],[-middle_stringers_y middle_stringers_y],'linewidth',2);
-plot([shear_top_web shear_top_web],[-middle_stringers_y -top_stringers_y],'linewidth',2);
-
-plot([0 shear_top_web],[top_stringers_y top_stringers_y],'linewidth',2);
-plot([0 shear_top_web],[-top_stringers_y -top_stringers_y],'linewidth',2);
-plot([shear_middle_web shear_top_web],[middle_stringers_y middle_stringers_y],'linewidth',2);
-plot([shear_middle_web shear_top_web],[-middle_stringers_y -middle_stringers_y],'linewidth',2);
-xlabel('shear stress (lb/in^2)','fontsize',16,'fontweight','bold');ylabel('Distance from Center (in)','fontsize',16,'fontweight','bold')
-set(gca,'FontSize',16,'fontweight','bold');
-
-%Alternate approach.. compute change in bending stress at each stringer to
-%find the change in shear load
-
-%at top stringer
-d_sigma = force * top_stringers_y / I;  %(lbs/in^2)
-d_force_top = d_sigma * stringer_A;
-
-%at middle stringer..
-d_sigma = force * middle_stringers_y / I;  %(lbs/in^2)
-d_force_middle = d_force_top + d_sigma*stringer_A;
-
-%check if load balances
-check_load = 2*d_force_top*4 + d_force_middle*4;
-
-
-
diff --git a/wing_scripts/wingAnalysis_190422.m b/wing_scripts/wingAnalysis_190422.m
deleted file mode 100644
index a7d65e2..0000000
--- a/wing_scripts/wingAnalysis_190422.m
+++ /dev/null
@@ -1,579 +0,0 @@
-%wing shear flow
-clear all;
-close all;
-
-
-
-
-Vx = 1; Vz = 1; My = 1;  %test loads will be applied individually
-
-%define a few
-numTopStringers = 6;
-numBottomStringers = 8;
-numNoseTopStringers = 4;
-numNoseBottomStringers = 4;
-
-t_upper = 0.02/12;
-t_lower = 0.02/12;
-t_upper_front = 0.02/12;
-t_lower_front = 0.02/12;
-t_frontSpar = 0.04/12;
-t_rearSpar = 0.04/12;
-
-frontSpar = 0.2;
-backSpar = 0.7;
-chord = 5;
-
-sparCaps(1).posX = frontSpar*chord;
-sparCaps(2).posX = frontSpar*chord;
-sparCaps(3).posX = backSpar*chord;
-sparCaps(4).posX = backSpar*chord;
-
-sparCaps(1).posZ = get_z(frontSpar,1)*chord;
-sparCaps(2).posZ = get_z(frontSpar,0)*chord;
-sparCaps(3).posZ = get_z(backSpar,1)*chord;
-sparCaps(4).posZ = get_z(backSpar,0)*chord;
-
-sparCaps(1).area = .1;
-sparCaps(2).area = .1;
-sparCaps(3).area = .1;
-sparCaps(4).area = .1;
-
-upperStringerGap = (sparCaps(3).posX - sparCaps(1).posX)/(numTopStringers + 1);
-lowerStringerGap = (sparCaps(3).posX - sparCaps(1).posX)/(numBottomStringers + 1);
-upperNoseStringerGap = (sparCaps(1).posX - 0)/(numNoseTopStringers + 1);
-lowerNoseStringerGap = (sparCaps(1).posX - 0)/(numNoseBottomStringers + 1);
-
-
-%set stringers spaced evenly along X axis betwen Spars
-%top Stringers
-for i=1:numTopStringers
-    topStringers(i).posX = sparCaps(1).posX + upperStringerGap*i;
-    topStringers(i).posZ = get_z(topStringers(i).posX/chord,1)*chord;
-    topStringers(i).area = .1;
-end
-
-%bottom Stringers
-for i=1:numBottomStringers
-    bottomStringers(i).posX = sparCaps(4).posX - lowerStringerGap*i;
-    bottomStringers(i).posZ = get_z(bottomStringers(i).posX/chord,0)*chord;
-    bottomStringers(i).area = .1;
-
-end
-
-%nose bottom Stringers
-for i=1:numNoseBottomStringers
-    noseBottomStringers(i).posX = sparCaps(2).posX - lowerNoseStringerGap*i;
-    noseBottomStringers(i).posZ = get_z(noseBottomStringers(i).posX/chord,0)*chord;
-    noseBottomStringers(i).area = .1;
-end
-
-%nose top Stringers
-for i=1:numNoseTopStringers
-    noseTopStringers(i).posX = upperNoseStringerGap*i;
-    noseTopStringers(i).posZ = get_z(noseTopStringers(i).posX/chord,1)*chord;
-    noseTopStringers(i).area = .1;
-end
-
-
-centroid.posX = sum([sparCaps.posX].*[sparCaps.area]) + ...
-    sum([topStringers.posX].*[topStringers.area]) + ...
-    sum([bottomStringers.posX].*[bottomStringers.area]) + ...
-    sum([noseTopStringers.posX].*[noseTopStringers.area]) + ...
-    sum([noseBottomStringers.posX].*[noseBottomStringers.area]);
-
-centroid.posX = centroid.posX / ( sum([sparCaps.area]) + sum([topStringers.area]) + ...
-    sum([bottomStringers.area]) + sum([noseTopStringers.area]) + sum([noseBottomStringers.area]));
-
-centroid.posZ = sum([sparCaps.posZ].*[sparCaps.area]) + ...
-    sum([topStringers.posZ].*[topStringers.area]) + ...
-    sum([bottomStringers.posZ].*[bottomStringers.area]) + ...
-    sum([noseTopStringers.posZ].*[noseTopStringers.area]) + ...
-    sum([noseBottomStringers.posZ].*[noseBottomStringers.area]);
-    
-centroid.posZ = centroid.posZ / ( sum([sparCaps.area]) + sum([topStringers.area]) + ...
-    sum([bottomStringers.area]) + sum([noseTopStringers.area]) + sum([noseBottomStringers.area]));
-
-%summing contributions for inertia terms
-Ix = 0; Iz = 0; Ixz = 0;
-
-for i=1:4 %spar caps
-    Ix = Ix + sparCaps(i).area*(sparCaps(i).posZ-centroid.posZ)^2;
-    Iz = Iz + sparCaps(i).area*(sparCaps(i).posX-centroid.posX)^2;
-    Ixz = Ixz + sparCaps(i).area*(sparCaps(i).posX-centroid.posX)*(sparCaps(i).posZ-centroid.posZ);
-end
-
-
-for i=1:numTopStringers %top stringers
-    Ix = Ix + topStringers(i).area*(topStringers(i).posZ-centroid.posZ)^2;
-    Iz = Iz + topStringers(i).area*(topStringers(i).posX-centroid.posX)^2;
-    Ixz = Ixz + topStringers(i).area*(topStringers(i).posX-centroid.posX)*(topStringers(i).posZ-centroid.posZ);
-end
-for i=1:numBottomStringers %bottom stringers
-    Ix = Ix + bottomStringers(i).area*(bottomStringers(i).posZ-centroid.posZ)^2;
-    Iz = Iz + bottomStringers(i).area*(bottomStringers(i).posX-centroid.posX)^2;
-    Ixz = Ixz + bottomStringers(i).area*(bottomStringers(i).posX-centroid.posX)*(bottomStringers(i).posZ-centroid.posZ);
-end
-for i=1:numNoseTopStringers %nose top stringers
-    Ix = Ix + noseTopStringers(i).area*(noseTopStringers(i).posZ-centroid.posZ)^2;
-    Iz = Iz + noseTopStringers(i).area*(noseTopStringers(i).posX-centroid.posX)^2;
-    Ixz = Ixz + noseTopStringers(i).area*(noseTopStringers(i).posX-centroid.posX)*(noseTopStringers(i).posZ-centroid.posZ);
-end
-for i=1:numNoseBottomStringers %nose bottom stringers
-    Ix = Ix + noseBottomStringers(i).area*(noseBottomStringers(i).posZ-centroid.posZ)^2;
-    Iz = Iz + noseBottomStringers(i).area*(noseBottomStringers(i).posX-centroid.posX)^2;
-    Ixz = Ixz + noseBottomStringers(i).area*(noseBottomStringers(i).posX-centroid.posX)*(noseBottomStringers(i).posZ-centroid.posZ);
-end
-
-%Ixz = -Ixz;
-
-%define webs
-
-%% web cell 1
-
-%upper webs
-numStringers = numTopStringers;
-stringerGap = upperStringerGap;
-webThickness = t_upper;
-tempStringers = topStringers;
-
-for i=1:(numStringers+1)
-    web(i).xStart = sparCaps(1).posX + stringerGap*(i-1);
-    web(i).xEnd = sparCaps(1).posX + stringerGap*(i);
-    web(i).thickness = webThickness;
-    web(i).zStart = get_z(web(i).xStart/chord,1)*chord;
-    web(i).zEnd = get_z(web(i).xEnd/chord,1)*chord;
-    if i==1
-        web(i).dp_area = sparCaps(1).area;
-        web(i).dP_X = 0;
-        web(i).dP_Z = 0;
-        web(i).qPrime_X = 0;
-        web(i).qPrime_Z = 0;
-    else
-        web(i).dp_area = tempStringers(i-1).area;
-        dx = web(i).xStart-centroid.posX; dz = web(i).zStart-centroid.posZ;
-        web(i).dP_X = get_dp(dx,dz,Vx,0,Ix,Iz,Ixz,web(i).dp_area);  %just Vx
-        web(i).dP_Z = get_dp(dx,dz,0,Vz,Ix,Iz,Ixz,web(i).dp_area);  %just Vz
-        web(i).qPrime_X = web(i-1).qPrime_X - web(i).dP_X;
-        web(i).qPrime_Z = web(i-1).qPrime_Z - web(i).dP_Z;
-    end
-    tempInt = get_int(web(i).xStart/chord,web(i).xEnd/chord,1)*chord^2;  %integral of airfoil function
-    triangle1 = abs( (web(i).xStart - sparCaps(1).posX)*web(i).zStart/2);
-    triangle2 = abs((web(i).xEnd - sparCaps(1).posX)*web(i).zEnd/2);
-    web(i).Area = tempInt + triangle1 - triangle2;
-    web(i).ds = get_ds(web(i).xStart/chord,web(i).xEnd/chord,1)*chord;
-    web(i).dS_over_t = web(i).ds / web(i).thickness;
-
-    web(i).q_dS_over_t_X = web(i).qPrime_X * web(i).dS_over_t;
-    web(i).q_dS_over_t_Z = web(i).qPrime_Z * web(i).dS_over_t;
-    web(i).two_A_qprime_X = 2*web(i).Area*web(i).qPrime_X;
-    web(i).two_A_qprime_Z = 2*web(i).Area*web(i).qPrime_Z;
-    web(i).qp_dx_X = web(i).qPrime_X *(web(i).xEnd-web(i).xStart);
-    web(i).qp_dx_Z = web(i).qPrime_Z *(web(i).xEnd-web(i).xStart);
-    web(i).qp_dz_X = web(i).qPrime_X *(web(i).zEnd-web(i).zStart);
-    web(i).qp_dz_Z = web(i).qPrime_Z *(web(i).zEnd-web(i).zStart);
-end
-webTop = web;
-web = [];
-
-%rear spar
-i=1;
-web(i).xStart = sparCaps(3).posX;
-web(i).xEnd = sparCaps(4).posX;
-web(i).thickness = t_rearSpar;
-web(i).zStart = sparCaps(3).posZ;
-web(i).zEnd = sparCaps(4).posZ;
-web(i).dp_area = sparCaps(3).area;
-dx = web(i).xStart-centroid.posX; dz = web(i).zStart-centroid.posZ;
-web(i).dP_X = get_dp(dx,dz,Vx,0,Ix,Iz,Ixz,web(i).dp_area);
-web(i).dP_Z = get_dp(dx,dz,0,Vz,Ix,Iz,Ixz,web(i).dp_area);
-web(i).qPrime_X = webTop(numTopStringers+1).qPrime_X - web(i).dP_X;
-web(i).qPrime_Z = webTop(numTopStringers+1).qPrime_Z - web(i).dP_Z;
-
-web(i).Area = (sparCaps(3).posX-sparCaps(1).posX)*sparCaps(3).posZ/2 + ...
-    abs((sparCaps(3).posX-sparCaps(1).posX)*sparCaps(4).posZ/2);
-web(i).ds = abs(sparCaps(3).posZ - sparCaps(4).posZ);
-web(i).dS_over_t = web(i).ds / web(i).thickness;
-
-web(i).q_dS_over_t_X = web(i).qPrime_X * web(i).dS_over_t;
-web(i).q_dS_over_t_Z = web(i).qPrime_Z * web(i).dS_over_t;
-web(i).two_A_qprime_X = 2*web(i).Area*web(i).qPrime_X;
-web(i).two_A_qprime_Z = 2*web(i).Area*web(i).qPrime_Z;
-web(i).qp_dx_X = web(i).qPrime_X *(web(i).xEnd-web(i).xStart);
-web(i).qp_dx_Z = web(i).qPrime_Z *(web(i).xEnd-web(i).xStart);
-web(i).qp_dz_X = web(i).qPrime_X *(web(i).zEnd-web(i).zStart);
-web(i).qp_dz_Z = web(i).qPrime_Z *(web(i).zEnd-web(i).zStart);
-
-webRearSpar = web;
-web = [];
-
-
-%lower webs
-numStringers = numBottomStringers;
-stringerGap = lowerStringerGap;
-webThickness = t_lower;
-tempStringers = bottomStringers;
-
-for i=1:(numStringers+1)
-    web(i).xStart = sparCaps(4).posX - stringerGap*(i-1);
-    web(i).xEnd = sparCaps(4).posX - stringerGap*(i);
-    web(i).thickness = webThickness;
-    web(i).zStart = get_z(web(i).xStart/chord,0)*chord;
-    web(i).zEnd = get_z(web(i).xEnd/chord,0)*chord;
-    dx = web(i).xStart-centroid.posX; dz = web(i).zStart-centroid.posZ;
-    if i==1
-        web(i).dp_area = sparCaps(4).area;
-        web(i).dP_X = get_dp(dx,dz,Vx,0,Ix,Iz,Ixz,web(i).dp_area);
-        web(i).dP_Z = get_dp(dx,dz,0,Vz,Ix,Iz,Ixz,web(i).dp_area);
-        web(i).qPrime_X = webRearSpar.qPrime_X - web(i).dP_X;
-        web(i).qPrime_Z = webRearSpar.qPrime_Z - web(i).dP_Z;
-    else
-        web(i).dp_area = tempStringers(i-1).area;
-        web(i).dP_X = get_dp(dx,dz, Vx,0,Ix,Iz,Ixz,web(i).dp_area);
-        web(i).dP_Z = get_dp(dx,dz, 0,Vz,Ix,Iz,Ixz,web(i).dp_area);
-        web(i).qPrime_X = web(i-1).qPrime_X - web(i).dP_X;
-        web(i).qPrime_Z = web(i-1).qPrime_Z - web(i).dP_Z;
-    end
-
-    tempInt = get_int(web(i).xEnd/chord,web(i).xStart/chord,0)*chord^2;  %integral of airfoil function
-    triangle2 = abs((web(i).xStart - sparCaps(1).posX)*web(i).zStart/2);
-    triangle1 = abs((web(i).xEnd - sparCaps(1).posX)*web(i).zEnd/2);
-    web(i).Area = tempInt + triangle1 - triangle2;
-    web(i).ds = get_ds(web(i).xStart/chord,web(i).xEnd/chord,0)*chord;
-    web(i).dS_over_t = web(i).ds / web(i).thickness;
-
-    web(i).q_dS_over_t_X = web(i).qPrime_X * web(i).dS_over_t;
-    web(i).q_dS_over_t_Z = web(i).qPrime_Z * web(i).dS_over_t;
-    web(i).two_A_qprime_X = 2*web(i).Area*web(i).qPrime_X;
-    web(i).two_A_qprime_Z = 2*web(i).Area*web(i).qPrime_Z;
-    web(i).qp_dx_X = web(i).qPrime_X*(web(i).xEnd-web(i).xStart);
-    web(i).qp_dx_Z = web(i).qPrime_Z*(web(i).xEnd-web(i).xStart);
-    web(i).qp_dz_X = web(i).qPrime_X*(web(i).zEnd-web(i).zStart);
-    web(i).qp_dz_Z = web(i).qPrime_Z*(web(i).zEnd-web(i).zStart);
-
-    %web(i).radCurv = ...   Example:  get_curve(web(i).xStart,web(i).xEnd,1)
-end
-webBottom = web;
-web = [];
-
-%front Spar
-i=1;
-web(i).xStart = sparCaps(2).posX;
-web(i).xEnd = sparCaps(1).posX;
-web(i).thickness = t_frontSpar;
-web(i).zStart = sparCaps(2).posZ;
-web(i).zEnd = sparCaps(1).posZ;
-web(i).dp_area = sparCaps(2).area;
-dx = web(i).xStart-centroid.posX; dz = web(i).zStart-centroid.posZ;
-web(i).dP_X = get_dp(dx,dz,Vx,0,Ix,Iz,Ixz,web(i).dp_area);
-web(i).dP_Z = get_dp(dx,dz,0,Vz,Ix,Iz,Ixz,web(i).dp_area);
-web(i).qPrime_X = webBottom(numBottomStringers+1).qPrime_X - web(i).dP_X;
-web(i).qPrime_Z = webBottom(numBottomStringers+1).qPrime_Z - web(i).dP_Z;
-web(i).Area = 0;
-web(i).ds = abs(sparCaps(2).posZ - sparCaps(1).posZ);
-web(i).dS_over_t = web(i).ds / web(i).thickness;
-
-web(i).q_dS_over_t_X = web(i).qPrime_X * web(i).dS_over_t;
-web(i).q_dS_over_t_Z = web(i).qPrime_Z * web(i).dS_over_t;
-web(i).two_A_qprime_X = 2*web(i).Area*web(i).qPrime_X;
-web(i).two_A_qprime_Z = 2*web(i).Area*web(i).qPrime_Z;
-web(i).qp_dx_X = web(i).qPrime_X *(web(i).xEnd-web(i).xStart);
-web(i).qp_dx_Z = web(i).qPrime_Z *(web(i).xEnd-web(i).xStart);
-web(i).qp_dz_X = web(i).qPrime_X *(web(i).zEnd-web(i).zStart);
-web(i).qp_dz_Z = web(i).qPrime_Z *(web(i).zEnd-web(i).zStart);
-
-webFrontSpar = web;
-web = [];
-
-
-
-
-%% web cell 2
-
-%lower nose webs
-numStringers = numNoseBottomStringers;
-stringerGap = lowerNoseStringerGap;
-webThickness = t_lower_front;
-tempStringers = noseBottomStringers;
-
-for i=1:(numStringers+1)
-    web(i).xStart = sparCaps(2).posX - stringerGap*(i-1);
-    web(i).xEnd = sparCaps(2).posX - stringerGap*(i);
-    web(i).thickness = webThickness;
-    web(i).zStart = get_z(web(i).xStart/chord,0)*chord;
-    web(i).zEnd = get_z(web(i).xEnd/chord,0)*chord;
-    dx = web(i).xStart-centroid.posX; dz = web(i).zStart-centroid.posZ;
-
-    if i==1
-        web(i).dp_area = sparCaps(2).area;
-        web(i).dP_X = 0;
-        web(i).dP_Z = 0;
-        web(i).qPrime_X = 0;
-        web(i).qPrime_Z = 0;
-    else
-        web(i).dp_area = tempStringers(i-1).area;
-        web(i).dP_X = get_dp(dx,dz,Vx,0,Ix,Iz,Ixz,web(i).dp_area);
-        web(i).dP_Z = get_dp(dx,dz,0,Vz,Ix,Iz,Ixz,web(i).dp_area);
-        web(i).qPrime_X = web(i-1).qPrime_X - web(i).dP_X;
-        web(i).qPrime_Z = web(i-1).qPrime_Z - web(i).dP_Z;
-    end
-    tempInt = get_int(web(i).xEnd/chord,web(i).xStart/chord,0)*chord^2;  %integral of airfoil function
-    triangle1 = abs((web(i).xStart - sparCaps(2).posX)*web(i).zStart/2);
-    triangle2 = abs((web(i).xEnd - sparCaps(2).posX)*web(i).zEnd/2);
-    web(i).Area = tempInt + triangle1 - triangle2;
-    web(i).ds = get_ds(web(i).xStart/chord,web(i).xEnd/chord,0)*chord;
-    web(i).dS_over_t = web(i).ds / web(i).thickness;
-
-    web(i).q_dS_over_t_X = web(i).qPrime_X * web(i).dS_over_t;
-    web(i).q_dS_over_t_Z = web(i).qPrime_Z * web(i).dS_over_t;
-    web(i).two_A_qprime_X = 2*web(i).Area*web(i).qPrime_X;
-    web(i).two_A_qprime_Z = 2*web(i).Area*web(i).qPrime_Z;
-    web(i).qp_dx_X = web(i).qPrime_X *(web(i).xEnd-web(i).xStart);
-    web(i).qp_dx_Z = web(i).qPrime_Z *(web(i).xEnd-web(i).xStart);
-    web(i).qp_dz_X = web(i).qPrime_X *(web(i).zEnd-web(i).zStart);
-    web(i).qp_dz_Z = web(i).qPrime_Z *(web(i).zEnd-web(i).zStart);
-
-    %web(i).radCurv = ...   Example:  get_curve(web(i).xStart,web(i).xEnd,1)
-end
-webLowerNose = web;
-web = [];
-
-%upper nose webs
-numStringers = numNoseTopStringers;
-stringerGap = upperNoseStringerGap;
-webThickness = t_upper_front;
-tempStringers = noseTopStringers;
-
-for i=1:(numStringers+1)
-    web(i).xStart = stringerGap*(i-1);
-    web(i).xEnd = stringerGap*(i);
-    web(i).thickness = webThickness;
-    web(i).zStart = get_z(web(i).xStart/chord,1)*chord;
-    web(i).zEnd = get_z(web(i).xEnd/chord,1)*chord;
-    dx = web(i).xStart-centroid.posX; dz = web(i).zStart-centroid.posZ;
-    if i==1
-        web(i).dp_area = 0;
-        web(i).dP_X = 0;
-        web(i).dP_Z = 0;
-        web(i).qPrime_X = webLowerNose(numNoseBottomStringers+1).qPrime_X - web(i).dP_X;
-        web(i).qPrime_Z = webLowerNose(numNoseBottomStringers+1).qPrime_Z - web(i).dP_Z;
-    else
-        web(i).dp_area = tempStringers(i-1).area;
-        web(i).dP_X = get_dp(dx,dz,Vx,0,Ix,Iz,Ixz,web(i).dp_area);
-        web(i).dP_Z = get_dp(dx,dz,0,Vz,Ix,Iz,Ixz,web(i).dp_area);
-        web(i).qPrime_X = web(i-1).qPrime_X - web(i).dP_X;
-        web(i).qPrime_Z = web(i-1).qPrime_Z - web(i).dP_Z;
-    end
-    tempInt = get_int(web(i).xStart/chord,web(i).xEnd/chord,1)*chord^2;  %integral of airfoil function
-    triangle2 = abs((web(i).xStart - sparCaps(2).posX)*web(i).zStart/2);
-    triangle1 = abs((web(i).xEnd - sparCaps(2).posX)*web(i).zEnd/2);
-    web(i).Area = tempInt + triangle1 - triangle2;
-    web(i).ds = get_ds(web(i).xStart/chord,web(i).xEnd/chord,1)*chord;
-    web(i).dS_over_t = web(i).ds / web(i).thickness;
-
-    web(i).q_dS_over_t_X = web(i).qPrime_X * web(i).dS_over_t;
-    web(i).q_dS_over_t_Z = web(i).qPrime_Z * web(i).dS_over_t;
-    web(i).two_A_qprime_X = 2*web(i).Area*web(i).qPrime_X;
-    web(i).two_A_qprime_Z = 2*web(i).Area*web(i).qPrime_Z;
-    web(i).qp_dx_X = web(i).qPrime_X *(web(i).xEnd-web(i).xStart);
-    web(i).qp_dx_Z = web(i).qPrime_Z *(web(i).xEnd-web(i).xStart);
-    web(i).qp_dz_X = web(i).qPrime_X *(web(i).zEnd-web(i).zStart);
-    web(i).qp_dz_Z = web(i).qPrime_Z *(web(i).zEnd-web(i).zStart);
-
-end
-webUpperNose = web;
-web = [];
-
-
-%front Spar
-i=1;
-web(i).xStart = sparCaps(1).posX;
-web(i).xEnd = sparCaps(2).posX;
-web(i).thickness = t_frontSpar;
-web(i).zStart = sparCaps(1).posZ;
-web(i).zEnd = sparCaps(2).posZ;
-web(i).dp_area = sparCaps(1).area;
-dx = web(i).xStart-centroid.posX; dz = web(i).zStart-centroid.posZ;
-
-web(i).dP_X = get_dp(dx,dz,Vx,0,Ix,Iz,Ixz,web(i).dp_area);
-web(i).dP_Z = get_dp(dx,dz,0,Vz,Ix,Iz,Ixz,web(i).dp_area);
-web(i).qPrime_X = webUpperNose(numNoseTopStringers+1).qPrime_X - web(i).dP_X;
-web(i).qPrime_Z = webUpperNose(numNoseTopStringers+1).qPrime_Z - web(i).dP_Z;
-web(i).Area = 0;
-web(i).ds = abs(sparCaps(1).posZ - sparCaps(2).posZ);
-web(i).dS_over_t = web(i).ds / web(i).thickness;
-web(i).q_dS_over_t_X = web(i).qPrime_X * web(i).dS_over_t;
-web(i).q_dS_over_t_Z = web(i).qPrime_Z * web(i).dS_over_t;
-web(i).two_A_qprime_X = 2*web(i).Area*web(i).qPrime_X;
-web(i).two_A_qprime_Z = 2*web(i).Area*web(i).qPrime_Z;
-web(i).qp_dx_X = web(i).qPrime_X *(web(i).xEnd-web(i).xStart);
-web(i).qp_dx_Z = web(i).qPrime_Z *(web(i).xEnd-web(i).xStart);
-web(i).qp_dz_X = web(i).qPrime_X *(web(i).zEnd-web(i).zStart);
-web(i).qp_dz_Z = web(i).qPrime_Z *(web(i).zEnd-web(i).zStart);
-
-webFrontSparCell2 = web;
-web = [];
-
-
-%check that q'*dx sums up to Vx
-
-Fx = sum([webTop.qp_dx_X])+webRearSpar.qp_dx_X+ sum([webBottom.qp_dx_X])+webFrontSpar.qp_dx_X;  %cell 1
-Fx = Fx + sum([webLowerNose.qp_dx_X])+ sum([webUpperNose.qp_dx_X]);  %cell 2
-Fx
-Fz = sum([webTop.qp_dz_X])+webRearSpar.qp_dz_X+ sum([webBottom.qp_dz_X])+webFrontSpar.qp_dz_X;  %cell 1
-Fz = Fz + sum([webLowerNose.qp_dz_X])+ sum([webUpperNose.qp_dz_X]);  %cell 2
-Fz
-
-%check that q'*dz sums up to Vz
-
-
-Fx = sum([webTop.qp_dx_Z])+webRearSpar.qp_dx_Z+ sum([webBottom.qp_dx_Z])+webFrontSpar.qp_dx_Z;  %cell 1
-Fx = Fx + sum([webLowerNose.qp_dx_Z])+ sum([webUpperNose.qp_dx_Z]);  %cell 2
-Fx
-Fz = sum([webTop.qp_dz_Z])+webRearSpar.qp_dz_Z+ sum([webBottom.qp_dz_Z])+webFrontSpar.qp_dz_Z;  %cell 1
-Fz = Fz + sum([webLowerNose.qp_dz_Z])+ sum([webUpperNose.qp_dz_Z]);  %cell 2
-Fz
-
-%%
-
-% sum up the ds/t and  q*ds/t to solve 2 equations, 2 unknowns
-
-% [A]*[q1s q2s] = B
-
-A11 = sum([webTop.dS_over_t])+webRearSpar.dS_over_t+ sum([webBottom.dS_over_t])+webFrontSpar.dS_over_t;
-A22 = sum([webLowerNose.dS_over_t])+ sum([webUpperNose.dS_over_t])+webFrontSparCell2.dS_over_t;
-A12 = -webFrontSpar.dS_over_t;
-A21 = -webFrontSparCell2.dS_over_t;
-
-B1_X = sum([webTop.q_dS_over_t_X])+webRearSpar.q_dS_over_t_X+ sum([webBottom.q_dS_over_t_X])+webFrontSpar.q_dS_over_t_X;
-B2_X = sum([webLowerNose.q_dS_over_t_X])+ sum([webUpperNose.q_dS_over_t_X])+webFrontSparCell2.q_dS_over_t_X;
-B1_Z = sum([webTop.q_dS_over_t_Z])+webRearSpar.q_dS_over_t_Z+ sum([webBottom.q_dS_over_t_Z])+webFrontSpar.q_dS_over_t_Z;
-B2_Z = sum([webLowerNose.q_dS_over_t_Z])+ sum([webUpperNose.q_dS_over_t_Z])+webFrontSparCell2.q_dS_over_t_Z;
-
-Amat = [A11 A12; A21 A22];
-Bmat_X = -[B1_X;B2_X];
-Bmat_Z = -[B1_Z;B2_Z];
-
-qs_X = inv(Amat)*Bmat_X;
-qs_Z = inv(Amat)*Bmat_Z;
-
-
-
-sum_2_a_q_X = sum([webTop.two_A_qprime_X])+webRearSpar.two_A_qprime_X+ sum([webBottom.two_A_qprime_X]);  %cell 1 qprimes
-sum_2_a_q_X = sum_2_a_q_X + sum([webLowerNose.two_A_qprime_X])+ sum([webUpperNose.two_A_qprime_X]);   %cell 2 qprimes
-sum_2_a_q_X = sum_2_a_q_X +  2*qs_X(1)*(sum([webTop.Area])+webRearSpar.Area+ sum([webBottom.Area]));
-sum_2_a_q_X = sum_2_a_q_X +  2*qs_X(2)*(sum([webLowerNose.Area])+ sum([webUpperNose.Area]));
-
-sum_2_a_q_Z = sum([webTop.two_A_qprime_Z])+webRearSpar.two_A_qprime_Z+ sum([webBottom.two_A_qprime_Z]);  %cell 1 qprimes
-sum_2_a_q_Z = sum_2_a_q_Z + sum([webLowerNose.two_A_qprime_Z])+ sum([webUpperNose.two_A_qprime_Z]);   %cell 2 qprimes
-sum_2_a_q_Z = sum_2_a_q_Z +  2*qs_Z(1)*(sum([webTop.Area])+webRearSpar.Area+ sum([webBottom.Area]));
-sum_2_a_q_Z = sum_2_a_q_Z +  2*qs_Z(2)*(sum([webLowerNose.Area])+ sum([webUpperNose.Area]));
-
-%shear center
-sc.posX =  sum_2_a_q_Z / Vz + frontSpar*chord;
-sc.posZ = - sum_2_a_q_X / Vx;
-
-
-% now consider the torque representing shifting the load from the quarter
-% chord to the SC  (need to check signs on these moments)
-
-torque_Z = Vz*(sc.posX - 0.25*chord);
-torque_X = -Vx*sc.posZ;
-
-
-Area1 = sum([webTop.Area]) + webRearSpar.Area + sum([webBottom.Area]);
-%check area
-Area1_check = get_int(frontSpar,backSpar,1)*chord^2 + get_int(frontSpar,backSpar,0)*chord^2;
-
-Area2 = sum([webLowerNose.Area]) + sum([webUpperNose.Area]);
-Area2_check = get_int(0,frontSpar,1)*chord^2 + get_int(0,frontSpar,0)*chord^2;
-
-
-%for twist equation  (see excel spreadsheet example)
-
-q1t_over_q2t = (A22/Area2 + webFrontSpar.dS_over_t/Area1)/(A11/Area1 + webFrontSpar.dS_over_t/Area2);
-
-q2t = torque_X/(2*Area1*q1t_over_q2t + 2*Area2);
-q1t = q2t*q1t_over_q2t;
-qt_X = [q1t;q2t];
-
-q2t = torque_Z/(2*Area1*q1t_over_q2t + 2*Area2);
-q1t = q2t*q1t_over_q2t;
-qt_Z = [q1t;q2t];
-
-
-
-% --- - add up all shear flows:  qtot = (qPrime + qs) + qt
-
-
-
-
-%--- insert force balance to check total shear flows ---
-
-% --- --
-
-
-%end
-
-sc
-
-
-%plotting airfoil cross-section
-
-xChord = 0:.01:1;
-xChord = xChord*chord;
-upperSurface = zeros(1,length(xChord));
-lowerSurface = zeros(1,length(xChord));
-
-for i=1:length(xChord)
-    upperSurface(i) = get_z(xChord(i)/chord,1)*chord;
-    lowerSurface(i) = get_z(xChord(i)/chord,0)*chord;
-end
-
-figure; hold on; axis equal; grid on;
-%plot(xChord,z_camber,'-')
-plot(xChord,upperSurface,'-k','linewidth',2)
-plot(xChord,lowerSurface,'-k','linewidth',2)
-plot([0 1],[0 0],'--k','linewidth',1)
-
-
-for i = 1:length(webTop)
-   vecX = [frontSpar*chord webTop(i).xStart webTop(i).xEnd];
-   vecZ = [0 webTop(i).zStart webTop(i).zEnd];
-   fill(vecX,vecZ,[0.9 0.9 0.9])
-end
-
-for i = 1:length(webBottom)
-   vecX = [frontSpar*chord webBottom(i).xStart webBottom(i).xEnd];
-   vecZ = [0 webBottom(i).zStart webBottom(i).zEnd];
-   fill(vecX,vecZ,[0.9 0.9 0.9])
-end
-
-for i = 1:length(webUpperNose)
-   vecX = [frontSpar*chord webUpperNose(i).xStart webUpperNose(i).xEnd];
-   vecZ = [0 webUpperNose(i).zStart webUpperNose(i).zEnd];
-   fill(vecX,vecZ,[0.7 0.9 1.0])
-end
-
-for i = 1:length(webLowerNose)
-   vecX = [frontSpar*chord webLowerNose(i).xStart webLowerNose(i).xEnd];
-   vecZ = [0 webLowerNose(i).zStart webLowerNose(i).zEnd];
-   fill(vecX,vecZ,[0.7 0.9 1.0])
-end
-
-   vecX = [frontSpar*chord sparCaps(3).posX sparCaps(4).posX];
-   vecZ = [0 sparCaps(3).posZ sparCaps(4).posZ];
-   fill(vecX,vecZ,[0.9 0.9 0.9])
-
-
-sparCapSize = 18;
-stringerSize = 18;
-plot([sparCaps(1).posX sparCaps(2).posX],[sparCaps(1).posZ sparCaps(2).posZ],'-k','linewidth',2)
-plot([sparCaps(3).posX sparCaps(4).posX],[sparCaps(3).posZ sparCaps(4).posZ],'-k','linewidth',2)
-plot([sparCaps.posX],[sparCaps.posZ],'.b','markersize',sparCapSize)
-plot([topStringers.posX],[topStringers.posZ],'.r','markersize',stringerSize)
-plot([bottomStringers.posX],[bottomStringers.posZ],'.r','markersize',stringerSize)
-plot([noseTopStringers.posX],[noseTopStringers.posZ],'.r','markersize',stringerSize)
-plot([noseBottomStringers.posX],[noseBottomStringers.posZ],'.r','markersize',stringerSize)
-plot(centroid.posX,centroid.posZ,'.k','markerSize',18)
-plot(sc.posX,sc.posZ,'.g','markersize',18)
-- 
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