How can I place a linear regression line (line of best fit) through both plots in this code, but only from the halfway point to the end?

I am trying to fit a linear regression line focusoed on only the second half of both plots in this provided code how can I do so? (for wind turbines, most power made on end of the blade so just the second half of the plot is needed to be focused on), but I would need a linear regression line or in other words a line of best fit similar to this example picture below

For example the solid line is what I already have (for both plots, but for example chord distribution is the first) within the plot and the dashed line is the linear fit line which represents the curve but only focused on the second half. I should've inlcuded this first of all hopefully it clears things up

txt data provided in comments

problem statemnt for example

Code......

% Given Data Problems 1-4
dd   = [0.0 0.3983 0.0066 0.0017 -0.0927 0.6330 0.6222
        0.5 0.4536 0.0066 0.0018 -0.0926 0.6172 0.6320
        1.0 0.5091 0.0068 0.0018 -0.0925 0.6013 0.6389
        1.5 0.5641 0.0069 0.0019 -0.0924 0.5857 0.6453
        2.0 0.6189 0.0070 0.0020 -0.0923 0.5699 0.6517
        2.5 0.6733 0.0072 0.0021 -0.0921 0.5540 0.6577
        3.0 0.7270 0.0073 0.0023 -0.0917 0.5358 0.6644
        3.5 0.7792 0.0075 0.0024 -0.0911 0.5135 0.6714
        4.0 0.8310 0.0078 0.0026 -0.0905 0.4921 0.6782
        4.5 0.8822 0.0080 0.0028 -0.0897 0.4682 0.6864
        5.0 0.9328 0.0083 0.0031 -0.0889 0.4464 0.6948
        5.5 0.9812 0.0086 0.0034 -0.0877 0.4199 0.7041
        6.0 1.0280 0.0090 0.0037 -0.0861 0.3896 0.7145
        6.5 1.0728 0.0094 0.0041 -0.0843 0.3581 0.7262
        7.0 1.1138 0.0100 0.0045 -0.0817 0.3214 0.7394
        7.5 1.1459 0.0107 0.0051 -0.0776 0.2766 0.7556
        8.0 1.1724 0.0117 0.0059 -0.0726 0.2228 0.7750
        8.5 1.1957 0.0128 0.0068 -0.0673 0.1745 0.7994
        9.0 1.2193 0.0139 0.0079 -0.0622 0.1382 0.8326
        9.5 1.2403 0.0149 0.0089 -0.0568 0.1102 0.9219
        10.0 1.2659 0.0161 0.0102 -0.0528 0.0907 0.9825
        10.5 1.2906 0.0175 0.0114 -0.0489 0.0728 1.0000
        11.0 1.3137 0.0191 0.0130 -0.0452 0.0602 1.0000
        11.5 1.3367 0.0208 0.0147 -0.0419 0.0518 1.0000
        12.0 1.3589 0.0226 0.0166 -0.0387 0.0458 1.0000
        12.5 1.3796 0.0247 0.0187 -0.0358 0.0412 1.0000
        13.0 1.3951 0.0273 0.0213 -0.0328 0.0368 1.0000
        13.5 1.4159 0.0297 0.0238 -0.0307 0.0345 1.0000
        14.0 1.4268 0.0330 0.0271 -0.0282 0.0316 1.0000
        14.5 1.4433 0.0360 0.0303 -0.0266 0.0300 1.0000
        15.0 1.4559 0.0396 0.0340 -0.0251 0.0282 1.0000
        15.5 1.4590 0.0443 0.0388 -0.0239 0.0264 1.0000
        16.0 1.4703 0.0485 0.0431 -0.0233 0.0253 1.0000
        16.5 1.4782 0.0532 0.0480 -0.0231 0.0241 1.0000
        17.0 1.4794 0.0590 0.0539 -0.0233 0.0230 1.0000
        17.5 1.4707 0.0663 0.0614 -0.0242 0.0220 1.0000
        18.0 1.4743 0.0723 0.0676 -0.0254 0.0214 1.0000
        18.5 1.4732 0.0792 0.0746 -0.0272 0.0208 1.0000
        19.0 1.4701 0.0867 0.0822 -0.0294 0.0201 1.0000
        19.5 1.4626 0.0950 0.0907 -0.0324 0.0196 1.0000
        20.0 1.4501 0.1043 0.1002 -0.0360 0.0190 1.0000];

alpha   = dd(:,1);      % Angle of attacks (Degreed)
CL      = dd(:,2);      % Lift coefficient
CD      = dd(:,3);      % Drag coefficient
Rh      = 0.75;         % Turbine hub radius (m)
Rt      = 15;           % Turbine blade tip radius (m)
Rht     = linspace(Rh,Rt,10); % r/R radius hub to tip (m)
Rr      = Rht/Rt;
B       = 3;            % Number of blades on the turbine
TSR     = 8;            % Tips-speed ratio

% Calculation Problem 1
CLD     = CL./CD        % Lift-to-Drag Ratio

CLD = 41×1

60.3485 68.7273 74.8676 81.7536 88.4143 93.5139 99.5890 103.8933 106.5385 110.2750 112.3855 114.0930 114.2222 114.1277 111.3800

<mw-icon class=""></mw-icon>

<mw-icon class=""></mw-icon>

TCL     = 1.0280;       % Lift coefficient associated with maximum lift-to-drag ratio
Talpha  = 6;            % Target angle of attack (degrees)

%Calculation Problem 2
Phi     = atand(2./(3*TSR*(Rr)))    % Local inflow angle (degrees)

Phi = 1×10

59.0362 28.1786 17.7004 12.8043 10.0080 8.2072 6.9530 6.0300 5.3228 4.7636

<mw-icon class=""></mw-icon>

<mw-icon class=""></mw-icon>

CrR     = Rt*(8*pi*sind(Phi))./(3*B*TCL*TSR);   % chord distribution
Beta    = Phi-Talpha

Beta = 1×10

53.0362 22.1786 11.7004 6.8043 4.0080 2.2072 0.9530 0.0300 -0.6772 -1.2364

<mw-icon class=""></mw-icon>

<mw-icon class=""></mw-icon>

subplot(2,1,1)
plot(Rht, CrR, 'LineWidth', 2)
xlabel('r/R')
ylabel('Chord Distribution (m)')
grid on

subplot(2,1,2)
plot(Rht, Beta, 'LineWidth', 2)
xlabel('r/R')
ylabel('Beta (degrees)')
grid on

% Problem 3 Linear Fit Line for Rht/CrR & Rht/Beta?

[Torsten]

To make the code work, we need your data as a .txt or .xls file, not as an image. Same for your second question in the forum.

[ryan]

Than you for your response, I would love to but MATLAB will not let me upload my .txt or .xls file for some reason. They are right handy but get an error everytime I try to submit them here and they're all under the 5 mb limit.

[Sam Chak]

Hi @ryan, I don't know what issue is, but perhaps you can directly copy/paste the numerals from the 'txt' file as shown below. Remember to click the indentation icon .

1	2	3	4	5
2	5	8	9	6
3	6	9	8	7
4	8	6	3	5
1	5	9	3	7
2	4	8	5	3
6	4	9	7	8
8	2	5	6	1
9	4	3	7	2

[ryan]

0.0 0.3983 0.0066 0.0017 -0.0927 0.6330 0.6222

0.5 0.4536 0.0066 0.0018 -0.0926 0.6172 0.6320

1.0 0.5091 0.0068 0.0018 -0.0925 0.6013 0.6389

1.5 0.5641 0.0069 0.0019 -0.0924 0.5857 0.6453

2.0 0.6189 0.0070 0.0020 -0.0923 0.5699 0.6517

2.5 0.6733 0.0072 0.0021 -0.0921 0.5540 0.6577

3.0 0.7270 0.0073 0.0023 -0.0917 0.5358 0.6644

3.5 0.7792 0.0075 0.0024 -0.0911 0.5135 0.6714

4.0 0.8310 0.0078 0.0026 -0.0905 0.4921 0.6782

4.5 0.8822 0.0080 0.0028 -0.0897 0.4682 0.6864

5.0 0.9328 0.0083 0.0031 -0.0889 0.4464 0.6948

5.5 0.9812 0.0086 0.0034 -0.0877 0.4199 0.7041

6.0 1.0280 0.0090 0.0037 -0.0861 0.3896 0.7145

6.5 1.0728 0.0094 0.0041 -0.0843 0.3581 0.7262

7.0 1.1138 0.0100 0.0045 -0.0817 0.3214 0.7394

7.5 1.1459 0.0107 0.0051 -0.0776 0.2766 0.7556

8.0 1.1724 0.0117 0.0059 -0.0726 0.2228 0.7750

8.5 1.1957 0.0128 0.0068 -0.0673 0.1745 0.7994

9.0 1.2193 0.0139 0.0079 -0.0622 0.1382 0.8326

9.5 1.2403 0.0149 0.0089 -0.0568 0.1102 0.9219

10.0 1.2659 0.0161 0.0102 -0.0528 0.0907 0.9825

10.5 1.2906 0.0175 0.0114 -0.0489 0.0728 1.0000

11.0 1.3137 0.0191 0.0130 -0.0452 0.0602 1.0000

11.5 1.3367 0.0208 0.0147 -0.0419 0.0518 1.0000

12.0 1.3589 0.0226 0.0166 -0.0387 0.0458 1.0000

12.5 1.3796 0.0247 0.0187 -0.0358 0.0412 1.0000

13.0 1.3951 0.0273 0.0213 -0.0328 0.0368 1.0000

13.5 1.4159 0.0297 0.0238 -0.0307 0.0345 1.0000

14.0 1.4268 0.0330 0.0271 -0.0282 0.0316 1.0000

14.5 1.4433 0.0360 0.0303 -0.0266 0.0300 1.0000

15.0 1.4559 0.0396 0.0340 -0.0251 0.0282 1.0000

15.5 1.4590 0.0443 0.0388 -0.0239 0.0264 1.0000

16.0 1.4703 0.0485 0.0431 -0.0233 0.0253 1.0000

16.5 1.4782 0.0532 0.0480 -0.0231 0.0241 1.0000

17.0 1.4794 0.0590 0.0539 -0.0233 0.0230 1.0000

17.5 1.4707 0.0663 0.0614 -0.0242 0.0220 1.0000

18.0 1.4743 0.0723 0.0676 -0.0254 0.0214 1.0000

18.5 1.4732 0.0792 0.0746 -0.0272 0.0208 1.0000

19.0 1.4701 0.0867 0.0822 -0.0294 0.0201 1.0000

19.5 1.4626 0.0950 0.0907 -0.0324 0.0196 1.0000

20.0 1.4501 0.1043 0.1002 -0.0360 0.0190 1.0000

[Sam Chak]

Hi @ryan, I merged the data with the code from your original post so that others can investigate the issue.

[ryan]

I am trying to fit a linear regression line focusoed on only the second half of a plot (for wind turbines, most power made on end of the blade so just the second half of the plot is needed to be focused on considering the x axis is the lenght of the wind turbine blade for both plots for example), but I would need a linear regression line or in other words a line of best fit similar to this example

For example the solid line is what I already have (for both plots, but for example chord distribution is the first) within the plot and the dashed line is the linear fit line which represents the curve but only focused on the second half. I need helpo figuring out how to create that dashed line (line of best fit) but to the conditions that it;'s at withi the picture (focused only on second half) should've inlcuded this first of all hopefully it clears things up

Answer 1

[Image Analyst]

Do you already have the "linear distribution" and "chord and twist distribution"? Is that what columns 2 and 3 are?

You are right that the tool to plot those distributions is plot(), or at least that's one way - you could also use bar(). If you don't already have those two distributions in variables, then I have no idea how to "determine suitable" vectors for them from your Problem 2 (which was not supplied to us here), and you should ask your instructor for help with that.

To plot only half of a vector you can do this

halfPoints = round(numel(y) / 2)
plot(x(1 : halfPoints), y(1:halfPoints), 'b-', 'LineWidth', 2);
grid on;

[ryan]

I believe I provided some more information ina comment above me that may be helpful if not elt me now thank you so much for helping me

Answer 2

[Sam Chak]

Hi @ryan

In purely math terms, do you mean to find the tangent line at the midpoint of the decaying beta curve? If so, I used math techniques to calculate the midpoint and draw the straight line. Of course, you can also use some built-in curve-fitting tools.

% Given Data Problems 1-4
dd   = [0.0 0.3983 0.0066 0.0017 -0.0927 0.6330 0.6222
        0.5 0.4536 0.0066 0.0018 -0.0926 0.6172 0.6320
        1.0 0.5091 0.0068 0.0018 -0.0925 0.6013 0.6389
        1.5 0.5641 0.0069 0.0019 -0.0924 0.5857 0.6453
        2.0 0.6189 0.0070 0.0020 -0.0923 0.5699 0.6517
        2.5 0.6733 0.0072 0.0021 -0.0921 0.5540 0.6577
        3.0 0.7270 0.0073 0.0023 -0.0917 0.5358 0.6644
        3.5 0.7792 0.0075 0.0024 -0.0911 0.5135 0.6714
        4.0 0.8310 0.0078 0.0026 -0.0905 0.4921 0.6782
        4.5 0.8822 0.0080 0.0028 -0.0897 0.4682 0.6864
        5.0 0.9328 0.0083 0.0031 -0.0889 0.4464 0.6948
        5.5 0.9812 0.0086 0.0034 -0.0877 0.4199 0.7041
        6.0 1.0280 0.0090 0.0037 -0.0861 0.3896 0.7145
        6.5 1.0728 0.0094 0.0041 -0.0843 0.3581 0.7262
        7.0 1.1138 0.0100 0.0045 -0.0817 0.3214 0.7394
        7.5 1.1459 0.0107 0.0051 -0.0776 0.2766 0.7556
        8.0 1.1724 0.0117 0.0059 -0.0726 0.2228 0.7750
        8.5 1.1957 0.0128 0.0068 -0.0673 0.1745 0.7994
        9.0 1.2193 0.0139 0.0079 -0.0622 0.1382 0.8326
        9.5 1.2403 0.0149 0.0089 -0.0568 0.1102 0.9219
        10.0 1.2659 0.0161 0.0102 -0.0528 0.0907 0.9825
        10.5 1.2906 0.0175 0.0114 -0.0489 0.0728 1.0000
        11.0 1.3137 0.0191 0.0130 -0.0452 0.0602 1.0000
        11.5 1.3367 0.0208 0.0147 -0.0419 0.0518 1.0000
        12.0 1.3589 0.0226 0.0166 -0.0387 0.0458 1.0000
        12.5 1.3796 0.0247 0.0187 -0.0358 0.0412 1.0000
        13.0 1.3951 0.0273 0.0213 -0.0328 0.0368 1.0000
        13.5 1.4159 0.0297 0.0238 -0.0307 0.0345 1.0000
        14.0 1.4268 0.0330 0.0271 -0.0282 0.0316 1.0000
        14.5 1.4433 0.0360 0.0303 -0.0266 0.0300 1.0000
        15.0 1.4559 0.0396 0.0340 -0.0251 0.0282 1.0000
        15.5 1.4590 0.0443 0.0388 -0.0239 0.0264 1.0000
        16.0 1.4703 0.0485 0.0431 -0.0233 0.0253 1.0000
        16.5 1.4782 0.0532 0.0480 -0.0231 0.0241 1.0000
        17.0 1.4794 0.0590 0.0539 -0.0233 0.0230 1.0000
        17.5 1.4707 0.0663 0.0614 -0.0242 0.0220 1.0000
        18.0 1.4743 0.0723 0.0676 -0.0254 0.0214 1.0000
        18.5 1.4732 0.0792 0.0746 -0.0272 0.0208 1.0000
        19.0 1.4701 0.0867 0.0822 -0.0294 0.0201 1.0000
        19.5 1.4626 0.0950 0.0907 -0.0324 0.0196 1.0000
        20.0 1.4501 0.1043 0.1002 -0.0360 0.0190 1.0000];

alpha   = dd(:,1);      % Angle of attacks (Degreed)
CL      = dd(:,2);      % Lift coefficient
CD      = dd(:,3);      % Drag coefficient
Rh      = 0.75;         % Turbine hub radius (m)
Rt      = 15;           % Turbine blade tip radius (m)
Rht     = linspace(Rh, Rt, 10001); % r/R radius hub to tip (m)
Rr      = Rht/Rt;
B       = 3;            % Number of blades on the turbine
TSR     = 8;            % Tips-speed ratio

% Calculation Problem 1
CLD     = CL./CD;       % Lift-to-Drag Ratio
TCL     = 1.0280;       % Lift coefficient associated with maximum lift-to-drag ratio
Talpha  = 6;            % Target angle of attack (degrees)

%Calculation Problem 2
Phi     = atand(2./(3*TSR*(Rr)));               % Local inflow angle (degrees)
CrR     = Rt*(8*pi*sind(Phi))./(3*B*TCL*TSR);   % chord distribution
Beta    = Phi-Talpha;

midpoint= mean([Rh, Rt])

midpoint = 7.8750

idx     = find(abs(Rht - midpoint) < 1e-3)

idx = 5001

dBeta   = gradient(Beta)./gradient(Rht);
m       = dBeta(idx)                % slope

m = -1.1265

c       = Beta(idx) - m*Rht(idx)    % y-intercept

c = 11.8904

point1  = m*Rht(1)   + c;
point2  = m*Rht(end) + c;

subplot(2,1,1)
plot(Rht, CrR, 'LineWidth', 2)
xlabel('r/R')
ylabel('Chord Distribution (m)')
grid on

subplot(2,1,2)
hold on
plot(Rht, Beta, 'LineWidth', 2)
plot([Rht(1) Rht(end)], [point1 point2], '--')  % tangent line
plot(Rht(idx), Beta(idx), 'o', 'LineWidth', 2)  % midpoint
hold off
xlabel('r/R')
ylabel('Beta (degrees)')
grid on

[ryan]

Hello @Sam Chak I tried your answer with this code right here...

%Given Data Problems 1-4
dd = load('NEWPROB6.txt') %Data loading for airfoil
alpha = dd(:,1); %Angle of attacks (Degreed)
CL = dd(:,2); %Lift coefficient
CD = dd(:,3); %Drag coefficient
Rh = 0.75; %Turbine hub radius (m)
Rt = 15; %Turbine blade tip radius (m)
Rht = linspace(Rh,Rt,10); %r/R radius hub to tip (m)
Rr = Rht/Rt;
B = 3; %Number of blades on the turbine
TSR = 8; %Tips-speed ratio
%Calculation Problem 1
CLD = CL./CD %Lift-to-Drag Ratio
TCL = 1.0280 %Lift coefficient associated with maximum lift-to-drag ratio
Talpha = 6 %Target angle of attack (degrees)
%Calculation Problem 2
Phi = atand(2./(3*TSR*(Rr))) %Local inflow angle (degrees)
CrR = Rt*(8*pi*sind(Phi))./(3*B*TCL*TSR); %chord distribution
Beta = Phi-Talpha
midpoint = mean([Rh, Rt])
idx = find(abs(Rht - midpoint) < 1e-3)
dBeta = gradient(Beta)./gradient(Rht);
m = dBeta(idx) 
c = Beta(idx) - m.*Rht(idx)
point1  = m*Rht(1)   + c;
point2  = m*Rht(end) + c;
subplot(2,1,1)
plot(Rht,CrR, 'LineWidth',2)
xlabel('r/R')
ylabel('Chord Distribution (m)')
grid on
hold on
subplot(2,1,2)
hold on
plot(Rht, Beta, 'LineWidth', 2)
plot([Rht(1) Rht(end)], [point1 point2], '--')  % tangent line
plot(Rht(idx), Beta(idx), 'o', 'LineWidth', 2)  % midpoint
xlabel('r/R')
ylabel('Beta (degrees)')
grid on

The plot I'm receiving

Error I'm receiving..

Answer 3

[Image Analyst]

Maybe try this (untested):

% x and y are your variables.  Replace them with whatever variable names you actually have.
plot(x, y, 'b-', 'LineWidth', 2); % Plot full curve
halfPoints = round(numel(y) / 2)
% Let's put a red vertical line at the half way point.
hold on;
xline(x(halfPoints), 'Color', 'r')
% Get the right half of the data.
xHalf = x(halfPoints : end);
yHalf = y(halfPoints : end);
% Fit the right half of the data to a line with polyfit
coefficients = polyfit(xHalf, yHalf, 1);
% Extend that line and get a vector covering 
% the whole original range of x.
xFitted = linspace(min(x), max(x), numel(x)); % Linearly spaced x samples.
%xFitted = x; % Or, you can use the same x as the original if you want.
% Get fitted y values by calling polyfit.
yFitted = polyval(coefficients, xFitted);
% Plot the fitted line as a cyan dashed line.
plot(xFitted, yFitted, 'c--', 'LineWidth', 2);
grid on;
legend('Original', 'Halfway line', 'Fitted', 'Location', 'north');
hold off;

[Sam Chak]

@Image Analyst, Tested, and it works perfectly. Thanks!

% Given Data Problems 1-4
dd   = [0.0 0.3983 0.0066 0.0017 -0.0927 0.6330 0.6222
        0.5 0.4536 0.0066 0.0018 -0.0926 0.6172 0.6320
        1.0 0.5091 0.0068 0.0018 -0.0925 0.6013 0.6389
        1.5 0.5641 0.0069 0.0019 -0.0924 0.5857 0.6453
        2.0 0.6189 0.0070 0.0020 -0.0923 0.5699 0.6517
        2.5 0.6733 0.0072 0.0021 -0.0921 0.5540 0.6577
        3.0 0.7270 0.0073 0.0023 -0.0917 0.5358 0.6644
        3.5 0.7792 0.0075 0.0024 -0.0911 0.5135 0.6714
        4.0 0.8310 0.0078 0.0026 -0.0905 0.4921 0.6782
        4.5 0.8822 0.0080 0.0028 -0.0897 0.4682 0.6864
        5.0 0.9328 0.0083 0.0031 -0.0889 0.4464 0.6948
        5.5 0.9812 0.0086 0.0034 -0.0877 0.4199 0.7041
        6.0 1.0280 0.0090 0.0037 -0.0861 0.3896 0.7145
        6.5 1.0728 0.0094 0.0041 -0.0843 0.3581 0.7262
        7.0 1.1138 0.0100 0.0045 -0.0817 0.3214 0.7394
        7.5 1.1459 0.0107 0.0051 -0.0776 0.2766 0.7556
        8.0 1.1724 0.0117 0.0059 -0.0726 0.2228 0.7750
        8.5 1.1957 0.0128 0.0068 -0.0673 0.1745 0.7994
        9.0 1.2193 0.0139 0.0079 -0.0622 0.1382 0.8326
        9.5 1.2403 0.0149 0.0089 -0.0568 0.1102 0.9219
        10.0 1.2659 0.0161 0.0102 -0.0528 0.0907 0.9825
        10.5 1.2906 0.0175 0.0114 -0.0489 0.0728 1.0000
        11.0 1.3137 0.0191 0.0130 -0.0452 0.0602 1.0000
        11.5 1.3367 0.0208 0.0147 -0.0419 0.0518 1.0000
        12.0 1.3589 0.0226 0.0166 -0.0387 0.0458 1.0000
        12.5 1.3796 0.0247 0.0187 -0.0358 0.0412 1.0000
        13.0 1.3951 0.0273 0.0213 -0.0328 0.0368 1.0000
        13.5 1.4159 0.0297 0.0238 -0.0307 0.0345 1.0000
        14.0 1.4268 0.0330 0.0271 -0.0282 0.0316 1.0000
        14.5 1.4433 0.0360 0.0303 -0.0266 0.0300 1.0000
        15.0 1.4559 0.0396 0.0340 -0.0251 0.0282 1.0000
        15.5 1.4590 0.0443 0.0388 -0.0239 0.0264 1.0000
        16.0 1.4703 0.0485 0.0431 -0.0233 0.0253 1.0000
        16.5 1.4782 0.0532 0.0480 -0.0231 0.0241 1.0000
        17.0 1.4794 0.0590 0.0539 -0.0233 0.0230 1.0000
        17.5 1.4707 0.0663 0.0614 -0.0242 0.0220 1.0000
        18.0 1.4743 0.0723 0.0676 -0.0254 0.0214 1.0000
        18.5 1.4732 0.0792 0.0746 -0.0272 0.0208 1.0000
        19.0 1.4701 0.0867 0.0822 -0.0294 0.0201 1.0000
        19.5 1.4626 0.0950 0.0907 -0.0324 0.0196 1.0000
        20.0 1.4501 0.1043 0.1002 -0.0360 0.0190 1.0000];

alpha   = dd(:,1);      % Angle of attacks (Degreed)
CL      = dd(:,2);      % Lift coefficient
CD      = dd(:,3);      % Drag coefficient
Rh      = 0.75;         % Turbine hub radius (m)
Rt      = 15;           % Turbine blade tip radius (m)
Rht     = linspace(Rh, Rt, 10001); % r/R radius hub to tip (m)
Rr      = Rht/Rt;
B       = 3;            % Number of blades on the turbine
TSR     = 8;            % Tips-speed ratio

% Calculation Problem 1
CLD     = CL./CD;       % Lift-to-Drag Ratio
TCL     = 1.0280;       % Lift coefficient associated with maximum lift-to-drag ratio
Talpha  = 6;            % Target angle of attack (degrees)

%Calculation Problem 2
Phi     = atand(2./(3*TSR*(Rr)));               % Local inflow angle (degrees)
CrR     = Rt*(8*pi*sind(Phi))./(3*B*TCL*TSR);   % chord distribution
Beta    = Phi-Talpha;

%% Ideas by Image Analyst
% -----------------------
x   = Rht;
y   = Beta;

% x and y are your variables.  Replace them with whatever variable names you actually have.
plot(x, y, 'b-', 'LineWidth', 2); % Plot full curve
halfPoints = round(numel(y) / 2)

halfPoints = 5001

% Let's put a red vertical line at the half way point.
hold on;
xline(x(halfPoints), 'Color', 'r')
% Get the right half of the data.
xHalf = x(halfPoints : end);
yHalf = y(halfPoints : end);
% Fit the right half of the data to a line with polyfit
coefficients = polyfit(xHalf, yHalf, 1);
% Extend that line and get a vector covering 
% the whole original range of x.
xFitted = linspace(min(x), max(x), numel(x)); % Linearly spaced x samples.
%xFitted = x; % Or, you can use the same x as the original if you want.
% Get fitted y values by calling polyfit.
yFitted = polyval(coefficients, xFitted);
% Plot the fitted line as a cyan dashed line.
plot(xFitted, yFitted, 'c--', 'LineWidth', 2);
grid on;
legend('Original', 'Halfway line', 'Fitted', 'Location', 'north');
hold off;

●

[ryan]

Hello @Image Analyst I adjusted my code to the one you provided just having one plot for now to simplify it, thank you very much. This is what I inputted and the output is lie the image below the code, just a vertical line, not sure what I'm doing wrong but what I see in your picture that you provided of the plot I can say that is exactly what i am looking to do, just not sure how I can turn my vertical line to be lie yours I must've done something.

Code...

%Given Data Problems 1-4
dd = load('NEWPROB6.txt') %Data loading for airfoil
alpha = dd(:,1); %Angle of attacks (Degreed)
CL = dd(:,2); %Lift coefficient
CD = dd(:,3); %Drag coefficient
Rh = 0.75; %Turbine hub radius (m)
Rt = 15; %Turbine blade tip radius (m)
Rht = linspace(Rh,Rt,10); %r/R radius hub to tip (m)
Rr = Rht/Rt;
B = 3; %Number of blades on the turbine
TSR = 8; %Tips-speed ratio
%Calculation Problem 1
CLD = CL./CD %Lift-to-Drag Ratio
TCL = 1.0280 %Lift coefficient associated with maximum lift-to-drag ratio
Talpha = 6 %Target angle of attack (degrees)
%Calculation Problem 2
Phi = atand(2./(3*TSR*(Rr))) %Local inflow angle (degrees)
CrR = Rt*(8*pi*sind(Phi))./(3*B*TCL*TSR); %chord distribution
Beta = Phi-Talpha
subplot(2,1,1)
plot(Rht,CrR, 'b-', 'LineWidth',2)
halfpoints = round(numel(CrR)/2)
xlabel('r/R')
ylabel('Chord Distribution (m)')
grid on
hold on
xline(Rht(halfpoints), 'Color', 'r')
RhtHalf = Rht(halfpoints : end)
CrRHalf = CrR(halfpoints : end)
coefficents = polyfit(RhtHalf, CrRHalf, 1)
RhtFitted = linspace(5, 10, 1)
CrRFitted = polyval(coefficients, RhtFitted)
plot(RhtFitted, CrRFitted, 'c--', 'LineWidth', 2)
grid on
legend('Original', 'Halfwayline', 'Fitted', 'Location', 'north')
hold off

Result :

[Image Analyst]

You misspelled coefficients and you didn't use linspace right. Try this:

% Given Data Problems 1-4
dd   = [0.0 0.3983 0.0066 0.0017 -0.0927 0.6330 0.6222
    0.5 0.4536 0.0066 0.0018 -0.0926 0.6172 0.6320
    1.0 0.5091 0.0068 0.0018 -0.0925 0.6013 0.6389
    1.5 0.5641 0.0069 0.0019 -0.0924 0.5857 0.6453
    2.0 0.6189 0.0070 0.0020 -0.0923 0.5699 0.6517
    2.5 0.6733 0.0072 0.0021 -0.0921 0.5540 0.6577
    3.0 0.7270 0.0073 0.0023 -0.0917 0.5358 0.6644
    3.5 0.7792 0.0075 0.0024 -0.0911 0.5135 0.6714
    4.0 0.8310 0.0078 0.0026 -0.0905 0.4921 0.6782
    4.5 0.8822 0.0080 0.0028 -0.0897 0.4682 0.6864
    5.0 0.9328 0.0083 0.0031 -0.0889 0.4464 0.6948
    5.5 0.9812 0.0086 0.0034 -0.0877 0.4199 0.7041
    6.0 1.0280 0.0090 0.0037 -0.0861 0.3896 0.7145
    6.5 1.0728 0.0094 0.0041 -0.0843 0.3581 0.7262
    7.0 1.1138 0.0100 0.0045 -0.0817 0.3214 0.7394
    7.5 1.1459 0.0107 0.0051 -0.0776 0.2766 0.7556
    8.0 1.1724 0.0117 0.0059 -0.0726 0.2228 0.7750
    8.5 1.1957 0.0128 0.0068 -0.0673 0.1745 0.7994
    9.0 1.2193 0.0139 0.0079 -0.0622 0.1382 0.8326
    9.5 1.2403 0.0149 0.0089 -0.0568 0.1102 0.9219
    10.0 1.2659 0.0161 0.0102 -0.0528 0.0907 0.9825
    10.5 1.2906 0.0175 0.0114 -0.0489 0.0728 1.0000
    11.0 1.3137 0.0191 0.0130 -0.0452 0.0602 1.0000
    11.5 1.3367 0.0208 0.0147 -0.0419 0.0518 1.0000
    12.0 1.3589 0.0226 0.0166 -0.0387 0.0458 1.0000
    12.5 1.3796 0.0247 0.0187 -0.0358 0.0412 1.0000
    13.0 1.3951 0.0273 0.0213 -0.0328 0.0368 1.0000
    13.5 1.4159 0.0297 0.0238 -0.0307 0.0345 1.0000
    14.0 1.4268 0.0330 0.0271 -0.0282 0.0316 1.0000
    14.5 1.4433 0.0360 0.0303 -0.0266 0.0300 1.0000
    15.0 1.4559 0.0396 0.0340 -0.0251 0.0282 1.0000
    15.5 1.4590 0.0443 0.0388 -0.0239 0.0264 1.0000
    16.0 1.4703 0.0485 0.0431 -0.0233 0.0253 1.0000
    16.5 1.4782 0.0532 0.0480 -0.0231 0.0241 1.0000
    17.0 1.4794 0.0590 0.0539 -0.0233 0.0230 1.0000
    17.5 1.4707 0.0663 0.0614 -0.0242 0.0220 1.0000
    18.0 1.4743 0.0723 0.0676 -0.0254 0.0214 1.0000
    18.5 1.4732 0.0792 0.0746 -0.0272 0.0208 1.0000
    19.0 1.4701 0.0867 0.0822 -0.0294 0.0201 1.0000
    19.5 1.4626 0.0950 0.0907 -0.0324 0.0196 1.0000
    20.0 1.4501 0.1043 0.1002 -0.0360 0.0190 1.0000];
%Given Data Problems 1-4
% dd = load('NEWPROB6.txt') %Data loading for airfoil
alpha = dd(:,1); %Angle of attacks (Degreed)
CL = dd(:,2); %Lift coefficient
CD = dd(:,3); %Drag coefficient
Rh = 0.75; %Turbine hub radius (m)
Rt = 15; %Turbine blade tip radius (m)
Rht = linspace(Rh,Rt,10); %r/R radius hub to tip (m)
Rr = Rht/Rt;
B = 3; %Number of blades on the turbine
TSR = 8; %Tips-speed ratio
%Calculation Problem 1
CLD = CL./CD %Lift-to-Drag Ratio

CLD = 41×1

60.3485 68.7273 74.8676 81.7536 88.4143 93.5139 99.5890 103.8933 106.5385 110.2750 112.3855 114.0930 114.2222 114.1277 111.3800

<mw-icon class=""></mw-icon>

<mw-icon class=""></mw-icon>

TCL = 1.0280 %Lift coefficient associated with maximum lift-to-drag ratio

TCL = 1.0280

Talpha = 6 %Target angle of attack (degrees)

Talpha = 6

%Calculation Problem 2
Phi = atand(2./(3*TSR*(Rr))) %Local inflow angle (degrees)

Phi = 1×10

59.0362 28.1786 17.7004 12.8043 10.0080 8.2072 6.9530 6.0300 5.3228 4.7636

<mw-icon class=""></mw-icon>

<mw-icon class=""></mw-icon>

CrR = Rt*(8*pi*sind(Phi))./(3*B*TCL*TSR); %chord distribution
Beta = Phi-Talpha

Beta = 1×10

53.0362 22.1786 11.7004 6.8043 4.0080 2.2072 0.9530 0.0300 -0.6772 -1.2364

<mw-icon class=""></mw-icon>

<mw-icon class=""></mw-icon>

subplot(2,1,1)
plot(Rht,CrR, 'b.-', 'LineWidth',2, 'MarkerSize', 20)
halfpoints = round(numel(CrR)/2)

halfpoints = 5

xlabel('r/R')
ylabel('Chord Distribution (m)')
grid on
hold on
xline(Rht(halfpoints), 'Color', 'r')
RhtHalf = Rht(halfpoints : end)

RhtHalf = 1×6

7.0833 8.6667 10.2500 11.8333 13.4167 15.0000

<mw-icon class=""></mw-icon>

<mw-icon class=""></mw-icon>

CrRHalf = CrR(halfpoints : end)

CrRHalf = 1×6

0.8852 0.7271 0.6166 0.5351 0.4725 0.4230

<mw-icon class=""></mw-icon>

<mw-icon class=""></mw-icon>

coefficients = polyfit(RhtHalf, CrRHalf, 1)

coefficients = 1×2

-0.0570 1.2388

<mw-icon class=""></mw-icon>

<mw-icon class=""></mw-icon>

RhtFitted = Rht; %linspace(5, 10, 1)
CrRFitted = polyval(coefficients, RhtFitted);
plot(RhtFitted, CrRFitted, 'c--', 'LineWidth', 2)
grid on
legend('Original', 'Halfwayline', 'Fitted', 'Location', 'north')
hold off

I encourage you to put back in the comments that I put in and that you removed. They help explain it and it's what all good programmers should do.

[ryan]

Hello @Image Analyst I changed the word coefficients, the linspace is a range of values starting with the smallest radius to the largest radius so that why its set from Rht to 1, but for some reason still getting this vertical line below the picture is my new code. I am not clearly surfe what to do from your guidance but am grateful for what youve given me thank you

%% Calculation Problem 2

%Given Data Problems 1-4

dd = load('NEWPROB6.txt') %Data loading for airfoil

alpha = dd(:,1); %Angle of attacks (Degreed)

CL = dd(:,2); %Lift coefficient

CD = dd(:,3); %Drag coefficient

Rh = 0.75; %Turbine hub radius (m)

Rt = 15; %Turbine blade tip radius (m)

Rht = linspace(Rh,Rt,10); %r/R radius hub to tip (m)

Rr = Rht/Rt;

B = 3; %Number of blades on the turbine

TSR = 8; %Tips-speed ratio

%Calculation Problem 1

CLD = CL./CD %Lift-to-Drag Ratio

TCL = 1.0280 %Lift coefficient associated with maximum lift-to-drag ratio

Talpha = 6 %Target angle of attack (degrees)

%Calculation Problem 2

Phi = atand(2./(3*TSR*(Rr))) %Local inflow angle (degrees)

CrR = Rt*(8*pi*sind(Phi))./(3*B*TCL*TSR); %chord distribution

Beta = Phi-Talpha

subplot(2,1,1)

plot(Rht,CrR, 'b.-', 'LineWidth',2, 'MarkerSize', 20)

halfpoints = round(numel(CrR)/2)

xlabel('r/R')

ylabel('Chord Distribution (m)')

grid on

hold on

% Assume x and y are your data vectors

xline(Rht(halfpoints), 'Color', 'r')

% Get halfway index

RhtHalf = Rht(halfpoints : end)

CrRHalf = CrR(halfpoints : end)

coefficients = polyfit(RhtHalf, CrRHalf, 1)

RhtFitted = linspace(5, 10, 1)

CrRFitted = polyval(coefficients, RhtFitted);

plot(RhtFitted, CrRFitted, 'c--', 'LineWidth', 2)

grid on

legend('Original Data', 'Linear Fit (2nd Half)');

hold off

[Image Analyst]

Why are you doing this

RhtFitted = linspace(5, 10, 1)

instead of the way I told you to do it? that literally gives only one points so there is only one output point to plot. Just watch:

RhtFitted = linspace(5, 10, 1) 

RhtFitted = 10

See? Just one point! Why are you only fitting from 5 to 10 instead of the right half of the curve?

I literally ran my code in Answers and it plotted correctly.