I know how to write the script to generate the plot. ALthough, I need help on ho
ID: 642906 • Letter: I
Question
I know how to write the script to generate the plot. ALthough, I need help on how to make the script identify the maximum of the curve.
Using MATLAB write a program (based on Betz's Law) that will model Betz's Law. The program must produce a plot that illustrates Betz's Law. The plot must be propertly titled, axis labeled and identified. The x-axis variable must use a minimum of 100 steps (I understood this as the x-axis on the plot). The program must also identify the point at which the maximum occurs. Which should be 59% according to Betz's Law.
Variables:
P=Power remaining in the wind downstream of the wind turbine
Po=Initial power available in the upstream wind
V1=Velocity of the upstream wind
V2=Velocity of the downstream wind.
The plot in the assignment looks like the plot on this webpage, at the bottom. It is just the standard Betz's Law plot.
http://ele.aut.ac.ir/~wind/en/stat/betzpro.htm
Here is my script file:
range = 0:0.01:1; %Defines the range of v
total = size(range,2);
for(i=1:total)
v(i) = range(i);
p(i) = 0.5 * ( 1-v(i)*v(i) ) * (1 + v(i));
end
figure();
plot(v,p),xlabel('v_2/v_1'),ylabel('P/P_0')
How can I modify this to give me the Identified Maximum?
Explanation / Answer
maximum efficiency oocurs when Ud/Uu=1/3 (i.e. when Ad/Au=3). The efficiency is then ?=16/27 ? 59%. This is the maximum achievable efficiency of a wind turbine and is known as the Betz limit