Extending Polyfit to Specified Y Value

Hi guys,

I am currently plotting a graph depicting the power required for a helicopter to hover at 1000 feet (PStd) compared to its gross takeoff weight (GTOW). I have used polyfit and polyval to plot a curve fitting through my found data but need to extend the curve to a known Y value (minimum takeoff weight of the helicopter - MinTOWD) so that I can extrapolate the power required to hover at that value. The current curve ends at 16670 (the lowest weight in my gathered data) but need to extend it to 10475.

%Import and Sort Data
data = xlsread('\\nask.man.ac.uk\home$\ClimbPower.xlsx','Sheet1');
GTOW = data(1:length(data),1);
PStd = data(1:length(data),2);

%Minimum Takeoff Weight
MinTOWD = 10475;

%Plot Data and Curve Fit
figure
plot(PStd,GTOW,'ks');
hold on
FitStd = polyfit(PStd,GTOW,3);
PolyStd = polyval(FitStd,PStd);
plot(PStd,PolyStd,'k--');
xlabel ('Power (kW)')
ylabel ('Gross Takeoff Weight (kg)')
title ('Power Required to Hover at 1000 Feet for Given Gross Takeoff Weight')
grid minor

Thanks in advance.

Jack

Answer 1

[Adam Danz]

After you compute the coefficients using polyfit(), you can use a different set of x values in polyval() to compute a new set of y values. The problem is, you don't know how far out you need to extend x in order to get to your desired y value. You can either solve the polynomial for y (not easy, see below) or you can just extend x in polyval() far enough that it will cover your desired y value. The 2nd option is a lot easier but might not result in an exact x value that precisely results in your desired y value. But depending on your x values in polyval(), you could get very close.

You're computing the 3rd degree polynomial which is (p are your coefficients)

y = p(1)*x^3 + p(2)*x^2 + p(3)*x + p(4)