Airfoil and Lift Coefficient Variation
Brandon Foster
MAE466
2/8/12
HW#2
1) I think about 1000 radial stations are required for a converged calculation. 2) The first plot is of a rotor with linear twist showing the lift coefficient variation with rbar in hover. The second plot is the lift coefficient max along the radius which looks to be about 1.2.
The maximum thrust of the rotor in hover in terms of thrust coefficient is 0.0183. Cpo = 2.5668e-004 Cpi = 0.0020 Cpt = 0.0022 Cpideal = 0.0017 Fig Mer = 0.7832 MATLAB CODE: First Code: This function integrates using the composite trapezoidal method of a function f(x) that is given in a set of n discrete points.
function I = IntPointsTrap(x,y) n = length(x)-1 a = x(1) b = x(n+1) h = (b-a)/n s = 0 for i = 2:n s = y(i)+s; end I = h/2*(y(1)+y(n+1))+h*s Second Code: s=sigma t=theta l=lambda a=alpha B = 4; rbar = .001:0.001:1; s = .1; a = (2.*pi)./(sqrt(1 - .4.*(rbar.^2))); t0 = 0.3; t1 = -.17; t = t0 + t1.*rbar; li = -(1/2).*((s.*a)./(8))+(sqrt((((s.*a)./(16)).^2)+((s.*a.*rbar.*t)./(8)))); f = (B./2).*((1-rbar)./li) F = (2./pi).*acos(exp(-f)); l = -(1/2).*((s.*a)./(8.*F))+(sqrt((((s.*a)./(16.*F)).^2)+((s.*a.*rbar.*t)./(8.*F)))); phi = l./rbar; ab = theta - phi; Cl = a.*ab; plot(rbar, Cl) dCt = (s./2).*Cl.*(rbar.^2) y = dCt(1:999); x = rbar(1:999); I = IntPointsTrap(x,y); Ct =I Cd = .0091 - .078.*ab + 1.02.*(ab.^2); dCp0 = Cd.*(rbar.^3); y = dCp0(1:999); I = IntPointsTrap(x,y); Cpo = I.*s./2 Cpi = 1.13.*(Ct^1.5)./(sqrt(2)) Cpt = Cp_o+Cp_i Cpideal = (Ct^1.5)./(sqrt(2)) FigMer =
MAE466
2/8/12
HW#2
1) I think about 1000 radial stations are required for a converged calculation. 2) The first plot is of a rotor with linear twist showing the lift coefficient variation with rbar in hover. The second plot is the lift coefficient max along the radius which looks to be about 1.2.
The maximum thrust of the rotor in hover in terms of thrust coefficient is 0.0183. Cpo = 2.5668e-004 Cpi = 0.0020 Cpt = 0.0022 Cpideal = 0.0017 Fig Mer = 0.7832 MATLAB CODE: First Code: This function integrates using the composite trapezoidal method of a function f(x) that is given in a set of n discrete points.
function I = IntPointsTrap(x,y) n = length(x)-1 a = x(1) b = x(n+1) h = (b-a)/n s = 0 for i = 2:n s = y(i)+s; end I = h/2*(y(1)+y(n+1))+h*s Second Code: s=sigma t=theta l=lambda a=alpha B = 4; rbar = .001:0.001:1; s = .1; a = (2.*pi)./(sqrt(1 - .4.*(rbar.^2))); t0 = 0.3; t1 = -.17; t = t0 + t1.*rbar; li = -(1/2).*((s.*a)./(8))+(sqrt((((s.*a)./(16)).^2)+((s.*a.*rbar.*t)./(8)))); f = (B./2).*((1-rbar)./li) F = (2./pi).*acos(exp(-f)); l = -(1/2).*((s.*a)./(8.*F))+(sqrt((((s.*a)./(16.*F)).^2)+((s.*a.*rbar.*t)./(8.*F)))); phi = l./rbar; ab = theta - phi; Cl = a.*ab; plot(rbar, Cl) dCt = (s./2).*Cl.*(rbar.^2) y = dCt(1:999); x = rbar(1:999); I = IntPointsTrap(x,y); Ct =I Cd = .0091 - .078.*ab + 1.02.*(ab.^2); dCp0 = Cd.*(rbar.^3); y = dCp0(1:999); I = IntPointsTrap(x,y); Cpo = I.*s./2 Cpi = 1.13.*(Ct^1.5)./(sqrt(2)) Cpt = Cp_o+Cp_i Cpideal = (Ct^1.5)./(sqrt(2)) FigMer =