Homework due April 6 0 Let U = 1 m/s, a= 1m, b = 0.8 m, and y'lD = 0. 0 Select one hundred evenly spaced points on a circular cylinder of z" = a...

Homework due April 6 0 Let U = 1 m/s, a= 1m, b = 0.8 m, and y'lD = 0.199. 0 Select one hundred evenly spaced points on a circular cylinder of z” = a 63"”
. b2
0 Use transformations 2’: z”+ zp’ and z = z’ + —, Z
to map these points into x-y plane and plot
airfoil shape 0 Plot pressure coefficients around a Joukowski
airfoil 0 Compute Lift x,’, = b — «a2 — .véz

the speed V at the surface of the airfoil V _ dw _ rim d3” of:
_ dE'. _ d3” dz: dz:
r
1—“? 5:” 2+f2¥r E”
V=U x } -Px
l—{b/ffl surface pressure coefficient of airfoil CP= $me = 1 ' (5)2

On the surface of cylinder - R = a
u = 0
R Stagnation point
. F
1:19 =-2U smB-Z— _’
. 7H1 Sin 95:11:20
sm GS = 315/3 1‘
xs=iVa2_YS2 ys=_m

Joukowski Airfoil Let zfi,(= x; + iyfp) be the position of the point P in the x’-y’
Plane and let 9 be the angle between the line PQ and the direction if of free stream.
F = 47raU sin 6 sine = yL/a,‘ F =47ryLU [I2 ZH n y f
w=U[z”+3+i2yp10g(;)] z =z —z,o 4. r '2
a2—_—y’i+(b~—xp)2 x}=b—‘Jaz-yp a, b determine the thickness and chord length; height of P
determines maximum chamber