b73579e4-5a90-4d03-b972-612109559c8f 13 3 5 decimal

&[DATE] &[TIME] - &[FILENAME]

Conformal mapping and Joukowsky Airfoil ...... adapted from Steven Finch ......

t 02 π * (π 64 / range :

Jo 52 :

a 125 / Jo * 2 - : b a 2 + (5 * π * 2 / cos 1 + : r 1 a - (2^b 2^+ sqrt : 31 sys

a b r 31 mat 0.08 0.191 0.94 31 mat

t f a r t cos * + : t g b r t sin * + : z j 12 / z 1 z / + (* : 31 sys

t z t f i t g * + vectorize : t h t z j Re vectorize : t k t z j Im vectorize : 31 sys

map circle foil 10.14 black 15 mat 31 sys :

circle t f vectorize t g vectorize augment : foil t h vectorize t k vectorize augment : 21 sys

The Joukowsky Circle mapped into Airfoil

map

The image of 'C' in the complex W-plane under the transformation is a simple closed curve with sharp tail @ W = 1 'C' is an oscillating circle around the anchor point [1, 0]

W 12 / z 1 z / + (* ≡