fuckyeahphysica:

In mathematics there is a concept known as ‘Conformal Mapping’ which allows you convert a given shape to a completely different one by making a transformation.

In the joukowski transform you take all the points on a circle and apply the following transform:

image

And the resulting transformed points resemble an aerofoil shape. Pretty cool huh ?

** Conformal mappings are a really cool topic in complex analysis but also equally extensive. If you want to know more about them click here

EDIT:

I forgot to mention that the transformation of a circle into an aerofoil is a very special case and the transformation of other shapes would yield distinct shapes. ( very different from an aerofoil )

Here’‘s what i mean:

Different circle

image

Triangle

image

Ellipse

image

Source : AT&T Archives

–. — — -.. / -.. .- -.–

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s