what is cl.c/cmac?and local lift coefficient formula

[Om Nagar]

i have seen structure people using it but dont know what it was?

[Rob McDonald]

It is normal convention to use capital letters CL to mean a 3D lift coefficient and cl to mean a 2D sectional lift coefficient.  The same for CD/cd and CM/cm.

c is the local chord

cmac is the mean aerodynamic chord -- which could be any average chord measure.

If we also use L as the total lift and l as the local 2D lift, then...

l = cl * q * c

and

L = CL * q * Sref

Where q is the dynamic pressure (0.5*rho*V^2) and Sref is the reference area of a wing.

We can also write

L=\int_-b/2^b/2  l dy

Lift is the integral over the span of the 2D sectional l times dy.

And we can write

S=\int_-b/2^b/2  c dy

For the area.

If you look at the Lift integral, you will see that the dynamic pressure - q - can be pulled out of the integral.  It is a constant over the span of the wing.

This gets us back to your question...

l = cl*c*q 

Is the 2D load.  However, this magnitude could be tiny (ounces per inch) or huge (many pounds per inch) depending on the dynamic pressure and size of our chord.  Think about an insect to a fighter plane.

So, we want a quantity that has the same shape -- but that is scaled to something meaningful and consistent for us.  We can keep the shape the same as long as we multiply or divide by constants.  These constants will scale the curve -- but not change the shape.

So, first we divide by q.

l/q = cl * c

Then we divide by an average chord

l/(q*cmac) = cl * c / cmac

This provides us with a curve of the load distribution on a wing -- but scaled in a way similar to CL for the airplane.  This way, we have a 'feel' for what a value of 0.5 means.  We can compare different aircraft and systems on a similar scale.

The load distribution is what structures people care about for applying the lift load to their wing.

It is also important for aerodynamicists because that is what they want to be elliptical in order to have minimum induced drag.

The lift load distribution is different than the lift coefficient distribution.  That (c/cmac) product is really important.  Think about a delta wing.  At the root, c is large -- but at the tip it is zero.

Hope this helps,

Rob

On Tue, Oct 4, 2022 at 12:19 PM Om Nagar <nagarde...@gmail.com> wrote:

i have seen structure people using it but dont know what it was?

--
You received this message because you are subscribed to the Google Groups "OpenVSP" group.
To unsubscribe from this group and stop receiving emails from it, send an email to openvsp+u...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/openvsp/47252094-2c6d-4479-bffb-d937079144d5n%40googlegroups.com.

[Om Nagar]

Thank you so much for the response

To view this discussion on the web visit https://groups.google.com/d/msgid/openvsp/CAEppYpETGXiSudqTWJgSZrTf7NEoZTQRduF91Kort0KvUzhV7Q%40mail.gmail.com.