Expert: Paul Soderman - 12/25/2009

Question
I am in need of an equation or series of equations that will allow me to find the density of air moving at a given speed.

This motion is assumed to be relative to a static surrounding medium also of air. This motion is assumed to be linear.

I am working on a personal project in which I would like to calculate the lift of an airfoil based on the density of specific regions of the surrounding air. I am attempting to apply this to a VTOL style craft. There being no forward motion requires the air above an airfoil to be moved elsewhere to reduce the pressure above the airfoil.

Given the air's movement above the airfoil and the non-moving air below, how would I calculate the difference in pressure?

Thank you very much for your time! I really appreciate any help you can lend.

Answer
I don't understand your plan in detail, but we can assume that subsonic flow is incompressible - density does not change with airspeed and can be computed from barometric pressure.  At transonic speeds near Mach one or supersonic speeds you must use compressibility equations that relate density to Mach number.

Airfoil pressures and velocities can be related from Beroulli's law:

delta P = rho V^2 /2  where delta P = Ptotal - Pstatic, rho = density, V = velocity, Ptotal = ram pressure, which is constant for a given airfoil flight speed, Pstatic = surface pressure on the airfoil.  The integral of surface pressures over the airfoil determines lift.  At zero airspeed, Ptotal and Pstatic are equal.

Without a full-blown CFD code your best bet to determine airfoil pressures is from published data such as in I. Abbott and A von Doenhoff:  Theory of Wing Sections.  An airfoil similar to yours has probably been tested somewhere.

This on-line computer code for airfoil performance prediction may also help:

http://www.mh-aerotools.de/airfoils/javafoil.htm
Paul