Mathematically model airflow over an aerofoil

[ChrisHarvey]

Hi!

I'm looking for someone who could explain how I can mathematically model airflow over an aerofoil using the "correct theory of lift" - Turning airflow.

I have tried several approaches but all fail because of one step... all textbooks I have read on the subject say that the airflow velocity parallel to the horizontal is constant. Therefore the air must accelerate over the aerofoil because velocity must change. The forces required for this to happen act on the aerofoil through the viscous forces of the air. I have however not even got this far in my model because...

Taking any equation for one surface of an aerofoil, at least two parts of it have a 0 gradient. When I differentiate this equation to get velocity, at these points I therefore have infinite velocity, which is obviously not the case.

Please can anybody guide me in the right direction as I am obviously doing something terribly wrong!?
Thanks, Chris

 

[quantumdude]

Come on now, you know bloody well this isn't atomic physics.

I'm moving this to the Aeronautical Engineering Forum, where it will probably get more attention.

 

[Tyro]

Originally posted by ChrisHarvey

I'm looking for someone who could explain how I can mathematically model airflow over an aerofoil using the "correct theory of lift" - Turning airflow.

Not exactly sure what you mean. Try looking up "Potential Flow Theory" or "Stream Function Theory", both of which are complementary (really just perpendicular to each other) theories in low speed inviscid aerodynamics.

Originally posted by ChrisHarvey

I have tried several approaches but all fail because of one step... all textbooks I have read on the subject say that the airflow velocity parallel to the horizontal is constant.

For a start, the velocity parallel to a surface need not be constant. Don't forget viscosity . The textbooks you were reading were probably (no offense) lower level aerodynamic ones or physics texts which don't deal with issues like separation or shear layers...

Originally posted by ChrisHarvey

Therefore the air must accelerate over the aerofoil because velocity must change. The forces required for this to happen act on the aerofoil through the viscous forces of the air. I have however not even got this far in my model because...

Taking any equation for one surface of an aerofoil, at least two parts of it have a 0 gradient. When I differentiate this equation to get velocity, at these points I therefore have infinite velocity, which is obviously not the case.

Please can anybody guide me in the right direction as I am obviously doing something terribly wrong!?
Thanks, Chris

See above. The maths can get quite detailed for all but the simplest geometries. At at introductory level, you are probably best off modelling your 'aerofoil' as a flat plate with a small inclination, or a semi-circle.