Mathematical Relationships in Aerodynamics — Lesson 1

This lesson covers the complex mathematical relationships between circulation and velocity in aerodynamics. It explains how to derive the relationship between gamma bar a x star and omega bar, and how to integrate these terms to find an expression for omega bar. The lesson also discusses the concept of non-dimensional variables and how they are used in these equations. It further explains how to derive the expression for pressure and how it relates to the velocity and circulation. The lesson also touches on the concept of reduced frequency and how it affects the disturbance in the airfoil. Towards the end, the lesson explains how to derive the expression for lift and moment in aerodynamics.

Video Highlights

00:15 - Explanation of the relationship between circulation and velocity, and the non-dimensional nature of the equation.
08:05 - Discussion on the relationship between pressure and velocity.
18:22 - Explanation of the Theodorson lift deficiency functions.
39:15 - Discussion on the concept of apparent mass and its effects.
58:14 - Explanation of the quasi-static and quasi-steady aerodynamics approximations.
70:26 - Explanation of the unsteady aerodynamic coefficients.

Key Takeaways

- The relationship between gamma bar a x star and omega bar is derived through complex mathematical equations.
- Non-dimensional variables are used in these equations to simplify the calculations and make the equations more universal.
- The expression for pressure is derived from the relationship between gamma bar a x star and omega bar.
- Reduced frequency is a concept that affects the disturbance in the airfoil. It is a non-dimensional parameter that represents the distance travelled by the disturbance in one oscillation.
- The expressions for lift and moment in aerodynamics are derived from the relationships between gamma bar a x star, omega bar, and pressure.