Aerodynamic analysis and computational modeling of lift generation
This project explores the aerodynamic principles governing flight through computational analysis of wing lift using Bernoulli's equation.
The fundamental principle behind lift generation is Bernoulli's equation, which relates pressure, velocity, and height in a flowing fluid:
$$P + \frac{1}{2}\rho v^2 + \rho g h = \text{constant}$$ where the height differences of two given points in a given streamline are small compared to velocity and pressure effects, so the difference in pgh between points is negligible. For this project, we take a reference point far upstream of the airfoil, where the air is nearly at rest and the height differences are negligible. The pressure at this point is defined as P_0. The code therefore uses the following equation to evaluate Pressure for a given freestream velocity, v:
$$P = P_0 - \frac{1}{2}\rho v^2$$
With Bernoulli's Principle stating that for horizontal flow, an increase in velocity must be accompanied by a decrease in pressure. The app allows the user to select from three parameters: Freestream velocity (m/s), Airfoil camber, and Angle of attack (deg), all given in a realistic range. The freestream velocity is the velocity at which air flows over the wing, the airfoil camber is the curvature of the wing, and the angle of attack is the angle in which the wing is tilted relative to the airflow. Users can also select a small, medium, or large plane corresponding to lift required for takeoff: Small = 1500 N/m, Medium = 3000 N/m, Large = 5000 N/m.
Pressure Distribution vs Airflow: The horizontal component of the freestream velocity for the top and bottom of the wing is scaled by 1+influence and 1-influence, respectively. "Influence" is modeled using a Gaussian curve, which decreases with distance from the wing surface. Bernoulli's equation is then used to compute pressures.
Lift vs Airspeed: The top and bottom pressures are calculated for each airspeed. The difference integrated over the chord length gives lift. The lift curve updates dynamically with parameter changes. This allows takeoff speed to be reduced by adjusting airfoil camber and angle of attack, without drastically increasing acceleration.