Equation Wall
"A picture is worth a thousand words, and an equation is worth a thousand pictures."
-Warren F. Phillips
What is the Equation Wall?
Our lab seeks to understand the fundamentals of aerodynamics.
We believe that a better understanding of fundamental physical and mathematical principles is key to unlocking the remaining mysteries of flight and fluid mechanics.
We agree with Warren Phillips's statement that "an equation is worth a thousand pictures."
Therefore, a wall in our lab is dedicated to posting equations we have discovered in this field.
Below is a sample of equations on our wall, and a short explanation for each.
Airfoil Theory
Wing Theory
The lift distributions that minimize induced drag for a rectangular wing with all-positive spanwise symmetric lift and an optimum weight distribution are as follows:
Prescribed gross weight, prescribed maximum stress, and prescribed chord length
Prescribed gross weight, prescribed maximum stress, and prescribed wing loading
Prescribed gross weight, prescribed maximum deflection, and prescribed wing loading
Prescribed net weight, prescribed maximum deflection, and prescribed stall speed
Panel Methods
Lifting-line theory relates vortex-generated lift to section aerodynamic properties. The governing equation for the G-H method (a dimensional, numerical, general lifting-line method) is:
