Fundamental Concepts
(This page reproduces some content in the online course that complements the AeroPython Jupyter notebooks.)
To start learning aerodynamics, you need a good foundation: an understanding of the physics and the basic models of fluid flow. You probably have studied this in a general course in fluid mechanics. But let's review.
At the heart of fluid mechanics are the principles of conservation of mass, momentum and energy.
To explain conservation of mass, we use a control volume and state that, since mass cannot be created or destroyed:
where is the mass flow rate (in or out of the control volume).
In words: the rate at which the mass within a control volume changes is equal to the net rate at which mass flows in or out of the control volume.
Watch this video "pencast," walking you through the derivation of the differential equation of conservation of mass. (Recorded some time ago for Prof. Barba's course in computational fluid dynamics.)
You remember Newton's second law for a system? The time rate of change of the linear momentum of a system is equal to the sum of external forces acting on the system.
Applying Newton's second law to a fluid, we transfer this statement from a system point of view to a control-volume point of view. All students of fluid mechanics need to master this process, by which we can derive the world-renowned Navier-Stokes equations.
Watch this video "pencast," walking you through the derivation of the differential equation of conservation of momentum. (Recorded some time ago for Prof. Barba's course in computational fluid dynamics.)
Pencast: derivation of the momentum equation https://youtu.be/_k38xJ_e8UU
Pencast: the Navier-Stokes equations https://youtu.be/aak3XNAuucU
Lecture by Doug McLean
Lecture by Doug McLean at the University of Michigan (October 2013), discussing several examples of erroneous ways of looking at aerodynamic phenomena.
Some of the topics covered include:
- Basic physics
- Newton's third law—often erroneously used to explain thrust.
- Lift explanations—full of misconceptions in textbooks and popular literature!
- Vorticity and the Biot-Savart law
- Lift and momentum in 3D
Biography of Doug McLean
Doug McLean is a retired Boeing Technical Fellow. At Boeing, he worked on CFD codes for transonic wing design, codes for airplane spanload optimization including the effect of structural weight, novel wingtip devices to reduce induced drag, transonic airfoil technology, swept-wing laminar flow, turbulent skin-friction reduction, and pressure-sensitive paint. He received a B.A. in physics from the University of California at Riverside in 1965 and a Ph.D. in Aerospace and Mechanical Sciences from Princeton University in 1970. He is the author of "Understanding Aerodynamics - Arguing from the Real Physics"(Wiley, 2012),
In this 1-min video released by the University of Cambridge in 2012, we see what happens when airflow moves around the curved surfaces of an airfoil. Pulses of smoke show that the airflow moves faster over the top of the airfoil, and reaches the trailing edge before the airflow under the bottom of the airfoil.
This video was made to help debunk one of the most prevalent and long-lasting misconceptions of aerodynamics: the idea of "equal transit time."
Read more on the Research News section of the University of Cambridge website.
— "How do wings work?" by Holger Babinsky, Physics Education, Vol. 38, 497 doi:10.1088/0031-9120/38/6/001
Fluid flow can be surprisingly complex. Generations of scientists and engineers have used flow visualization to help them unravel the puzzles of fluids. We need to understand four basic concepts of visualization: path line, streak line, time line and stream line. We will use just the first 13 minutes of this classic video, part of a series made in 1961 by initiative of Prof. Ascher Shapiro of MIT (you can stop watching after that, for the purposes of this lesson).
Watch the video, pay close attention, and attempt the quiz questions!
At the end of this learning sequence, you'll find explanations of streakline, pathline and streamline.