The physics of flight
Welcome! I am so excited to dive into the physics of flight with you. It is a beautiful blend of physical laws working together to make giant metal tubes glide effortlessly through the sky.
To help me tailor our journey, what is your main goal for learning about the physics of flight, and how much prior background do you have in physics or aviation?
I have some science background and want to understand the deep aerodynamic math.
Since you have a science background and want to dive straight into the deep mathematical and physical principles of aerodynamics, let's skip the superficial hand-waving and construct the physics of flight from first principles. Our journey begins by analyzing how a massive aircraft negotiates the fluid atmosphere using the vector balance of the four fundamental forces of flight.
The Dynamic Vector Balance
When an aircraft is in steady, straight, and unaccelerated flight, it exists in a state of dynamic translational equilibrium. While introductory textbooks often simplify this as a perfect cross where lift equals weight and thrust equals drag, the actual vector equations require summing all components acting on the vehicle's mass. Because the engine's thrust vector is often inclined relative to the flight path by the , a portion of thrust actually supports the aircraft's weight, while a portion of lift can act rearward. To formalize this equilibrium, we analyze the system along the flight path (longitudinal axis) and perpendicular to it (normal axis).
If we perturb this equilibrium by changing our engine output or adjusting our control surfaces, the system obeys Newton's second law, prompting linear or angular acceleration. For example, if thrust exceeds drag, the net forward force accelerates the aircraft's mass, which in turn increases the velocity of the air flowing over the wings. Because aerodynamic forces scale quadratically with velocity, this velocity change immediately alters the lift and drag forces until a new equilibrium state is established. Let's look at how these four forces are distributed spatially on a flying aircraft.
Aerodynamic force vectors for a commercial airplane in steady climbing flight.
I have generated a visualization above to help you visualize how these force vectors act on different physical points of the aircraft—specifically, how weight acts through the center of gravity while lift and drag act through the . Before we dive into the partial differential equations that describe the fluid flow generating these forces, we need to examine how we mathematically model lift and drag themselves. Ready to look at the lift and drag equations?