The Basic Lift Equation — Page 77, Lesson 84

Let’s start with the definition, because everything else hangs off it. Lift is the net force generated normal to the relative airflow or flight path of the aircraft. “Normal” means at 90° to it. So if the aircraft is flying along a path, the lift force acts perpendicular to that path, not along it. That’s the professional definition, and it matters because it separates lift from drag, which acts along the flight path. Now, where does this force come from? Lift results from a pressure differential between the top and bottom surfaces of the wing. The air accelerates over the top surface, and as it accelerates, its pressure drops. So you get lower pressure on top, higher pressure on the bottom, and that difference produces the net upward force we call lift. And that force is captured by the basic lift equation: L = ½ ρ V² CL S. Let me unpack each symbol, because correct interpretation of this formula is a key element in understanding Principles of Flight. L is the lift force. ρ, the Greek letter rho, is the air density. V is the true airspeed of the aircraft through the air. CL is the lift coefficient. And S is the wing area. The ½ is just a constant from the physics of dynamic pressure. Now, a note on CL. For this initial examination, we state that CL is determined by angle of attack. That is true, but CL is also influenced by the shape or profile of the surface and other factors, which we’ll amplify in later sections. So for now, think of CL as the coefficient that captures how the wing’s angle of attack affects lift. Let’s think about what the aircraft actually needs. An aircraft spends most of its time in straight and level flight. So how much lift is required? The same as the weight. Consider that at any moment in time, weight is constant, so lift must be constant. That’s a key constraint. Now, while generating that required lift force, the less drag the better, because drag has to be balanced by thrust, and thrust costs money. So we want efficiency. The value of lift divided by drag is a measure of aerodynamic efficiency. This has a maximum value at one particular angle of attack. For a modern wing, that optimum is about 4°. If you maintain that optimum angle of attack, you achieve maximum aerodynamic efficiency. And here’s an important note: maximum CL and minimum CD are not obtained at best L/D. So the angle of attack that gives you the best lift-to-drag ratio is not the one that gives you the highest lift coefficient or the lowest drag coefficient. They’re different points. Now let’s tie this back to the physics of generating lift. Lift is generated by that pressure differential between top and bottom surfaces. Pressure is reduced by the air accelerating over the top surface. And the wing area must be big enough to generate the required lift force. So S, the wing area, is a design factor you size to meet the lift requirement. Now, here’s where altitude comes in. Air gets thinner as altitude increases. If you keep the speed of the aircraft through the air constant as altitude increases, the amount of air flowing over the wing in a given time decreases, and lift decreases. Why? Because ρ, the air density, is dropping, and lift depends on ρ. So to keep lift constant as altitude increases, you must maintain a constant mass flow. As air density decreases with altitude, the speed of the wing through the air — that’s the true airspeed, TAS — must be increased. Let me give you a concrete example. If you refer to the ICAO Standard Atmosphere chart, the air density at 40,000 feet is only one quarter of the sea level value. So at 40,000 feet, to keep lift constant, TAS must be doubled. Let me walk through that logic. We assume the optimum angle of attack of 4° is maintained for aerodynamic efficiency, and the wing area is constant. At 40,000 feet, air density is ¼ of sea level. So to maintain dynamic pressure — and hence lift — constant, the speed through the air must be doubled. Why does doubling the speed compensate for a quarter of the density? Because V is squared in the equation. If ρ drops by a factor of 4, you need V² to increase by a factor of 4, which means V doubles. That’s the relationship. And here’s the deeper reason: TAS is squared because essentially we are considering the kinetic energy of the airflow. The kinetic energy equation is KE = ½ m V². So the V² in the lift equation reflects that the dynamic pressure, and hence the lift, scales with the square of the airspeed. So let me summarize the whole picture. Lift equals ½ times air density times true airspeed squared times the lift coefficient times wing area. In straight and level flight, lift equals weight, which is constant. To maintain that constant lift as you climb and density drops, you must increase true airspeed, and because V is squared, a quarter density requires double the speed. And throughout, you want to hold the optimum angle of attack of about 4° to maximize aerodynamic efficiency, remembering that best L/D is not where CL is maximum or CD is minimum. That’s the basic lift equation and how it governs your flight.