Answers from page 78 — Page 106, Lesson 117

Let’s start with the lift curve comparison in Figure 5.28, because that’s the heart of this page. I’m going to walk you through the five questions and answers that explain why cambered and thicker aerofoils behave the way they do. First, the graph itself. We’re plotting section lift coefficient, which we write as CL, against section angle of attack in degrees. The vertical axis is CL, the horizontal axis is angle of attack. On that graph we have three curves: a symmetrical section with 6% thickness, a symmetrical section with 12% thickness, and a cambered section with 12% thickness. The labels on the figure tell us two big results: camber gives an increase in CLMAX, and greater thickness gives a 70% increase in CLMAX. So thickness alone, going from 6% to 12% on a symmetrical section, buys you a 70% jump in the maximum lift coefficient. Now question (a): why does the cambered aerofoil section have a significantly higher CLMAX than a symmetrical section of the same thickness? The answer is about the streamtube over the top surface. At approximately the same stall angle, the cross-sectional area of the streamtube over the top surface is smaller for the cambered section, and the section change is more gradual. Because the streamtube is narrower, the air has to accelerate more over the top surface. Greater acceleration means a bigger pressure differential — lower pressure on top, higher pressure below — and that bigger pressure difference is what produces the higher maximum lift coefficient. Question (b): for the same angle of attack, why do the symmetrical sections generate less lift than the cambered one? Remember the definition: angle of attack is the angle between the chord line and the relative airflow. At the same angle of attack, the cross-sectional area of the symmetrical section’s upper surface streamtube is larger. A larger streamtube means less acceleration of the air, so a smaller pressure differential, and therefore less lift. Question (c): why does the cambered section of 12% thickness generate a small amount of lift even at slightly negative angles of attack? At small negative angles of attack, the cambered aerofoil is still providing a reduced cross-sectional area streamtube over the top surface. Even though the angle is negative, the camber shape still squeezes the streamtube on top, so it still generates a small pressure differential — and that small pressure differential produces a small amount of lift. Question (d): for a given angle of attack, the symmetrical section of 6% thickness generates the smallest amount of lift. How can that be favourable? This is the high-speed jet transport point. At the high speeds at which modern high-speed jet transport aircraft operate, a thin wing can generate the required lift force with minimum drag caused by the formation of shock waves. So the thin symmetrical wing’s weakness at low speed is exactly what makes it efficient at high speed — less shock-wave drag. The full explanation of shock waves comes in later chapters, but that’s the reason. Question (e): what are the disadvantages of the symmetrical section of 6% thickness? It will give a high minimum speed, requiring complex high-lift devices to enable the aircraft to use existing runways. So the thin symmetrical wing needs a high speed just to stay airborne, and to get it down to runway speeds you need sophisticated high-lift devices. Now, the rest of the page is a set of practice questions. I’m not going to read them all out — these are the book’s practice questions, so let’s try them one at a time.