This prevented the fighter from flying supersonic limiting the top speed to Mach 0.98, which put its role and capabilities as an interceptor in question. To overcome this problem, the program of the F102 went through a major redesign. In less than half a year, the new prototype, with a longer and narrower fuselage in the mid-section, broke the sound barrier and reached a top speed of Mach 1.22, exceeding all expectations and allowing it to enter production. In just 118 days, the F102 went from being just a simple failure to a major success, nearly setting new speed records. But then, what was exactly the secret of this new design? How could such a tiny change have such a big effect?
At the beginning of the 1940s, the engineers of the time already had a wide knowledge of aeronautical science. Through wind tunnel testing, they looked for ways to reduce aerodynamic drag in an effort to design even faster aircraft. Everything starts with the drag equation: one-half of the density of the air times the square of the airspeed, the drag coefficient, and the wing reference area of the plane. If you look closely, drag is proportional to the square of the speed. This means that if we double the airspeed, drag increases by 4, and if we triple it, then drag increases by nine. However, this was not the reason why the F102 was unable to break the sound barrier.
The problem was rather the drag coefficient.
In incompressible flows, that is, well below the speed of sound, we encounter two types of drag: parasitic and induced. The parasitic is the most obvious of all. It is produced by the simple friction of the air with the surface of the plane. For that reason, its coefficient depends mostly on the shape of an object. In 2 dimensions, for example, a square has a drag coefficient of 1.05. If we rotate the square 45 degrees so that the corner faces the wind, the coefficient decreases to 0.80, almost 20% less. If we turn it into a circle, then it decreases to almost half and finally if we give it the shape of an airfoil, the coefficient drops to 0.04. The smaller the coefficient, the less drag the body will create.
Regarding induced drag, we have already said that it is produced by the creation of wingtip vortices, especially when aircraft fly at low speeds. Although the vortices never disappear, they get smaller as the plane accelerates. In this graph we can see the change of both drag forces with respect to the airspeed. As you can see, once an airplane reaches a certain speed, parasitic drag becomes predominant.
However, as we get closer to the sound barrier, air begins to behave very differently. At a speed of around Mach 0.72, that is, at 72% of the speed of sound, the airflow traveling above the airfoil accelerates to almost sonic speeds, but without reaching Mach 1. This is the so-called Critical Mach number, where the airflow always remains at subsonic speeds. Once we exceed the critical Mach, a shock wave appears on the upper surface of the airfoil, which can sometimes even be seen from inside a plane. The flow ahead of the shock wave is supersonic and all other areas are subsonic. As we continue to accelerate, the shock wave begins to move backwards, and another one appears in the lower surface. Both shock waves then begin to move backwards and meet at the trailing edge.
If we continue increasing the airspeed, another shock wave appears in front of the airfoil until it is attached to the leading edge. Once they come together, the airflow is supersonic everywhere. Shock waves also produce wave drag; whose effect can be seen in this graph. Here is the critical Mach number. If we continue to accelerate, we reach the Divergence Mach number, where the coefficient increases drastically until it reaches the sound barrier. This was the reason why the F102 could not reach supersonic speeds.
The engineers of the time knew about the existence of shock waves and wave drag but did not know what their value depended on. None except one. Richard Whitcomb, a NASA engineer, discovered that wave drag depended on the variation of the cross-sectional area of an aircraft, hence the name "area rule."
Let's use the first version of the F102 as an example. If we measure the cross-sectional area of the fighter from the nose to the tail, we obtain this graph. As it can be seen, there is a steep drop in the area after the middle section of the plane. This sudden change in area is what maximizes wave drag. By reducing the size of the fuselage where it meets the wing, just like a Coke bottle, the change in cross-sectional area was smoothed out, getting closer to the ideal shape and allowing the fighter to break the sound barrier.
Although no commercial aircraft of that era operated at a cruise speed high enough to require an area-ruled fuselage shapes, Whitcomb did find ways to improve their performance. In 1958, he developed a special fuselage addition on the forward part of the upper fuselage which greatly reduced wave drag, and which resembles the fuselage fairing that was later used in the Boeing 747. Shortly after, Whitcomb also discovered anti-shock bodies, which are aerodynamic fairings located above or below the wing that decelerate the airflow ahead of the shock wave, reducing the size of the wave and increasing the performance of aircraft. Anti-shock bodies produce supercritical flow, a concept that would lead to the discovery of supercritical airfoils. But that is a topic for another day.
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