The need for speed

Ever since the inception of flight, we have been looking for ways to make air travel safer, cheaper and faster. Even though the former two of these goals is being expanded upon with each new generation of aircraft, the latter has been seemingly ignored lately. The last (and basically only) commercial supersonic aircraft, the Concorde, ended service in 2003. The Concorde was a technological marvel, being able to fly at speeds well over twice of what any other commercial airliner could fly at (or indeed can fly at), cutting transit times between many locations in less than half. Since its retirement, the fastest commercial planes only fly at around Mach 0.85, a speed which could be achieved by airliners as many as 60 years ago. This might make you wonder why air travel speeds have stagnated in the last few decades, and why there is a barrier at Mach 0.85 that modern aircraft can’t seem to overcome. In this module, we’re going to take a look at the reasons for this barrier, how it can be overcome, and some other challenges of high speed flight.

The only close up photo of the Concorde in supersonic flight; it was so fast that it had to slow down for the chase plane

Why are wings swept back?

You might have noticed at some point that for some reason, basically every single high performance aircraft flying today has exhibits what are called swept wings. The wings of these aircraft are angled back instead of being perpendicular to the fuselage almost unanimously. Why is this? Sweeping the wings back doesn’t change the area of the wings, so it shouldn’t affect the amount of lift it generates. It can’t be for structural reasons – if anything, swept back wings are harder to make structurally sound than straight ones. In fact, sweeping wings back does almost nothing at low speeds, which is why small general aviation aircraft like the iconic Cessna 172 do not have wing sweep. However, at higher speeds, particularly in the transonic region of about Mach 0.75 to Mach 1.0, sweeping the wings back causes a huge reduction in drag.

Contrast the straight wings of a Cessna 172 (above) with the angled wings of a Boeing 747 (below)

Remember in the first section of this week, we talked about how one of the effects of the shape of the wing was to increase the speed of the airflow over the wing? Well, at higher speeds, this increase in velocity of the local airflow actually causes it to go supersonic. To keep it very brief, the fact that the flow is supersonic means that sound waves going upstream along the flow (i.e. along the direction of motion of the aircraft) get “stuck” and cannot proceed further. This causes pressure to build in that region, leading to the formation of shock waves. This has the dual effect of both increasing the drag and decreasing the lift of the wing. This means that travelling at the same speed requires more thrust to counteract the added drag, which as you can tell is not ideal when fuel efficiency is one of, if not the most important factors in air travel.

The solution to this problem is – you guessed it – swept wings. By decreasing the angle at which the airflow meets the wings, some of the airflow is deflected along the leading edge of the wing instead of over it. More importantly however, the flow is no longer parallel to the chord (basically the line joining the two ends) of the wing, meaning that its effective velocity over the chord has been reduced. So, the speed at which shock waves will begin to form (known as the critical Mach number) will increase, making the aircraft more efficient at those speeds.

This does have the side effect of marginally reducing the amount of lift the wing generates, but this can be easily compensated for by slightly increasing the area of the wings. Or another approach that could be used is a swing wing design like the one used on the F-14 Tomcat and B-1 Lancer. This design incorporates wings that can change their sweep angle in flight, giving both the benefits of maximum lift generation thanks to extended wings at low speed, and the large reduction in drag at high speeds (albeit at the cost of much higher complexity).

An F-14 Tomcat showing off both the swept and unswept modes of its wings

The area rule

Moving on to the next have you ever noticed item on our list, we have jet engines that are conspicuously mounted in front of or behind the wings of the aircraft, and never directly under or over them, basically without exception. Another curious design choice related to the same phenomenon is the presence of these things on the wings –

Called anti-shock bodies, these pod-like structures protect the delicate actuation mechanisms of the flaps, but they also serve another important purpose: reducing the drag on the aircraft at high (transonic to be specific) speeds. Now when I first learned this fact, I was bamboozled to say the least. If anything, stuff like that should increase drag, right?

As with many things related to aerodynamics, it isn’t that simple. Although normal frictional drag is the only real concern at low speeds and behaves much the way you would expect it to, at higher speeds a new form of drag (known as wave drag) starts to come into effect. This wave drag is exactly what we discussed when talking about swept wings. Caused by the formation of shock waves at transonic speeds, wave drag causes an extremely sharp increase in drag as the aircraft approaches the speed of sound. This increase is so great that for a time people thought that it would be impossible to exceed the speed of sound, hence the term sound barrier. But wait! Take a look at this graph below which shows the coefficient of drag plotted against Mach number –

As the aircraft passes through Mach 1, the coefficient of drag actually starts to decrease. This means that even though the overall amount of drag continues to increase (as it’s proportional to the square of the velocity), the rate at which it increases is reduced. So paradoxically, it’s actually (relatively speaking) more efficient to fly at Mach 2 than it is to fly at Mach 1!

To understand this, it is necessary to realize that wave drag is essentially caused by the formation of shock waves. These shock waves are created wherever the airflow around the aircraft goes from subsonic to supersonic, or vice versa. As the aircraft accelerates into the transonic regime, shock waves begin to form as airflow in some regions becomes supersonic.

However, as the aircraft itself exceeds Mach 1, the number and intensity of shock waves reduces as the oncoming air is now already supersonic, meaning that it doesn’t undergo that transition when being accelerated over the wing that it did earlier. At even greater speeds, the transitions of the airflow through the sound barrier continue to decrease, and so does wave drag.

Now what does all of this have to do with the placement of engines and the strange drag-reducing properties of the anti-shock bodies? This is where the area rule comes in. Discovered by Richard T. Whitcomb, the area rule essentially says that the wave drag produced by an aircraft depends on the distribution of cross sectional area along its length. Basically, if you were to cut the plane along its width at every point and look at the resulting area of the newly exposed portion, the way this area changes affects the wave drag acting on the plane. This is because at transonic speeds, the airflow isn’t compressible like it is at lower speeds, and so any increase in drag due to a change in cross sectional area in one part of the plane will not be localized and will affect all parts of the plane equally. So, it is necessary that all of the aircraft’s cross sectional area be taken into account when trying to smooth the change in cross sectional area as is done conventionally by making the nose and tails of aircraft pointed.

Putting the engines in front of the wings provides a smoother transition to the leading edge of the wing, which is the thickest part of it and thus has a very large cross sectional area. Towards the back of the wing, the anti-shock bodies help to compensate for the tapering cross sectional area of the wing and also help provide a transition into the area behind the wing. Thus, they help to ease the transition between these points, providing a smoother change in cross sectional area and reducing the drag at transonic speeds. Incidentally, this is also the reason why the characteristic hump of the Boeing 747 was extended on newer versions; this helped make the change in cross sectional area of the aircraft near the front smoother (seen above) and so by the area rule, reduced drag, making it more efficient. All of these reasons combined explain the near-static speed of modern airlines at about Mach 0.85. So, the next time you see an airliner, just think about how much work went into designing every single shape and curve that you see.

Assignments on efficiency in high speed flight

  1. Besides sweep angle, what other optimizations are made to airliner wings to make them more efficient at high speeds?
  2. What techniques besides the ones mentioned in the text are used to reduce wave drag at transonic and supersonic speeds?
  3. Most aircraft wings have a small built-in angle of attack of a couple of degrees. How does this affect aircraft in cruise in terms of the area rule?

Further research