Synopsis of Wendy's PhD work 

The growth of air travel for commercial and defense purposes far exceeds improvement in fuel economy in these industries. With increasingly disastrous consequences of climate change, scientific research on fuel savings in aircraft operation is crucial! Wendy’s PhD work looks at evaluating fuel-saving benefits in aircraft flight.

Have you ever wondered why birds fly in 'V' formation during migration?

Birds intuitively know that there are regions behind the leading bird, where they conserve energy. The same physics applies to an aircraft. When an aircraft is in flight, like a bird, it generates something called a ‘wake vortice’ that induces a non-uniform wind distribution behind it. An aircraft behind this leading aircraft experiences this non-uniform wind distribution, and it has been demonstrated that there is a “sweet spot” which leads to reduced ‘drag force.’ Drag force sometimes called ‘air resistance’ is a force acting opposite to the relative motion of a moving object. Imagine an athlete running and there is wind blowing in the opposite direction. The wind is imposing a drag force on the runner causing him to work harder than he would have to, if he was running in the same direction as the wind. The same effect happens to any moving object, and the drag force is directly proportional to the surface area. That is the larger the area of an object, the higher the drag force on it. Consequently, an aircraft experiencing more drag force, will require more fuel to accelerate. So, imagine the benefits in fuel economy if we could fly two or more aircraft carriers in their calculated ‘sweet spots’ during flight! This form of flight is referred to as formation flight.

Aircraft liners are significantly larger than birds, hence their ‘sweet spots’ are not as easily defined. In addition, for aircraft carriers, there are strict aviation guidelines (for safety) that dictate the minimum distance between two carriers. That is, a trailing carrier must be in a ‘sweet spot’ that is a safe distance from the leading carrier. Wendy’s dissertation looked at different metrics to obtain the sweet spot from a leading carrier following aviation guidelines, and evaluated the benefits in fuel saving.

As outlined in Wendy's dissertation, the static sweet spot is the point behind the leading aircraft where the lift: drag ratio is highest. However, this is not the position where a trailing aircraft will require minimal thrust during flight. That is referred to as a dynamic sweet spot. Wendy’s thesis outlines how to calculate the aerodynamic force and induced moments to determine the static sweet spot, and dynamic sweet spot, respectively. Below is a list of notable conclusions from her work:

  • If the trailing aircraft is at least as large as the lead, there is a noticeable difference between the static and dynamic sweet spots. This is an important consideration when trying to take advantage of formation flight for large carriers.
  • Larger trailing aircrafts, experience induced aerodynamic moments from the leading aircraft. The moment of a force is a measure of its tendency to cause a body to rotate about a specific point. Therefore, to stabilize the aircraft and prevent it from rotating, 'control effector' flaps are deflected. Have you ever been on a plane and seen those tiny flaps on the wings? Those are control effector flaps, there to induce moments that can control how the plane rotates. However, recall that drag force is proportional to surface area. If you deflect flaps to stabilize the plane you are increasing the drag force! This detracts from fuel savings you are trying to achieve with formation flight. Wendy showed in her thesis, that you can generate moments that help stabilize the plane by internal fuel transfer and differential thrusting. A typical aircraft carrier has multiple engines and fuel tanks. So, if you can move weight (fuel) around, and/or thrust the plane engines in a defined way, you can stabilize the plane without having to use external control effectors (flaps). Hence, you can recover some of the losses to drag and maximize overall efficiency. Have you ever tried to get two kids stable on a see-saw? When you move the heavier kid closer to the center and move the lighter kid farther away, you are essentially trying to equalize the ‘moments.’

 Illustration of  'upwash’ that leads to reduced drag benefits for trailing aircraft and consequently, fuel savings. 

Illustration of  'upwash’ that leads to reduced drag benefits for trailing aircraft and consequently, fuel savings. 

  • As the leading carrier, travels it consumes fuel and gets increasingly lighter, hence generating less lift to trailing aircraft. From Wendy's calculations, this reduction in lead aircraft weight decreases benefit, but does not nullify formation benefit, in flights as long as 6.5 hours.

  • No additional detrimental impact to a person located in trailing aircraft during flight formation, even with atmospheric turbulence.

Fuel savings >20% demonstrated in this work is significant, especially to aviation fuel economy. Jet fuel is not cheap! Moreover, the aviation industry needs to keep up with fuel efficiency improvements in the automobile industry, for example. Wendy’s research paves the way for flight formation consideration for large aircraft carriers!