Up, Away and Rudderless..

Prandtl D in flight (photo: courtesy http://www.nasa.gov website)

On October 28, 2015, at the NASA’s Armstrong Flight Research Center, a boomerang shaped aircraft model( flying wing), remotely piloted, made a graceful flight after a bungee like launch. The 25 foot wingspan model was in the air for just about 1 minute and 33 seconds and made a soft landing on the dry lake bed.

Prandtl -D with streamers showing the vortices(photo: courtesy http://www.nasa.gov website)

However, the short flight could forever change the way airplanes have been flying so far. Spearheading this effort, NASA Chief Scientist Al Bowers, used German Aerodynamicist’s 1933 theory of minimum induced drag and bending moment to come up with a design that could

  1. overcome adverse yaw without using a vertical fin or rudder.
  2. result in 11% reduction in total aircraft drag due to span load.
  3. result in 20-30% efficiency gain due to elimination of the rudder.
  4. resultant improvement of of 15.4% in propulsive efficiency.

Let us take a closer look at the component that matters most in flying – wings. Wings help birds and airplanes fly. How? By generating lift. And what factor decides the lift generated? Wing Loading!

In simple language, wing loading is the effort required by the wings to support the aircraft weight in flight. It is denoted by a ratio of the total aircraft weight(W) and the total area of the wings(S). Units used are N/sq.mtr  or  lbs/sq.ft.

wing loading

Higher wing loading means smaller wings, greater take off and landing speeds, higher stall speed, poor maneuvering, reduced drag etc.

Lower wing loading means larger wings, lower takeoff and landing speeds, lower stall speed, better maneuvering, increased drag etc.

The shape and size of the wing decides the wing loading. As of now, till today, almost all the aircraft wings are designed using the elliptical span load. The problem with elliptical span loaded wings is that they generate an “adverse yaw” while turning.

Adverse yaw

For example, if the airplane is turning right, it would increase the lift on the outer wing(left) and reduce the lift on the inner wing(right) resulting in a bank or partial roll. Now the wing that generates more lift, in this case left wing, also generates more induced drag at the wing tip resulting in a net force against the direction of the turn which is called adverse yaw. The vertical fin or the rudder helps counter this adverse yaw.

However, the rudder extracts its price by way of weight and drag.

Bell Spanload
Bell Shaped Span Load wing
Elliptical Spanload
Elliptical Span Load wing


Birds on the other hand, do not have a rudder but still turn effortlessly and even sharply. How do they do that? Bell span load wings! In a bell span load wing, the resultant force at the wingtip is twisted forward which results in an induced thrust instead of drag. Applying that to our air plane turning right, this induced thrust at the wing tip results in a net force in the direction of the turn creating a proverse yaw. So if you have to turn right, just increase the lift at the wing tip of the left wing and voila, the airplane would turn right without the need of a rudder!

That’s how birds fly and turn and like Al Bowers said “They never told us about it!”

Albatross in flight

It is still a puzzle as to why aviation experts and airplane designers took almost 80 years to take cognizance of and put Ludwig Prandtl’s Bell span load theory into practice. However, the best part is yet to come. Al Bowers and Dave Berger, a NASA Armstrong aeronautical engineer have come up with an idea for Prandtl-M which is planned for flight on Mars in 2020.

Prandtl-M (photo: courtesy http://www.nasa.gov website)


The plan for Prandtl M is to glide for about 10 minutes in the Martian atmosphere at about 2000 feet, overfly some of the proposed future landing sites for a manned mission to Mars and send back high resolution photographs of the landing sites.

Turns out that the bell shaped span load is the best solution for the adverse yaw problem without a rudder, reducing drag and getting much better efficiencies and explaining the mysteries of bird flight.