A Viscoelastic Problem: I believe I can fly

Paper airplanes are one of the greatest inventions of the modern world. With some cheap and readily available scrap paper, any 3 year old child can become an aeronautical engineer. Your correspondent has whiled away a large portion of his childhood folding these little devices; I have been completely mesmerized by how a well-designed airplane glides across a room. Having two nephews these days once again allows me ample excuse to design and fold planes to my heart's content without being accused of engaging in childish pursuits.

Fig 1. Aerodynamicist #1 with design #23

Typically, I set myself these rules when designing the aircraft:
1. One sheet of paper per aircraft only.
2. No additional material, i.e. paper clips, staples
3. No adhesives
4. No tearing

However, I will break these rules as quick as you can say Wright brothers if the result is a more spectacular flight. In fact, I frequently tear little ailerons on the wings for fine tuning.

After some initial calculations, experiments and literature review, I will like to share the following observations:

Induced drag: to minimize induced drag, the wings should be of high aspect ratio, i.e. long and slender in the direction perpendicular to the fuselage. it might be tempting to suppose the sharp delta wing (space shuttle/triangular wings) might be more efficient for "cutting" through the air. However, they are actually inefficient lifting geometries at these speeds. (You need to be well over the speed of sound for delta wings to be efficient).

Fig 2. Delta Wing Paper Dart: inefficient aerodynammics

Balance: a head heavy plane is more dynamically stable; but will have a strong tendency to nose down. Generally speaking, trimming the the centre of gravity to be slightly less than 1/4 chord length from the leading edge of the wing is ideal. The quarter chord point is both the centre of lift and neutral point; the trimmed aircraft will fly at a steady angle of attack. This thin airfoil theory was derived in the 1920s by the greatest aerodynamicist, my hero: Prof. Ludwig Prandtl, who amongst other things, also brought us boundary layer theory. It is amazing what a man sitting at a desk can come up with.

Fine tuning is key: Little adjustments to the ailerons, and dihedral makes a large difference. While the effect of ailerons are pretty obvious, it is not obvious how dihedral affects flight characteristic. A positive dihedral increases the lateral stability: the plane is less likely to roll over. However, it does increase the tendency to swerve to the side. I recommend a very gentle positive dihedral: less than 10 deg +ve for optimal flight.

The world record for paper airplane flight endurance is 27.6s! His strategy is to throw the plane as high and fast as possible, and let it glide down slowly. Hence the design has two conflicting requirements, one is a low drag stage in which the plane needs to acquire altitude as rapidly as possible, while the other is a high lift-drag ratio stage in which the plane glides slowly down. A 8s flight is considered a crash by this guy.