All about winglets

ABOUT WINGLETS
by Mark D. Maughmer
Over the past ten years, from initially being able to do little to improve
overall sailplane performance, winglets have developed to such an
extent that few gliders leave the factories without them. They are now a
familiar sight to nearly every soaring pilot. Few, however, really
understand what winglets do.
Understanding Drag
A winglet’s main purpose isto improve performance by reducing drag. To understand
how this is done, it is first necessary to understand the distinction between profile drag
and induced drag.
Profile drag is a consequence of the viscosity, or stickiness, of the air moving along the
surface of the airfoil, as well as due to pressure drag (pressure forces acting over the front
of a body not being balanced by those actingover its rear). As a wing moves through
viscous air, it pulls some of the air along with it, and leaves some of this air in motion.
Clearly, it takes energy to set air in motion. The transfer of this energy from the wing to
the air is profile drag.
Profile drag depends on, among other things, the amount of surface exposed to the air
(the wetted area), the shape of the airfoil, and its angleof attack. Profile drag is
proportional to the airspeed squared. Readers interested in a more thorough explanation
of these concepts are directed to refs. 1 and 2.
To measure an airfoil’s profile drag in a wind tunnel, a constant-chord wing section is
made to span the width of the wind-tunnel test section. In this way, the airflow is not free
to come around the wing tips. There is thus noflow in the spanwise direction -- the wing
section behaves as if it belonged to a wing of infinite span.
Induced drag is the drag that is a consequence of producing lift by a finite wing. If a
wing is producing lift, there must be higher pressure on the underside of the wing than on
the upper side. Thus, there is a flow around the wingtip from the high-pressure air on the
underside of the wingto the low-pressure air on the upper side (fig. 1). In other words,
there is spanwise flow on the finite wing that was not present on the infinite wing (fig.
2). This spanwise flow is felt all along the trailing edge as the flow leaving the upper
surface moves inward while that on the lower surface moves outward. As these opposing
flows meet at the trailing edge, they give rise to a swirlingmotion that, within a short
distance downstream, is concentrated into the two well-known tip vortices. Clearly, the
generation of tip vortices requires energy. The transfer of this energy from the wing to the
air is induced drag.
This process can be idealized as a “horseshoe” vortex system (fig. 3). As a consequence
of producing lift, “an equal and opposite reaction” must occur -- air must begiven a
downward velocity, or downwash. With this downwash comes spanwise flow, tip
vortices, and induced drag. The goal is to minimize this drag by minimizing the amount
of energy used in producing the required downwash -- to reduce the energy that is
“wasted” in creating unnecessary spanwise flow and in the rolling up of the tip
vortices.
In observing the flowfield around the wing in Fig.2,it should be clear that the greater the
span, the less the tip effect is felt on the inboard portions of the wing. That is, the greater
the span, the more “two-dimensional like” will be the rest of the wing and, consequently,
the less its induced drag. As the span approaches infinity, the downwash and induced
drag approach zero. Likewise, if the wing is not producing lift, there will be nodownwash and thus no induced drag.
It is found that the induced drag is a function of the inverse of the square of the airspeed--
it is smallest at high speeds and increases as the aircraft slows down. It also depends on
the weight squared divided by the span squared, (W/b)2, how much weight each foot of
wing is asked to support. Thus, it increases with the square of the aircraft weight and...