February 19, 2005
Induced drag reduction, the natural way.
As almost everyone must have noticed the wings of all bird have ragged outline to their trailing edges produced by the tips of the feathers but on the other hand since the early days aircraft have always had smooth trailing edges (probably because it looks more efficient!).
When early aerodynamicists were researching bird’s wings it was assumed that the saw tooth trailing edges were basically due to the requirements for the fold of the wings and nothing to do with aerodynamics. Even the oldest fossils of feathered birds show the typical ragged trailing edge. The shape does not appear to have changed much over millions of years. Darwinian theory would suggest that this feature would change over time or at least this feature would not have remain the same across all bird species if it did not have a very significant purpose. It would appear that there is an advantage in having a feather like trailing edge. Looking closely at each feather, each one is slightly different from the next (just as fingers on a hand are different). It would appear that each feather over time has developed their own particular shape for a very specific purposeand and the increase in efficiency must be significant for the system not to have canged over the millenia
Lift line theory gives a series of vortices produced along the trailing edge. The effect on a wing is that these combine downstream to produce a single large tip vortex. It would appear that the use of the wing feather ends on bird’s trailing edge is to stabilise these vortices and prevent them migrating towards the tip. They appear to act the same as wing fences but in a much more subtle way and for no extra wetted area.
Winglets are used to break up the strength of the tip vortex. Spillman tips were tried to emulate the pectoral tip feathers on birds, but they were neither long enough nor of variable incidence. There was also nothing to limit the span wise flow, so the tip vortex was already fairly powerful before it was trying to be dispersed. Recent aerodynamic developments appear to be to using small vortex generators to achieve similar a sort of result of stabilising the spanwise flow.
Looking at bird’s wings. Sea birds with large span have relatively smooth trailing edges inboard and the ends of the feather slowly gets more pronounced toward the Tip, with relatively small pectoral feathers. Large land birds on the other hand with their limited available span have much more pronounced trailing edge feathers and large pectoral feathers. These feathers have an advantage in that they are flexible and adjust automatically to the loads imposed so that they are near optimum for all stages of flight. A modern equivalent is the flexible mast and sail on high-speed sailboards. It can also be seen that birds preen their feathers frequently and the trailing edge arrangement of the feathers is important to them.
Tests on wings with stepped trailing edges have at times produced some unexpected reductions in drag, but so far there has been no systematic research on the subject.
The use of a saw tooth trailing edge on a wing should have the effect of reducing the span wise flow thus reducing induced drag and also improving the flow near the stall. An added bonus would also be reduction in wake turbulence and probably less noise.
Since this is basically a vortex system it should be more efficient at higher Reynolds numbers.
Ian Hannay, Fleet, Hants. UK 2005
Maximum Lift from an Aerofoil System
Basics
Most research on achieving the maximum possible lift from an aerofoil system has ignored the fact that there could be a physical limit to the maximum achievable lift in a uniform flow.
Theories
From disc actuator theory (windmill) the maximum energy that can be extracted from the flow is one third of the total energy passing through the disc.
From circulation theory the maximum lift (Cl) possible is 4*П = (12.56) with total circulation. Therefore combining the two theories the maximum sustained total force is 4.П/3 = (4.19). This is the total force, not just lift but the combination of Lift and Drag. That is √ (Cl2+ Cd2) = 4.18 Note that for this Cl is based upon the total projected of the foil not just that of the basic foil. From this it can be seen that when trying to achieve maximum possible lift it is important that the drag is minimised. This is a fact that is normally ignored when trying to achieve maximum lift.
With a basic lift slope of 2.П/rad, the angle of attack for maximum lift works out at 2/3.Пrad (38°). This is from the angle of zero lift, not the geometric angle of attack of the basic foil and is independent of aspect ratio.
Discussion
Total forces higher than 4.19 can be achieved for very short period by hysteresis but then the total force drops very significantly (stalls). Birds use this feature when coming into land and frequently leave their wings extended as the lift has by then dissipated.
Higher sustained lift can only be achieved when additional force is applied to the flow. Such as blown flaps or boundary layer control. In these conditions the additional lift will always be less than the extra energy applied.
All experimental information appears to indicate that maximum lift is achieved at >2/3 rad (38˚) true angle of attack. The classic Handley-Page experiments gives a greater total force, but this is most likely due to the tunnel blockage that would cause the flow to be boosted over the foils and would indicating what is in effect a blown flap system. The Douglas experiments on the DC9 show a basic physical angle of attack of 39° and a true Cl max of just over 3.0. No drag figures are given. Tests on delta wings show maximum angles of attack of up to 38˚.
With conventional aerofoil sections giving they maintain attached flow to around 15°, it should only need three foils in series to achieve maximum lift at a true 38° angle of attack. Any high lift configurations should not need more than three segments; except possibly in the landing configurations were additional drag rather than absolute lift is an important factor.
The figures given above may not be exact but from the evidence available they are in the right ball park and fit the theories.
From the idea that there is a maximum force availble it would appear that sections with falt topped pressure distibutions would probabley be better than peaky sections for achieving maximum lift.
Ian Hannay, Fleet, Hants UK 2005