1 - General design requirements

The basic concept of the model was specified in the winter just after the World Championships F3B in Holland in 1991. The model should be relative small, agile, fast and light.

The model should also have a three piece wing, T-tail because of the not so high rated handling qualities of V-tailed models (fig.1) Empty weight goal around 2.2 kg to manage duration task despite of the low camber airfoils. The maximum weight required for speed should also be low to keep good launch performance in low wind conditions.

1991 World championship results were evaluated together with the most remarkable and succesfull models at that time such as the: Electra (Wright), Eagle (Wurts), Spojalo (Stahl), Spark (SAF team) Ellipse (J.Mueller).

Broad flaps as found on the Spark V and Vektor (Rotte) models seemed to enhance launch altitude and should give easy flight path control during landing.

Airfoil choice should be based on the wish for very good speed results, and advantage at distance in good thermal conditions. The duration task should be achievable with a better than average launch and low empty starting weight.

2 - Low Reynolds number airfoil characteristics - a refresher on separation bubbles.

F3B sailplanes typically operate at chord Reynolds numbers between ca. 100.000 and 600.000, right within the low Reynolds number regime. In this regime a complex transition process takes place. This transition process is not abrupt and my take place when the boundary layer is separated from the airfoil surface. The laminar boundary layer separates easily from the surface due to the deceleration on the aft part of the airfoil. In the laminar boundary layer the kinetic energy of the flow in the thin layer of air near the airfoil surface is not high enough to overcome the adverse pressure gradient.
The separated flow forms a free-shear layer which is highly unstable and soon transitions to turbulent. Only then does the flow reattach to the airfoil surface because of the stronger kinetic energy exchange in the turbulent layer. Downstream of the reattachment point, the fresh turbulent boundary layer is capable of negotiating much higher adverse pressure gradients without separation than the laminar boundary layer.

This laminar separation, transition to turbulent followed by reattachment enclose a region of recirculation flow called the 'Laminar Separation Bubble' (fig. 2)

The presence of this bubble is the principal reason for degradation in performance at low Reynolds numbers. Transition of the boundary layer while separated yields bad starting conditions of the turbulent boundary layer. This means it gets thicker and is more sensitive to separation near the trailing edge.

The bubble gives mainly pressure drag due to its effect on the pressure distribution and the resulting thick wake behind the airfoil. In the bubble, the region of separated flow, the skin friction is low. Problems with the bubble are greatest on the upper surface were the flow is accelerated the most, followed by the necessary pressure recovery, or slowing down of the flow.

Drag reduction of low Reynolds number airfoils has to concentrate on reducing the size of the laminar separation bubble while keeping a long laminar flow trajectory. To reduce the bubble the laminar boundary layer has to be destabilized to induce a transition, just before separation occurs.

One method is using turbulators like zigzagtape fixed to the airfoil surface. With this method it's necessary to design the airfoil so that the place where the laminar boundary layer tends to separate doesn't move along the airfoil surface too much with variations of the angle of attack.

(One example of this type of airfoil , with incorporation of flap deflections in the design phase is: DU86-084/18)

A second method to reduce the size of the bubble is to destabilize the laminar boundary layer by a long, gradual pressure recovery so as to slow the flow down from its highest speed gradually, without separation, until natural transition occurs. The region of the pressure distribution with gradual pressure recovery is called a 'Bubble Ramp'.

Both methods of reducing the separation bubble size have trade offs:

In the case of the turbulators fixed on the airfoil surface the wide speed range of F3B models means that the turbulators, when optimized for thermal flying at low speeds are much too effective in creating turbulence during the speed task. Conversely, turbulators optimized for the speed task doesn't work at all at lower speeds were the (thin) tape is immersed in the larger separation bubble. The width of the useable speed range of a zigzag tape turbulator is illustrated in (Fig. 3) This figure shows measurements of a typical airfoil with and without zigzag tape, together with the theoretical drag of the airfoil when the separation bubble could be eliminated without losses.

So the effect of (mechanical) turbulators is highly sensitive to the speed of the model. (3d turbulators like zigzag-tape have a broader operating range than 2d strips but still can not completely cover the Reynolds range of an F3B model.)

Pneumatic turbulators are well known also, the low dynamic pressure during the duration task in F3B is not enough to eliminate the bubble completely however on an airfoil designed for use with turbulators through the whole flight envelope. At the lowest Reynolds number the laminar boundary layer is pretty stable near the turbulator position as it is intended that the laminar boundary layer reaches the same chordwise point without natural transition at the highest (design) Reynolds number. This is common to the airfoils designed for use with turbulators. At high speeds it could be necessary to reduce the turbulator flow rate ( by remote control in F3B). Windtunnel experiments are a must to optimize the turbulator effect.

In the case of the bubble ramp or destabilizing region, a large part of the airfoil contour is dedicated to destabilize the boundary layer in a natural way. This process is highly sensitive to the Reynolds number. For a particular Reynolds number and angle of attack there's only one airfoil shape possible that gives natural transition just at the point were the laminar boundary layer would otherwise separate from the surface. When the Reynolds number is lower, a separation bubble will develop because the boundary layer is to stable, when the Reynolds number is higher, transition will occur to far upstream resulting in more friction drag because of a longer turbulent flow trajectory.

Where the Eppler program so far shows only bubble warnings with little effect on the shape of the drag polar, ISES shows a deformation of the laminar drag bucket due to separation bubbles similar to the polars measured in windtunnels. This gives easier insight in the behaviour of different airfoil shapes with variation in Reynolds number.

A large part of the Fletcher wing, the entire rectangular middle section, uses a slightly modified version of the RG14 airfoil by Rolf Girsberger as basis. Consequently this airfoil will mainly dictate the performance of the whole wing. Main reason to use an airfoil based on RG14, apart from the low drag at low lift coefficients, was the positive effect expected from this airfoil together with a broad 28.5 % flap.

The flap hinge at 28.5 % happened to be exactly at the kink in the pressure distribution of the lower side of the airfoil (fig. 6). This has two effects:

a.

When deflecting the flap a few degrees for distance flight in "non raceable air" or for duration flight, the pressure distribution of the lower side is kept very smooth with only a little dent in the airfoil contour (fig. 7 & 8). At +2 degrees flap setting the pressure distribution shows much similarity with the MH32 or MH885215 (Hepperle) airfoils wich promise very good distance flight performance, but in turn could benefit from a small negative flap deflection in speed.

b.

Speed can be flown with zero flap deflection were the tape hinge roughness can trip the laminar boundary layer so that the laminar separation bubble, just under the flap, will be reduced. That this effect actually happens could be confirmed by the reduction in noise from the wing when the model reaches maximum speed compared to other models with RG14, at the beginning of the speed task.

If we use the same specification of minimum separation bubble problems during the speed task and minimum drag just above Cl= 0 for the tip airfoil we should use for the tip a different airfoil because of the lower Reynolds number alone.

But there are more requirements for the tip airfoil that make it useful to use a different airfoil in the wing tip than in the root.
Most wings have a taper of at least 0.7 to obtain an approximately elliptical lift distribution for minimum induced drag. Aspects we should consider are:

• Tip chord Reynolds number is ca. 70 % from Reynolds number at wing root.
• Speedrange at the tip is wider than at root. In flat turns the speed of the inboard tip could be very low. Here tip stall could easily occur
• Angle of attack variations at wingtips are larger due to turns and rol manoeuvres.
• Abrupt drag changes with angle of attack can lead to yaw instabilities. (induced by turbulence or uncoordinated controlling of the model)

The airfoil SD7003 of Selig and Donovan has extensive bubble ramps on upper and lower surface (fig. 9). Calculations and measurements show almost no influence on the drag polar due to separation bubbles at a Reynolds number of 100.000 (Soartech 8) SD7003 has almost the same thickness and camber as RG14 but with a different thickness distribution. SD7003 has a more rounded nose and a sharper trailing edge. The round nose makes the drag polar rounder and wider. Stall characteristics of a model with RG14 at the root and SD7003 at the tip should not be too bad. The more as SD7003 shows no hysteresis effect near Cl-max in the measurements as published in Soartech 8. Airfoils with a sharp nose sometimes show an hysteresis loop in the Cl-alfa line near Cl-max due to a large flow separation. Near Cl-max a laminar separation occurs just behind the sharp nose and a 'long bubble' can be formed. When the angle of attack is increased further, the bubble bursts and gives a sudden increase in drag, consequently giving a nasty stall behaviour.

SD7003 is not expected to show such behaviour, instead a gradual increase in drag near Cl-max and a small los in lift just above Cl-max should give a more predictable stall behaviour and relaxed low speed characteristics.

The airfoil transition from root to tip can take place without washout and with an elliptical lift distribution by using an approximation of an elliptical planform with trapezoids. A minor correction on the elliptical planform was made because of the Reynolds number related drop in lift at the tip and to (further) prevent tipstall during turns where small differences in airspeed occur between inboard and outboard wingtip.

A possible measure to prevent tipstall and make the plane more friendly is using more camber at the tip together with the then necessary washout. When the airfoil thickness is kept the same, the tip wil drop out of the low drag bucket at high speeds. To prevent this the airfoil could be made thicker but then the airfoil will become more sensitive to the low Reynolds number at the tip. The thick airfoil will develop larger separation bubbles and will have more abrupt changes in drag with changing angle of attack wich could lead to yaw instabilities. To investigate the effect of airfoil thickness polars of thick versions of RG14 where calculated.

To compare RG14 & SD7003 new calculations were made with the ISES programm. Then RG14 was modified to match it better with SD7003 and make it less sensitive to separation. This modifications did not show a drag reduction from the calculations, but it could be expected from practical experience and measurements of other airfoils. Most Girsberg and Eppler airfoils have a rather steep pressure recovery in the last few percent of the upper surface. This can lead to turbulent separation at high angles of attack or with large positive flap deflection This effect is mostly not correctly predicted by the airfoil analysis programs but could have the same effect on the drag as a rather thick trailing edge.

The original steep pressure recovery was smoothed out, resulting in a sharper trailing edge (fig. 6) and less camber in the last few percent of the airfoil, more like SD7003. Also the curve in the lower surface pressure distribution around 73 % chord became less pronounced.

After creating the new airfoil coordinates of the modified RG14 a third airfoil geometrical exactly in between the tip and the root airfoil was determined (fig. 10). The polars of this airfoil are compared to the polars of SD7003 and the modified RG14 to check if nothing unexpected occurs in the transition from root to tip airfoil.

Fig. 11 shows that the intermediate airfoil rivals the root and tip airfoils in allround performance. At Re=400.000 the minimum drag of the airfoil DD92-8415 is just as low as the minimum drag of DD92-8416 (the modified RG14)

This figure shows also very well the influence of the Reynolds number on airfoils of different shape but with nearly the same tickness and camber. At Re=100.000 SD7003 has lower minimum drag, At Re=400.000 DD92-8416 has lower minimum drag. The SD7003 airfoil holds longer at high Cl, near Clmax, than the root airfoil.

In the complete polars of the airfoils (fig. 12,13,14) the Cl-alfa and Cm-alfa characteristics can be found. Important to note is that the Cm-alfa and Cl-alfa lines are less smooth when larger separation bubbles occur on the airfoils.

Ripples in the Cl-alfa line are often larger than the difference in Cl-alfa(0) between the different airfoils. Using only one airfoil in the whole wing is no guarantee for zero induced drag of the complete wing at its theoretical zero lift angle. The variation in Reynolds number always gives a variation in lift along the span of a tapered wing. In the situation of DD92-8416 transitioning to SD7003 the difference in zero lift angle seems reasonably low in practical situation. Single polars of the root and tip airfoil at relative Reynolds numbers that correspond with their chord difference in the Fletcher wing are shown in fig. 15 to compare in particular their actual Cl-alfa lines.

6 - Concluding remarks

7 - Sources:

 1- D. Althaus, Windkanalmessungen an den Profilen RG12 und RG14
                FMT-Kolleg 1, VTH GmbH, Baden-Baden, Germany 1988

 2- F. Donker Duyvis, L.M.M.Boermans, Entwurf und Windkanal-
                Messungen des F3E und F3B Profils DU86-084/18,
                FMT-Kolleg 6, VTH GmbH, Baden-Baden, Germany 1988

 3- M. Hepperle, Neue Profile fuer Elektro-Pylon modelle
                FMT-Kolleg 10, VTH GmbH, Baden-Baden, Germany 1991

 4- M. Selig, Donovan, Fraser, Airfoils at Low Speeds, Soartech 8
                H.A.Stokely, Virginia, USA, 1989