The following seminar lecture was presented at West Virginia University on Friday, February 12, 1971, under the auspices of the Department of Aerospace Engineering and the Department of Theoretical and Applied Mechanics. The author, Dipl. Ing. Klaus Holighaus has kindly consented to its publication in these Proceedings.


by Klaus Holighaus

The application of fiberglass in the construction of sailplanes is growing steadily and calls for sailplane wings of growing span and higher aspect ratio. Consequently sailplanes with a span of 72 feet and an extreme aspect ratio of more than 30 are already flying.

Due to this present high level of performance, it is getting more and more difficult to further increase the performance without increasing the span and aspect ratio of the wing. It should be mentioned however, that there is a loss in performance due to an unfavorable wing planform for wings with very high aspect ratio. Although this loss in performance decreases relatively with increasing aspect ratio; when compared with the total performance of the sailplane, the choice of an optimum wing planform is necessary for obtaining top overall performance. As seen in Diagram 1, the induced drag, which increases directly with the aspect ratio, is, except for the profile and parasite drag, the most important drag of a sailplane, especially at high lift coefficients.

[Figure 1]

An extremely high aspect ratio maintaining normal span gives wing chords which result in a reduction of the Re-numbers far below one million. Therefore, when choosing the airfoil, special attention is to be paid to the "high lift - low drag" relation of the airfoil polar at low Re-numbers. Further to this, planform and airfoil of a wing should be chosen in such a manner as to obtain a high degree of aileron efficiency, especially at low speeds, without too much increase in drag, considering that the glider spends 50 percent of its flight time circling, where low speed and highly banked turns are required. When projecting a sailplane it is one of the designer's prime responsibilities to find an optimum compliance of these three criteria.

First let us take the planform. As you all know, the wing with a finite span has an induced drag of:

[Figure 0]

The value delta C-sub-Di is exclusively determined by the deviation of the lift distribution from the theoretically optimum planform, that is, the elliptical form. This means you have to choose a planform and an aerodynamic twist which allows a possibly true elliptical lift distribution. The difficulty is to obtain the widest possible CL range, but maintain a low speed lift distribution which gives good-natured stalling characteristics.

Let us look at the following three diagrams:

[Figure 2]

In Diagram 2, the left curve shows a wing with an untapered rectangular planform. It can be seen at once that the delta C sub Di quickly reaches a value of about 20 percent of the airfoil drag. As you will see later, this wing form, however, has an excellent stalling characteristic, especially with an additional aerodynamic twist. Therefore, this form is still applied on power planes. On high performance sailplanes, however, this form is out of the question, though a wing of such construction would be very economical.

Something better is the normal tapered wing on the right in Diagram 2. The minimal losses in performance are obtained from the double tapered planform with no aerodynamic twist (right in Diagram 3), and secondly from a planform comprised of a constant chord rectangular center section with a tapered outer wing and a twist of -3 degrees along the span (left in Diagram3 ). The latter planform, however, is rarely used due to the necessary washout in the wing, and because the low thickness of the airfoil section associated with the reduced chord at the wing root produces constructional difficulties, and lower stiffness of the wing.

[Figure 4]

Diagram 4 shows clearly the stalling characteristics of the different wings.

The elliptical wing has a uniform lift coefficient over the entire span and from this an elliptical lift distribution or product CL * c.

The rectangular wing in comparison, however, requires a lower CL at the outer wing than at the root, because there is more wing area at the outer part of the wing than necessary when compared with the optimum elliptical planform.

Looking at the bottom of Diagram 4 we see the CL * c distribution of different wings. In the case of the rectangular wing we notice that the CL * c of the outer wing is greater than optimum as indicated at point A , and at the inner wing the product CL * c is below optimum as indicated at point B . This situation will give the glider the tendency to pitch down symmetrically since the maximum CL is obtained on the inner wing earlier than near the wing tip, which prevents the glider from rolling motions at the stall.

In the case of the tapered outer wing planform however, we have the contrary characteristic. Its wing area compared with the optimum elliptical one is too low at the outer part of the wing, so its C L - c product is greater than necessary at the inner wing as indicated at point Y and is below optimum at the outer wing shown on the diagram at point X. This means the maximum CL is mainly required on the outer wing, especially at low Re-numbers. Normally the one wing stalls earlier than the other because of a slight skidding motion or bank, and the sailplane tends to pitch down asymmetrically and shows a tendency to spin.

The double tapered wing, however, shows again the most favorable characteristic. It approximates almost the elliptical lift distribution and even requires a low CL at the outer wing. Therefore, the choice should be a double tapered planform if you have a high class aerodynamic wing in mind.

Now let us come to the choice of the airfoil. Different from power planes, jet airliners or jet fighters, which usually require low airfoil drag only at a specific speed (like cruising speed), sailplanes require low drag over the entire speed range, from the maximum speed with a lift coefficient of CL = 0.15, down to the minimum stalling speed with about CL = 1.4. Unfortunately, the minimum drag increases steadily with increasing width of the laminar bucket, so you have to pay for a wide laminar bucket with a drop in high speed performance.

It is evident that a way should be found to displace the small laminar bucket with low drag coefficients by changing the airfoil camber by means of flaps. This is realized by the application of camber changing flaps with about 17 to 20 percent of wing chord and with deflections of about -8 to +15 degrees. Plotting the laminar buckets, thus obtained, onto one another, the envelope of these curves represents a new polar curve, which shows a clear superiority compared with the polar curve of an extreme high speed airfoil such as RACA 662-415 or of airfoil NACA 63-618 with a wide laminar bucket (see Diagram 5). Airfoils with respect to the foregoing were developed by Professor Wortmann in recent years, known as Fx 61-131 and Fx 67-K 150, and also by Professor Eppler, whose best known airfoil is the Eppler 348K. These airfoils have been investigated by Dipl.-Ing. Althaus in the laminar wind tunnel of the university at Stuttgart.

[Figure 5]

The designer of today prefers the mentioned camber flap profiles for the construction of very high performance sailplanes. Since these profiles have a laminar flow of 80 percent of chord, they call exclusively for glass fiber sailplanes with the well known high degree of surface quality.

Unfortunately all the camber-flap airfoils known at present show a noticeable sensitivity to Re-numbers. As you see from Diagram 6, the drag coefficient increases considerably when reducing the Re-numbers from 1.5 to 1.0 million. The loss is yet higher when reducing the Re-numbers to 0.75 million. On modern sailplanes, however, they might be even lower in the outer wing area. This fact is limiting the further increase of the aspect ratio.

[Figure 7]

Looking at Diagram 7, You notice clearly the optimum of the total drag for a specific aspect ratio.

[Figure 0]

Diagram 8 shows the dependence of the optimum total drag on the lift coefficient. Diagram 9 shows the relation between the optimum aspect ratio and the span. Analyzing the curves you find in the CL-range at the best gliding ratio of a sailplane (CL about 0.7) the optimum aspect ratio of 31 for a 72 foot glider. These results, have been realized exactly on the 22-meter (72 foot) sailplane NIMBUS which won the Open Class World Championships last year.

Finally, let us turn to the problem of aileron efficiency at high CL values and low Re-numbers. This problem has also been investigated in the laminar wind tunnel at Stuttgart, where very informative measurements on highly developed laminar airfoils were carried out.

[Figure 10]

The results obtained from these measurements primarily show that it is of the greatest importance to seal the aileron slots in order to avoid considerable losses in drag and aileron efficiency. Diagram 10 clearly shows the necessity for seals. The drag increases considerably, the laminar bucket becomes smaller, and the obtained maximum CL decreases. The difference becomes even greater with increasing positive aileron angles. Due to the negative pressure at the upper and the positive pressure at the lover surface of the airfoil, a flow is going through the aileron slot from the lover to the upper surface, even with undeflected ailerons, which results in a separation of airflow just at the aileron hinge line.

The aileron chord is also of great importance. Conventional airfoils with a short laminar flow showed increasing aileron efficiency at increasing aileron chord. This does not prove correct anymore on high grade laminar profiles. As you see from Diagram 11, the aileron efficiency even decreases with increasing chord at positive deflections. It shows that an aileron deflection of more than B = +10 degrees and b = -20 degrees is no longer worthwhile. The increase in drag is considerable in the case of a 36 percent aileron chord, due to the aforementioned separation of laminar flow at the hinge line. This is clearly represented by the drag polar curve of Diagram 12.

[Figure 12]

As mentioned before, soaring flight means circling flight for rather a long period which requires aileron deflections, where you have to observe exactly the mentioned problems if you do not want unexpected losses in performance.

All the foregoing statements result in the fact that the design of wings for modern high performance sailplanes does not involve strength and stiffness problems only, but all the aforementioned delicate problems which have to be taken into consideration very thoroughly and patiently, if you want to obtain substantial improvements compared with conventional designs.

Sensational improvements as it was possible in earlier times, for instance by the application of new airfoils, are no longer to be realized, regarding the present status of aerodynamic reseaxch. To improve today the best gliding ratio about only one point means hard brainwork and much money. Nevertheless, during the past 30 years the best gliding ratio could be improved from 40 up to 50.

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