Effects of the step in lift-curves of wing profiles with flaps

 

by Karel Termaat 

 

Introduction (third alinea modified since publication in S&G)

 

Some years ago, I found that when landing our new sailplane it usually made a couple of bumps onto the ground before it decided to stay there; very interesting to friends observing your flying skills with the new toy of course.  Another surprising thing happened to me with this sailplane when I made a long cross-country flight, came back a little late and low and decided to divert from my shortest route to the airfield to an area where small flocks of cumulus clouds were still forming. To my surprise I could not climb there, even though the air was quite turbulent and going up on average. I tried another identical spot with the same disappointing result. I flew out of this promising area and found a weak smooth thermal which brought me home. Quite a frustrating experience. 

 

After a while, my son Ronald and I began to suspect the lift-curve of the wing of having an unusual part at the lower speeds, which could explain our findings that pitch control just prior to touching down had hardly any effect on sink rate and that the good climbing performance of our new sailplane degraded substantially when circling in turbulent thermals.

 

Because of our observations we contacted prof. ir. Loek Boermans at Delft Technical University. "We improved the not so good climbing performance of a standard class sailplane in turbulent conditions already some years ago”, he said.  “A new wing profile and winglets were applied. Apart from a recent phone call of Ronald flying at the EC in Leszno, I heard no complaints about the climbing performance of the new breed of sailplanes with flaps though I was indeed worried about this. I advised Ronald to fly somewhat faster in turbulent thermals with more banking angle. I think there are ways to solve this problem also for sailplanes with flaps as we did for the standard class glider”. 

 

Shortly after the meeting, prof. Boermans came up with a slightly redesigned profile promising a better climbing rate in turbulent conditions while maintaining optimum glide rates. I myself started to develop some software of my own to better understand the effects of the flatter part in the lift-curves of modern sailplanes with flaps and came up with a couple of practical ideas when flying in turbulent air or when landing at low speed. Slightly modifying the wing profile is of course no option to pilots having one of the current breed of high performance sailplanes.

 

The lift-curves:       

 

The lift of a sailplane is controlled by the well known lift formula:  L = ½.r.V2.S.CL .  With this formula, together with the CL-a graph we can study the performance of a sailplane in smooth and turbulent air. Modern wings are quite thin to minimise profile drag and are normally operated at small values of a within the so called ‘laminar drag bucket’ where maximum length’s of laminar boundary layers on both the upper and under surfaces of the wing are realized. The lift formula shows that at low thermalling speeds or when landing, Cl must be as large as possible to properly carry the weight of the sailplane. Maximising CL at low speeds and small values of a is controlled by a balancing process, where with increasing a the lift in the forward section of the wing grows as expected, while the lift on the aft part of the wing breaks down at about the same rate because of earlier laminar boundary layer transitions and flow seperations at the flap hinge area. The net effect of this is that the mean lift coefficient remains about constant over quite some interval of a, especially for the larger flap settings, as shown in figure 1.

 

So, a linear relationship between CL and a, as common in earlier years of wing design, does not apply to modern wing profiles with flaps. Almost all have a more or less horizontal step in their lift curves. Beyond the step, CL increases again because of a retarding effect in the break down process of the lift until the airflow starts fully detaching from the wing surface and the sailplane stalls.

 

 

Figure 1: Measured CL- a curves (typical for any modern sailplane)

 

Landing

 

Now consider the case of a pilot on finals to the airfield close to touching down. No water in the sailplane (mass=450kg) and FL=20°, ie in the landing position. Assume an approach speed V = 76km/h. Then from formula (2) it folows that CL = 1.46. The FL=20° curve of figure 1 indicates that for this value of CL, a = 2.5° which is just in front of the step as indicated. In rounding off prior to touching the ground, the pilot lifts the nose of the sailplane to increase a with the idea of slowing down the descent rate of the sailplane.  a increases alright, but CL doesn’t do that unless the nose of the sailplane is tilted so high that a has increased from 2.5° to more than 7.0°. Only then CL will increase to above 1.46 and the sailplane will stop its downward motion. Usually a pilot’s action in rotating the sailplane over this large angle is too cautious. The sailplane will contact the ground prematurely and will usually bounce a couple of times. Bumpy landings are quite familiar to pilots flying modern competition sailplanes and can frequently be observed. The solution to this problem is to stay more in front of the step region by flying a little faster than the minimum approach speed and use airbrakes rather than pitch to control descent rate. Once on the ground, good wheelbrakes should be applied to bring the sailplane to a halt. 

 

Flying through turbulences

 

In turbulent air, serious changes in a occur because of vertical movements of air hitting the wing surface. When gliding straight on at small values of a close to 0°, which is usually the case, one can see from the CL- a graphs of figure 1, that upgusts will increase CL and downgusts will decrease CL in the same manner. On the average CL will stay constant with time and no altitude gain or loss appears in this situation where gusts have a random distribution in strength and direction. But especially at low wing loading one may expect a rough ride because of significant positive and negative accelerations due to the more or less strong variations in CL with time.

 

However, now consider a sailplane flying nose up with a = 4.0° and FL=15°, where CL=1.40 as indicated in figure1. So right at the beginning of the step where upgusts have no effect on CL, since an increase of some degrees in a falls right into the step where CL is constant. However, downgusts will reduce a with the same some degrees, thereby reducing CL. So CL swaps between 1.40 for positive gusts, and some lower value, say 1.20 for negative gusts. On average CL = 1.30, i.e. 7 % less than the 1.40 required to carry the weight of the sailplane. Therefore the sailplane starts a dynamic downward motion as long as the turbulences are present. Not what one really wants of course.

 

A computer routine

 

To get a better insight into the climb rate of the sailplane under turbulent conditions I wrote a small, but effective, computer routine. The first part of the routine is an outer loop, which is rather straightforward and describes vertical speed as the difference between thermal climb rate and polar descent rate in smooth thermals for 300 values of circling speeds in a practical range.

 

I used a theoretical thermal model with a parabolic shape and accurate speed polars as measured by Idaflieg (the German academic flight test group). I used cubic spline functions to make the ploar curves accessible to the computer routine as a function of flying speed. The straight flight sink rate data of the polar were corrected for mass and bank angle. With these formulae for the thermal model and polar descent rate, stable climbing rate as a function of flying speed can be calculated as:   Vs_(th+pol) = Vs_thermal + Vs_polar   ......(3) (purple curve in figure 3)

 

To calculate the additional effect of turbulence, some sensible dynamics equations had to be defined. In the computer routine, these equations are enclosed in an iterative inner loop having small time steps dt =  0.01s. Turbulence is described as sine waves with a time constant of 2 seconds and random amplitude. In this way the effect of turbulence, Vs_gusts, is calculated during 30 seconds for each of the 300 flying speeds considered and plotted in graphs (blue curve in figure 3). Then total climbing rate is:  Vs_total = Vs_(th+pol) + Vs_gusts ......(4) (black curve in figure 3)

 

A key issue in the routine is the application of Newton’s second law to find the vertical speed, Vs(t), of the sailplane from the forces acting on the wing due to the airgusts present.

 

Results of calculations with the routine

 

Figure 2 shows the development of vertical speed Vs(t) of the sailplane for the first couple of turbulence gusts, Vg(t), encountered. One can say that the results are quite dramatic when looking at the blue Vs(t) curve which averages out at -0.59m/s. The sine wave shapes of the turbulence can be recognised, as well as their randomised amplitudes. More erratic forms are likely of course, but these are not expected to make a significant difference to the results of this analysis.

 

 

Figure 2: Development of sink rate Vs(t) due to sine wave shaped turbulences.

 

More practical results with the computer routine are given in figure 3 which shows one of the many graphs studied. The a line shows the step as expected. Considering a smooth thermal, a best climbing rate of Vs_total = Vs_(th+pol) = 1.80m/s is obtained. Circling with a speed just above something like 100km/h is OK and comfortable, but of course this is dependent on the shape of the thermal.

 

Considering also the turbulence in figure 2, total climbing rate is now Vs_total = Vs_(th-pol) + Vs_gusts as indicated. For speeds above, say, 120km/h, the defined turbulence has no effect because a is small (even negative) and quite less than 4.0° where the step in the CL-a curve for FL=15° begins.  Then positive and negative gusts cancel out as is shown by the Vs_gusts curve. However, for speeds less than 120km/h, positive gusts raise a to into the flat part of the  CL-a curve of figure 1 and give a reduced contribution and at 99km/h no contribution at all to the lift of the wing. Negative gusts however still fully reduce CL as usual.  Therefore with turbulences present, the nice total climbing rate of 1.80m/s at 100km/h for the smooth thermal is dramatically reduced to 1.20m/s only, a loss of 33 per cent. The only way out of this is to circle some 10km/h faster. In this case a climbing rate of  about 1.40m/s is attained at a speed of 110km/h. So, still a loss of 22 per cent due to the turbulence.

 

To get a beneficial effect out of random air gusts, a pilot may try to fly with an a just behind the step in the CL-a curve where positive gusts push the sailplane up and negative gusts have no effect. Figure 3 promises a nice climbing rate when circling with a speed of say 96km/h. Some pilots seem succesful in doing so, however the sailplane may be rather difficult to control and high drag may deminish this special effect substantially.

 

Other calculations with the routine show that having a dip in the lift curve is still worse than a flat step, but some earlier high-performance sailplanes have that. A small positive gradient in the step area, as suggested by Loek Boermans,  improves climbing rate with turbulences present quite considerably, so this looks the way to go in the design process of new wing profiles. Just now, some new sailplanes having this idea are coming on the market.

 

 

 

Figure 3: Reduced climbing rate in a turbulent thermal

 

It should be mentioned that the above calculations were performed assuming that the effects of the flat part in the liftcurve occur at the same moment over the total span of the wing. This not the case however due to the random distribution of turbulences in size and in space and because of different wing profiles and Re-numbers in the spanwise direction of the wing. Therefore the results of the above calculations maybe somewhat exaggerated for the practical situation.

 

In conclusion

 

Recent optimisations of wing profiles with flaps have resulted in CL-a curves with a more or less ‘flat part’ in the lower speed range. Because of this, landing behaviour and climbing performance in turbulent thermals are somewhat disappointing.

 

This article shows that pilots can partly take care of these drawbacks by flying with a (angle of attack) well in front of the ‘step’ in the CL- a curve.

 

The main actions to achieve that are:

 

a. When trying to make perfect landings, approach speeds should be a little higher than usual and speed brakes gently applied rather than pitch to finely control the descent rate in rounding off just before touching the ground.

b. When optimising total climbing rate in turbulent thermals, flying speed and bank angle should be higher than a pilot would usually prefer.

c. Thermals should be entered with redundant speed to avoid that the sudden upflow encountered pushes a into the step area.

 

This study shows that slightly modifying the CL-a curve with a positive gradient in the step area will improve sailplane performance substantially. A better control of the descent rate during landing will then be possible and an increase in average climbing rate of some 20 per cent may be expected when circling in turbulent thermals. I understand that only minor modifications of the wing profile are necessary to obtain these improvements without a penalty in the high speed range of the sailplane (as suggested by Prof. Ir. Loek Boermans).

 

Acknowledgement

 

I would like to thank my friends for the inspiring discussions about the step in the CL-a curve of modern sailplanes – especially my son Ronald and Loek Boermans, both of whom gave in their own specific way of practical experience and theoretical knowledge, a substantial support in the realisation of this work. Additionally the books and articles of John Anderson, Helmut Reichmann, Fred Thomas, Loek Boermans and others and many articles found on the internet were also quite inspiring.

 

ir. K.P. Termaat

Arnhem, NL

20 oct. 2011