Introduction
It has been recognized from the beginning of the development of the sailplane that the key to performance improvement was in drag reduction. It has been also known that the total drag consisted of three major components: induced, profile, and parasite drag. The development started first in reducing the parasite drag by elimination of struts, wires, open cockpit, etc. Then, it continued in decreasing the induced drag by using high aspect ratio. The third stage of the development is going on at the present time, when the major effort is concentrated on lowering the profile or friction drag, since the possibilities of induced and parasite drag reduction are nearly exhausted.
During the second stage of Development, the continuous efforts for lower and lower drag led to the idea of the flying wing design. This offered the complete elimination of the parasite drag in addition to lighter weight and lower cost. But, at the same time, numerous problems of stability and control were to be overcome. These difficulties discouraged most of the designers, but the Horten brothers took up the problem with great determination and basically solved it. It is most remarkable that the fourth of their models, the Horten IV, was already better, or at least equivalent in performance to those of conventional design, which were developed with all the experience gained through dozens of previous models. This successful development, however, was interrupted by the war, and the last two models of the line, the Horten IVb and Horten VI, remained unevaluated.
Since the war, the emphasis in sailplane development has been concentrated mostly on the profile or friction drag reduction of conventional types. The adoption of laminar airfoils and new technology brought significant progress, and the seemingly ultimate gliding ratio of 40 to 1 has been reached. But, in this state of development when the greatest effort is necessary to eliminate one or two thousandths from the profile drag coefficient, the presence of the parasite drag due to the fuselage and tail becomes more and more annoying, and the idea of the flying wing configuration comes into prominence again.
For this reason, as a part of the sailplane research program conducted by the Aerophysics Department of Mississippi State University, an investigation was projected into flying wing sailplanes, and a Horten IV was chosen for that purpose as the most advanced design of its class.
Preliminary performance measurements of the Horten IV were made by the DFS in comparison flight with the D-30 Cirrus in 1943, and reported by Hans Zacher [2].
It was pointed out that, although the Horten IV was one of the best performing sailplanes of that time, the actual performance was well below that expected.
The basic aim of our research was to find out why the estimated performance could not be achieved and whether or not the factors causing the lower performance are inherent in the flying wing design.
Preliminary flight tests at Mississippi State University showed even lower performance than reported by Zacher. Since the plane wasn't in good condition at that time, it was decided to overhaul it, improving the wing surfaces as much as possible and making some modifications on the center section, such as streamlined housing for the nose skid and improved canopy contour. Finally, the projected flight tests were conducted in the fall of 1959, and the results of the evaluation are presented here.
Results of Recent Performance Measurements
Figure 1 shows the performance curves. The test points of several Sights are indicated by different symbols. The points were weighed according to the customary method [3], and those of full weight have solid symbols. In addition to our measurements, the former DFS test results are also indicated. They are adjusted to W=366 kg, the gross weight of the recent tests.
The best gliding ratio of the Horten IV was expected to be 0.37. The flight tests, however, indicated considerably lower performance. Nevertheless, there are some differences between the flight test points. While the drag polars in Figure 2 almost coincide at low lift coefficients, the deviation between them becomes larger and larger as the lift coefficient increases. In other words, the slope of the linearized drag polar is steeper according to the DFS measurements, which means better span efficiency. It should be noted, however, that the span efficiency is affected by the C.G. position, and it is not given for the DFS test. If the C.G. was located considerably farther back in the DFS test, or if the two planes were not the same, the disagreement is understandable.
The most important performance and aerodynamic data are summarized in table 1.
Three features of the aerodynamic characteristics are most remarkable.
(1.) The minimum drag ^{C}D_{min }= 0.0125, is Barely lower than that of a good conventional design of that time in spite of the elimination of the fuselage and tail ^{C}D_{min }was 0.0135 for the D-30 "Cirrus", and 0.015 for the DFS "Reiher" [4].
(2.) The drag rapidly increases with the lift coefficient, that is, the slope of the linearized drag polar is extremely shallow, which means poor span efficiency or low effective aspect ratio.
(3.) The maximum lift coefficient, ^{C}L_{max }= 1.125, is relatively low also.
Analysis of the Drag Components
The performance measurements represented only the first step in our investigation. As mentioned before, the basic aim was to find out the reasons for the unusual behavior and to make clear the interaction of the several influential factors. For this a detailed study of the individual drag components was necessary, or in other words, the drag polar was to be broken down into its elements.
The Profile Drag
The profile drag was measured at several places along the span by means of an integrating wake rake. The method is described in Reference 5. The measured profile drag polars, Figure 3, have the following features: Going outward along the span, the drag increases considerably. This is partly due to the decrease of Reynolds number, but most likely is due to the lack of cleanliness of the airfoil caused by elevon surfaces, dive brakes, and drag rudders.
In the case of the innermost test section, the minimum profile drag coefficient ^{c}d_{pmin} =0.009. Then the drag gradually increases at the higher lift coefficients, and amounts to ^{C }_{dp} =0.015 at C_{L} =1.125.
Although, in view of the present state of the art, an airfoil of such a high drag is considered very unfavorable, it was not worse than other contemporary airfoils [4, 6]
For the rest of the test sections, the airfoils are not clean due to dive brakes and control surfaces. At the second and third test section there is a rapid drag increase at high lift coefficients. This is generated by turbulent separation, which occurs on that part of the wing as an initiation of the stall.
For the fourth test section, the rate of drag increase with lift coefficient is much greater than for the inner sections, but there is no rapid growth in drag at high lift coefficients.
This is because the center elevon has large negative deflection which results in higher drag at moderate lift coefficients, but does not allow separation at the high lift coefficients.
The outermost test section has approximately two and one-half times higher drag than the innermost one. Numerous factors, such as contour and surface imperfections, drag rudder, low Reynolds number, large control surface-chord ratio, etc., contribute to develop this extremely high drag at the wing tip. It is peculiar that the minimum drag occurs at C _{L} =0.4, and below that the drag increases again. The probable reason for this is the discontinuity in profile contour which causes the flow to separate from the drag rudder when the elevon has zero or positive deflection, while the overhanging nose of the Frisetype elevon creates rapidly increasing drag at high lift coefficients when large negative deflection is applied.
Based on the sectional profile drag measurements, the spanwise profile drag distribution and resultant profile drag polar were determined. Figure 4 shows the local profile drag coefficients along the span. These curves, multiplied by the local chord length, represent the effective drag distribution and the resultant profile drag is calculated as:
The results are given below.
Resultant Profile Drag Coefficients
CL | 0.2 | 0.4 | 0.6 | 0.8 | 1.0 | 1.05 | 1.125 |
^{C}Dp | 0.0115 | 0.0120 | 0.0132 | 0.0151 | 0.0179 | 0.0208 | 0.0223 |
Induced Drag
The induced drag coefficient is defined as:
where the factor represents the induced drag increment due to the deviation of spanwise lift distribution from elliptic, which would give the minimum induced drag. It is customary to express the induced drag coefficient also as:
that is, to consider the induced drag increment as a consequence of decreased effective aspect ratio where
and e, the span efficiency, is defined as
The low span efficiency of the Horten IV indicated that the induced drag increment might be very high because of the heavy twist and control deflection. Therefore, a detailed calculation was carried out concerning the spanwise lift distribution and actual induced drag.
The factor is determined by the spanwise lift distribution which is affected mainly by the taper, sweep, twist, and Control deflection. The spanwise lift distribution was calculated according to O. Schrenk's approximate method, supplemented by Weissinger's correction for sweep [7, 8, 9].
The most unusual among the influencing factors considered is the control deflection. In low speed flight the center and outboard elevons are deflected up as much as 15 degrees, which results in a considerably decreased effective local angle of attack or lift coefficient.
The elevator deflection angles are shown as a function of the lift coefficient in Figure 5. This was obtained by collating the curves , where ^{* }represents the displacement of the control grip and ° is the control surface deflection in degrees.
According to theory, a small control deflection results in a change of effective angle of attack defined by the control power derivative
This change in angle of attack due to control deflection was considered as additional twist, and the resultant lift distribution calculated accordingly.
Figure 6 illustrates the deviation of the lift distribution from the elliptic for the wing with basic twist only, and for that with control deflection included. Too examples are presented: C_{L }= 1.00, and C_{L} = 0.25. As can be seen, at high lift coefficient, the large negative control deflection greatly increases the deviation of the (c_{l}c) curve from the elliptic, while the basic twist results in minor difference.
However, at low lift coefficients, the control deflection, being positive, decreases the effective twist and brings the resultant lift distribution closer to the elliptic than it is for the wing of basic twist.
The induced drag increment was calculated by the formula [Reference 10]:
where a_{1} and a_{n} are the Fourier coefficients of the (c_{l}c) lift distribution curves.
The results are summarized in figure 7, where is plotted versus C_{l}. The effect of taper, sweep, twist, and control deflection can be delineated clearly. The extreme taper causes an induced drag increment of about 2.5 per cent, as compared to an elliptical planform. The sweep, by shifting the load toward the tips, counteracts the taper and reduces to about l.5 per cent. Contrary to the former two factors, in which cases is constant with the lift coefficient, the twist results in a rapidly increasing as the lift coefficient decreases. This is true because the basic load distribution due to twist remains unchanged, while the additional load distribution determined by the planform proportionally decreases with the lift coefficient and, since the load distribution is the sum of the two above, at low lift coefficients, the effects of the twist become more and more predominant.
While = 2.5 per cent at high lift coefficients, it has grown to = 59 per cent at C_{L} = 0.25. The control deflection required to trim has an alleviating effect on the induced drag increment due to twist at the lower lift coefficients. The actual conditions are represented by the heavy curve which includes the effect of all influencing factors. By reference to this, it can be seen that = 35 per cent at ^{C }L_{max} and gradually decreases to = 24 per cent at C_{L}= 0.5. Below C_{L} = 0.5, increases again, but not nearly so rapidly as in the case of the twisted wing without control deflection.
Parasite Drag
The parasite drag of a flying wing is supposed to be negligible, since the frontal and wetted area of the fuselage are very small compared to the entire wing area. Tuft observations on the Horten IV however, indicated intense separation on the rear part of the cockpit hatch which implies a source of considerable parasite drag. Figure 8 shows tuft photographs of the canopy at two typical speeds. As can be seen, the separated region diminishes as the speed increases. Figure 9 presents the extent of separation evaluated from tuft photographs. The attitude of the plane as well as the angle of flight path, pitch, and angle of attack; are given also. The steep nose up attitude of the canopy at high lift coefficients, which incorporates severe adverse pressure gradients, is apparently the major source of the separation.
Since there is no practical method available for measuring the parasite drag numerically, it is determined indirectly by subtracting the profile and induced drag from the measured total drag. The remainder is considered parasite drag.
Breakdown of the Drag Polar
In Figure 10, the drag polar is divided into the major components discussed in the foregoing paragraphs. The induced drag consists of two parts: the theoretical value, that associated with an elliptic lift distribution; and the increment, due to the actual conditions. The former part being proportional to the square of the lift coefficient, appears in the linearized drag polar as a straight line with a slope determined by the geometric aspect ratio. At the maximum lift coefficient, this part amounts to about 35 per cent of the total drag. The other part, the induced drag increment, progrcssively increases with the lift coefficient, and at C_{L }= 1.00, results in about 30 per cent higher induced drag than the theoretical. Thus, the total induced drag amounts to about 46 per cent in low speed flight.
The parasite drag is negligible at low lift coefficients, but begins to grow gradually between C_{L} = 0.4, and 0.7. Above C _{L} = 0.7, the separation from the canopy expands rapidly and the parasite drag rises from 3 to 14 per cent of the total.
The profile drag forms a major part of the total drag throughout the entire speed range, and becomes more and more predominant at low lift coefficients. It is 90 per cent at C_{L} = 0.2. It can be seen that the main responsibility for the lower than expected performance rests with the high profile drag and its intense growth with lift coefficient.
On the basis of the Figure 10, the low span efficiency can be explained also. The span efficiency is defined as the ratio between the slopes of the theoretical and actual induced drag polars plotted in linearized form: C_{l}^{2} versus C_{D}. In other words, it is the ratio of the effective and geometric aspect ratio. Simplified theoretical considerations often assume, however, that the profile and parasite drag are constant, that is, the total drag polar is parallel to the actual induced drag polar. Hence, it is a general practice to express the span efficiency as the ratio between the slopes of the theoretical induced drag polar and the total drag polar. This is, however, not precise, since in practice both the profile and parasite drag are subject to change with the lift coefficient, and the slope of the total drag polar is accordingly different from that of the actual induced drag polar.
In the case of the Horten IV, using the slope of the total drag polar, the span efficiency appears to be 53 per cent, however, the actual span efficiency, using the induced drag increment, is 76 per cent.
A further weakness of the Horten IV, which was not clearly understood, is the low maximum lift coefficient. This can be cleared also by studying the lift distribution at minimum speed.
In Figure 11, the actual local lift coefficient is plotted along the span for C_{L} = 1.125. The peak value, ^{C }L_{max} = 1.36, occurs at about 35 per cent of the half span, that is, somewhat inboard of the elevons. Tuft observations revealed that intense separation exists at the same place when the plane flies at the minimum speed. This means that the stall is initiated there, that is, the local lift coefficient reaches its maximum possible value. Since ^{C }L_{max} for a given airfoil depends primarily upon the Reynolds number, the maximum available lift coefficient for the rest of the wing can be estimated. Accordingly, ^{C}L_{max} {} 1.4 for the wing root (Re = 1.7x10^{6}) and ^{C}L_{max }{} 1.00 for the tip (Re = 0.4x10^{6}). In figure 11, the maximum available local lift coefficient is also indicated. The difference between this and the curve of actual lift coefficient, designated as lift reserve, indicates the margin of safety against tip stall.
As can be seen, the local lift coefficient reaches the limit of the stall once at the third half span and once more at the outer end of the inboard elevon, but remains far below the limit on the outboard part of the wing due to the highly deflected control surfaces. This implies a great safety margin against tip stalling, but simultaneously results in a considerable loss in lift. This is why the resultant maximum lift coefficient, ^{C}L_{max} = 1.125, is so low although the airfoil itself has a normal ^{C}L_{max} = 1.3 to 1.4, at the Reynolds numbers concerned. For comparison, the lift coefficient distribution for the wing without control deflection is given also in Figure 11. This shows that the local lift coefficient would exceed the available limit over the outer portion of the wing, resulting in tip stall. Consequently, some negative control defection at the tips is necessary, however, much less would be sufficient to provide favorable stall characteristics than actually is applied.
Possible Performance Improvements
On the basis of the foregoing drag analysis, the possibilities of performance improvement will be discussed below. This is based on a calculation in which we assumed several successive improvements in the drag components, which are believed reasonable in the present state of development. These improvements are the following:
Figure 13 demonstrates the result of these improvements on the gliding performance. Curve No. 1 is the present state; Nos. 2, 3 and 4, show the performance if only one of the three drag components were improved at one time. Thus, the importance of the several modifications can be seen clearly. Namely, the complete elimination of the parasite drag would affect the performance mostly at low speeds, and the best gliding ratio would be barely increased (Curve No. 2). The reduction of the induced drag increment to 10 per cent would increase the best gliding ratio from 29.5 to 32 only (Curve No. 3). But a considerable improvement follows when the profile drag is reduced. Curve No. 4 was obtained by using the imaginary profile drag polar marked as "A" in Figure 12. The best gliding ratio rises to 40, and the performance at high speed, that is, the penetration ability, is greatly increased. Curves No. 5 and 6 show the improvement, if in addition to the above profile drag reduction, the parasite drag were eliminated and the induced drag were decreased in the formerly described manner. In this case, a remarkable improvement appears in the low speed region, and the best gliding ratio becomes 41.5 and 43.5 respectively. Finally, the Curve No. 7 represents the ultimate performance which could be achieved with the other imaginary profile drag polar marked "B" in Figure 12, naturally assuming the above mentioned improvements in induced and parasite drag. In this case, the best gliding ratio would be 48, a really phenomenal one.
Conclusions
The present investigation has basically cleared the conditions by which the performance of the Horten IV was limited. However, a large margin of improvement seems to be possible by means of proper drag reduction. An up-to-date flying wing of the size of the Horten IV should be able to reach a best gliding ratio of nearly 50 to 1. In the case of one of the very best conventional designs, like the Phoenix, such a high performance seems to be feasible only if extensive boundary layer control were applied. This verifies that the flying Wing design is not an obsolete idea, but is worthy of development
It is beyond the scope of this paper to deal with the stability and control characteristics in detail, nevertheless, the author wishes to note that, in his opinion, the handling of the Horten IV is not essentially more difficult than that of any other high performance sailplane. The extremely good natured stalling and circling characteristics, as well as the excellent landing maneuverability are to be noted especially. The prone position of the pilot is believed to provide a more natural sensation of fight than the conventional sitting position; in addition, it provides incomparable visibility for landing and navigation. On the other side of the balance, however, the marginal directional stability, unusual response for rudder control coupled with pitch, and above all, the wing tip flutter, appearing above 140 km/h, should be noted.
Drawing the final conclusions; we summarize once more the major deficiencies of the Horten IV and outline the possible ways of improvement in Table II.
Two of the suggested improvements are of primary importance, that is, the use of a low drag laminar airfoil and the elimination of large control deflection by some means, for example, by variable sweep or center of gravity. The variable sweep seems to be fairly practical, however' a more detailed consideration is necessary to find out which would be the more favorable way. To do this, of course, the stability and control characteristics are to be taken into consideration also.
Since the keystone of the performance improvement lies in the use of a laminar airfoil, this, in the case of the Horten IV, would mean a complete reconstruction of the airframe. Therefore, further development seems more reasonable through a new design, in which all the experiences gained so far as well as the latest technology of construction could be utilized. This does not mean, however, that there is no further use for the Horten IV as far as further research is concerned. For example, for the sake of further development it would be necessary to evaluate the stability and control characteristics, as was done for the performance. Moreover, it would be very useful to make an experiment on variable sweep before adopting it for a new design and the Horten IV seems to be suitable for this experiment.
We, at Mississippi State University, have planned to continue this work; through further evaluation and study toward a new flying wing design, in which the brave old Horten IV would be reincarnated. The tragic death of Dr. August Raspet, who was the leading spirit in this aspiration, however, has made the chances of realizing this plan very uncertain.
Symbols
A.C. | m | Aerodynamic center |
b | m | Wingspan |
c | - | Chord length |
CG | - | Center of gravity |
CD | - | Total drag coefficient |
CL | - | Resultant lift coefficient |
cl | - | Section lift coefficient |
^{C}Dp | - | Resultant profile drag coefficient |
^{c}dp | - | Section profile drag coefficient |
^{C}Di | - | Induced drag coefficient |
e | - | Span efficiency |
Re | - | Reynolds number |
S | m^{2} | Wing area |
V | km/h | Calibrated airspeed |
W | kg | Gross weight |
w | m/sec | Sinking speed |
y | m | Distance perpendicular to the symmetry axis |
a | deg. | Angle of attack |
- | Factor of induced drag increment | |
E | deg. | Elevon deflection angle |
- | Gliding ratio | |
y | Deg. | Glide path Angle |
deg. | Pitch angle | |
- | Geometric aspect ratio | |
eff | - | Effective aspect ratio |
Measured aerodynamic and performance data
DFS* | MSU** | |
CDmin | 0.01175 | 0.0125 |
CLmax | 1.17 | 1.125 |
_dCL Rad-1
d |
_ | 4.35 |
CLmax
^{C}Dmin |
99.5 | 90 |
max = (L/D)max | 31.5 | 29.5 |
e | 63% | 53% |
eff | 13.4 | 11.3 |
wmin m/sec | 0.59 | 0.70 |
Vwmin km/h | 60 | 70 |
Vmin km/h | 52 | 59.5 |
Vmax km/h | 76 | 82 |
V=20 km/h | 130 | 126 |
** Actual tested gross weight W=366 kg. CG 1.38 meters from nose point (see figure 5)
TABLE II
Summary of the evaluation of Horten IV concerning the
performance
Deficiency | Reason | Possible way of improvement | |
1 | Obsolete airfoil | Use of laminar airfoil | |
High profile drag | 2 | Disturbance of the airfoil by control surfaces, dive brakes and drag rudders. | Smaller but more effective control surfaces with sealed gaps. Different arrangement of dive brakes and rudders |
3 | Excessive control deflection | Variable sweep or CG to provide trim | |
4 | Low Reynolds number at the tip due to high taper ratio | Moderate taper ratio | |
High induced drag | Excessive twist, control deflection, and taper | Variable sweep or CG to provide trim, less taper | |
High parasite drag | Separation from the canopy | Different canopy arrangement | |
Low maximum lift coefficient | Excessive control deflection, excessive taper | Variable sweep or CG and, perhaps, variable twist, less taper |
Span | 20 | m |
Wing area | 18.8 | m^{2} |
Aspect ratio | 21.3 | |
Dihedral | 5 | degrees |
Sweep-back (1/4 chord line) | 17 | degrees |
Twist | 7.1 | degrees |
Wing root chord | 1.55 | meters |
Wing tip chord | 0.28 | meters |
Taper ratio | 5.55 | |
Airfoil sections | Reflexed, individual design | |
Total area of elevon surfaces | 3.16 | m^{2} |
Ratio of the elevon surfaces to the total wing area | 16.8 | % |
Total wetted area | 41 | m^{2} |
Ratio of the wetted area to the total wing area | 2.18 | |
Empty weight (present condition) | 266 | kg |
Gross weight (recent flight tests) | 366 | kg |
Wing loading (recent flight tests) | 19.5 | kg/m^{2} |
Acknowledgments
This work was done under the sponsorship of the United States Army Transportation Command and Office of Naval Research. Dr. August Raspet, Head of the Aerophysics Department, took the initiative in this study and gave full support and inspiration. A special appreciation is due to Mr. Rudolf Opitz, who saved the Horten IV from deterioration, rebuilt and flew it with remarkable success in the U.S. National Contest of 1951, as well as In the early flight tests at Mississippi State University then introduced the author to flying the plane and gave over much of his vast experience on flying wings.
References
A hard copy of this document is available from:
TWITT
P.O. Box 20430
El Cajon, CA 92021
Price is $5.00 US. Add $2.00 for foreign postage. Be sure to ask for the "Performance analysis of the "Horten IV" Flying Wing.
The author of this report "Dezso George-Falvy" delivered a presentation
at the 1997 National Soaring Museum Flying Wing Symposium.