Differential Twist Wings for Better Solution Upgrade of Advanced Flying Wings Combined with LEX and Tail | The Design Analysis and Configuration | Aspect Ratio Review

A flying wing is a tailless fixed-wing aircraft that has no definite fuselage, with its crew, payload, fuel, and equipment housed inside the main wing structure. The flying wing may have various small protuberances such as pods, nacelles, blisters, booms, or vertical stabilizers. Whereas the flying wing seeks to maximize cruise efficiency at subsonic speeds by eliminating non-lifting surfaces. Lifting bodies generally minimize the drag and structure of a wing for subsonic, supersonic and hypersonic flight, or spacecraft re-entry. All of these flight regimes pose challenges for proper flight safety.

Similar aircraft designs, that are not technically flying wings, sometimes casually referred to as such. These types include blended wing body aircraft and lifting body aircraft, which have a fuselage and no definite wings. The basic flying wing configuration became an object of significant study, often in conjunction with other tailless designs. Tailless aircraft have been experimented with since the earliest attempts to fly.

Caused of flying wing lacks conventional stabilizing surfaces and the associated control surfaces; in its purest form the flying wing, suffers from the inherent disadvantages of being unstable and difficult to control. These compromises are difficult to reconcile, and efforts to do so can reduce or even negate the expected advantages of the flying wing design, such as reductions in weight and drag. Moreover, solutions may produce a final design that is still too unsafe for certain uses, such as commercial aviation.

A wing that is made deep enough to contain the pilot, engines, fuel, undercarriage and other necessary equipment will have an increased frontal area, when compared with a conventional wing and long-thin fuselage. This can actually result in higher drag and thus lower efficiency than a conventional design. Typically, the solution adopted in this case is to keep the wing reasonably thin, and the aircraft is then fitted with an assortment of blisters, pods, nacelles, fins, and so forth to accommodate all the needs of a practical aircraft.

The problem becomes more acute at supersonic speeds, where the drag of a thick wing rises sharply and it is essential for the wing to be made thin. No supersonic flying wing has ever been built.

Directional stability: for any aircraft to fly without constant correction, it must have directional stability in yaw. Flying wings lack anywhere to attach an efficient vertical stabilizer or fin. Any fin must attach directly onto the rear part of the wing, giving a small moment arm from the aerodynamic center, which in turn means that the fin is inefficient and to be effective the fin area must be large. Such a large fin has weight and drag penalties, and can negate the advantages of the flying wing. The problem can be minimized by increasing the wing sweepback and placing twin fins outboard near the tips, as for example in a low-aspect-ratio delta wing, but many flying wings have gentler sweep back and consequently have, at best, marginal stability.

Another solution is to angle or crank the wing tip sections downward with significant anhedral, increasing the area at the rear of the aircraft when viewed from the side.

The frontal area of a swept wing as seen in the direction of the airflow depends on the yaw angle relative to the airflow. Yaw increases the drag of the leading wing and reduces that of the trailing one. With enough sweepback, differential drag is sufficient to naturally re-align the aircraft.

A complementary approach uses differential twist or wash out, together with a swept back wing planform and a suitable airfoil section. Due to the necessity for elevons to be located near the wingtips, the one on the upward-moving wing causes drag that impedes turning as it deflects the high-pressure airflow under the wing. Described as "bell shaped lift distribution" across the span of the wing, with more lift in the center section and less at the tips due to their reduced angle of incidence, or washing out. The restoration of outer lift by the elevon creates a slight thrust for the rear (outer) section of the wing during the turn. When displaced, this vector essentially pulls the trailing wing forward to compensate for the "adverse yaw" caused by the elevon. It did not work well in practice.

Yaw control: in some flying wing designs, any stabilizing fins and associated control rudders would be too far forward to have much effect, thus alternative means for yaw control are sometimes provided.

One solution to the control problem is differential drag: the drag near one wing tip is artificially increased, causing the aircraft to yaw in the direction of that wing.

A consequence of the differential drag method is that if the aircraft maneuvers frequently then it will frequently create drag. So flying wings are at their best when cruising in still air: in turbulent air or when changing course, the aircraft may be less efficient than a conventional design.

Design Principle:

Design principle of advanced flying wing in the bases of differential twist wings has to be narrower span for main wings to 12.9 meters, and continue the span till 27.9 meters for expanded wingspan. Main wings to provide imaginary fuselage must be set highly swept by 54 degrees, while expanded wings, sweep back by 22 degrees, is to provide more stability for trapezoidal. The transition form, where the trailing-edge is straight, is equivalent to cropped delta planform, while the trailing-edge is tapered will be equivalent to trapezoidal planform, sweeps forward by 36 degrees.

 To implement the design principle into the bases of modern aircraft design, that is by placing angle 60 degrees at 1.5 cm right from zero-point at horizontal line. Configuration of the angle performs span of main wings to 12.9 meters. Then begin from the root, drawing a line sweeps back by 54 degrees forming leading-edge of trapezoidal, and make straight line from tip to tip forming delta planform. Continue expanding the span till 27.9 meters sweeps back by 25 degrees. Since the main wings based on trapezoidal, it is necessary to complete the trapezoidal design at first. From the root of the span, draw a line sweeps back by 22 degrees, then joining its wing tip to wing tip with straight line to form span of the trapezoidal and the cropped. Finally finish the trapezoidal with tapered trailing-edge sweeps forward by 36 degrees.

The configuration is then called differential twist wings that combines two type of wings with different angles. Main wings based on trapezoidal wings while expanded wings based on swept wings. As differential twist wings, both wings have different twist or sweep of leading-edge and also different configurations. However, main configuration, design analysis and aspect ratio come to trapezoidal as main wings. Benefit of applying trapezoidal in main wings is that trapezoidal wings have three major configurations: delta planform, the cropped and tapered trailing-edge as described. Each element provides benefit and configuration, even possibility to install many control surfaces in flying wings design.

Differential twist of flying wings requires highly swept for main wing, the trapezoidal, and narrower span to provide imaginary fuselage and to provide longitudinal stability. Sweep of leading-edge by 54 degrees gives proportional sweep and configuration for trapezoidal and other elements in flying wings design. The stability of imaginary fuselage can be measured from the square formed by the configuration where it shaped into a square extends downward not extend to the side or not shaped into a cube shape. So that, configuration of trapezoidal in which contain delta planform, the cropped and tapered trailing-edge provides low wings loading with aspect ratio of span to root chord will be in range 0.40 to 0.55 and value of golden ratio of fuselage length to wingspan reaching 1.618 even if combined with LEX and by adding tail. For the flying wings to fly as if it’s a fighter, parameter low wings loading has to be fulfilled since the very first time the trapezoidal is designed. And the advantages of trapezoidal are then forced to the highest limit by configuring it in such way and equip the trapezoidal with many control surfaces and aerodynamic surfaces as it requires.

Delta planform in trapezoidal configuration is highly sweep of leading-edge by 54 degrees. Configuration of the delta provides longer root than the span. Wing square formed by the configuration extends downward with aspect ratio of span to root chord 0.73. Meaning, high wings area to provide stability without losing control by reducing drag.

Since flying wing does not really have fuselage, so imaginary fuselage is the very first time to do in designing the flying wing besides longitudinal stability. Imaginary fuselage can be trapezoidal wing itself that configured in such way as lifting-body configuration. Or it can be aerodynamic surfaces such as cockpit, pods and tapered long tail.

The delta planform, main imaginary fuselage, is then configured in such way as lifting-body configuration to provide lift by its own wings. Onto the delta is then attached cockpit and other control surfaces such as group leading-edge in which configuration is product of angle 60 degrees and leading-edge. As compact design, configuration of cockpit and group leading-edge described. Imaginary root of leading-edge on the left hand will intersect with angle 60 degrees on the right hand. From the intersection line, it deflected downward to leading-edge. Straight line that intersects with vertical line will be root of group leading-edge, sweeps along the leading-edge. While cockpit width is automatically formed by downward lines on the left and right hands.

The cropped, it has more complex configurations than delta planform. On the cropped lies aerodynamic center and gravity center at once. Aerodynamic center lies on tip to tip of flaps, while gravity center lies on tip to tip of delta planform, currently equivalent with tip to tip of the cropped. Gravity center in differential twist wings is product of root of angle 22 degrees that formed by the cropped. Gravity center always lies in front of aerodynamic center. Determining position of aerodynamic and gravity center is the next parameter to define in aircraft design.

 Further, the cropped from tip to wing tip formed by angle 22 degrees. The cropped is transition form, where trailing-edge is straight. Square of the cropped 33.62 square meters. So, the cropped is such conventional straight wings with high wings loading to help to stabilize the delta planform running forward the cropped. Configuration of the cropped provide basic configuration of other elements that attached on it.

 

Tapered trailing-edge of trapezoidal is the most complex configurations where the configurations must match with the cropped. If something dismisses, then configuration of both or one of them must be changed. The very first thing to define the sweep of tapered trailing-edge is aspect ratio of span to root chord. Total number of lengths of tapered trailing-edge, the cropped and delta planform must fulfill low wings loading, then configuration can continue to next step. The sweep and the span of trapezoidal play key role in the designing process. Onto tapered trailing-edge attached engines and some other control surfaces, such as flaps and additional flaps. Onto trailing-edge is also attached directional stabilizer and tail. The very tapered of trailing-edge enable all possibilities.

 Flaps, configuration of flaps produce aerodynamic center. In trapezoidal configuration, flaps sweep along the trailing-edge of trapezoidal. Due to the trailing-edge sweeps forward, then aerodynamic center lies at tip of the flaps. Tip to tip of the flaps is where aerodynamic center located. In design, configuration of flaps can be described. Downward line of tip of group leading-edge will intersect with angle 22 degrees of the cropped. The intersection line will be tip of the flaps, sweeps along the trailing-edge. Width of the flaps determined by sweep of angle 22 degrees, or by sweep of trailing-edge, even by width of group leading-edge. As compact design, if configuration of one element is changed, other elements will (be) change(d) too. For useful explanation this statement about flaps configuration is that if sweep of angle 22 degrees decreased, then square of the cropped will follow decreased, either ability of the cropped to stabilize the delta planform. In other hand, intersection line of the angle with downward line of group leading-edge will get higher. As consequence, width of the flaps will get higher and ability of the flaps to stabilize the cropped delta planform will get higher too. And overall stabilizing surfaces will remain.

Since the flying wing is double engines, span of flaps must share its space with engines room and the tail. Then span of flap on right hand decreases to about 3.8 meters. The condition decreases ability to stabilize the trapezoidal. To solve the problem, sweep of flaps must be changed to get more and higher square of flaps. It can be done by moving root of the flaps to intersection line of wing tip to wing tip of expanded wings. Or at intersection line of imaginary trailing-edge with vertical axis.

Flying wing does not have horizontal stabilizing surfaces, ventral fins. It lacks anywhere to install ventral fins. As replacement of ventral fins, flying wing requires additional flaps installed on top of main wings. Currently the additional flaps installed running forward the main flaps. Additional flaps then configured to be able to move upright while main flaps move downright.

 Expanded wing is swept wings to provide additional stability and control for main wings. It is conventional swept wings to improve take-off and landing characteristic. Or it might be variable swept wings to reduce drag while flying in fully swept at supersonic speed.

Distance from tip to tip and wing tip to wing tip of trapezoidal provides basic configuration for expanded wing and sub-elements of the wings. As compacted design, major configuration provides basic configuration for other elements and control surfaces.

Width of the cropped, 2.606 meters to attach swept wings on the left and right hands. Leading-edge of the swept wings sweeps back by 25 degrees while the trailing-edge is imaginary tip of angle 22 degrees of the cropped.

 

Aileron on the swept wings is then formed begin at aerodynamic center sweeps along the trailing-edge of swept wings. Root of aileron is at straight line with tip of flap on the right hand. Angle 22 degrees of the cropped will intersect with imaginary line of trailing-edge of trapezoidal. Begin at wing tip to wing tip of imaginary line of the intersection line then drawing a line sweep back by 22 degrees. So, root of aileron will be at the straight line with tip of flaps. Precisely at aerodynamic center.

 

Adding tapered tail is to provide more stability and control, as well as combining with LEX instead of nose. Tapered tail at the back provides imaginary fuselage for flying wings since the flying wings do not really have fuselage. The tail appears as aerodynamic surface in which sides lean outward.

Other possible configuration of differential twist in flying wings design is to re-design the span and the sweep of differential twist wings. The span may come to trapezoidal or might come to swept wings. Another possibility configuration can come to the sweep of trapezoidal leading-edge. Reason of re-designing process is to provide desired requirements and stabilities of designing flying wings.

 There are two parameters to measure aerodynamic characteristics of main wings, the trapezoidal, that is aspect ratio of wingspan square to wings area which is equivalent to aspect ratio of span to root chord. The aspect ratio describes wings area that produces wings loading for the trapezoidal which to provide lift and stability while flying at high speed. And the second parameter is ability of trapezoidal in which the trapezoidal itself must be able to fly independently if formed into a paper plane model.

 

As a compact design, the straight line from wingtip to wingtip of expanded wing must connect and join with imaginary root chord of tapered trailing-edge of trapezoidal. Either aileron, flap, and group leading-edge, formed from running lines surround the square of the design. And many others. Compact design will be important parameter in modern aircraft design.

To this point, the flying wings can fly smoothly if formed into a paper plane model. But it is still unstable enough to implement it in real flying wings because additional longitudinal stabilizer isn’t installed yet: LEX. Installing the LEX will increase length of second imaginary fuselage of flying wings intended to provide longitudinal stability. In addition, installing LEX would be better than attaching nose at the front. More descriptions and how to install LEX can be found in my previous article.

In design, LEX is a triangle formed by two angles 60 degrees that standing side by side and meet on either side of its perpendicular. The triangle is angle 60 degrees at 1.5 cm right from zero-point at horizontal line, while the left angle is a mirror design of the right angle. The two angles will be roughly equilateral triangle in shape. That is the basic design of LEX. And as every line running and flow, imaginary root of leading-edge of trapezoidal wing will intersect with the perpendicular on the left hand, and in turn. From the intersection line, draw a backward line to the leading-edge of trapezoidal, then make straight line from tip to tip forming span of the LEX. Group leading-edge of the trapezoidal may be formed from the root of the span sweeps back along the leading-edge. And then finish the LEX by forming it into cropped delta. The LEX can be formed into cropped delta, but it will be better to form it into fixed-cropped delta by fixing the cropped into a lean outward shape. A fixed-cropped delta of LEX is better in shape and aerodynamic if combined with trapezoidal configuration.

Trapezoidal wing that can be combined with LEX is trapezoidal in which sweep of leading-edge lower than 60 degrees. If the same or higher than that, the sweep of the leading-edge will not match with LEX, since the LEX is triangle formed by two angle 60 degrees. This also can be measured by dividing square of trapezoidal to square of LEX where group leading-edge will be too narrow to install. In addition, fully swept of trapezoidal does not need LEX neither canards.

 The aspect ratio may help to analyze if the LEX match with the trapezoidal, or configuration of the trapezoidal must be changed to match the LEX. Possibility to attach LEX is highly sweep of leading-edge by 54 degrees or lower. However, LEX or LERX in trapezoidal configuration is not included in parameter of aspect ratio of span to root chord to define low wings loading because trapezoidal has three major configurations as described above.

To prove stability of the flying wing based trapezoidal, it can be formed into paper plane model for second time in which the flying wing contain of main trapezoidal wing, second expanded wing and as well as LEX. The flying wing shall fly more smoothly than previous paper plane model.

Directional stability:

Since flying wings lack anywhere to attach an efficient vertical stabilizer or fin, it became urgent to find proper placement to attach the fin directly onto the rear part without giving small moment of arm. Just like a conventional fin, the fin attached point upright onto the tail, and the fin must be all-moveable fin, wider in span, and single fin. The tapered trailing-edge sweep forward by 36 degrees enable all possibility to attach directional stabilizing surface, the fin.

 General rules applied in vertical stabilizer, the fin must be large area, and shorter root with wider span is better than longer root and narrower span. But proper placement of the fin is the main rule in flying wing design. And it is rather different in configuration since the design of vertical stabilizer point upright from aerodynamic center along the tapered tail. Therefore, the basis of modern aircraft design can help to configure the design. If aerodynamic center is the root of the fin, then vertical line is a line that mounted upward from the root perpendicular to the tapered tail. And the tapered tail itself will be the horizontal line. From the root, then draw a vertical line sweeps forward by 48 degrees till it reaches span 1.5 meters, then make vertical straight line from tip to horizontal line. Then continue making line from root to tip sweeps forward by 10 degrees. Again, make vertical straight line from tip to horizontal line forming span of the fin. The configuration results enough area of mounted upright fin 1.5 meters from the root, since the fin must have large area to provide directional stability. And for aerodynamic purposes and some other configurations, trailing-edge of the fin can be wider at the rear sweeps back by 12 degrees from its tip, and top of the fin must be tapered, not flat.

Single fin with large area attached onto the tail is a realistic and possible configuration for flying wing design since the fin is configured as required and placed at proper placement. Flying fin does not need double fins to control yaw. The fin has been designed with large area and set as all-moveable fin. So, it can provide directional stability.

Tail as expanded trailing-edge, tail design is a very tapered trailing-edge of trapezoidal sweeps forward by 80 degrees. Tail length can be up to 4.5 meters. Tapered tail length measured from root of trailing-edge to root of tail. As part of directional stability, tail has both sides lean outward sweeps by 26 degrees if measured from the back bottom. The tail is straight at bottom and curve at the top. Such tail appears an aerodynamic surface to provide directional stability and to improve parameter of golden ratio.