Trapezoidal Wings of Sukhoi Su-57 Design (should be) for 6th Generation Upgrade | Design Analysis and Configuration | Aspect Ratio Review

A trapezoidal wing is a straight-edge or sweep-edge and tapered wing planform. It may have any aspect ratio and may or may not be swept. The trapezoidal wing we’ll talk about  in this design analysis and configuration is trapezoidal in which leading-edge sweep back while trailing-edge sweep forward: a trapezoidal wing of Sukhoi Su-57 combined with LERX as well as adding tail as should be. And note that this article will be updated regularly according to the progress of my analysis, and will be equipped with more descriptions, illustrations and design analysis, as well as equations of the parameters.

These are the advantages and disadvantages of such trapezoidal wings configuration:

Advantages:

Ÿ  Better performance than delta wings at transonic speed and during transition to and from supersonic conditions.

Ÿ  Do not require upwards deflection of the trailing-edge control surfaces for pitch control and therefore do not lose lift.

Ÿ  The center of lift lies further forward and therefore the tail must not lie too far back on the fuselage.

Ÿ  Preferred for stealth aircraft.

Ÿ  Flaps can be easily used.

Disadvantages:

Ÿ  High wing loading.

Ÿ  Stall at much lower angles of attack than delta wings.

This problem is overcome using Leading Edge (Root) eXtensions (LEX or LERX) and/or canards.

The thin, highly swept wings, short-span, low-aspect-ratio of trapezoidal configuration offer some advantages for high-speed flight. It can provide low aerodynamic drag at high speeds, while maintaining high strength and stiffness. The advantages of trapezoidal wings currently implemented in Sukhoi Su-57 stealth aircraft. As we can see, the designers' talent of Sukhoi Design Bureau that make Su-57 better and more advance than the competitor. It was revolutionary trapezoidal wings design and can be upgraded to 6th generation.

Requirements of 6th generation aircraft: hypersonic speed, stability, maneuverability, stealthy, advanced trapezoidal, engine thrust without afterburner, powerful radar, etc. Trapezoidal wings combined with LERX, I'm sure, will be wings design and wings configurations of 6th generation aircraft, as well as swept forward wings.

In my analysis, Sukhoi Su-57 has lack in wing configurations, that is the sweep of leading-edge, either lack in length of fuselage. So that I’d like to re-design, if I may say, Sukhoi Su-57 stealth aircraft for 6th generation upgrade. Parameters used in re-designing process is the aspect ratio, where aspect ratio and other features of the planform often used to predict the aerodynamic efficiency of a wing because the lift-to-drag ratio increases with aspect ratio. Second is the design analysis of the wing, as the aircraft design often classified by its wing configurations. Sometimes we cannot ignore that esthetics may be included in the re-designing process of the aircraft.

In aeronautics, the aspect ratio of a wing is the ratio of its span to its mean chord. It is equal to the square of the wingspan divided by the wings area. Thus, a long, narrow wing has a high aspect ratio, whereas a short, wide wing has a low aspect ratio. While wing configuration is arrangement of lifting and related surfaces. Modern combat aircraft may be described either as cropped compound delta with (forwards or backwards) swept trailing-edge, or as sharply tapered swept wings with large leading-edge root extensions (LERX).

Chord, or root chord, as one of the parameters used in this analysis, is the imaginary straight line joining the leading-edge and trailing-edge of an airfoil. The chord length is the distance between the trailing edge and the point where the chord intersects the leading-edge. The point on the leading-edge used to define the chord may be either the surface point of minimum radius or the surface point that maximizes chord length. The chord of a wing, stabilizer and propeller determined by measuring the distance between leading and trailing-edges in the direction of the airflow.

Familiarization of terms used in this design analysis may help to continue re-designing process of the aircraft design. The terms maybe included in descriptions of the design analysis.

Sukhoi Su-57 capability if compared with previous generation of Sukhoi aircraft, Su-27, maneuverability of Su-57 is less than the previous generation. The reason is high wings loading causes high wings area of trapezoidal wings design and configuration that implemented in Su-57. It may influence stability and maneuverability of the aircraft. We intend to build a fighter aircraft not a passenger air plane. So, we need low wings loading. The wings design and configuration of Su-57 needed to re-design and make drastic measure. Loosing maneuverability is the main problem required to solve correctly. This article intended as contributions to Sukhoi Design Bureau and great affections to Russia from people of Indonesia.

Sukhoi Su-57 has been built and has shown its capability to the world. If there is something lack in it or something going on, it is our duty to analyze and give best recommendations how the aircraft design should be.

Suggested design in this analysis is highly swept of trapezoidal wings by increasing the sweep of leading-edge. And for purposes of stealthy and reducing high wings area, the sweep of leading-edge set as fully swept by 60 degrees. But the configuration will then produce very long fuselage of the aircraft which is not good for a fighter. So, highly swept by 54 degrees of leading-edge is recommended. Re-designing the swept of trapezoidal will affect all measurements and parameters, that is to improve lift-to-drag ratio, as well as design characteristic of the wings and esthetics to be better. And let’s start analyzing the trapezoidal and find the advantages of this design analysis.

Design principles of the suggested highly swept of trapezoidal wings: the line of maximum chord is swept at an angle, usually forward. This increases the sweep of leading-edge by 54 degrees, and increases the sweep of the trailing-edge by 12-15 degrees. And at the same time to re-design narrow wingspan to 14.1 meters. The transition form, where the trailing-edge is straight, equivalent to a cropped delta planform while the trailing-edge is tapered will be equivalent to trapezoidal planform. The trapezoidal is then configured into an inverted shape of a kite and tested of being able to fly independently if combined with LERX and tail. Force the trapezoidal advantages to the highest limits.

The basis of modern aircraft design can help the re-designing process of the geometric descriptions. That is by placing angle of 60 degrees at 1.7 cm right from zero-point at the horizontal line. Configuration of this angle will perform 14.1 meters of wingspan. Then begin to draw a line from root to tip sweeps back by 54 degrees to form leading-edge of the wings. Make straight line from tip to tip, the span of wing, will perform delta of the wings. Again, at the root of the span draw a line from root to tip sweeps back by 15 degrees, and make straight line from wingtip to wingtip, the wingspan, to perform cropped delta. And finally tapered trailing-edge sweeps forward by 12 degrees. The configurations result a trapezoidal wing which is like an inverted shape of a kite. So, general rule applied for the trapezoidal: longer root is better than wider span of the wings: span of wings must be balanced by the length of root chord. So, the horizontal stability has been performed since the very first time trapezoidal is designed. And that the inverted kite can fly smoothly if formed into a paper plane model. If the design principle and configuration fulfilled, the kite model does not matter to fly independently in inverted shape or either to fly in such a kite. All we have to do is then where to put aerodynamic center and gravity center of the trapezoidal wings.

Useful explanations of the trapezoidal configuration are wingspan set to narrow, 14.1 meters, to reduce wings area, since trapezoidal has additional wings area at the cropped and tapered trailing-edge of the wings. Delta shape of the trapezoidal wings is then analyzed. The sweep of leading-edge is that formed by 54 degrees, higher than those of previous generation of trapezoidal wings. While current sweep of Su-57 is 52 degrees. The highly swept by 54 degrees give proportional sweep of leading-edge for trapezoidal if measured from aerodynamic and design analysis. While sweep by 52 degrees produce high wings area and increases drag at high angle-of-attack that esthetically bad design.

Cropped delta of the trapezoidal wings swept back by 15 degrees provide enough area to help improve stability for the delta shape. Area of the cropped then calculated from 14.1 time 1.9 meters, which is equal to 26.79 square meters. Enough wings area to fly a glider. And in that area lies aerodynamic center of trapezoidal as well as control surfaces configuration may appear on it.

Tapered trailing-edge of the trapezoidal provide similar stability and configuration with cropped delta for trapezoidal wings and control surfaces. Sweep forward for trailing-edge by 12 degrees provide proportional configuration for flaps sweep along the trailing-edge. If higher than that, flaps shape will be unproportionable. While aileron will be automatically formed by the design.

More on trapezoidal design analysis, span of wing must be lower than root chord, then square of span of wing will form itself into rectangular shape, extend downwards not extend to the side. This rule is implemented in aircraft design not in air plane design, where the aircraft requires low wings loading while moving in the air at supersonic speed. Extending the rectangular downwards will increase wingspan square significantly while extending to the side may increase wings area. Sweep of leading-edge plays key role in extending the rectangular shape. And if divided span of wing by root chord, the value will be in range from 4.0 to 5.5, the value describes standard low wings loading for fighter aircraft, where sweptback wing has the lowest value followed by cropped delta and trapezoidal wing.

And for useful measurements for trapezoidal and design analysis, it is necessary to include parameters in design analysis and while in re-designing process for trapezoidal wings.

Trapezoidal wings, due to very low aspect ratio of wingspan square to wings area, the sweep of leading-edge must be as high as possible more than those of previous generation of trapezoidal wings. So that the aspect ratio will not be too low since trapezoidal wings have large number of wings area, larger than delta wings, and even sweptback wings.

The aspect ratio is directly proportional to wingspan square and inverse to wings area. It can be meant the wings area must be balanced by wingspan square. Measurement of the aspect ratio produces standard low aspect ratio for fighter aircraft which is value in range 4.0 - 5.5. If wingspan is constant since the wingspan set to narrow, 14.1 meters, then wings area decreasing. But if compared with wingspan square, the aspect ratio will be still very low as requirement of low aspect ratio for fighter aircraft.

Wingspan square of the wings measured from wingtip to wingtip times chord, distance from root of leading-edge to root of tapered trailing-edge. If divided wingspan square by wings area, the value will be higher than 5.5. Higher than requirements.

To analyze more specific the above parameter, it is necessary to correspond the wingspan square to aspect ratio of span b, divided by root chord Cr:

The aspect ratio is equivalent to previous one. This parameter is more specific to measure aspect ratio of right or left wing separately. Value of the aspect ratio will be in range 0.40-0,55 which is standard low aspect ratio of wing for fighter aircraft.

Since span of trapezoidal wings set to narrow, then square of span of the wing will follow to narrow, followed by decreasing area of the wing if compared with span of wing square. Then the aspect ratio of span to root chord is very high. 

For useful simplification of the parameter, if leading-edge of the wing sweeps back by 45 degrees, then the aspect ratio will be equal to 1. Mean that length of span will be same as tip chord and square of the wing will form itself into a cube shape. As consequence, high wings area if compared with wingspan square.

From the measurement, seems trapezoidal wings lack in length of root chord. But although the root chord increased by increasing the sweep of tapered trailing-edge, it does not help much because it will be followed by increasing area of the wing. The result is constantly very high of the aspect ratio. It must be something else goes wrong with trapezoidal configuration.

Let’s correspond to another parameter: wing area of trapezoidal, in general. If wing area of general trapezoidal wings symbolized with A, the span s, root chord Cr, and tip chord Ct, then wings area of general configuration of trapezoidal may be calculated by:

According to the calculation, if root chord increased, then mean chord increasing followed by increasing wings area, where wing area measured from span times mean chord. If divided wingspan square by wing area, then aspect ratio will be very high. From the calculation we can see that trapezoidal wings lack in length of tip chord.

Resulting a very low aspect ratio of wingspan square to wings area, caused by lack in length of chord and high wings area, caused by tapered trailing-edge, are the next problems of trapezoidal wings that required to solve correctly. There are two options to solve the problem: first option is sharply tapered sweep of trailing-edge, and the second one is highly swept of trapezoidal wings by increasing the sweep of leading-edge. The second option is better solution with many advantages as described.

Re-designing highly sweep of leading-edge will be followed by increasing tip chord of the wing, as well as the root chord will automatically change its position far back at the root equal to increasing of tip chord. The highly sweep will then followed by increasing square of wingspan significantly while wings area almost withstands with its value. As consequent, highly swept of leading-edge in trapezoidal wings affect all measurements: increasing both root and tip chord followed by increasing wingspan square significantly, withstand the value of wings area by increasing the mean chord. In other words, wingspan square increases but wings area mostly constant. So that the very low aspect ratio of wingspan square to wings area solved to be proportionally low as requirement of low aspect ratio for fighter aircraft.

In contrast, a low aspect ratio of wing allows the high pressure on the bottom of the wing to escape more easily, resulting in a larger vortex and greater drag.

The wings loading w, is then given by the lift L, divided by the area:

In aerodynamics, wing loading is the total weight of an aircraft divided by the area of its wing. The stalling speed of an aircraft in straight, level flight is partly determined by its wing loading. An aircraft with a low wing loading has a larger wing area relative to its mass, as compared to an aircraft with a high wing loading. High wings loading result a high stalling speed with marginal take-off and landing characteristics and a corresponding high level of take-off and landing accidents.

In level flight, the amount of lift is equal to the gross weight. Lift is the component of this force that is perpendicular to the oncoming flow direction. Lift is always accompanied by a drag force, which is the component of the surface force parallel to the flow direction.

The faster an aircraft flies, the more lift can be produced by each unit of wing area. Consequently, faster aircraft generally have higher wing loadings than slower aircraft. This increased wing loading also increases takeoff and landing distances. A higher wing loading also decreases maneuverability.

Wing loading is a useful measure of the stalling speed of an aircraft. Wings generate lift owing to the motion of air around the wing. Larger wings move more air, so an aircraft with a large wing area relative to its mass (i.e., low wing loading) will have a lower stalling speed. Therefore, an aircraft with lower wing loading will be able to take off and land at a lower speed (or be able to take off with a greater load). It will also be able to turn at a greater rate.

However, I realize, highly swept of the wings corresponded to take-off and landing characteristic can be observed in wind tunnel or some other observation instruments.

The wing of a fixed-wing aircraft provides the lift necessary for flight. wing geometry affects every aspect of an aircraft's flight. The wing area will usually be dictated by the desired stalling speed but the overall shape of the planform and other detail aspects may be influenced by wing layout factors. The wing can be mounted to the fuselage in high, low and middle positions. The wing design depends on many parameters such as selection of aspect ratio, taper ratio, sweepback angle, thickness ratio, section profile, washout and dihedral. The cross-sectional shape of the wing is its airfoil. The construction of the wing starts with the rib which defines the airfoil shape. Ribs can be made of wood, metal, plastic or even composite materials.

As the disadvantage of trapezoidal wings, require LERX, it is necessary to consider this overall wings area of aspect ratio in trapezoidal wings combined with LERX:

Consideration of the parameter is total number of wings area and LERX area increase significantly. Then highly sweep of leading-edge of trapezoidal wings solve the problem by balancing the wings and LERX area with overall wingspan square, measured from root of LERX to root of tapered trailing-edge of the wings, where the square increases higher than wings area, then mean chord increased by highly sweep of leading-edge which followed by increasing both root chord and tip chord. Whereas high wings loading balanced by length of the chords followed by increasing overall wingspan square. So that the aspect ratio will be constantly low. As well as high loading of the wings resulted a high stalling speed with marginal take-off and landing characteristics and a corresponding high level of take-off and landing accidents, shall be managed so well.

For purpose of stealthy, the sweep of LERX in Su-57 design is then changed same as the sweep of leading-edge, 52 degrees. Then span of LERX will be automatically longer, while tip chord and root chord decreased equivalent to decreasing sweep of the LERX. And finally shape the LERX into large fixed cropped-delta. The configurations then followed by increasing LERX area if compared with square of the LERX. I don’t think it is good idea because total number of wings area and LERX area increase significantly, another reason is width of LERX then does not fit with width of nose where width of nose increases reversely with decreasing the sweep of LERX, either not fit with length of nose and even not fit with span of wing. As consequence, group leading-edge will get wider. But in fact, group leading-edge of Su-57 is narrow. It is not compact design according to this design analysis and configuration. The true LERX design is to re-arrange the shape of equilateral triangle formed by two angle 60 degrees, not to change its sweep or to move its position since it has been placed at proper placement. However, something good I see in Su-57 design is LERX then functioned as canards. It is unique design of LERX and no such design before.

There must be another solution for purpose of stealthy in LERX design which is still under construction in this design analysis and configuration. For this moment I just can say that sweep of LERX must be higher than leading-edge, then LERX will flow the air outwards towards the tip, away from fuselage, before it splitted by leading-edge of the wings. If the sweep of LERX and leading-edge is the same, then the LERX will not work properly as desired. The LERX will be just additional wings running forward the leading-edge. And the second, note that the sweep of nose, LERX and leading-edge decreased gradually from 70 to 60 degrees and finally decreased by 54 degrees at leading-edge. It fulfilled rule of all wings must lie inside the conical shock wave generated by the fuselage nose of an aircraft that flying at supersonic conditions.

Momentary solution for LERX design in Su-57 is let it be as equilateral triangle formed by two angle 60 degrees in which sides meet at perpendicular lines, and let the advanced canards as should be. This solution is better, while analyzing new approach of diagonal sweeps surround square of delta planform on trapezoidal configuration: As the angle-of-attack increases, the leading-edge of the wing generates a vortex which energizes the flow on the upper surface of the wing, delaying flow separation, and giving the delta a very high stall angle.

Implication of the highly swept of trapezoidal wings, where both root and tip chord increased, is longer wings size at the back that will affect overall fuselage length in tail design. The highly sweep of the leading-edge is perpendicular with the length of tip chord, either perpendicular with the root chord of the wings. That case will enable to design longer fuselage at the back. Longer fuselage at the back if combined with expand length of nose, it would be a miracle design that no other designers ever thought before. Possible explanation to this statement is both aerodynamic and gravity center have been performed properly since the very first time the trapezoidal is designed. Where the aerodynamic center lies between root of tip and root of wingtip and either center of lift of trapezoidal wings will change position far forward in front of aerodynamic center. Aerodynamic center, in design, is product of flaps configuration, that is at straight line of tip of flaps. While center of lift or gravity center is product of ventral fins configuration.

As flaps can be easily used, designing flap in trailing-edge of the wings either group leading-edge, can be easily performed by following the running line in square of aircraft design. Flaps in trailing-edge can be designed begins at fuselage at the back in which intersect with line of wingspan of trapezoidal, then make line sweeps along the trailing-edge until it intersects and join with angle 20 degrees of wingspan, while aileron is automatically shaped by the design. 

As the advantages of re-designing highly swept of trapezoidal wings are low aspect ratio of wings will have a higher roll angular acceleration than one of high aspect ratio, because a high aspect ratio of wing has a higher moment of inertia to overcome. In a steady roll, the longer wing gives a higher roll moment because of the longer moment arm of the aileron. Low aspect ratio wings are used on fighter aircraft, not only for the higher roll rates, but especially for longer chord and thinner airfoils involved in supersonic flight. Capability of maneuverability shall be managed properly.

Most important advantage of designing that such highly angle of leading-edge is there will be enough space, I prefer say proper space, to design LERX as should be. Proper LERX design is at the running forward from the leading-edge of the wing, at the root of the wings to a point along the fuselage. That is at the angle of 60 degrees of The Basis of Aircraft Design as described before, where the angle can be functioned as LERX. The true LERX design is to re-arrange the shape of angle of 60 degrees, not to change its position since it has been placed in proper placement.

As we know, leading-edge root extension (LERX) is a small fillet, typically roughly triangular in shape, running forward from the leading-edge of the wing root to a point along the fuselage. LERX induces controlled airflow over the wing at high angles of attack, so delaying the stall and consequent loss of lift.

A leading-edge extension (LEX) is a small extension to an aircraft wing surface, forward of the leading-edge. The primary reason for adding the extension is to improve the airflow at high angles of attack and low airspeeds, to improve handling and delay the stall. A dog tooth can also improve airflow and reduce drag at higher speeds

Corresponding LERX with leading-edge of the wings, leading-edge root extension can be straight or curved as it is an extension of the leading-edge that has similar configurations. LERX is formed from angle 60 degrees where configuration of the angle performs span of the wing. In other hand, configuration of LERX can help to define group leading-edge. And many other configurations.

In design, LERX is two triangles standing side by side that meet on either side of its perpendicular. The triangle is angle 60 degrees at 1.7 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 bases design of LERX. And as every line running and flow, imaginary root of leading-edge of trapezoidal will intersect with the perpendicular side of the triangle on the left hand, and in turn. From the intersection line, draw a backward line to the leading-edge of the trapezoidal, then make straight line from tip to tip forming span of the LERX. 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 LERX by forming it into cropped delta. The LERX can be formed in cropped, but it will be better to form it into fixed-cropped delta by fixing the cropped into a lean outward. A fixed-cropped delta of LERX is better in shape and aerodynamic if combined with trapezoidal configuration.

As well as LERX come along with nose, running forward from the leading-edge of the wings to a point along the fuselage, nose design affected by the angle of leading-edge, the angle of 60 degrees, and LERX itself: nose placement and shape measured from the three elements. The configuration of the three elements will affect nose, and the design automatically compacted by itself. So that one element to the others are unified and inseparable. 

Nose design, the fuselage at the front, corresponded to angle of 60 degrees is quite challenged, as well as challenging in wingspan design and configuration. The challenge of nose design is how to measure length of nose and width. Length of nose shall be flip horizontal copy of equilateral triangle formed by two angles of 60 degrees, the two angles that stand side by side and meets at its perpendicular line. Copying the triangle results another equilateral triangle with two longer side, in which shorter side stands at the horizontal line, at tip of the angle 60 degrees, and the longer side stands at the root, at the vertical line I would say. Length of nose is then measured from root of the longer side of the angle. That is true measurement and configuration in length of nose.

As compacted design, width of engine room at the back of fuselage then can be defined from running line of angle 60 degrees and length of nose. Imaginary root of right angle 60 degrees will intersect with left straight horizontal line of nose at about 2.4 cm from vertical axis to the left hand. From that intersection point, then deflect the line downward to the fuselage at the back. It will be width of engine room on the left hand. And in turn. So, the total number of engine room width, fuselage at the back, will be 4.8 meters. Other configurations that can be defined by the deflected line are vertical fins and flaps.

Nose width on the left hand is where the imaginary line of the right leading-edge intersect with the left angle of 60 degrees, either nose width on the right hand. The higher the angle of leading-edge the narrower the nose width, and more space for LERX. Seems wing’s sweep and the angle of 60 degrees would like to lead talented designer(s) to design nose of the aircraft as should be.

As every line running and flow through the aircraft design square, many running forward or backward, and even horizontally, the angle line will do so. Many of the lines might intersect and cross-meet with each other at a certain point, and others deflected to other side. Talented designer(s) shall see the phenomenon as guide to design proper placement, shape, length, and width of nose in the aircraft design. Following and playing with the running lines in aircraft design is impressive analysis. This approach has been analyzed and proved in Sukhoi Su-27 design. 

The configurations result expanded length of nose, that will affect the aspect ratio of fuselage square to fuselage area:

The aspect ratio must be higher than 1. The higher the aspect ratio, better performance the aircraft. Meaning the fuselage area must be as narrow as possible. Sukhoi Su-27 design has proved the advantages of the parameter. And now Su-57 for upgrade to 6th generation turn.

As well as challenging in nose and wingspan design, tail and its elements do so. The challenging of this design is the horizontal tail fins (ventral fins): besides many parameters need much considerations, placement and shape, pointing gravity center by ventral fins is  another challenge.

Tail is all-moveable fins that often referred to as stabilizer. Aircraft stabilizer is an aerodynamic surface, typically including one or more moveable control surface, that provide longitudinal (pitch) and/or directional (yaw) stability and control. Longitudinal stability and control, the horizontal tail fins, may be obtained with other wing configurations, including canard, tandem wing and tailless aircraft. Trapezoidal wings actually do not require tail fins, but for stability and maneuverability Sukhoi Su-57 implemented tail fins to its design. Applying all possible elements to design advanced aircraft.

To design ventral fins, the horizontal stabilizer, the first thing to do is to finish flaps design. Deflected line of imaginary root of angle 60 degrees as described before will intersect with straight line of wingspan. The intersection point will be root of flaps. From that point then make line sweep along the trailing-edge of trapezoidal till it intersects with angle 20 degrees of wingspan line. Finally make straight line from tip to tip. The aerodynamic center lies on it, in front of wingspan line. While aileron will be automatically formed by the design.

Defining root of ventral fins is where aerodynamic line intersects with line of engine room width. Then designing the fins begin by drawing a line from the root to tip sweeps leading-edge of trapezoidal. And then ventral fins designed in such way to fulfil rule longer root is better than wider span of ventral fins. Then square of the fins will form itself into rectangular shape that extends downward.

Parameter used to design tail fins similar to parameter of the wing, that is aspect ratio AR, span of fins b, divided by mean chord Cr:

The parameter leads to design angle of ventral fins as if equal to wings leading-edge or higher than that. Particularly in trapezoidal wings, the angle of fins is equal to wings. In such case, the parameter leads to measure chord, longer root is better than wider span of fins. Then aspect ratio shall be below than 1. And then finish the tail fins design by drawing line of trailing-edge of the fins sweeps forward a half of tapered trailing-edge of the wings.

Ventral fins design has secret function, that is pointing center of gravity of aircraft design in general. Where imaginary root of the fins pointing the center of lift: pointed in front of aerodynamic center. It will happen only when root of fins placed at proper placement: at straight line of wingspan along with fuselage, which is same as at straight line of cropped delta of tapered trapezoidal wings. As the center of lift of trapezoidal wing lies further forward and therefore the tail must not lie too far back on the fuselage.

More specific to determine root chord of the fins is as every line running and flow through aircraft design. That is when imaginary hypotenuse line of angle of 60 degrees deflected vertically by imaginary square line of aircraft design and then intersect with line of wingspan. Following the running line determine root chord of the fins will perform the true width of room of air intakes of the engines.

Corresponding the square of wingspan and LERX to square of ventral fins, is another challenge of fins design.

 

Square of the ventral fins is not more than a quarter if compared with square of wingspan. Means that ventral fins, as stabilizer, does not need big square but proper placement and configuration. And length of root chord of the fins not more than the length of imaginary tip chord of the fins. That’s general rule of ventral fins design.

Sukhoi Su-27 and Su-57 have unique own tail design as should be. As the tail is part of ventral fins function, refers to as stabilizer, where tail length measured from imaginary tip chord of ventral fins, in which line from tip to tip of the chords intersect with root of fuselage will be the length of the tail design. Length of the tail will be length of fuselage at the back. Length of the fuselage affected by length of imaginary tip chord of the fins, which is a product of sweep of leading-edge of the wings. The higher angle of the leading-edge the longer tail at the back. That’s the reason why modern Sukhoi aircrafts have own tail as should be. Applying all possible elements to design advanced aircraft.

To this point, designing that such trapezoidal wings combined with LERX, and equipped with ventral fins, then applying in paper plane model, would be a miracle: it can fly as if it was a flying wing. The trapezoidal wings can fly even though without nose and vertical fins. That’s the advantage of this design analysis.

Lifting body configuration, a fixed-wing aircraft or spacecraft configuration in which the body itself produces lift. In contrast to a flying wing, which is a wing with minimal or no conventional fuselage, a lifting body can be thought of as a fuselage with little or no conventional wing. Whereas a 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.

Vertical stabilizer, or fin(s) of an aircraft, are typically found on the aft-end of the fuselage, and are intended to reduce side slip and provide direction stability. On aircraft, vertical stabilizer generally pointed upward. This upright mounting position has two major benefits: The drag of the stabilizer increases at speed, which creates a nose-up moment that helps to slow down the aircraft and prevent dangerous overspeed; and when the aircraft banks, the stabilizer produces lift which counters the banking moment and keeps the aircraft upright in the absence of control input. If the vertical stabilizer was mounted on the underside, it would produce a positive feedback whenever the aircraft dives or banks, which is inherently unstable. The trailing-end of the stabilizer is typically movable, and called the rudder; this allows the aircraft pilot to control yaw.

General rules of ventral fins design as mentioned above, also implemented in vertical stabilizer, or fins: the square of fins, as vertical stabilizer, is almost a half if compared with square of span of wing. Other rule are proper placement and configuration, but shorter root and wider span of the fins is better than longer root and narrower span. And it is rather different in configuration since the design of vertical stabilizer mounted upright from aerodynamic center. Therefore, the basis of aircraft design can help to configure the design of fins. If aerodynamic center is the root of the fins, then vertical line is the line that mounted upward from the root perpendicular to the fuselage. And the fuselage itself will be the horizontal line. Consider that trapezoidal while has single engine or two engines. Typically, in trapezoidal wings have two engines. In such case, root chord of vertical fins lies at straight line in front of root chord of ventral fins. From the root, then make line upward sweeps back by 42 degrees, until it reaches span of 2.1 – 2.7 cm (range 0.60) from the root to tip chord of the fin. Make vertical straight line from tip chord to root (to horizontal line). Then continue to make line from root to tip sweep back by 10 degrees. Again, make vertical straight line from tip chord to root. The configuration results a high mounted upright of fin, 2.1 – 2.7 meters from the root, since square or span of fin is almost a half of the wing.

For purposes of stealthy aircraft, span of the fins reduced to 1.5 meters (also in range 0.60 below from 2.1) from the root, and then configure the fins lean outward by 5 - 10 degrees. It depends on designer’s talent to design shape of the fins while equipped with rudder or to design fins as all-moveable vertical stabilizer without rudder. In such condition, longer root is better than wider span of fins, and square of the fin is about a quarter of the wing.

Important parameter that almost forgotten by Sukhoi and the competitor is aspect ratio of square of aircraft design to fuselage area:

The square of aircraft design is an imaginary square surrounding the aircraft design which can be generally calculated from length times width. Length is measured from root of nose to root of tail, either width measured from span of wings. The square describes minimal area required to park the aircraft and minimal diameter of wind tunnel to observe aircraft aerodynamic characteristics. Fuselage area is total area of all elements that implemented to design the aircraft, these are wingspan, LERX, fuselage, fins, ventral fins, etc.

Other analysis of the parameter is how much the empty space square is left from overall square of aircraft design. The empty space must be wider in square than fuselage area, then aspect ratio higher than 1. Meaning that fuselage area of the aircraft must be as narrow as possible. 

The empty space can be calculated by subtract square of aircraft design from fuselage area.

Explanation of this parameter is if we want to speed quickly through the air, we're better off in a long, thin vehicle - something like a plane or a train - that creates as little disturbance as possible: planes and trains are tube-shaped for exactly the same reason that we swim horizontally with our bodies laid out long and thin. Likewise, an aircraft wing is designed to be smooth to reduce drag.

Finally reaching value of the golden ratio of 1.618 of overall fuselage length divided by wingspan:

Fighter aircraft design cannot really touch the value of golden ratio. Sometimes the value reached lower or higher than that. In this design analysis, the ratio of trapezoidal higher than that, while the ratio of Sukhoi Su-57 is lower. But at least we try to reach value of the ratio by increasing the sweep of leading-edge that will produce longer wings at the back and reduce wings area.

Trapezoidal design, due to very high wings area caused by tapered trailing-edge, the value of golden ratio can not really be touched even by decreasing the sweep of leading-edge to 50 degrees. If that happed, we need to consider previous parameter: very low aspect ratio caused by high wings area of trapezoidal wings.

Useful solution to the problem is deviation, where the amount by which a single measurement differs from a fixed value such as the mean. And set the narrow wingspan till 14.1 meters with sweep of leading-edge by 54 degrees, then length of fuselage measured from root of nose to root of imaginary tip chord of ventral fins. It provides length of fuselage about 24 meters, then the ratio will be 1.702 which is higher. Benefits of the configuration are lower wings area with low wings loading, reaching the ratio rationally and lift-to-drag ratio shall be managed correctly.