Effects of Symmetric Wing Sweep Angle Variations on the Performance and Stability of Variable-Sweep Wing Aircraft

Abstract

Research on morphing aircraft that can change geometry to achieve the desired performance and stability under different flight conditions has been ongoing for many years. This study provides a conceptual-level, preliminary analysis of the impact of symmetrically changing the wing sweep angle on aircraft performance and stability. The T-37B-like aircraft is selected as a base to compare the results with T-37B’s known data. The T-37B-like aircraft is modeled in both Digital DATCOM and Open VSP software. Changes in aircraft performance and stability are demonstrated for changes in the wing sweep angle between −10° and 40°. When 0° and 40° wing sweep configurations are compared, it is observed that the 40° wing sweep configuration performs better in terms of climb and range, but worse in terms of takeoff distance, glide, approach, and radius of turn. In terms of static stability, it has a positive effect on longitudinal stability. While it does not significantly affect lateral stability overall, it contributes positively to stability around the roll axis. Changing the symmetrical wing sweep angle is expected to improve certain performance and stability parameters while degrading others. A symmetrical variable-sweep wing offers advantages by adjusting to the optimal sweep angle for each flight phase. Thus, benefits can be fully utilized, and drawbacks minimized. However, it entails design, mechanical, weight, and financial costs. Therefore, whether the performance and stability benefits outweigh these costs must be evaluated on an aircraft-specific basis.

1. Introduction

When designing an aircraft, parameters such as wing configuration, fuselage dimensions, vertical and horizontal tail, empty weight, fuel weight, maximum takeoff weight, and maximum payload are selected to fulfill the flight requirements.

All aircraft designed are expected to be suitable for all flight conditions as much as possible. However, no aircraft can be suitable for all conditions. Aircraft designs are optimized for only specific types of flight missions. For instance, passenger aircraft are designed for long-range performance, whereas fighter aircraft are designed for high-speed acceleration and maneuverability. Technological advancements in aviation have driven the pursuit of increased efficiency and performance. Hence, studies have begun to be conducted on morphing technology that can provide optimal performance under various flight conditions [1].

Adapting to different flight conditions requires large-scale modifications to the aircraft. In this case, morphing technologies first begin with the modification of the aircraft’s external shapes. To adapt to a changing mission, changes in the wing area, wing span, wing aspect ratio (AR), and wing sweep angle are targeted. For instance, an aircraft that flies effectively at low speeds is expected to have a low-sweep wing and a high wing aspect ratio. On the contrary, an aircraft that flies effectively at high speeds is expected to have a high-sweep wing and a low wing aspect ratio. Therefore, considerable shape modifications on the aircraft are required to fulfill both opposite conditions [2].

Studies usually focus on backward, i.e., positive changes in the wing sweep angle. However, forward, i.e., negative changes in the sweep angle also have positive effects. Aircraft can operate effectively at high angles of attack due to the forward sweep angle change. Aircraft with a backward sweep angle change stall under this flight condition. Since the stall begins at the wing tips, the ailerons lose control. Due to a forward sweep angle change, the stall occurs first at the wing root, and the ailerons maintain their full effectiveness. The X-29 aircraft, designed by the Grumman company, is the most prominent example of this condition [3].

Aircraft can obtain higher L/D ratios due to varying sweep angles. Thus, they can perform stably at low speeds, take off from much shorter runways by achieving lower stall speeds, and have lower approach speeds. Additionally, as a result of changing sweep angles, higher range values can be achieved by reducing the drag force on the aircraft, particularly at high speeds, and improved maneuverability can be obtained by increasing acceleration values. Such studies can focus not only on changing the aircraft sweep angle, but also on increasing the aircraft wing length, modifying the wing profile, and changing the wing geometry using flexible materials.

In 2002, Bowman, Sanders, and Weisshaar [4] evaluated the effects of changeable aircraft geometry on aircraft performance and investigated the benefits that could be obtained by changing the geometry of aircraft with large wing structures. The study was inspired by eagles’ ability to change their wing structures under different flight conditions. The change in the aircraft’s drag force, its effects on the turning radius, the change in the L/D ratio, fuel consumption, and cruise flight were examined, and the impact of the sweep angle change on the mentioned issues was evaluated by creating a sample mission profile. The drag polar equation changed with the change in sweep angle, and a fuel consumption benefit was provided due to the change in wing area, L/D change, and decreased drag force.

In 2017, Lipton, Wood, and Kuindersma [3] developed a forward (negative) sweep wing design for small aircraft in Massachusetts to investigate the controllability and performance of forward (negative) sweep change in high AoA maneuvers. The aerodynamic effects of forward sweep angle change in the AoA range between −25° and 75° were obtained using a wind tunnel. Non-linear dynamic modeling was performed using the obtained data. It was demonstrated that the change in the forward wing sweep angle of the aircraft altered the pre-stall lift characteristics, the moment on the pitch axis, and the longitudinal stability characteristics. The forward wing sweep angle change in the simulated high AoA maneuvers performed better than a straight wing.

Neal, Good, Johnston, Robertshaw, Mason, and Iman (2004) [5] designed a UAV whose wing sweep angle could be changed between 0° and 40° and whose wing length could be increased by 44%. Due to the configuration change, the drag force was reduced, the lift force was increased, and the minimum drag force could be obtained. It was also shown that changing the wing sweep angle and length was beneficial.

Ma, Ge, Song, and Pei [6] conducted the stability and trim analyses of a multi-selective variable-sweep-angle UAV in 2021. Different sweep angles yielded the best results for longitudinal and lateral dynamic stability.

Numerous similar studies have investigated the effects of changing the aircraft’s geometry on its performance and stability. A review of scientific studies, the aircraft produced in the past, and future research shows that changing the aircraft’s geometry has quite a significant effect on its performance. Studies on the subject are ongoing to achieve the best performance in multiple missions with an aircraft.

Although numerous aircraft are designed and manufactured, there are few for which design parameters, aerodynamic and stability coefficients, and information on weight, mass inertia, and engine performance are shared. Furthermore, since the purpose of this study is to calculate the effects of sweep angle changes, the selected aircraft should have a flat wing structure. Information on weight and mass inertia, stability coefficients, and engine performance is needed. After examining the aircraft for which the relevant information is shared, it is decided that it would be appropriate to take the T-37B training aircraft as a basis for the present study. Analyses are conducted on a model we create using technical drawings and data from the literature for the T-37B training aircraft, which we refer to as the T-37B-like aircraft. The current study conducts a conceptual-level, preliminary analysis of the impact of symmetrically changing the wing sweep angle on aircraft performance and stability.

Performance and stability calculations are also repeated for changes in the wing sweep angle between −10° and 40°. For the T-37B-like aircraft, the effects of symmetric changes in the wing sweep angle on both performance and stability are addressed.

2. Materials and Methods

The current study aims to conduct a performance and stability analysis of fixed-wing aircraft with variable-sweep wings. Instead of designing an aircraft from scratch, an existing aircraft is selected as the base. The aim here is not to reach the exact design of the existing T-37B aircraft, manufactured by Cessna Aircraft Company, Wichita, KS, USA, but to obtain a base design that yields results close to its known data.Therefore, we will refer to our design as a T-37B-like aircraft.

First, we will compare the data from the T-37B aircraft in open sources with the data from our T-37B-like aircraft. We expect the two aircraft, which are not identical but share the same outline, to have similar characteristics. In this way, we will verify the analyses for the T-37B-like aircraft.

Information on the T-37B aircraft, which we target in terms of design, is presented. The T-37B was designed by the Cessna company as a two-person twin-jet training aircraft. The first XT-37 and T-37A models used the J69-T-9 engine. The higher-performance J-69-T-25 engine was used in the later T-37B and T-37C aircraft.

Table 1. T-37B design specifications.

Design Specifications	Value
Length	29.3 ft
Height	9.2 ft
Wing Length	33 ft
Wing Width	5.47 ft
Empty Weight	4056 lb
Wing Area	201 ft2
Max. Takeoff Weight	6574 lb
Engine	2 × Continental J69-T-25
CG Position	27% MAC
Ixx	7985 slugft2
Iyy	3326 slugft2
Izz	11,183 slugft2
Engine Thrust	1025 lbf
Max. Speed	369 kts (0.65 Mach)
Wing Type Root	NACA 2418
Wing Type Tip	NACA 2412

lists the parameters used in the T-37B aircraft’s design [7,8].

Figure 1 shows the side and top views used for the aircraft design.

Afterward, we use the T-37B-like aircraft as a base and analyze the effects of different sweep angles on aircraft performance. We use digital DATCOM (USAF, March 1976 version) and Open VSP software (version 3.27.1) to obtain the aircraft’s aerodynamic and stability derivatives. It should be noted that the present analysis relies on Digital DATCOM and OpenVSP, which are widely used in conceptual design studies but have inherent limitations. Digital DATCOM is based on empirical and semi-empirical methods, and therefore its accuracy decreases outside the subsonic–transonic regime and for non-conventional configurations. Likewise, OpenVSP employs vortex lattice and panel methods under the rigid-body assumption, which restricts its capability to capture non-linear aerodynamic effects such as stall, flow separation, and aeroelastic deformations. Additionally, both tools assume fixed mass properties and do not account for control surface effectiveness variations. Several previous studies have demonstrated their ability to provide reliable aerodynamic estimations, particularly for conventional aircraft geometries [9,10,11,12,13]. Since the sweep angle variation investigated in our work falls into this category of conventional configurations, these tools are considered appropriate for the scope of the current research. No cross-validation with high-fidelity CFD or wind-tunnel experiments has been performed at this stage, as the primary aim of this work is to conduct a conceptual-level investigation to demonstrate general aerodynamic and stability trends due to symmetric sweep angle variations. Consequently, the results presented here should be interpreted as indicative tendencies rather than precise quantitative predictions.

2.1. Digital DATCOM

DATCOM software (USAF, March 1976 version) estimates aerodynamic coefficients, stability, and control coefficients for fixed-wing aircraft. Although initially developed for use by the US Air Force, it has been frequently utilized for academic purposes. By modeling aircraft geometry and flight conditions, aerodynamic and stability coefficients, as well as drag polar equations, can be obtained. Furthermore, trim analysis can be performed under different flight conditions by allowing elevator changes using the trim module [14].

AID (Aircraft Intuitive Design) is integrated into MATLAB 2016a version, and the DATCOM connection is provided. Using the program, a 3D model of the aircraft is created first. The CG position is determined, and aircraft inertia and weight information are defined (Figure 2).

It is assumed that there is a mechanism in the design for wing sweep angle change, and that the wing sweep angle changes starting from 10 ft behind the wing tip. The change in CG is ignored. The wing root section is modeled as NACA 2418, and the tip section as NACA 2412. It is assumed that a NACA 0012 airfoil is used in the horizontal stability wings.

Figure 3 displays changes in aircraft geometry with the change in the wing sweep angle.

Table 2. Geometric effect of wing sweep angle variation.

Change in Sweep Angle	Wing Span	NP (Neutral Point)
−10°	32.88 ft	34% MAC
−5°	32.97 ft	37% MAC
0°	33 ft	39% MAC
10°	32.88 ft	38% MAC
20°	32.54 ft	37% MAC
40°	31.24 ft	40% MAC

contains wing sweep angle change, wing span, and neutral point location.

2.2. Open VSP

OPEN VSP (Open Vehicle Sketch Pad) is an open source parametric aircraft design program developed by NASA, which performs 3D modeling of aircraft. It designs and analyzes aircraft quickly with the help of computers. In addition to the direct input of CAD files, it also enables MATLAB version R2022b and Python (3.10.13) connections [15].

The present study designs and analyzes the T-37B-like aircraft using the OPEN VSP program version 3.27.1 (Figure 4). The aircraft geometry and assumptions used in DATCOM are utilized exactly in the OPEN VSP program. The program performs analyses using the vortex lattice and panel methods. OPEN VSP uses the Carlos pressure correlation method for the stall model solution [16,17].

3. Performance Calculations and Analyses

The mission profile of our T-37B-like aircraft design is determined first, and the aerodynamic coefficients for the flight conditions in

Table 3. Flight conditions.

Flight Phase	Altitude	Speed
Takeoff	0 ft	90 kts
Climb	5000–15,000 ft	280 kts (2000 ft/s)
Cruise Flight	39,000 ft	0.65 Mach
Descent	39,000–24,000 ft	0.65 Mach
Glide	24,000–10,000 ft	-
Approach	5000 ft	95 kts

are calculated. The programs DATCOM and OPEN VSP are used for calculations and analyses, and the calculations are compared in both programs. The results are compared with the T-37B data in the literature [7,18]. It is concluded that the results are satisfactory for both programs.

3.1. Takeoff Performance

Table 4. Data on takeoff performance.

Speed	Distance	MTOW	Stall Speed
90 kts	650 m (2130 ft)	2890 kg (6570 lb)	75 kts

contains data available in open sources on the takeoff performance of the T-37 aircraft [19,20].

The J69-T-25 engine, manufactured by Teledyne CAE, Toledo, OH, USA, is used in the T-37B aircraft.

Table 5. Specifications of the J69-T-25 engine.

Engine Model	Type	Max. Thrust	Max. SFC	Weight
J69-T-9	Turbojet	1050 lb	1.14	364 lb

lists data on the J69-T-25 engine [7,21].

The corrected properties graphs [7] are used to determine the gross thrust, TSFC, and mass airflow for any atmospheric condition and throttle setting. According to the calculations, the J69-T-25 engine produces 1.461 lb of thrust during takeoff. To calculate the takeoff performance, the stall speed must be determined using Equation (1):

$$V_{Stall}=\sqrt{{\displaystyle \frac{2W}{\rho S{C}_{Lmax}}}}$$

(1)

It is assumed that there is no wind during takeoff, with takeoff calculations based on standard gravity (1 g).

The variation in $C_L$ with respect to AoA is obtained using OPEN VSP and DATCOM (Figure 5). The $C_{L_{max}}$ value is taken from the graph. The takeoff weight is assumed to be 6300 lb, and the runway altitude is assumed to be at sea level.

The stall speed is calculated to be 80.2 kts. This value is quite close to the stall speed in the open sources specified in Table 4.

When comparing Open VSP and DATCOM decoders, a 12% difference in the maximum CL value was calculated.

Since there is no information, such as wind conditions and altitude at which the stall speed is determined, the calculated stall speed (80.2 kts) is considered acceptable. Details of the average acceleration method used in the present section to calculate the takeoff distance can be found in Ref. [7].

According to this method, the takeoff distance $S_G$ is calculated by finding the average acceleration $a_{avg}$ (Equations (2) and (3)):

$$S_G={\displaystyle \frac{1}{a_{avg}}} {\displaystyle \frac{V_G^2}{2}}$$

(2)

$$a_{avg}={\displaystyle \frac{g}{W}}[T-D_{avg}-{\mu }_r\left(W-L_{avg}\right)]$$

(3)

At sea level, the J69-T-25 engine in the T-37B aircraft produces a maximum thrust of 975 lb. Since there are two J69-T-25 engines on the aircraft, a total of 1950 lb of thrust is produced. Using the program DATCOM, the aircraft’s polar equation is obtained as $C_D$ = 0.025 + 0.054 ${C_L}^2$. The takeoff distance $S_G$ is calculated to be 2007 ft following the steps of the average acceleration method. Compared to the information on takeoff performance in Table 4, a difference of 5.87% is found, which is considered acceptable.

In Figure 6, $C_L$-AoA graphs are created separately for different sweep angle configurations.

The maximum CL values obtained from DATCOM and OpenVSP solvers were compared for different wing sweep angles, and differences of about 10–14% were observed.

Take-off distances for each configuration are calculated using the average acceleration method and shown in Figure 7.

According to the takeoff performance calculations for the T-37B aircraft, the negative sweep angle change does not affect the takeoff performance. Furthermore, the positive sweep angle change does not significantly increase the takeoff distance, whereas the 40° sweep angle change does. It is concluded that the takeoff performance of the flight with the 0° sweep angle change is quite effective.

3.2. Climb Performance

Table 6. Climb performance data.

Altitude	Speed	Rate of Climb
0–5000 ft	120 kts	55 ft/s
5000–15,000 ft	280 kts	33.3 ft/s
15,000–24,000 ft	280 kts	33.3 ft/s
24,000–39,000 ft	0.6 Mach	16.6 ft/s

presents data on the climb performance of the T-37B aircraft [19].

The flight conditions between 5000 ft and 24,000 ft in Table 6 are used in the takeoff performance calculations.

Table 7. RPM variation by flight phase.

Flight Phase	RPM
Idle	38%
Level Flight	80%
Climb	90%
Takeoff	100%

contains the RPM percentage values of the J69-T-25 engine during various phases, including idle, level flight, climb, and takeoff [22,23].

The thrust of the J69-T-25 engine is 975 lb in Table 5. Considering that the T-37B aircraft is equipped with two J69-T-25 engines, the total maximum thrust is evaluated as 1950 lb. Since the resulting difference is 2.6%, it is considered negligible, and the model’s accuracy is validated. Figure 8 shows the visual representation of the resulting drag force. The blue lines represent induced drag, the red line represents parasitic drag, and the orange line represents total drag. The green asterisk shows the maximum drag value at the aircraft’s maximum speed.

The variation in thrust with altitude is experimentally expressed in Equation (4). Here, the value x is assumed to be 0.7, unless otherwise stated [17]:

$${\displaystyle \frac{T}{T^{\ast }}}={\left({\displaystyle \frac{\rho }{{\rho }^{\ast }}}\right)}^x$$

(4)

If the aircraft’s RPM value during climb is 90%, the aircraft produces 1540 lb of thrust during the climb.

Equation (5) is used to calculate the drag force [7]:

$$D=T_R=\left[{\displaystyle \frac{1}{2}} C_{D_0} \rho S\right]V^2+\left[{\displaystyle \frac{2K{\left(nW\right)}^2}{\rho S}}\right]V^2$$

(5)

where $T_R$ is the required thrust, $C_{D_0}$ is the zero-lift drag coefficient, $\rho$ is the air density, S is the wing reference area, V is the flight velocity, K is the induced drag factor, n is the load factor, and W is the aircraft weight.

Rate of Climb (ROC) (Equation (6)) is calculated using Equations (4) and (5).

$$Rate of Climb (ROC)=V\left({\displaystyle \frac{T-D}{W}}\right)$$

(6)

Table 6 shows the aircraft’s rates of climb. To verify the accuracy of the calculation, the rates of climb are calculated separately for the altitudes of 5000, 15,000, and 25,000 ft using Equation (6).

Upon evaluating the results at three altitudes, a high rate of climb is obtained at a low altitude, and the rate of climb decreases with increasing altitude. Figure 9 displays the results. Since the value closest to those in Table 6 is obtained at an altitude of 5000 ft, the calculation is made at an altitude of 5000 ft while assessing the impact of a change in sweep angle on the climb. Figure 10 shows the change in the rates of climb according to configurations with changing sweep angles.

The rate of climb varies with the difference between constant engine thrust and aircraft drag force. Accordingly, it is assumed that the aircraft engine thrust is constant, and the drag force decreases with the increasing wing sweep angle of the T-37B aircraft. In this decrease criterion, the aircraft’s rate of climb increases with the increasing wing sweep angle. The aircraft’s drag polar equation and aerodynamic coefficients are calculated using the program DATCOM.

3.3. Range Performance

Table 8. Cruise flight performance data.

Altitude	Speed	Range
39,000 ft	0.65 Mach	800 Nm

contains information from open sources on the cruise flight performance of the T-37B aircraft [19,20].

First, calculations are made for the configuration with a 0° sweep angle, and the results obtained are compared with the values in Table 8, accepted as a reference. Afterward, the results are repeated for the configurations with −10°, −5°, 0°, 10°, 20°, and 40° sweep angles.

To obtain the maximum range, the throttle lever adjustment should provide a minimum fuel flow without the aircraft losing altitude. Range calculation is one of the most important criteria in an aircraft’s design. The range capacity of aircraft has changed considerably over the years. The main reason for the said changes is that developing technology advances engine technologies that consume less fuel and ensure more thrust. When performing range calculations, it is first assumed that the thrust produced by the aircraft is equal to the thrust required for the aircraft, i.e., the drag force [7].

Range calculations differ in supersonic and subsonic cases. Since the cruise speed of the T-37B aircraft is 0.65, it is evaluated in the subsonic case. Range calculations are performed for a constant altitude and constant speed. This equation is also defined as the Breguet range equation (Equation (7)):

$$R=\sqrt{{\displaystyle \frac{2W}{\rho S}}}\left({\displaystyle \frac{2}{TSFC}}\right) \left({\displaystyle \frac{{C_L}^{\frac{1}{2}}}{C_D}}\right)\left(\sqrt{W_0}- \sqrt{W_1}\right)$$

(7)

Furthermore, it is shown that the range expression is realized when the value of ${\displaystyle \raisebox{1ex}{${C_L}^{\frac{1}{2}}$}\!\left/ \!\raisebox{-1ex}{$C_D$}\right.}$ is maximum, which is provided under the condition $C_{D_0}=3{{KC}_L}^2$ [7].

The maximum takeoff weight of the T-37B aircraft is 6574 lb, and its empty weight is 4056 lb [3]. Considering that a particular amount of fuel is consumed during the taxiing time from engine start to takeoff of the aircraft, the aircraft’s weight is accepted as 6300 lb for the takeoff and stall speed calculations. Considering that the aircraft is a two-person training aircraft, the total mass of the two pilots and equipment weight are accepted as 200 kg, i.e., 440 lb. If the remaining weight difference is evaluated as the aircraft fuel, the total fuel weight of the T-37B aircraft is accepted as 2078 lb.

The model of our T-37B-like aircraft is established using DATCOM. Elevator trim calculations for each flight condition are performed using the program DATCOM.

The trim analysis obtains an elevator trim value of −1.37° for the configuration with a 0° sweep angle. The drag polar equation is obtained as $C_D=0.024+0.054{C_L}^2$ according to the specified flight conditions.

A range value of 765 Nm is obtained for the configuration with a 0° sweep angle. When compared to the 800 Nm range value in Table 8, a difference of 4.37% is calculated, which is acceptable.

The sequence of procedures mentioned above are repeated for configurations with −10°, −5°, 10°, 20°, and 40° sweep angles, as for the configuration with a 0° sweep angle.

Trim analysis is conducted to calculate the cruising range at a constant altitude in each sweep angle case (Figure 11), and the polar equation is obtained (

Table 9. Drag Polar Equations Corresponding to Various Wing Sweep Configurations.

Change in Sweep Angle	Drag Polar
−10°	$C_D=0.024+0.054{C_L}^2$
−5°	$C_D=0.024+0.054{C_L}^2$
0°	$C_D=0.024+0.054{C_L}^2$
10°	$C_D=0.024+0.054{C_L}^2$
20°	$C_D=0.024+0.056{C_L}^2$
40°	$C_D=0.024+0.061{C_L}^2$

).

Drag force does not change considerably for configurations with −10°, −5°, 0°, 10°, and 20° sweep angles. Figure 12 displays the results. In this case, a change in thrust value can be ignored.

Since the thrust value does not change significantly, it is assumed that there is no change in RPM and TSFC values. Figure 13 and Figure 14 show RPM and TSFC change for configurations with different sweep angles, respectively.

Figure 15 presents changing range values.

The most significant factors in the range change in cruise flight can be evaluated as the amount of fuel to be spent on the aircraft and the drag force on the aircraft in the specified flight condition. Drag force on the aircraft does not change significantly in cases other than the configuration with a 40° sweep angle. Therefore, thrust, RPM, and TSFC do not change. The resulting changes are ignored, since they are very small. A decrease in drag force is calculated in the configuration with a 40° sweep angle. Accordingly, an increase in range is calculated, but it is evaluated as not very large. One of the main reasons for this is that the polar equation that corresponds to the 40° sweep angle in Table 9 differs from the other equations.

3.4. Descent and Glide Performance

This section examines the descent and glide performance of the aircraft, focusing on its aerodynamic efficiency and stability characteristics during unpowered flight conditions. The analysis provides insight into how wing sweep variations influence glide capability and overall flight performance.

Table 10. Information on descent performance.

Altitude	Speed	Rate of Descent
39,000–24,000 ft	0.65 Mach	83.3 ft/s
24,000–10,000 ft	300 kts	83.3 ft/s

contains information on the descent performance of the T-37B aircraft [19].

Maximum endurance and longest glide distance calculations are made for glide performance. After the longest glide distance for the configuration with a 0° sweep angle is calculated, calculations are repeated for configurations with −10°, −5°, 10°, 20°, and 40° sweep angles. The effects of sweep angle change on glide performance are evaluated.

Glide performance is the condition in which the aircraft does not produce thrust. Figure 16 displays the relationship between altitude, glide angle, and glide distance during glide. Equation (8) expresses this connection.

$$R=H\left({\displaystyle \frac{L}{D}}\right)$$

(8)

The initial altitude is considered the most significant factor that impacts the glide distance. Whereas the maximum range is obtained with the condition $C_{D_0}=K{C_L}^2$, the maximum endurance is obtained with the condition ${3C}_{D_0}=K{C_L}^2$ [7].

Considering that the flight will start at 39,000 ft and end at 24,000 ft for the glide performance in line with the above-mentioned flight conditions, the glide altitude difference is calculated to be 15,000 ft. Drag polar equations are recalculated for each configuration with a different sweep angle. The maximum range calculation is made using the information obtained from the calculations and presented in Figure 17.

There is no difference in range for configurations with −10°, −5°, 0°, and 10° sweep angles. However, the range decreases in configurations with 20° and 40° sweep angles. Engine thrust in descent performance is the most evident difference between descent and glide performances. It is assumed that there is no acceleration during the flight for descent performance.

First, calculations are made for the configuration with a 0° sweep angle. Upon evaluating the information in Table 10, it is assumed that the aircraft descends from 24,000 ft to 10,000 ft at 300 kts. In this case, the drag force on the aircraft is calculated separately for 24,000 ft and 10,000 ft. The drag force on the aircraft is 646 lb for 24,000 ft and 971 lb for 10,000 ft. While performing the calculations, these two values are averaged, and the drag force is calculated to be 808 lb.

It is assumed that the engine throttle lever of the T-37B aircraft is set at 38% RPM during descent (Table 7). The thrust force corresponding to a 38% RPM value is calculated to be 90 lb. Since there are two engines on the aircraft, a total thrust of 180 lb will be obtained. In this case, when the impact of the density change depending on the air altitude on the engine thrust is calculated, the total thrust is computed to be 105 lb.

The angle of descent is calculated to be 8.8° using Equation (9):

$$sin\left(\gamma \right)={\displaystyle \frac{D-T}{W}}$$

(9)

Using this value, the descent speed is calculated to be 77.42 ft/s by switching from the aircraft speed to the vertical descent speed. In Table 10, the descent speed is 83.3 ft/s, and there is a difference of 7% between them. Considering that the calculated difference is negligible, the calculations are repeated for configurations with −10°, −5°, 10°, 20°, and 40° sweep angles (Figure 18).

The calculations show that drag force decreases depending on the aircraft sweep angle change. It is assumed that there is no acceleration on the aircraft. In this case, since the throttle lever setting on the aircraft does not change, the thrust force does not change either. Therefore, since the drag force decreases, it is quite normal for the aircraft descent speed to decrease. However, if there were acceleration during descent on the aircraft, or if the aircraft were moving with a negative pitch angle (nose down), the calculated results could differ.

3.5. Approach Performance

The review of the literature on the aircraft’s approach performance shows that it approaches at 95 kts [19]. It is assumed that it approaches a runway at sea level and there is no wind. The aircraft weight is assumed to be approximately 4500 Ilb. The approach speed is basically accepted to be 1.3V_Stall [24]. In this case, the stall speed and the final approach speed are obtained for the configuration with a 0° sweep angle.

The stall speed is calculated using Equation (10):

$$V_{Stall}=\sqrt{{\displaystyle \frac{2W}{\rho S{C}_{Lmax}}}}$$

(10)

Figure 19 shows the $C_{L_{max}}$ change depending on the sweep angle change, while Figure 20 displays the change in approach speeds.

The approach speed of our T-37B-like aircraft is calculated to be 89 kts for a 0° sweep angle. The literature reports that the approach speed of the T-37B aircraft is 95 kts. Hence, there is a 6% difference between the two values. It is thought that the main reason for this difference is the aircraft configuration and weight. As mentioned above, the aircraft weight is accepted to be 4500 lb. Considering that the aircraft’s empty weight is 4056 lb, it can be thought that approximately 100 lb of fuel remains on the aircraft in this configuration. The resulting 6% difference is acceptable, and the change in the aircraft wing sweep angle adversely impacts the approach speed.

3.6. Maneuver Performance

In the literature, no information could be obtained on the V-n diagram, n_max value, radius of turn, and rate of turn of the T-37B aircraft. Therefore, only the calculations made for configurations with different sweep angles are compared among themselves. Since the maneuver performance will change according to the aircraft weight, calculations are made for different weights.

The equations utilized for the constant-altitude turn maneuver are given below (Equations (11)–(17)) [25,26]:

$$W=L\mathrm{c}\mathrm{o}\mathrm{s}\left(\Phi \right)$$

(11)

$$m\left({\displaystyle \frac{V^2}{r}}\right)=L\mathrm{s}\mathrm{i}\mathrm{n}(\Phi )$$

(12)

$$\cos \left(\Phi \right)={\displaystyle \frac{W}{L}}$$

(13)

$$n={\displaystyle \frac{W}{L}}$$

(14)

$$\Phi =arccos\left({\displaystyle \frac{1}{n}}\right)$$

(15)

$$R={\displaystyle \frac{V^2}{g\sqrt{n^2-1}}}$$

(16)

$$\omega ={\displaystyle \frac{g\sqrt{n^2-1}}{V}}$$

(17)

where W is the aircraft weight, L is the lift force, Φ is the bank angle, m is the aircraft mass, V is the flight velocity, R is the turn radius, g is the gravitational acceleration, n is the load factor, and ω is the turn rate.

In this case, when Equations (16) and (17) are evaluated, it is seen that values R_min and $\omega$_max depend on values V and n. This can be explained by the situation where the highest load factor is at the lowest speed. Equation (18) presents the value n_max using the relevant equations [25,26]:

$$n_{max}={\left\{{\displaystyle \frac{\frac{1}{2}\rho V^2}{K\left(W/S\right)}}\left[{\left({\displaystyle \frac{T}{W}}\right)}_{max}-{\displaystyle \frac{1}{2}}\rho V^2{\displaystyle \frac{C_{D_0}}{W/S}}\right]\right\}}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}$$

(18)

Values of n_max are calculated according to the weight change of the T-37B aircraft and given in Figure 21.

The highest load factor value of our T-37B-like aircraft is 6.0 g (Figure 21). As seen in Figure 21, the aircraft configuration with a weight of 4500 lb is evaluated as the configuration closest to this condition. Therefore, the aircraft weight will be taken as 4500 lb in the ongoing calculations. Figure 22 shows values of n_max corresponding to the speed values depending on the change in the aircraft sweep angles.

As seen in Figure 2, a difference in the value n_max is observed only at a 40° sweep angle change. The value n_max is at a speed of 275 kts in all sweep angle changes.

Figure 23 presents the value n_max to be obtained according to the change in sweep angles at a speed of 275 kts.

To obtain values R_min and $\omega$_max, calculations are performed with the acceleration values to be obtained for different speeds using Equations (16) and (17) and presented in Figure 24 and Figure 25.

Upon evaluating the calculations from Figure 24, the lowest radius of turn is obtained at a speed of 80 kts. However, since 80 kts would be very close to the stall speed of the T-37B aircraft, a speed of 100 kts is selected to show the impact of changing sweep angles on the radius of turn. Figure 26 shows the change in the turning speed depending on the speed value.

Considering the results from Figure 25, the highest turning speed value is obtained at 100 kts. Figure 27 displays the change graph of the highest turning speed (at 100 kts) depending on the sweep angle.

3.7. V-n Diagram

The maximum load value provides detailed information on the aircraft’s structural limits and maneuver performance. Unwanted structural deformations occur on the aircraft if this limit is exceeded during the maneuvers performed in the course of the flight. To prevent this, V-n diagrams are drawn when designing all aircraft and included in the aircraft technical documents.

The impact of sweep angle change is attempted to be determined by drawing V-n diagrams for the configurations of the T-37B-like aircraft with changing sweep angles. The literature reports that the structural limit of the T-37B aircraft is 6.67 g. Therefore, the highest load factor ($n_{max}$) in Equation (19) is accepted to be 6.67 g [27].

The first curve of the V-n diagram is calculated as the stall curve and is cut by the value in Equation (19). The curve’s right corner is limited by the highest dynamic pressure.

Table 11. C_Lmax change according to sweep angle change.

Sweep Angle (°)	CLmax
−10	1.397
−5	1.406
0	1.408
10	1.391
20	1.369
40	1.132

contains $C_{L_{max}}$ changes according to changing sweep angles.

$$V^{\ast }=\sqrt{{\displaystyle \frac{n_{max}}{\rho C_{Lmax}}}{\displaystyle \frac{W}{S}}}$$

(19)

V-n diagrams are drawn for configurations with changing sweep angles in Figure 28.

For the T-37B aircraft, the structural load limits depend on speed and sweep angle. As the sweep angle increases, a given g-force can be maintained at higher speeds, and the maximum achievable g-force also occurs at a higher speed.

4. Stability Calculations and Analysis

The present section examines the change in stability characteristics for the T-37B-like aircraft’s configurations with changing sweep angles. Stability calculations are examined under two headings: static and dynamic.

4.1. Static Stability

The moment values acting on the aircraft must be 0 when evaluating the aircraft’s static stability. This condition can also be called the trim condition. Equations (20) and (21) express the aerodynamic pitching moment $M_A$ on the aircraft as follows:

$$M_A=C_m\left(qSc\right)$$

(20)

$$C_m=C_{m0}+C_{m_a}\alpha +C_{m_{\delta e}}{\delta }_e+C_{m_{ih}}{i}_h$$

(21)

As seen in Equation (21), moment $C_m$ can be explained by the changes in $\alpha$ (AoA), δ_e (elevator control surface change), and i_h (the angle of the horizontal stabilizer with the x-body axis). Here, value AoA, providing the C_m = 0 equality, can be defined as the aircraft’s trim point.

The most important factor for providing longitudinal positive stability requirement must be $C_{m_a}<0$. $C_{m_a}$ can be called the stability derivative, while $C_{m_{\delta e}}$ can be called the basic control derivative [7].

First, the longitudinal stability status of the T-37B-like aircraft for the configuration with a 0° sweep angle is examined (Figure 29).

For an aircraft of this type, the wing generally constitutes about 15% of the total empty weight [28,29]. Within the wing itself, approximately 70–80% of the structural weight is concentrated in the inner sections near the root [29]. In this study, sweep angle variation is applied only to part of the wing, meaning that the shift affects only a small fraction of the total aircraft weight. Consequently, while about 95% of the mass remains unchanged, only ~5% of the weight shifts slightly rearward, making the CG displacement negligible for the scope of this preliminary analysis.

The DATCOM program is used to examine the aircraft’s stability derivative. It is assumed that the T-37B-like aircraft has a weight of 6360 lb, CG is 27%, that the sweep angle change does not change the CG position, that the aircraft is in cruise flight at a speed of 0.459 Mach at an altitude of 30,000 ft, and that there is no wind.

When C_m change depending on AoA change is examined in the configuration with a 0° sweep angle, it is calculated that $C_{m_a}$ < 0 in both program results. Since the T-37B-like aircraft is designed as a training aircraft, the results are satisfactory, as expected. The longitudinal static stability of the T-37B-like aircraft is examined in the analyses conducted using the DATCOM program for configurations with different sweep angles (Figure 30).

Figure 30 shows that value $C_{m_a}$ increases negatively with the increasing sweep angle, and the aircraft becomes more stable. The negative increase in the sweep angle value makes the aircraft more unstable. In this case, it can be concluded that the positive increase in the sweep angle value positively affects the aircraft’s longitudinal stability.

A slope difference of about 5% was observed in the $C_m$–AoA curves between DATCOM and OpenVSP.

Considering lateral static stability, the moments acting on the aircraft must be 0, similar to longitudinal static stability. Equations (22) and (23) express aerodynamic rolling moment L_A and aerodynamic yawing moment N_A that occur on the aircraft [7]:

$$L_A=C_l\left(qSc\right)$$

(22)

$$N_A=C_n\left(qSc\right)$$

(23)

To provide the lateral static stability requirement, $C_{l_{\beta }}$ < 0 and $C_{n_{\beta }}$ > 0 [23].

By accepting that the same assumptions made for longitudinal static stability are made for lateral static stability, the change in $C_l$ and $C_n$ moments depending on the side slip angle β of the T-37B-like aircraft in the configuration with a 0° sweep angle is examined using the OPEN VSP program (Figure 31).

Figure 31 shows that $C_l$ < 0 and $C_n$ > 0 for the configuration with a 0° sweep angle, i.e., it is lateral static stable. Since the T-37B-like aircraft is designed as a training aircraft, the results are satisfactory, as expected. The analyses conducted using the OPEN VSP program for configurations with different sweep angles can be compared in Figure 32.

Figure 32a shows that the aircraft meets the condition $C_l$ < 0 and is stable in all sweep angle changes. The aircraft’s stability on the roll axis increases in the positive direction as the aircraft wing sweep angle increases positively. As seen in Figure 32b, the aircraft fulfills the condition $C_n$ > 0 and is stable in configurations with all sweep angles. Changing sweep angles do not have any significant effect on the stability of the yaw axis.

4.2. Dynamic Stability

Dynamic stability provides insight into the aircraft’s stability when it is removed from the trim or balance conditions. Dynamic stability typically involves the oscillations that occur when the aircraft tries to return to its original position. If the oscillations decrease over time, the aircraft has positive dynamic stability. If the oscillations increase over time, the aircraft has negative dynamic stability. If the aircraft oscillations remain the same over time, it has neutral dynamic stability. This issue should not be confused with static stability. Despite being statically stable, an aircraft may have positive, neutral, and negative dynamic stability [18].

Although the previous section examines the longitudinal and lateral static stability behavior of the T-37B-like aircraft, the current section investigates only the longitudinal dynamic stability. Therefore, the aircraft’s three-degree-of-freedom longitudinal motion analysis is conducted, and the motion variables are obtained as α, u, and θ. Equation (24) is obtained when the fourth-degree characteristic equation of the longitudinal motion is written as follows [7]:

$$\left(s^2+2{\zeta }_{SP}{\omega }_{N_{SP}}+{{\omega }_{N_{SP}}}^2\right)\left(s^2+2{\zeta }_{PH}{\omega }_{N_{PH}}+{{\omega }_{N_{PH}}}^2\right)$$

(24)

where s is the Laplace variable, ${\zeta }_{SP}$ and ${\omega }_{N_{SP}}$ are the damping ratio and natural frequency of the short-period mode, respectively, and ${\zeta }_{PH}$ and ${\omega }_{N_{PH}}$ are the damping ratio and natural frequency of the phugoid mode, respectively.

The short period mode has a complex root and a high damping and natural frequency. The phugoid mode (long period) has a complex root and a low damping ratio and natural frequency.

For a short period, ${\omega }_{N_{SP}}$ can be expressed by Equation (25), whereas ${\zeta }_{SP}$ can be expressed by Equation (26) [7,18]:

$${\omega }_{N_{SP}}\approx \sqrt{-M_{\alpha }}\approx \sqrt{{\displaystyle \frac{{-C}_{m_{\alpha }}{q}_{1}Sc}{I_{yy}}}}$$

(25)

$${\zeta }_{SP}\approx {\displaystyle \frac{-\left(M_q+\frac{Z_{\alpha }}{U_1}+{-M}_{\dot{\alpha }}\right)}{2{\omega }_{N_{SP}}}}$$

(26)

where ${\omega }_{N_{SP}}$ is the natural frequency of the short-period mode, $M_{\alpha }$ is the pitching-moment derivative with respect to angle of attack, $C_{m_{\alpha }}$ is the non-dimensional pitching-moment coefficient derivative with respect to angle of attack, $q_1$ is the dynamic pressure at the reference flight condition, S is the wing reference area, c is the mean aerodynamic chord, $I_{yy}$ is the aircraft moment of inertia about the pitch axis, ${\zeta }_{SP}$ is the damping ratio of the short-period mode, $M_q$ is the pitching-moment derivative with respect to pitch rate, $Z_{\alpha }$ is the vertical force derivative with respect to angle of attack, $U_1$ is the trim flight speed, and $M_{\dot{\alpha }}$ is the pitching-moment derivative with respect to the rate of change of angle of attack.

For the phugoid mode roots, ${\omega }_{N_{PH}}$ is obtained using Equation (27), and ${\zeta }_{PH}$ using Equation (28) [7,18]:

$${\omega }_{N_{PH}}\approx \sqrt{-{\displaystyle \frac{Z_{u}g}{U_1}}}\approx \sqrt{{\displaystyle \frac{g\left(q_{1}S\right)(C_{L_u}+2C_{L_1})}{{U_1}^{2}m}}}$$

(27)

$${\zeta }_{PH}={\displaystyle \frac{1}{\sqrt{2}}}{\displaystyle \frac{C_{D_1}}{C_{L_1}}}$$

(28)

where ${\omega }_{N_{PH}}$ is the natural frequency of the phugoid mode, $Z_u$ is the derivative of vertical (Z) force with respect to forward speed u evaluated at the trim, g is the gravitational acceleration, $U_1$ is the trim flight speed, $q_1$ is the dynamic pressure at the trim condition, S is the wing reference area, $C_{L_u}$ is the derivative of the lift coefficient with respect to forward speed u (at trim), $C_{L_1}$ is the lift coefficient at the trim, m is the aircraft mass, ${\zeta }_{PH}$ is the damping ratio of the phugoid mode, and $C_{D_1}$ is the drag coefficient at the trim.

Table 12. Dynamic stability data for the T-37B aircraft.

Altitude	30,000 ft	Speed	0.459 Mach (456 ft/s)
g	32.18 lb/ft2	$C_{L_1}$	0.378
Weight	6360 lb	$C_{L_{\alpha }}$	5.15
Wing Area (S)	182 ft2	$C_{D_0}$	0.02
Wing Length (b)	33.8 ft	$C_{D_1}$	0.03
Wing Width (c)	5.47 ft	$C_{m_{\alpha }}$	−0.7 rad/s
Dynamic pressure (lb/ft2)	92.7	$C_{m_q}$	−14.9
CG	27.0%	$M_{\alpha }$	−19.42 1/s2
Ixx	7990 slug/ft2	$M_q$	−2.48 s−1
Iyy	3330 slug/ft2	$M_{\dot{\alpha }}$	−1.15 s−1
Izz	1120 slug/ft2	$Z_{\alpha }$	−442.46 (ft/s2)
Ixz	−1120 slug/ft2

lists the dynamic stability coefficients of the T-37B aircraft found in the literature [7,18]. Dynamic stability coefficients are obtained for the configurations of the T-37B-like aircraft with different sweep angles, and the calculated values are compared.

${\omega }_{N_{SP}}$ = 4.89 1/s is obtained using Equation (22). Using Equation (23), ${\zeta }_{SP}=0.438$ is calculated. In this case, the characteristic equation for the short period mode can be defined as s² + 4.32s + 24.35. The equation’s roots are found as λ₁ =$-$2.1650 + 4.3958 i and λ₂ = $-$2.1650–4.3958 i.

Equations (24) and (25) are used for the phugoid mode calculations. ${\omega }_{N_{PH}}=$0.0998 s⁻¹ and ${\zeta }_{PH}=$ 0.06272 are calculated. The characteristic equation for the phugoid mode can be defined as s² + 0.0125s + 0.0099. The equation’s roots are found as λ₃ = $-0.0063$ + 0.0993 i and λ₄ = $-0.0063$ − 0.0993 i.

Figure 33 shows the representation of four different complex roots of the short period and phugoid modes calculated for the T-37B-like aircraft.

Upon examining the equation’s roots for the 0° sweep angle change, it is calculated that the phugoid mode damping and frequency are quite low compared to the short period mode, which is an expected condition, as mentioned in the previous sections. Furthermore, the real axis equivalents of the roots of both modes are negative. In this case, the aircraft can be considered dynamically stable on the longitudinal axis, as expected. Additionally, the characteristic equations obtained are answered according to the step function inputs given using the MATLAB Simulink program (version R2022b) and are presented in Figure 34.

Figure 34a shows that the aircraft damps in a short time in the short period mode against the step function given as input. Hence, the simulation time is as short as 4 s. As seen in Figure 34b, the aircraft damps in a long time in the phugoid mode against the step function given as input, which is expected, as explained in the previous sections. Therefore, the simulation time is determined to be 500 s to examine the damping clearly. The T-37B-like aircraft is dynamically stable in both modes on the longitudinal axis in the configuration with a 0° sweep angle.

The dynamic stability of the T-37B-like aircraft is examined according to the changing sweep angles and is presented in

Table 13. Frequency, damping, and characteristic equations according to sweep angles.

Sweep Angle (°)	Mode	${\mathit{\omega }}_{\mathit{N}}$ (sn−1)	ζ	Equation
−10	Short Period	3.972	0.545	s2 + 4.33s + 15.78
	Phugoid	0.0998	0.624	s2 + 0.0125s + 0.0099
−5	Short Period	4.508	0.479	s2 + 4.32s + 20.32
	Phugoid	0.0998	0.626	s2 + 0.0125s + 0.0099
0	Short Period	4.934	0.438	s2 + 4.32s + 24.35
	Phugoid	0.0998	0.627	s2 + 0.0125s + 0.0099
10	Short Period	5.759	0.376	s2 + 4.34s + 33.17
	Phugoid	0.0998	0.624	s2 + 0.0124s + 0.0099
20	Short Period	4.677	0.463	s2 + 4.33s + 21.87
	Phugoid	0.0998	0.0623	s2 + 0.0124s + 0.0099
40	Short Period	5.28	0.404	s2 + 4.27s + 27.92
	Phugoid	0.0998	0.645	s2 + 0.0146s + 0.0093

.

As seen in Table 13, the equations’ roots are obtained by solving the characteristic equations. Figure 35 displays the roots in the short period mode according to changing sweep angles, and Figure 36 shows the roots in the phugoid mode according to changing sweep angles.

As seen in Table 13, the characteristic equation roots for the phugoid mode are the same for all sweep angle changes, except for the configuration with a 40° sweep angle. In this case, Figure 36 shows that the roots are calculated as the same for configurations with −10°, −5°, 0°, 10°, and 20° sweep angles. For the configuration with a 40° sweep angle, even if the difference is calculated, it is very small. Figure 37 demonstrates the response of the aircraft in the phugoid mode for the 40° sweep angle change and the 0° sweep angle change, which is the most obvious difference.

Figure 37 shows that the aircraft damps faster in the configuration with a 40° sweep angle and that the stability is positively affected in the phugoid mode. Figure 38 presents the responses of the aircraft in the short period mode according to changing sweep angles.

Figure 38 presents the responses of the aircraft in the short period mode according to changing sweep angles. It is seen that the aircraft is dynamically stable in the short period mode. As expected, although the aircraft is stable earlier between −10° and 10° sweep angle changes, this situation does not continue at 20° and 40° sweep angle changes. Whereas the positive increase in the aircraft sweep angle has a positive effect in cases changing between −10° and 10°, it has an uncertain impact at 20° and 40° sweep angle changes.

5. Conclusions

The present study conducted the performance and stability analysis of a fixed-wing aircraft with a symmetrical variable wing sweep angle. The impact of a symmetrical change in sweep angle on performance and stability was evaluated. The T37-B aircraft was used as the basis for this investigation.

The T-37B-like aircraft was modeled using the DATCOM and OPEN VSP programs, and the values obtained were found to be consistent with the data from the literature review. The performance model was established, and it was determined to agree with the published performance values. Then, the effect of the aircraft sweep angle was examined. Concerning the performance calculations, the most significant differences were observed between 0° and 40° sweep angles. Hence, all comparisons below were made for the two cases.

It was found that the symmetrical change in the wing sweep angle adversely affected the takeoff performance and increased the takeoff distance by 12% in the case of a 40° sweep angle change. The change in sweep angle positively affected climb performance, increasing it by 11%. It reduced the aircraft’s drag force by 5.2% during the cruise flight and increased the range by 1%. It reduced the range by 5.8% in the glide flight, so the 40° sweep angle change had a negative effect in this aspect. It was calculated that, in the descent case, the descent speed decreased by 4%, similar to gliding, and the sweep angle change adversely affected it. Upon evaluating the approach performance, an 8% increase in approach speed was calculated, and it was observed that the sweep angle change negatively affected it. A 12% increase in the radius of turn and a 12% decrease in the turning speed were calculated. The impact on the radius of turn and turning speed was evaluated as negative.

It was shown that a positive symmetrical change in the aircraft wing sweep angle by 40° increased the longitudinal static stability, while a negative symmetrical change affected the stability negatively. In terms of lateral static stability, it was shown that the symmetrical change in the wing sweep angle did not have a significant effect on the yaw axis, but it had a positive stability-enhancing effect on the roll axis. Dynamic stability analyses were performed only on the longitudinal axis. It was found that the 40° sweep angle change in the phugoid mode had a positive effect, and the aircraft damped faster compared to other sweep angles. In the short period mode, the sweep angle change in the negative direction adversely affected stability, while the change in the positive direction had a positive impact on stability.

It is expected that changing the symmetrical wing sweep angle will positively affect some aircraft performance and stability parameters while negatively affecting others. The advantage of a variable-sweep wing structure is achieved by adjusting the wing’s sweep angle to the most favorable sweep angle value during the flight phase. Therefore, all advantages can be utilized, while disadvantages can be avoided by changing the configuration. However, a symmetrical variable wing sweep configuration will have some design, mechanical, weight, and financial costs. Therefore, whether the performance and stability benefits justify these costs must be evaluated on an aircraft-specific basis.

When the effect of the symmetric variable-sweep wing configuration on aircraft performance and stability is considered specifically for the T-37B-like aircraft, the performance and stability are increased in the positive direction; nevertheless, the increase is not at the desired level. This can be explained by the fact that, in the T-37B-like aircraft, the symmetric sweep angle change can only be applied to a certain part of the wing, not the entire wing, due to the engines’ position. Therefore, the effect of the symmetric variable-sweep wing configuration was limited. Additionally, many aircraft on which the wing sweep angle change has been applied have been manufactured and have successfully performed their missions. However, upon evaluating the aircraft produced in this design concept, it is seen that they have quite wide flight conditions. On the other hand, the T-37B aircraft cannot exceed a speed of 0.7 Mach with its design and engine thrust force.

Integrating higher-fidelity CFD simulations and experimental studies is identified as an important direction for future work. This study performed a conceptual-level, preliminary analysis of the effects of symmetric wing sweep variations on aircraft performance and stability. While the present results highlight general aerodynamic and stability trends, further research is required for higher-fidelity validation. In particular, CFD-based flow analyses, together with optimization and sensitivity studies, are considered important directions for future work.

Future research will extend this preliminary study by incorporating aeroelastic effects and mass–stiffness variations of the sweep mechanism, which are not captured under the rigid-airframe assumptions of DATCOM and OpenVSP. We clarified this in the manuscript and noted that investigating transonic conditions (Ma ≈ 0.8–0.9) with higher-fidelity CFD or experiments will be pursued as future work.

It should be noted that nonlinear stall and departure phenomena may arise at high sweep angles. These effects, however, are beyond the scope of this preliminary study, which focused on steady aerodynamic and stability trends. Future work will address these nonlinear behaviors using higher-fidelity methods.