Aerodynamics Caused by Rolling Rates of a Small-Scale Supersonic Flight Experiment Vehicle with a Cranked-Arrow Main Wing

Abstract

A small-scale supersonic flight experiment vehicle is being developed at Muroran Institute of Technology as a flying testbed for verification of innovative technologies for high-speed atmospheric flights, which are essential to next-generation aerospace transportation systems. Its baseline configuration M2011 with a cranked-arrow main wing with an inboard and outboard leading edge sweepback angle of 66 and 61 degrees and horizontal and vertical tails has been proposed. Its aerodynamics caused by attitude motion are required to be clarified for six-degree-of-freedom flight capability prediction and autonomous guidance and control. This study concentrates on characterization of such aerodynamics caused by rolling rates in the subsonic regime. A mechanism for rolling a wind-tunnel test model at various rolling rates and arbitrary pitch angle is designed and fabricated using a programmable stepping motor and an equatorial mount. A series of subsonic wind-tunnel tests and preliminary CFD analysis are carried out. The resultant static derivatives have sufficiently small scatter and agree quite well with the static wind-tunnel tests in the case of a small pitch angle, whereas the static directional stability deteriorates in the case of large pitch angles and large nose lengths. In addition, the resultant dynamic derivatives agree well with the CFD analysis and the conventional theory in the case of zero pitch angle, whereas the roll damping deteriorates in the case of large pitch angles and proverse yaw takes place in the case of a large nose length.

1. Introduction

Innovation in technologies for high-speed atmospheric flights is essential for the establishment of supersonic/hypersonic and reusable space transportation. It is quite effective to verify such technologies through small-scale flight tests repeatedly in practical high-speed environments prior to incorporation in large-scale vehicles. Thus, we are developing a small-scale supersonic flight experiment vehicle as a flying test bed. Its baseline configuration M2011 with a cranked-arrow main wing and a single Air Turbo Ramjet Gas-Generator-cycle (ATR-GG) engine [1] has been proposed. Its aerodynamics, including static stability and controllability, have been investigated through intensive static wind-tunnel tests [2].

In the recent phase of the development study, a 1/3-scale prototype vehicle with a model-scale jet engine has been designed and fabricated. Its flight tests are being carried out in the subsonic regime to measure its flight characteristics onboard as well as investigate the capability of guidance/control systems. However, several prototype vehicles have lost control and crashed during their maneuvers, including turning. Thus, the numerical flight simulation is indispensable to predict the flight characteristics of the vehicle and establish autonomous guidance and control sequence on the basis of the predicted flight characteristics. For this purpose, aerodynamics caused by attitude motion are of interest. For example, the roll damping effects denoted by $C_{lp}$ determine the terminal rolling rate in the condition of equilibration between the rolling moment caused by aileron deflections and roll damping moment [3]. In addition, the proverse/adverse yaw effects due to the roll rate, denoted by $C_{np}$, determine the possibility of the so-called “roll reversal”, i.e., “aileron departure” in conjunction with the proverse/adverse yaw effects due to aileron deflection $C_{n{\delta }_a}$, the directional stability $C_{n\beta }$, and dihedral effects $C_{l\beta }$ [4]. In the roll reversal phenomena, the rolling rate deteriorates, and the rolling motion takes place in the direction opposite to the aileron deflection.

There are various efforts for establishing methodologies for characterization of such aerodynamics, including wind-tunnel testing and CFD analysis [5,6,7,8,9,10,11,12]. Regarding vehicle configurations with cranked-arrow wings, quasi-static characterization with various sets of pitch and roll angles, i.e., sets of angles of attack and sideslip, have been carried out by some researchers [13,14,15] for delta and cranked-arrow wings. However, quantitative aerodynamics caused by rolling rates of vehicles with cranked-arrow wings have not been characterized and reported.

On the other hand, large-scale dynamic test techniques have been proposed by national research centers [6,7,8,9,10], but they cannot be applied to the present small-scale development project. Thus, this paper aims to evaluate aerodynamics caused by rolling rates of the proposed supersonic flight experiment vehicle in the subsonic regime by our own small-scale test technique.

In Section 2, the baseline configuration M2011 is outlined. In Section 3, the conventional theory for predicting aerodynamics due to rolling rates is described, and its drawbacks are discussed. Methods of wind-tunnel tests, CFD analysis, and data reduction are introduced in Section 4. Their results are discussed in Section 5. Then, Section 6 outlines our conclusions.

2. The Baseline Configuration M2011

The baseline configuration M2011 with a single Air Turbo Ramjet Gas-Generator-cycle (ATR-GG) engine has been designed as shown in Figure 1 and

Table 1. Dimensions of the baseline configuration M2011.

Dimension	Value
Wingspan	2.41 m
Wing Area	2.15 m2
Fuselage Diameter	0.3 m
Overall Length	Nose-A: 5.8 m (Propellants 80 kg)
	Nose-B: 6.8 m (Propellants 105 kg)
	Nose-C: 7.8 m (Propellants 130 kg)

. A diamond wing section of 6% thickness with a sharp leading-edge is adopted for the main wing and the tails. The planform of the main wing is a cranked arrow with an inboard and an outboard leading-edge sweepback angle of 66 and 61 degrees, respectively. Such a combination of the wing section with a sharp leading-edge and the planform with a crank is quite favorable both for reduction in wave drag during supersonic flights, as well as for generation of stable leading-edge separation in the subsonic regime. Note that the leading-edge separation, the subsequent large-scale longitudinal vortices above the main wing, and the resultant low pressure on the upper surface of the main wing are the origin of the lift generation in cranked-arrow wings in the subsonic regime. It is quite distinct from conventional rectangular, tapered, and moderately sweptback wings where a low pressure generated on the shoulder portion of the wing section in accordance with its profile and the Kutta condition is the origin of lift generation.

In addition, a high-wing configuration with a dihedral of 1.0 degree is adopted in order to attain sufficient roll stability. Three fuselage lengths, 5.8 m, 6.8 m, and 7.8 m, are considered tentatively for various quantities of propellants loaded for various missions.

3. The Conventional Theory

The conventional theory [3,16,17] assumes that the airflow around the main wing is uniform in the spanwise direction. In the case of rolling motion in such a uniform flow field, a straight distribution of up- and down-wash flows around the main wing is induced by the rolling rate, and the resultant distribution of the increment in the local angle of attack and in the local lift force vector will give the roll damping and adverse yaw, as illustrated in Figure 2a,b.

Thus, the aerodynamics caused by rolling rates are described by the following Equations (1) and (2). The rolling rate is non-dimensionalized by Equation (3).

$$C_{lp}=-{\displaystyle \frac{4a_0}{S{b}^2}}{\int }_0^{{\displaystyle \frac{b}{2}}}c\left(y\right)y^{2}dy$$

(1)

$$C_{np}=-{\displaystyle \frac{4}{S{b}^2}}\left(C_L-{\displaystyle \frac{\partial C_D}{\partial \alpha }}\right){\int }_0^{{\displaystyle \frac{b}{2}}}c\left(y\right)y^{2}dy$$

(2)

$$\widehat{p}=p·{\displaystyle \frac{b}{2U_0\cos \theta }}$$

(3)

Here, $C_l$ is the rolling moment coefficient, $C_n$ is the yawing moment coefficient, $a_0$ is the lift curve slope of the main wing, $S$ is the main-wing area, $b$ is the wingspan, $c\left(y\right)$ is the chord length of the main wing at the lateral location $y$, $C_L$ is the lift coefficient, $C_D$ is the drag coefficient, $\alpha$ is the angle of attack, $p$ is the dimensional rolling rate, $\widehat{p}$ is the non-dimansionalized rolling rate, $U_0$ is the freestream airspeed, and ${( )}_p$ is the derivative with respect to $\widehat{p}$.

Evaluated values for the proposed aerodynamic configuration M2011 by the theoretical procedure are listed in

Table 2. Stability derivatives evaluated by the conventional theory.

Derivative	Evaluated Value
$C_{lp}\left[{\mathrm{r}\mathrm{a}\mathrm{d}}^{-1}\right]$	−0.245
$C_{np}\left[{\mathrm{r}\mathrm{a}\mathrm{d}}^{-1}\right]$	0.0117

.

Such a uniform flow assumed in the conventional theory will not be the case for the cranked-arrow wings above which leading-edge separations and resultant large-scale vortex systems are dominant. Thus, practical wind-tunnel tests and CFD analysis are indispensable for evaluation of aerodynamics due to rolling rates.

4. Wind-Tunnel Tests and CFD Analysis

4.1. Experimental Apparatus and Methods

In order to investigate such aerodynamics by wind-tunnel tests, a mechanism for rolling an assembled set of a vehicle model, an internal balance, and a sting is designed and fabricated using a stepping motor and an equatorial mount as illustrated in Figure 3. The stepping motor is controlled by a digital program on a PC, and then actuation with precise repeatability is realized.

The internal balance is the custom-made Model RT03 designed and fabricated by Ryoei Technica Co., Ltd., Kamakura, Japan. The stepping motor is the off-the-shelf Model PKE5913MC fabricated by Oriental Motor Co., Ltd., Tokyo, Japan. The equatorial mount and the sting are of the authors’ own design and fabrication.

The vehicle model is of 7/60 scale, i.e., its wingspan is 0.28 m. An intensive series of wind-tunnel tests are carried out using a Goettingen-type subsonic wind tunnel at Muroran Institute of Technology. The dimension of its open-jet test section is 0.45 m × 0.45 m, as shown in Figure 4. The blockage ratio of the present vehicle model to the test section is 1.9% at an angle of attack of zero and 13.3% at 20 degrees. Test conditions are various combinations of a non-dimensional rolling rate of 0.002 through 0.025 rad⁻¹, a pitch angle of 0 through 20 degrees, and an airspeed of about 20 m/s. The Reynolds number is about 1.9 × 10⁵ with respect to the mean aerodynamic chord of the main wing, and the Mach number is 0.059.

The electric noise is caused by electromagnetic interference between the digital control circuit for the stepping motor and the strain amplifier circuit for the balance. It can be reduced by applying an electromagnetic shield of grounded metal-mesh cover around each of the circuits, as well as using a separated power supply for each circuit. The mechanical noise caused by the vibration of the vehicle model is reduced by applying an appropriate low-pass filter to the balance signals. In addition, the scatter of acquired data is assessed through multiple measurements at each test condition.

The coordinates and the force/moment components are defined for aircraft as illustrated in Figure 5. Here $X$, $Y$, and $Z$ are the body-fixed axes along which the force components $F_X$, $F_Y$, and $F_Z$ are defined, as well as around which the rolling moment $M_X$, the pitching moment $M_Y$, and the yawing moment $M_Z$ are also defined. On the other hand, the lift $L$ and the drag $D$ are defined with respect to the airflow vector.

4.2. Data Analysis Methods

An example of acquired data is shown in Figure 6, where stepwise positive and negative calibration signals, measurement with roll actuation without airflow, and that with airflow appear in this order. As indicated by the PM (potentiometer signal), a right half stroke, a left full stroke, a right full stroke, and a left half stroke are applied in this order in each roll actuation. Various effects such as gravitational and centrifugal forces can be eliminated by differencing the measurements with and without airflow. The aerodynamic forces and moments are evaluated by comparison between the calibration and the balance signals where each calibration signal for each force/moment channel corresponds to the rated load of the balance channel.

Obtained aerodynamic coefficients show a hysteresis curve, as shown in Figure 7, which is for the rolling moment coefficient caused by rolling actuation. The red lines are linear approximations of the curve around the vertical intercepts and are expressed by Equations (4) and (5), in which the angles of attack and sideslip are evaluated from the angles of pitch and roll by using Equation (6).

$$C_{l1}=C_{l\beta }\beta +C_{lp1}\widehat{p}+\epsilon$$

(4)

$$C_{l2}=C_{l\beta }\beta +C_{lp2}(-\widehat{p})+\epsilon$$

(5)

$$\alpha ={\tan }^{-1}\left({\displaystyle \frac{\cos \mathsf{\phi }\sin \mathsf{\theta }}{\cos \mathsf{\theta }}}\right), \beta ={\sin }^{-1}\left(\sin \phi \sin \theta \right)$$

(6)

Here, $\epsilon$ is a zero-point shift in the measured data due to asymmetry in the wind-tunnel flow and the vehicle model alignment. The dynamic derivative is evaluated by differencing these equations, i.e., by Equation (7), whereas the static derivative $C_{l\beta }$ is evaluated as the slope of the approximate straight lines.

$$C_{lp}={\displaystyle \frac{C_{lp1}+C_{lp2}}{2}}={\displaystyle \frac{C_{l1}-C_{l2}}{2\widehat{p}}}$$

(7)

4.3. CFD Analysis

Preliminary CFD analysis is also carried out for the flow conditions equivalent to wind-tunnel tests using a business-class PC with a limited memory and CPU capability. The physical space to be analyzed is composed of concentric double spheres illustrated in Figure 8 where the vehicle model is located at their center. An unstructured tetrahedral mesh with about four million cells is generated using POINTWISE V17.1.R2. The mesh in the inner sphere is fixed to and rotated with the vehicle model whereas that between the inner and the outer spheres are stationary. The ANSYS FLUENT R17.2.0 is utilized with the Spalart–Allmaras turbulence model to solve the flow field. The primary conditions and settings are listed in

Table 3. Conditions and settings for CFD analysis.

Category	Item	Setting
Vehicle model	7/60-scale wind-tunnel test model, wingspan 0.282 m
Mesh generation	type	unstructured tetrahedral
	spacing	body surface: 1 mm inner and outer half circle: 60 points
	number of cells	about four million
CFD analysis	Boundary Condition	body surface	Wall
		inner spherical surface	Interface, 1 m radius
		outer spherical surface	Pressure-far-field, 2 m radius
	Governing equation	three-dimensional Navier–Stokes
	Spatial Discretization	second-order upwind differencing
	Fluid	air/ideal gas
	Viscosity model	Sutherland
	Turbulence model	Spalart–Allmaras
	Mach number	0.6

. Evaluated aerodynamic coefficients are analyzed by the procedure equivalent to that described in Section 4.2.

5. Results and Discussions

Static rolling and directional stability derivatives, $C_{l\beta }$ and $C_{n\beta }$, for the Nose-C configuration at pitch angles of 5–20 degrees are shown in Figure 9. Note that the sideslip angle $\beta$ does not appear in the case of zero pitch angle in accordance with Equation (6). Thus, the static derivatives cannot be evaluated in such cases. It is clearly shown that the present static derivatives have sufficiently small scatter, i.e., small widths of error bars, and are in good agreement with static wind-tunnel tests in the case of a small pitch angle. In addition, the static rolling stability, i.e., the dihedral effect, is almost independent of the pitch angle, whereas the static directional stability deteriorates in the case of large pitch angles.

The static derivatives for the three types of nose length are compared in Figure 10 where the derivatives are averaged with respect to the rolling rates. The static rolling stability is almost independent of the nose length, whereas the static directional stability deteriorates in the case of large pitch angles and large nose lengths.

The dynamic derivatives for the Nose-C configuration are shown in Figure 11 in comparison with the CFD analysis and the conventional theory. The present results of wind-tunnel tests at zero pitch angle show good agreement with the CFD analysis and the conventional theory within the range of scatter, i.e., the widths of error bars. In addition, the roll damping effect, i.e., negative $C_{lp}$, deteriorates at larger pitch angles. The adverse yaw effect, i.e., negative $C_{np}$, seems to exist at zero pitch angle, whereas the proverse yaw, i.e., positive $C_{np}$, appears at large pitch angles.

Regarding the error bars in Figure 11, the following considerations can be provided: In this study, each error bar denotes the standard deviation, i.e., the degree of scatter, of the data acquired by several measurements in each condition. In the present dynamic wind-tunnel tests with rolling rates, acquired aerodynamic coefficients fluctuate as illustrated by the wavy shape of the hysteresis curve in Figure 7. Such fluctuation is caused by (1) fluctuation of the leading-edge separation flow dominant on cranked-arrow wings, (2) electromagnetic noises generated by the digital control system of the stepping motor, and (3) mechanical vibration of the vehicle model, the balance, and the support sting. The first cause is inevitable around delta and cranked-arrow wings because the leading-edge separation and the resultant fluctuating vortex flows are inherent, as they are the origin of lift generation. The second one has been reduced intensively in this study by applying an electromagnetic shield on the control circuit of the stepping motor, but it might be imperfect. The third one is somewhat inevitable in the present low-cost wind-tunnel tests in the university laboratory with low-rigidity apparatus in comparison with high-cost ones in national research centers.

Such fluctuation of aerodynamic coefficients affects the dynamic components $C_{lp}\widehat{p}$ in Equations (4) and (5) and $C_{np}\widehat{p}$. Then, the scatter of the dynamic derivatives $C_{lp}$ and $C_{np}$ is large for small values of the rolling rate $\widehat{p}$, and small for large values of $\widehat{p}$. Such characteristics of the scatter are clearly shown by the magnitude of the error bars in Figure 11. In addition, dependency of the derivatives on the pitch angle $\theta$ is also clearly shown.

On the other hand, the fluctuation has little effect on the average slope of the hysteresis curve, i.e., the static derivative $C_{l\beta }$, in Figure 7 and Equations (4) and (5), and similarly on $C_{n\beta }$. Then the error bars in Figure 9 and Figure 10 are small.

The dynamic derivatives for the three types of nose length are compared in Figure 12, where the derivatives are averaged with respect to the upper three rolling rates at which the error bars are relatively small. The roll damping effect is almost independent of the nose length. And the proverse yaw takes place in the Nose-C configuration, specifically at pitch angles of 5 to 10 degrees. There might be some interference between the flow separated at the long nose and the vortex system above the main wing at these pitch angles.

The present results, averaged with respect to the upper three rolling rates, are tabulated in

Table 4. Comparison of the results for static derivatives by several methods and flight test data of existing airplanes [10] at pitch angles around zero.

Derivative	$\mathbf{Present} \mathbf{Dynamic} \mathbf{Wind} \mathbf{Tunnel} \mathbf{Tests}, \mathbf{Nose}\text{-}\mathbf{C}, \mathit{\theta }$$=5 \mathbf{deg}., \mathit{p}$-Averaged	$\mathbf{Static} \mathbf{CFD}, \mathbf{Nose}\text{-}\mathbf{C}, \mathit{\theta }$ = 0 deg.	$\mathbf{Static} \mathbf{Wind} \mathbf{Tunnel} \mathbf{Tests}$ [2], $\mathbf{Nose}\text{-}\mathbf{C}, \mathit{\theta }$ = 0 deg.	$\mathbf{Boeing} 747$ [10], $\mathit{\theta }$ = 2.5 deg.	$\mathbf{Lockheed} \mathbf{F}\text{-}104\mathbf{A}$ [10], $\mathit{\theta }$ = 2 deg.
$C_{l\beta }\left[{\mathrm{r}\mathrm{a}\mathrm{d}}^{-1}\right]$	−0.156	−0.0970	−0.106	−0.0951	−0.0930
$C_{n\beta }\left[{\mathrm{r}\mathrm{a}\mathrm{d}}^{-1}\right]$	0.117	0.126	0.146	0.210	0.242

and

Table 5. Comparison of the results for dynamic derivatives by several methods and flight test data of existing airplanes [10] at pitch angles around zero.

Derivative	$\mathbf{Present} \mathbf{Dynamic} \mathbf{Wind} \mathbf{Tunnel} \mathbf{Tests}, \mathbf{Nose}\text{-}\mathbf{C}, \mathit{\theta }$$=0 \mathbf{deg}., \mathit{p}$-Averaged	$\mathbf{Present} \mathbf{CFD}, \mathbf{Nose}\text{-}\mathbf{C}, \mathsf{\theta }=0 \mathbf{deg}., \mathit{p}$-Averaged	$\mathbf{Conventional} \mathbf{Theory}, \mathbf{Nose}\text{-}\mathbf{C}, \mathit{\theta }$ = 0 deg.	$\mathbf{Boeing} 747$ [10], $\mathit{\theta }$ = 2.5 deg.	$\mathbf{Lockheed} \mathbf{F}\text{-}104\mathbf{A}$ [10], $\mathit{\theta }$ = 2 deg.
$C_{lp}\left[{\mathrm{r}\mathrm{a}\mathrm{d}}^{-1}\right]$	−0.248	−0.212	−0.245	−0.320	−0.272
$C_{np}\left[{\mathrm{r}\mathrm{a}\mathrm{d}}^{-1}\right]$	−0.219	0.0499	0.0117	−0.0200	−0.0930

in comparison with those by other methods and flight test data for existing airplanes [10] with different configurations. The selected airplanes are the Boeing 747 as a conventional configuration with a relatively large main wing and the Lockheed F-104A as a supersonic configuration with a small main wing, although both of their main wings are not cranked but straight tapered. The rolling rate is not reported for the existing airplanes, thus the present results by dynamic wind-tunnel tests and CFD analysis are averaged with respect to the rolling rate, for the sake of convenience of comparison.

Regarding the evaluation of the static derivatives $C_{l\beta }$ and $C_{n\beta }$ shown in Table 4, it should be noted again that in the present dynamic wind-tunnel tests at a pitch angle of zero, the sideslip angle does not appear and static derivatives $C_{l\beta }$ and $C_{n\beta }$ cannot be evaluated, whereas it is not the case in the static wind-tunnel tests and CFD analysis where the sideslip angle sweeps at a pitch angle of zero. Thus, the results of the present dynamic wind-tunnel tests listed here are for the case of a small non-zero pitch angle. The values for the existing airplanes are reported to have been derived from subsonic flight tests at small trim angles of attack.

The rolling stability derivative $C_{l\beta }$ evaluated from the present dynamic wind-tunnel tests is larger by about 50% than the other treatments and existing airplanes. The difference would be due to the difference in the pitch angle.

The directional stability derivative $C_{n\beta }$ from the present wind-tunnel tests is slightly smaller than the other treatments and smaller by half than the existing airplanes. The former difference would also be due to the difference in the pitch angle. The latter deterioration is considered to be caused by the large nose-length of the present Nose-C configuration, which is shown also in Figure 10b.

The absolute value of the roll damping derivative $C_{lp}$ derived from the present dynamic wind-tunnel tests agrees well generally with other treatments and the Lockheed F-104A, but smaller than the Boeing 747, which is probably because of the difference in their wingspans. The present yaw derivative $C_{np}$ disagrees with the other treatments and existing airplanes. The negative value of the present $C_{np}$ at zero pitch angle implies a kind of adverse yaw effects which will enhance the side-slip angle and consequent dihedral effects in rolling motion. This would cause the so-called “aileron departure”, i.e., “roll reversal” phenomena, where the rolling motion deteriorates and takes place in the direction opposite to the aileron deflections. However, $C_{np}$ at larger pitch angles is positive, as shown in Figure 11b and Figure 12b. This proverse yaw effects would reduce the roll reversal phenomena. Quantitative prediction of such phenomena requires numerical flight simulation using the aerodynamic data acquired partially by the present study.

6. Conclusions

In the course of the development study of the small-scale supersonic flight experiment vehicle, its aerodynamics caused by attitude motion are required to be clarified for six-degree-of-freedom prediction of its flight capability, including the roll reversal phenomena, and for the design of autonomous guidance and control in the subsonic regime including taking-off and landing. Thus, this study concentrated on characterization of such aerodynamics caused by rolling rates in the subsonic regime. A mechanism for rolling a wind-tunnel test model at various rolling rates and arbitrary pitch angle was designed and fabricated using a programmable stepping motor and an equatorial mount. A series of subsonic wind-tunnel tests and preliminary CFD analysis were carried out.

The resultant static derivatives have sufficiently small scatter and agree quite well with the static wind-tunnel tests in the case of a small pitch angle. The static directional stability derivative deteriorates in the case of large pitch angles and large nose lengths. This would cause the so-called roll reversal phenomena.

In addition, the resultant dynamic derivatives agree well with the CFD analysis and the conventional theory in the case of zero pitch angle. The roll damping deteriorates in the case of large pitch angles and the proverse yaw takes place in the case of a large nose length. This proverse yaw would reduce the roll reversal phenomena. There are effects of such enhancement and reduction simultaneously, and quantitative numerical flight analysis is needed for prediction of roll reversal phenomena.

Regarding future studies, more precise and extensive CFD analysis with improvement in mesh generation and turbulence model selection is required. In addition, because the blockage ratio is somewhat large and the Reynolds number is small in the present wind-tunnel tests, efforts for measurement at a larger Reynolds number without the blockage problem are indispensable. Such methodology is already being prepared by car-mounted running tests using a 1/3-scale prototype vehicle where measurements are carried out in the open air at the Reynolds number equivalent to the flight condition of the prototype vehicle [19].

Moreover, the flow field behavior and the mechanism of the deterioration of the static and dynamic derivatives and generation of the proverse/adverse yaw should be clarified through flow-field visualization. Some preliminary results by wind-tunnel tests and corresponding CFD analysis are shown in [20]. Furthermore, the acquired static and dynamic derivatives will be applied to six-degree-of-freedom flight analysis of the proposed supersonic flight experiment vehicle and its 1/3-scale prototype in order to predict the probability of roll reversal phenomena.