The requirements for aircraft stability and control were derived from the RFP. The main requirement to fulfill is that the stabilizers must fold to conform to the constraints of the G-sized sonobuoy canister.
3.2.2. Tail Design and Control Surface Sizing
The size constraints of the Flying Fish were the main factor for consideration in the tail design layout. Twin vertical tails were selected as they are able to fold easily along the fuselage. The vertical tails were treated as one total stabilizer for calculations, as recommended by Raymer [
18]. The aspect ratios chosen for both the vertical and horizontal stabilizers are within the valid range of the Polhammus formula to estimate their 3D lift curve slope,
, which is used in the calculation of the stability derivatives.
Table 4 displays the geometric parameters for the tail.
The design for the tail involved using vertical and horizontal tail volume coefficients (
to size the tail. Historical data suggest a range for
from 0.35 to 0.5 and a
range from 0.02 to 0.04 [
18]. Typical tail sizing reflects the fact that the tail area is embedded in the fuselage. However, the Flying Fish has an abnormally large fuselage at the point where the tail connects to the body. Thus, the areas for the horizontal and vertical stabilizers used in the volume coefficient equations reflect the planform areas exposed to the freestream air. The tail configuration parameters from
Table 4 yield a
of 0.45 and a
of 0.028, both within the recommended range.
One of the primary areas of concern in the deployment of the Flying Fish is when the aircraft falls out of the canister and unfolds its wing and stabilizers. This maneuver is detailed in
Section 3.5. As the wings unfold, the natural lifting direction of the wing impedes the unfolding action as the wing attempts to unfold over itself. To ensure that the wing unfolds, spoilerons on the wing will prevent the lift from counteracting the direction in which the wing unfolds, as shown in
Figure 7.
The spoilerons are 20% of the chord and 63% of the span, as seen in
Figure 7. They were sized from a combination of historical guidelines and car testing. Car-top testing was conducted, with the car starting at 20.1 m/s and decelerating until the wing was able to open, deploy, and lock. With no spoilerons, the wing opened, deployed, and locked at 2.23 m/s. With spoilerons, the wing was able to open, deploy, and lock at 11.2 m/s. Further testing of the spoilerons is recommended to ensure that unfolding and locking will occur during the pullout maneuver that occurs upon the jettison from the G-sized canister. Greater detail of the refined mechanical folding mechanism is provided in
Section 3.4.2.
The Flying Fish is outfitted with all-moving rudders and all-moving elevators. All-moving surfaces were selected to provide enough control authority for the aircraft to pull up during the 2 g pullout maneuver. In addition, all moving control surfaces are easier to manufacture at the scale of this UAV. Raymer suggests that a full 6 degree of freedom dynamic analysis is required to determine whether the control surfaces are sufficient in size to provide the proper control authority the aircraft needs throughout its flight regime [
18]. Due to time constraints, the team decided to prove the Flying Fish’s control authority in the 2 g pullout maneuver through flight testing. It was shown through flight testing that the pitch authority was sufficient for pullout, allowing for the transition to steady level flight at the terminus of the maneuver.
3.2.3. Stability
Static stability was determined using four parameters: static margin (SM), the coefficient of pitching moment due to AoA (
), the coefficient of yaw moment due to sideslip (
), and the coefficient of roll moment due to sideslip
. To be stable, the following criteria must be met: SM must be positive,
must be negative,
must be positive, and
must be negative. These stability derivatives, as well as the static margin, were found using equations from Napolitano’s
Aircraft Modeling and Simulation [
19] and calculated at the cruise condition.
Table 5 displays these key parameters. One key assumption made was that the fuselage did not generate any lift and its contribution to the aircraft’s aerodynamic center was negligible. This assumption was validated through the wind tunnel testing of the fuselage. It should be noted that the values acquired from using Napolitano’s equations are estimations derived from larger aircraft. Thus, the team decided to learn more through flight testing for validation.
The Flying Fish’s static margin is estimated to be 0.15 and the aircraft’s aerodynamic center is predicted to be 0.178 m aft of the nose. During flight testing, it was shown that the actual aerodynamic center lies more forward than predicted. The center of gravity, CG, was then moved to 0.136 m aft of the nose, from the original CG location of 0.165 m. was calculated to be −1.554 (rad−1). The negative value means a small disturbance will result in the aircraft pitching back to steady level flight. These values predict that the aircraft is longitudinally stable, which was validated through flight testing.
The incidence of the horizontal tail at cruise, , was calculated to be −3.4°. The incidence of the horizontal tail can be experimentally derived through flight testing since it is fully variable.
For lateral/directional stability,
was calculated to be −0.071 (rad
−1) and
was calculated to be 0.138 (rad
−1). These values satisfy the stability criteria. The main contributor to
is the high-mounted wing. However,
is not in the range for typical aircraft, which is −0.28 to −0.082 [
19]. However, adding 5° of dihedral would change
to −0.09, which would be within the typical range. To add any amount of dihedral to the main wing, a proposed idea involved cutting the tips of the center portion of the main wing at an angle, resembling a bevel cut.
Despite being statically stable, the flight test results demonstrated that the Flying Fish is sensitive to environmental conditions, roll and spiral instability, and over-control. Details of flight testing are discussed in
Section 4. Sensitivity to environmental conditions and roll instability is likely due to a low roll mode time constant and not having enough roll stability, despite the high-mounted wing. A solution to this problem could be to incorporate polyhedral on the outboard wings to increase the roll stability and push
into the nominal range for typical aircraft. The Flying Fish’s spiral instability was predicted using the Blaine Rawdon parameter, B, as shown in Equation (1).
In the equation above, Υ is the dihedral of the wing in degrees, is the vertical tail moment arm, b is the wingspan, and is the lift coefficient. To be considered spirally stable, B must be greater than five. Since the current design of the Flying Fish does not incorporate dihedral, the corresponding Blaine Rawdon parameter becomes zero. However, 15° of dihedral yields a value of 5.03, predicting that the aircraft would be stable in the spiral mode. Launch UAV made the decision to not include dihedral to not reduce the wing planform area. The reduction in the planform area would have increased the aircraft’s stall velocity, which was already relatively high for an aircraft of its size. With no dihedral, the aircraft would have to avoid the spiral mode through pilot skill and the pilot’s corrective inputs.
To address the problem of being over-controlled, the receiver used during flight testing incorporated control limiters for all control surfaces. The limits were derived experimentally, where the spoilerons were limited to ±10°, elevator to ±30°, and rudder to ±5°. Being over-controlled is a direct result of the all-moving elevator and rudder as well as oversized spoilerons relative to other aircraft.