In this section, a brief overview of the coefficients assessed through balance-force measurements in the wind tunnel is presented.
Knowledge of these three coefficients is essential for the effective design and control of the bioinspired MAV, ensuring its ability to fly safely and efficiently. As a result, this paper focuses on the analysis of the following three coefficients obtained experimentally.
where
is the lift force,
the aerodynamic drag,
the pitching moment,
the air density,
the wing reference surface,
the mean aerodynamic chord, and
the free stream velocity.
4.1. Measurements with External Balance
Figure 9 shows the lift coefficient (
) obtained with the five bioinspired horizontal stabilizers by force balance measurements in the wind tunnel, with zero tail incidence angle.
It is clearly observed that the lift coefficient () increases with the angle of attack until reaching a maximum value () when . This increase in lift coefficient is practically linear up to low angles of attack (). After the maximum lift coefficient (), there is a sharp decrease in lift, which corresponds to the stall condition, that is, the lift is reduced rapidly, therefore the vehicle is not able to fly.
At low angles of attack (), the lift coefficient shows similar values between all horizontal stabilizers. However, when the angle of attack is higher (), a slight difference between them can be appreciated. The maximum value of is obtained for the Horizontal-Wedge-Shaped stabilizer (HW-tail), being higher than the Square-Fan-Shaped stabilizer (HSF-tail), being higher than the Forked-Shaped stabilizer (HFK-tail), higher than the Rounded-Fan-Shaped stabilizer (HRF-tail), and higher than the Notched-Shaped stabilizer (HN-tail).
Figure 10 shows the aerodynamic drag coefficient (
) obtained with the five bioinspired horizontal stabilizers by force balance measurements in the wind tunnel.
In all bioinspired horizontal stabilizers, the values of the aerodynamic drag coefficient () at all angles of attack are practically the same; only HFK and HN-tails show slight differences at very high angles of attack, around .
The aerodynamic drag coefficient () increases with the angle of attack. At low angles of attack, between , the aerodynamic drag coefficient presents a typical value of these vehicles, with values less than 0.1. The minimum drag coefficient () is obtained during the cruise phase between .
Figure 11 shows the polar curve obtained for the five bioinspired horizontal stabilizers by force balance measurements in the wind tunnel.
Figure 12 shows the aerodynamic efficiency (
) obtained for the five bioinspired horizontal stabilizers by force balance measurements in the wind tunnel.
The aerodynamic efficiency values vary slightly among the different horizontal stabilizers across all angles of attack. However, all of them present a similar trend, that is, as the angle of attack increases, the efficiency also increases until reaching a maximum value () at the angle of attack of . In this flight condition, preferable for take-off and landing flight phases, the highest value of is achieved with the HSF-tail () followed in descending order by the configurations of HW, HN, HRF, and HFK.
For higher angles of attack (), the aerodynamic efficiency decreases progressively until reaching the stall condition, where a sharp loss of efficiency occurs.
The most interesting region is presented for the cruise flight (), where again the highest value of aerodynamic efficiency is obtained with the Squared-Fan-Shaped stabilizer (HSF-tail). As a consequence, this horizontal stabilizer becomes the best candidate for implementation on the vehicle, as it has the potential to enhance the autonomy and range of the vehicle.
Figure 13 shows the pitching moment coefficient (
) obtained for the five bioinspired horizontal stabilizers by force balance measurements in the wind tunnel. These measurements are taken at the reference point
, located at
from the nose of the MAV (
Figure 14). This is a fixed point joining the MAV and the external balance and is located near the aerodynamic center of the vehicle (
).
The aerodynamic center of the vehicle (
) can be easily calculated by applying the following expression:
where
is the slope of the pitching moment coefficient obtained directly from
Figure 14 and
is the slope of the lift coefficient obtained from
Figure 9 . Therefore, the aerodynamic center of the vehicle is placed at
from the nose of the vehicle (see
Figure 13).
The five bioinspired stabilizers show similar values of during all angles of attack. Notably, these configurations are longitudinal stables, as the curves intersect with the X-axis with negative slopes () during the cruise flight phase. Consequently, the MAV can maintain stable and level flight with relatively low angles of attack () without requiring a constant force on the horizontal stabilizer to maintain its attitude during flight. In other words, the MAV naturally maintains equilibrium during the cruise flight, avoiding a tendency to ascend or descend. This natural equilibrium, with during the cruise flight, is crucial for both the efficiency and safety of the vehicle.
It can be seen that all bioinspired horizontal stabilizers present with an angle of attack between .
A summary of the relevant aerodynamic parameters with the values of the best horizontal stabilizers is presented in
Table 4.
Table 5 presents the variations of these aerodynamic parameters between different horizontal stabilizers, providing a clearer representation of how these parameters increase or decrease. Based on this data, it can be concluded that the Squared-Fan-Shaped stabilizer (HSF-tail) is the selected implementation solution for the MAV.
Table 6 summarizes the values of the aerodynamic efficiency (
) during cruise flight (
) for the five bioinspired horizontal stabilizers.
4.2. Deflection-Horizontal Stabilizer
After selecting the horizontal stabilizer HSF-tail as the solution for implementation on the MAV, a detailed study of stabilizer deflection is conducted to investigate the influence of aerodynamic forces under various conditions. This experimental analysis is crucial for acquiring deep aerodynamic insights and ensuring the longitudinal stability and control of the vehicle during flight.
The horizontal stabilizer is tested at different angles of incidence, from
, to
, with an interval of
. When the angle of incidence is negative, the stabilizer exhibits an upward deflection, whereas when it deflects downward, the angle of incidence is positive (see
Figure 15). Within each angle of incidence, the entire range of angles of attack is studied.
Figure 16 shows the lift coefficient (
) for the HSF-tail with all angles of incidence. It is obvious that as the angle of incidence becomes negative (upward deflection), the lift coefficient decreases in all ranges of angles of attack compared to the stabilizer with a zero angle of incidence (orange curve). On the contrary, when the angle of incidence is positive (downward deflection), the lift coefficient is higher than that of the zero angle of incidence. The data clearly shows that the greater lift coefficient is obtained at an angle of incidence of
.
Similar to the impact on lift force, the variation of the horizontal stabilizer deflection will also influence the aerodynamic drag characteristics.
Figure 17 shows the aerodynamic drag coefficient (
) for the HSF-tail at various angles of incidence.
The aerodynamic drag variation due to horizontal stabilizer deflection will depend on the angle of attack, the orientation of the wing, and the flight conditions. In this context, it is observed how negative angles of incidence (upward deflection) result in an increased aerodynamic drag coefficient when compared to the zero angle of incidence (). In contrast, positive angles of incidence yield reduced values of aerodynamic drag over the entire range of angles of attack in comparison to the zero angle of incidence. The lowest aerodynamic drag coefficient is achieved when employing an angle of incidence of .
Figure 18 shows the pitching moment coefficient
curve for all angles of incidence measured at the reference point
. As in the previous cases, adjusting the horizontal stabilizer deflection leads to observable changes in the pitching moment coefficient. Deflection of the stabilizer should shift the pitching moment curve by adjusting the trim angle of attack (the angle of attack at which the pitching moment coefficient is zero) without substantially changing the pitching moment slope.
In the case of zero angle of incidence (), the moment coefficient curve intercepts the X-axis at approximately at , providing a MAV longitudinal stable under this condition. As the angle of incidence becomes negative, the curves shift upward with respect to the curve corresponding to the zero angle of incidence, increasing the pitching moment coefficient. The opposite occurs when the angle of incidence becomes positive, the curves shift downward, and the value of decreases.