Experimental analysis of aircraft directional control effectiveness

Abstract

Aircraft directional control effectiveness is analyzed through experiments in wind tunnel. Control surfaces on low aspect ratio lifting surfaces exhibit different lifting capabilities compared to those with high aspect ratio. Such behavior must be carefully considered in the preliminary design phase to avoid any overestimation in size, weight, costs and emissions. Traditional sizing methodologies are based on coupling the effects of the wing planform (e.g. aspect ratio) at low angles of control surface deflection with the effects of wing section (e.g. chord ratio) evaluated on section data in the full range of control surface deflection, so that the non-linear aerodynamics is inherited from 2D data, completely neglecting the different aerodynamic behavior of a low aspect ratio wing at high angles of deflection. To fill this gap, an experimental wind tunnel test campaign on a generic regional turboprop aircraft model with a modular vertical tail with rudder has been performed. Results indicate that the aircraft design methodologies present in public literature underestimate the control surface effectiveness at high angle of deflections by 15% to 25%, leading to an average overestimation of control surface size.

Introduction

There are conditions in which the aircraft flight path lies outside the aircraft longitudinal plane. In this case, the projection of the velocity vector in the horizontal plane forms an angle with the aircraft centerline: the angle of sideslip β. The problem of aircraft stability and control is to keep the aircraft in equilibrium at the desired angle of sideslip [1], which is usually zero.

There are several flight conditions or maneuvers that introduce sideslip. These must be opposed by some yawing moment to keep the desired sideslip angle. This yawing moment is usually supplied by a control surface, i.e. the rudder, installed on a vertical, low aspect ratio lifting surface, i.e. the vertical tailplane, which should be located with the greatest possible distance aft the center of gravity. See Fig. 1 for reference.

The sizing of the vertical tail is driven by several requirements, depending on the flight phase and aircraft configuration [2], [3], [4]. In particular, for multi-engine airplanes, an engine failure at take-off is the critical condition, as the anti-symmetric thrust at low speed yields to a significant yawing moment that must be opposed by the vertical tail to keep the aircraft controllable within $5^{\circ }$ bank angle [5], [6]. The complex aerodynamics developed in such condition is shown in [7].

Unconventional configurations, such as aircraft with distributed propulsion, may employ differential thrust as a mean to reduce or eliminate the vertical tail and be still compliant with regulations, although aero-propulsive interactions and system robustness must be carefully investigated, while different safety criteria could be applied [8], [9], [10], [11].

As performance and maneuverability are key aspects for military aircraft, investigations on the use of thrust vectoring [12] and jet actuators [13] proved better control capability and effectiveness, while reducing the vertical tail size or even eliminating it. This leads to additional benefits as drag and weight reduction as well as a smaller radar cross-section, but it adds the complexity, mass and costs of the active control system.

As hundreds of accidents involving propulsion system failures on multi-engine airplanes resulted in killing thousands of people [14], it is fundamental that aircraft controllability and performance must be adequate also after engine failure. This involves control surface sizing and effectiveness.

The aircraft yawing moment may be expressed in the usual formulation

$$N=q_{\infty }Sb{C}_N$$

where $q_{\infty }$ is the flow dynamic pressure, S is the reference wing area, b is the reference wing span, and $C_N$ is the yawing moment coefficient, which may be exploded in

$$C_N=C_{N_0}+C_{N_{\beta }}\beta +C_{N_{{\delta }_r}}{\delta }_r+C_{N_{{\delta }_a}}{\delta }_a$$

where $C_{N_0}$ is a term accounting for asymmetries, $C_{N_{\beta }}$ is the rudder-fixed directional stability derivative, β is the sideslip angle, $C_{N_{{\delta }_r}}$ is the directional control derivative, also known as rudder control power, ${\delta }_r$ is the rudder deflection angle, $C_{N_{{\delta }_a}}$ is the yawing moment derivative due to ailerons deflection, and ${\delta }_a$ is the aileron deflection angle. The quantities of interest are positive as indicated in Fig. 1.

Aircraft directional stability has been widely discussed in [15], [16], [17], [18], [19]. As concern directional control, it can be shown that [1]

$$C_{N_{{\delta }_r}}=\frac{d{C}_L}{d{\alpha }_v}\frac{d{\alpha }_v}{d{\delta }_r}{\eta }_v\overline{V_v}$$

where $d{C}_L/d{\alpha }_v$ is the lift curve slope of the vertical tail, $d{\alpha }_v/d{\delta }_r$ is the control surface effectiveness, ${\eta }_v$ is the dynamic pressure ratio (accounting for wing-body and propeller wake, if any), and $\overline{V_v}$ the vertical tail volume coefficient, which is a scaling factor of reference parameters $S_v{l}_v/Sb$, stating how big ($S_v$) and far ($l_v$) is the vertical tail with respect to the wing area S and span b.

It should be clear that the magnitude of the yawing control moment N, once frozen the geometry of the aircraft wing-body, is driven by the rudder control power $C_{N_{{\delta }_r}}$. Thus, the aircraft designer may act on the terms of Eq. (3).

As concern the first term, the lift curve slope of the vertical tail $d{C}_L/d{\alpha }_v$, shortly written as $C_{L_{{\alpha }_v}}$, is limited by some considerations on the required aircraft directional stability [2]. This term may include most of the aerodynamic interference among the main aircraft components [20], but it has been shown that the interference factors are different from the case of sideslip without rudder deflection [21].

The second term $d{\alpha }_v/d{\delta }_r$ is also known as rudder control effectiveness τ. This parameter relates the rudder deflection ${\delta }_r$ to an equivalent change in the local angle of attack ${\alpha }_v$. Its magnitude, with a theoretical maximum value of 1, depends on the vertical tail planform and decreases with rudder deflection ${\delta }_r$, because of non-linear aerodynamic effects.

The last two terms are often grouped as ${\eta }_v\overline{V_v}$, indicating a direct proportionality between the rudder control power $C_{N_{{\delta }_r}}$ and the vertical tail area $S_v$.

A standard design procedure for multi-engine airplanes provides the sizing of the vertical tail planform area $S_v$ to comply with the (airborne) minimum control speed $V_{\text{MC}}$, which is 1.13 the aircraft stall speed in take-off conditions for large airplanes [5], [6]. The sizing of the vertical tail area $S_v$ depends from the values of the vertical tail lift curve slope $C_{L_{{\alpha }_v}}$ and rudder effectiveness τ. If these are not sufficient to achieve the desired rudder control power, an increase in volume coefficient is necessary (see again Eq. (3)). By assuming negligible changes in vertical tail planform and moment arm, a larger volume coefficient means a larger vertical tail area. This yields to an increase in weight (including a rearward shift of the aircraft center of gravity), parasitic drag, cost, and emissions. Moreover, it can be shown that an excessively large vertical tail area increases directional stability at the expense of controllability at high sideslip angles, limiting cross-wind landing capability [17]. Therefore, the rudder effectiveness τ should be chosen to match the desired minimum control speed in take-off and to effectively counteract cross-winds in landing.

Although methods to calculate the rudder effectiveness τ are presented in major aircraft design books, e.g. Ref. [4], [20], [22], recent numerical analyses and wind tunnel tests on the twin-engine Tecnam P2012 utility airplane (Fig. 2, Fig. 3a and Ref. [23], [24]) provided high values of the rudder effectiveness, as shown in Fig. 4a. Moreover, numerical analyses on a variety of rudder geometries (partly described in Ref. [21]) also provided a higher control effectiveness with respect to semi-empirical methods for generic vertical tail planforms, as shown in Fig. 3b and Fig. 4b. The last figure also highlights that the effect of the Reynolds number is not significant in the range between 1 and 5 millions.

Conversely, results of semi-empirical methods are in better agreement with wind tunnel data on horizontal tails. Fig. 5a presents the calculated elevator effectiveness for the Tecnam P2012 horizontal tail with aspect ratio

, whereas Fig. 5b presents data extracted from the work of Garner [25] on a horizontal tail with

.

Thus, it appears that semi-empirical methods underestimate the control surface effectiveness of short aspect ratio lifting surfaces (

) from 15% to 25% at high deflection angles. This pushed for further investigations on the subject.

To understand the phenomenon, pressure and velocity distributions calculated with RANS simulations in Simcenter STAR-CCM+ at the mean aerodynamic chord station of a generic vertical tail [21], without sideslip and with rudder deflected, have been compared with the same quantities on the same airfoil section in a 2D simulation. Fig. 6 shows that the airflow is completely separated on the 2D control surface at high angle of deflection, while the section extracted from the 3D simulation has only a mild separation, indicating a three-dimensional effect that is missing in two-dimensional flow.

A literature review seems to confirm this hypothesis. The method for the calculation of the rudder effectiveness reported by Roskam [20] is taken from the USAF DATCOM [26], which seems to provide only a generic approach to estimate the effectiveness of a control surface applied to a lifting wing (or lifting surface). In fact there is no specific difference in the approach among flaps, ailerons, and lower aspect ratio lifting surfaces like tails. The effect of

on effectiveness seems to be particularly relevant for low aspect ratio vertical tails (

between 1.5 and 3.0). Instead, the experimental results reported in DATCOM are taken from section data at several deflection angles. As a matter of fact, a 2D section is like a 3D planform of infinite aspect ratio [27].

Similarly, Torenbeek [4] calculates the flap, elevator, and rudder effectiveness as the product of two terms: a 2D factor accounting for chord ratio and a 3D correction factor including the non-linear effects of deflections. Interestingly, the method refers to the work of Lowry and Polhamus [28], also cited by Perkins and Hage [1] and Roskam [20], which include data on short aspect ratio wings, whereas the correction factor for the non-linear effects of the rudder deflection has been taken from DATCOM tables [26], which are made up of 2D section data taken from NACA reports.

In the first half of the XX century, the NACA conducted extensive wind-tunnel investigations to determine the aerodynamic characteristics of control surfaces to supply data for design purposes. Most of these data were resumed and published in the NACA Wartime Report L-663 by Sears [29]. Other reports that contributed with aerodynamic data of control surfaces are: Ilk [30], including the effect of Mach number on flap effectiveness, with a max deflection of ${10}^{\circ }$; Leroy Spearman [31], evaluating flap effectiveness and hinge moments at several deflection angles; and Cahill et al. [32], who do not calculate flap effectiveness, but include many data on lift increment and hinge moments. These are amongst the references that are used in DATCOM to test its method for the effectiveness of plain flaps. The average error on the 2D lift increment at all deflection angles is 7.75% [26].

In the same fashion of other aircraft design textbooks, McCormick [22] provides charts which data are taken from summaries of section data for flaps [33], [34]. He also formulates a very simple method to estimate the rudder effectiveness for low angles of deflection, based on the Weissinger approximation representing the flapped airfoil with two point vortices.

In this work, a wind tunnel investigation on several vertical tail planforms with rudder is presented to characterize the rudder effectiveness of short aspect ratio lifting surfaces and to provide charts useful in aircraft design and performance analysis. Section 2 describes the wind tunnel model, the test matrix and the setup of the experimental investigations. Section 3 provides a discussion on the results. Conclusions are drawn in Sec. 4.