Effect of Tail Dihedral Angle on Lateral Directional Stability Due to Sideslip Angles and Disturbance - Final Edit

8/19/2019 Effect of Tail Dihedral Angle on Lateral Directional Stability Due to Sideslip Angles and Disturbance - Final Edit

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Effect of Tail Dihedral Angle on Lateral Directional

Stability due to Sideslip Angles

Nur Amalina Musa∗, Shuhaimi Mansor†, Airi Ali‡, and Mohd Hasrizam Che Man§

Faculty of Mechanical Engineering, Universiti Teknologi Malaysia, Skudai, Johor, 81310, Malaysia

This paper will describe the aerodynamic characteristic of complete aircraft equipped

with conventional tail and V-tail configurations. Based on lateral-directional stability, the

introduction of tail dihedral angle can significantly affect the yaw stability derivative of an

aircraft. The wind tunnel test was conducted for sideslip angle, from -25◦ to 25◦ and the

results were used to verify the CFD works. Good agreements were achieved at a lower

sideslip angle which is below 15◦. Then, CFD will be used to study the flow field around

the tail region and figure out the effect on the directional stability. This study found that

during sideslip condition, conventional tail stall at a lower sideslip angle and only effective

at lower sideslip condition. This study shows that the V-tail configuration provide anadvantage at higher sideslip condition. The interactions of V-tail vertical tailplane slightly

increase rolling stability thus causes the reductions in yawing motion.

Nomenclature

β Sideslip angleb Wing spanLf Length of fuselageS w Wing surface areac̄ Wing mean chordbt Tail spanc Tail chordC l Rolling moment coefficientC y Side force coefficientC n Yawing moment coefficientC nβ Yawing moment due to sideslipC yβ Side force die to sideslipC lβ Rolling moment due to sideslipCFD Computational Fluid DynamicsT 35 Conventional tail◦ Degree

I. Introduction

Recently, aviation industry progressively seek for aircraft designs which not only look good but better inperformance. This leads to the introduction of unconventional design in order to improve aerodynamic

characteristics. One of them is tail part. The tail provides stability and control to aircrafts and it has theability to restore the aircraft from perturbation in pitch, yaw and roll. It is vital that the aircraft is stablein handling the moments created from various disturbances while maintaining the body under control [1].

∗PHD student, Department of Aeronautics, Automotive & Ocean Engineering and AIAA member†Associate Professor, Department of Aeronautics, Automotive & Ocean Engineering‡Research Officer, Aeronautical Laboratory§Research Officer, Aeronautical Laboratory

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American Institute of Aeronautics and Astronautics


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Meanwhile, aerodynamicist believes that tail surfaces add wetted area and structural weight hence theyoften sized as small as possible. Although in some cases this is not optimal, the tail is generally sized basedon the required control power [2]. There are attempts to completely remove tails from aircraft in order toreduced aerodynamic drag and weight, however, this result in poor handling qualities which affects safety.But the development of fly by wire flight control system technology made it possible to design a taillessaircraft like B-2 [3].

Based on that, lots of unconventional empanage have been design including v-tail configuration whichremoved the vertical tail. Basically ,vertical tail provides lateral directional stability, yaw damping and

effective directional control [3]. In performance point of view, the disadvantages of vertical tail are increasedin aerodynamic drag and weight penalties [3]. While from the stability and control point of view, thedisadvantages of vertical tails is the reduction in their directional stability as the effectiveness of yaw controlcontribution was reduce at the higher angle of attack. In this case, V-tail need to cater the role provides byvertical tail [3]. The control surface for the V-tail aircraft is known as ruddervator where the combinationbetween rudder and elevator work to control the pitching and yawing motions of the aircraft. The firstaircraft which introduce the V-tail design was Beech Model 35 Bonanza which was first produced in 1947but was grounded due to safety reason. At this moment, lots of unmanned aerial vehicle used V-tail as itprovides fascinating features.

Nowadays, unmanned aircraft is widely developed for aerial observation and scientific research. Varioustypes and unmanned aircraft configurations were developed in order to fulfill their specific operations andmission requirements. The required flight performance of an UAV is the ability to fly for a very longendurance. The important criteria needed to satisfy this requirement is to design UAV which have highlift to drag ratio and low trimmed drag. Some studies have suggested that a V-tail configuration has lowtrimmed drag due to the reduction in number of parts and wetted area compared to conventional tail [4].Since less parts are required for V-tail, its help reduce the weight of aircraft [5]. Furthermore, it is alsoreported that the V-tail configuration may reduce radar detection[5].Beside the advantages mentioned, thereare frequent reports that there are problems associated with stability and control of a V-tail aircraft[6]. V-tailconfiguration for unmanned aerial vehicle (UAV) design produces cross-coupling effect between yawing androlling moment causing UAV lateral stability and directional control to be unsatisfactory[4]. There are manycases of pilot complaints on the difficulties on flying the V-tail aircraft (Beech Model 35 Bonanza) using aruddervator control input. Several fatal accidents had been reported due to loss of ruddervator control of the V-tail aircraft especially on lateral motions[7]. It is clear that the application of V-tail for unmannedaircraft may cause similar issues on flying and handling qualities on lateral motions especially in dutch rollmode [6].The problems may even be worse if the aircraft is flying under gusty conditions.

II. Methodology

Developing an aircraft requires an accurate aerodynamic data, therefore lots of numerical studies andexperiments were conducted throughout the research. This helped to reduce potential mistake which canaffect the design process [8] and predict the performance of the aircraft itself. Computational Fluid Dynamic(CFD) simulation offer lower cost to evaluate and optimize the design compared to wind tunnel testing butthe accuracy of the data only valid for lower condition and it is proven through this study.

In this research, wind tunnel test data was used to correlate and validate CFD results. The simulationsettings such as meshing technique and turbulence model which gives good agreements with the experimentwere retain to study the flow field around the tail area. The CFD also helped to visualize and capture thespecific aerodynamic phenomena around the tail region.

A. Wind Tunnel Test Model

A one fifth Scale UTM-UAV model constructed using fiberglass was used in the experiment. The tail part ischangeable in order to test different tail configurations. There are three sets of V-tail with different dihedralangle (35◦, 47◦ and 55◦) and one conventional tail set. The dihedral angle is measured from horizontal planeto the tail chord plane and the selection of angle were based on NACA Report [9]. The span for vertical andhorizontal stabilizer for the conventional tail were derived from 35◦ V-tail projection areas to the horizontaland vertical planes, hence, the total references area would be the same[4]. This is due to the fact that, basedon isolated tail theory, in order V-tail to have the same stability parameters as the conventional tail, they

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must have equal areas [10]. Selection of dihedral angle starts at 35◦ and the value is arbitrary [11]. V-tailwith 35◦ dihedral angle was taken to be the baseline tail part for the projected conventional tail. The mainwing of the aircraft was equipped with 1◦ anhedral angle. The parameters of the model are listed in Table1.

Table 1. Summary of Model Parameter

Parameter V-tail (35◦) V-tail (47◦) V-tail (55◦) T-tail (35◦)

Wing span,b (m) 0.791 0.791 0.791 0.791Length of fuselage,Lfc (m) 0.51 0.51 0.51 0.51

Wing surface area,S w (m3) 0.067432 0.067432 0.067432 0.067432

Wing Mean chord,c̄ 0.0852 0.0852 0.0852 0.0852

Tail span,bt (m) 0.282 0.282 0.282 0.231

Tail chord,c 0.062 0.062 0.062 0.062

(a) V-tail with 45◦ dihedral angle (b) V-tail with 55◦ dihedral angle

(c) Conventional tail with Projected Area from 35◦ di-hedral angle

(d) V-tail with 35 dihedral angle (Baseline)

Figure 1. Configurations of wind tunnel test models

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B. Test Set up

This research measured the aerodynamics characteristics from a wind tunnel test and the prediction of vortexstructure using computational fluid dynamic (CFD). The wind tunnel tests for V-tail configurations wereconducted at the speed 40m/s for various sideslip angles, β from -25◦ to 25◦ with 5◦ of increment. CFDanalysis results were validated for V-tail configurations with the same conditions with the wind tunnel test.CFD analysis were then carried out for V-tail and T-tail configurations for sideslip angle, β = 0◦, 5◦, 10◦,15◦, 20◦, 25◦, 30◦ and 35◦.

1. Computational Fluid Dynamics (CFD)

CFD analyses for both configurations (V-tail with dihedral angle, 35◦ and T-tail) were performed using acombination of structured and unstructured meshing methods. The structured meshing method producedan initial layer with controlled size of less than 6.125 mm high over the model surface. The CFD analysiswas solved using κ − ω SST turbulence model.

2. Wind Tunnel Testing (WT)

The static wind tunnel tests were conducted in the 1.5 m × 2 m × 6 m closed circuit Universiti TeknologiMalaysia Low Speed Tunnel (UTM-LST).This facility is capable to provide maximum wind speed of 80 m/swith maximum turbulence intensity approximately 0.01 % across the test section. The model was mountedon a single strut support while the model angle of attack was fixed to zero degree. Forces and momentssensed by the model were measured using JR3 Six Component Balance. This sensor is capable to returnthree aerodynamic forces and moments and it is placed under the test section floor. The Balance MomentCenter (BMC) is located at the center of this sensor. The sideslip angles were changed by rotating the tunnelturn table and all data have been corrected for tares caused by model strut support.

III. Results

All results presented here are referred to the aircraft center of gravity (CG). The forces and momentsresult related to lateral stability are presented in body axis.

A. Reynolds Sweep Test

In order to determine the suitable test speed, Reynolds sweep tests were conducted at various wind speedsfor zero angle of attack and zero yaw angles. The drag coefficient is then evaluated to find a range of windspeeds where the drag coefficient is independent of the wind speed. The wind speed was varied from 10 m/sto 50 m/s with 5 m/s increments. The Reynold sweep results is presented in Figure 2, from which it is foundthat at 30 m/s and above the drag coefficients were almost identical. The test speed can be selected fromany wind speed fall within this range. However, it is still dependent on the sensitivity of the sensor. Sincethe model is small, the force sensed by sensor will be small at the lowest speed in the range. The effect dueto any small changes in the model may not be detected if the wind speed is too low. The selection should bemade by taking this consideration into account. Hence, wind speed of 40 m/s which correspond to Reynoldsnumber of 0.2064×106 based on wing model chord was selected to be a test speed throughout this study.

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Figure 2. Uncorrected coefficient of drag with variation of wind speed in Reynolds sweep test

B. CFD Result compares with Wind Tunnel Test Data

All CFD analyses have been carefully post processed. The coefficients of side force, yawing moment androlling moment from numerical and experimental study were plotted for comparison and validation purposes.Result from the numerical for side force and rolling moment show a good agreement with experimental datafor sideslip angles up to 25◦ while for Yawing moment, the result is matched only up to 15◦. Side forceand yawing moment coefficients for conventional tail are almost identical compared to 35◦ V-Tail from thesideslip angle of 0◦ to 15◦. Table 2 shows the derivatives related to lateral stability calculated for low sideslipangle (0◦ to 15◦). Compared to experimental data, numerical method is able to predict the derivative of thismodel with maximum error of 6.5%. As to understand the V-tail with wing fuselage combination, additionalfactors such as downwash and sidewash associated with the wing fuselage vortex must be considered [9].

Figure 3. Yawing moment coefficient against sideslip angle

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Figure 4. Side force coefficient against sideslip angle

Figure 5. Rolling moment against sideslip angle

Table 2. Lateral Stability Derivative for Numerical and Experimental data

Derivative(Deg−1) CFD Conventional Tail CFD V-Tail Wind Tunnel V-Tail V-Tail Error(%)

C nβ 0.0546 0.0595 0.0622 -4.37

C yβ -0.3432 -0.3721 -0.3496 6.42

C lβ -0.1173 -0.1628 -0.1553 4.82

As the relative strength of aircraft directional stability and dihedral effect will determine several lateral-directional characteristics of the aircraft itself. V-tail contributes to strong directional stability as comparedto Conventional tail but at the same time V-tail also generate higher rolling moment and this will lead tothe cross-coupling problem when aircraft start to yaw. Conventional tail has a less directional stability andit is likely to induce spiral instability which caused the roll and yaw motion to be slightly decreased due todamping effect cause by vertical tailplane . Referring to aerodynamic principal which indicates the changesin dihedral angle can alter the angle of attack along span wise tail section while aircraft in sideslip mode,this leads to change in lift distribution along span wise section of the tail which altered the lateral directionalaerodynamic derivatives [12].

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(a) Wake region at rudder for Conventional tailconfiguration at sideslip angle 15◦

(b) Streamwise vortex generated by fuselage cross-flow for V-tail configuration at sideslip angle 30◦

Figure 6. Non-linear response of Conventional tail and V-tail configuration

The non-linear response of Conventional tail configuration is starts at sideslip angle, 15◦ due to the stall

of vertical tail (rudder) as shown in Figure 6(a). On the other hand, Figure 6(b) shows the non-linearresponse of V-tail configuration start at sideslip angle of 30◦ due to the stream wise vortex generated by thefuselage cross flow [3].

Figure 7. Static pressure distribution at sideslip angle 15◦

As shown by numerical analysis, the front wing fuselage generated asymmetric downwash airflow to therear tail. This effect will destroy the vortex formation on the V-tail [5].

C. Effect of Tail Dihedral Angle on Directional Stability

National Advisory Committee for Aeronautics (NACA) have conducted a lots of wind tunnel test as to gain

understanding in aircraft directional stability but they dealt with geometries which differ from the typicalcivil aircraft. This is due to the fact that all the test were motivated by World War II where the result wereused to design new fighter aircrafts [13][14].The understanding was basically developed based on certaingeometry but yet not accurate to be applied to any typical civil aircraft. In this research, a typical civilaircraft with different V-tail dihedral angle were used to obtain a basic understanding on aircraft directionalstability characteristics.

Considering special case during wind tunnel test, when the direction motion remains unchanged butaircraft is yawed, hence the sideslip and yaw angle are related by relation, ϕ = -β . Due to response of sideslip motion in wind tunnel test, typically both yawing and rolling moment are created [15]. The aircraftsaid to have a stable in roll if C lβ < 0. Roll moments are created when the aircraft starts to sideslip and

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depends on the arrangement and design of vertical tail. The rolling moment produced by vertical tailstends to bring back the aircraft to the wing level attitude. The introduction of tail dihedral angle werealso contributes to the production of side force during sideslip and created an aditional effect in directionalstability.

(a) Yawing Moment (b) Rolling Moment

Figure 8. Experimental results of comparison between yawing and rolling moment characteristics

Figure 9. Experimental results of side force versus yaw angle

A conventional tail configuration is added in the experiment to see how V-tail will perform compared to

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Table 3. Yawing and Rolling Moment Derivatives for DifferentDihedral Angle

Tail Configuration Dihedral Angle (deg) C nβ C lβV-tail 35 0.0016 -0.0028

V-tail 47 0.0032 -0.0061

V-tail 55 0.0041 -0.0062

Conventional tail 0 0.0025 -0.0041

the conventional tail. However a fair comparison can only be achieved if these two tails configuration havethe same projection area. This is due to the fact that a V-tail of same span but with different dihedral anglewill produce different projection area; hence, the side force is expected to be much larger at high dihedralangle. Since the yawing moment is a product of the side force, one can expect that higher V-Tail dihedralangle will provide better lateral stability.

The projection area for the conventional tail used in this experiment is equivalent to the baseline configu-ration (35◦ V-tail). The gradient of yawing moment due to sideslip angle, C nβ for Conventional tail is higherthan baseline configuration which indicates that V-tail is less stable directionally than conventional tail.However, this is only true for low sideslip angle (-10◦ ≤ β ≤ 10◦). Referring to Figure 8, at sideslip angle, β = ± 15◦, the yawing moment for V-tail aircraft still in linear region while yawing moment for conventional

tail start to flat out indicating the aircraft is going to stall. This is due to the fact that conventional tailis always positioned in serious asymmetric downwash region created by wing fuselage, which will not createany additional lateral forces [5][14][6][16].

The roll stability is also reduced in V-tail configuration; however, the linear region is still present inconventional tail for higher sideslip angle. Based on Figure 9, V-tail aircraft is slightly more sensitive to theside flow as the horizontal components of lift on the two surface combine to produces a net side force to thatopposes the sideslip motion and is proportional to the sideslip angle [4] and this will make the aircraft morevulnerable to turbulence especially side gust at lower sideslip angle.

It can be conclude that if dihedral angle is too small; it will generate less yaw stability effect duringflight while if it is too large, it will affect the longitudinal stability but it also can make directional stabilityrecovery moment too excessive causing the aircraft to lose the power to control the rudder during slidingmotion. Because of this, aircraft could start to rotate and enter the tail spin condition [5].On the other hand,too much dihedral angle can cause safety issues in Dutch roll modes especially during high speeds as in thecase of F4U Corsair and the V-tailed Beechcraft Bonanza are famous victim of this effect.

Based on NACA Report, 47◦ dihedral angle provide a better longitudinal and lateral stability as comparedto Conventional tail [9]. This is due to the decrease in the rate of change of effective downwash with angleof attack due to the high tail position and the favorable effect of sidewash at the tail. V-tail must replacehorizontal stabilizer as close as possible as a reservation for static stability and control in extreme situationsin order to avoid sudden stall [10] .

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Figure 10. Variation of Directional Stability with Tail Dihedral Angle

Figure 11. Eigenvalues for different V-tail configuration

Neglecting the Dutch roll problem at high speeds, tail dihedral angle boosts the yawing stability of theaircraft. Figure 10, shows that, the C nβ value increased as higher dihedral angle were applied due to thereason that higher dihedral angle provide better directional stability. This is true as the eigenvalues for allV-tail configurations are located at the left side with negative real parts of the S-plane plot which lies instable region. Note that the eigenvalues for V-tail with 55◦ dihedral angle is located further left from the

imaginary axis compared to those with lower dihedral angles, indicating stable condition. As the dihedralangle reduces, the eigenvalues moves towards positive side, indicating less stable conditions. These showsthat the V-tail with greater dihedral angle will have greater degree in directional stability as it eigenvaluesare moves away from unstable region as shown in S-plane plot. Higher yawing moment provides a betterstability and controllability during landing and takeoff in crosswind conditions [17]. In terms of lateralhandling qualities, the important parameters are the vertical tail surface and the dihedral angle as thechanges of these two parameters will imply positive changes to the stability derivatives C nβ and C lβ; hence,satisfy the Spiral and Dutch roll mode based on Routh conditions [18].

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D. Study Tail Contribution Only

In this section, the test was made in such a way as to measure the moments contributed by the tail surfaceitself.

(a) Yawing moment (b) Rolling Moment

(c) Side force

Figure 12. Tail contributions to directional stability

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Table 4. Lateral Stability Derivative for Numerical and Experimental data

Tail Configuration Dihedral Angle, deg (◦)Shaded Area, deg(◦)based on YawingMoment Plot (Positive Region)

V-tail 35 0.447705

Conventional tail 0 0.425456

Figure 12 show that tail plays a vital role in determining the stability and performance of the aircraft. Thegraph compares the two types of configurations which is wing-fuselage without tail and with the completeaircraft configurations as to determine the tail contribution to directional stability of the aircraft. It is foundthat V-tail contributes 5% to directional stability to the aircraft compared to conventional tail.

IV. Conclusion

The static wind tunnel test focusing on effect of directional stability was used to verify the CFD simula-tion. The results agreed with the experiment up to 25◦ sideslip angle and the simulation was used to analyzeflow field around the tail area. V-tail with 35◦ dihedral angle was chosen as the baseline configuration. Thispaper investigates the effect of different tail dihedral angles and tail type to the aerodynamics characteristicsof the same wing body fuselage. The conventional tail was constructed based on projection area of the V-tail.Introducing dihedral angle in tail design caused the increment in rolling moment. Wind tunnel test has beendone as to eliminate the effect of interaction between wing-body fuselage and found that V-tail produce abetter directional stability.

References

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2Roskam, J., Aiplane Design (Part III:Layout Design of Cockpit, Fuselage, Wing and Empennage: Cutaways and Inboard Profile), DARCorporation, Kansas, USA, 2002, pp. 249-279.

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9Polhamus, R.C., and Moss, J., “Wind-Tunnel Investigation of the Stability and Control Characteristics of a CompleteModel Equipped with a Vee Tail,” NACA TN-1478, Washington,DC, 1947.

10Purser, E.P. and Campbell, J.P., “Experimental Verification of a Simplified Vee-Tail Theory and Analysis of AvailableData on Complete Models with Vee-Tails,” NACA TR-823, Washington,DC, 1944.

11Greenberg, H., “Comparison of Vee-Type and COnventional Tail Surfaces in Combination with Fuselage and Wing inthe Variable-Density Tunnel,” NACA TN-815, Washington, DC, 1941.

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large aspect ratio tailless flying wing aircraft,” Chinese Journal Aeronautic , Vol. 27, No. 5, Oct. 2014, pp. 1149-1155.13House, A.O., and Wallace, R., “Wind-Tunnel Investigation of Effect of Interference on Lateral-Stability Characteristics

of Four NACA 23012 Wings, an Elliptical and Circular Fuselage and Vertical Fins,” NACA TR-705, Washington, DC, 1941.14Nicolosi, F., Della Vecchia, P., and Ciliberti, D., “An Investigation on Vertical Tailplane Contribution to a Aircraft

Sideforce,” Aerospace Science Technology , Vol. 28, No. 1, Jul. 2013, pp. 401-416.15Nelson, R.C., Flight Stability and Automatic Control , 2nd ed., McGraw-Hill International Editions, New York, 1998.16Abzug, M.J., “V-Tail Stalling at Combined Angles of Attack and Sideslip,” Journal Aircraft , Vol. 36, No. 4, Jul 1999,

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Effect of Tail Dihedral Angle on Lateral Directional Stability Due to Sideslip Angles and Disturbance - Final Edit