1American Institute of Aeronautics and Astronautics

Stability and Control Characteristics of a NewFAR23 Airplane

Kasim Biber*

Biber Aeronautical Research, Istanbul, Turkey 34870

Wind tunnel tests were conducted for a power-off and stick-fixed 1/12 scale model of a high-wing FAR 23 cargo transport airplane at a Reynolds number of 0.92 million and Mach number of0.2. Tests included simultaneous measurements of six-component force and moment by using thetunnel external balance. Effects of flap, elevator, rudder and aileron on longitudinal and lateral-directional aerodynamics were investigated in stability axis system. Pertinent static stability andcontrol derivatives were obtained and used for the analysis of airplane open loop dynamic stabilityand response. The airplane in its cruise flight phase appears to achieve better than level 3longitudinal flying qualities. Changes are suggested in size and shape of airplane components forimprovement in design.

Nomenclaturec = mean aerodynamic chordCD, CL, CY = drag, lift and side force coefficientCD0 = drag coefficient for zero-angle of attackCD1 = drag coefficient for flightCL0 = lift coefficient for zero-angle of attackCL1 = lift coefficient for flightCLmax = maximum lift coefficientCM, Cn, Cl = pitching, yawing and rolling moment coefficientCMCL = variation of pitching moment coefficient with lift coefficientCLα CDα, CMα = lift, drag and pitching moment coefficient slopeCLα

. , CMα. = variation of lift, and pitching moment coefficient with the rate of change of angle of attack

CLδf = variation of lift coefficient with flap angleCLδe, CDδe, CMδe = variation of lift, drag and pitching moment coefficient with elevator angleCLu, CDu, CMu = variation of lift, drag and pitching moment coefficient with air speedClβ, Cnβ, CYβ = variation of rolling, yawing and side force coefficient with sideslip angleClδr, Cnδr, CYδr = variation of rolling, yawing and side force coefficient with rudder angleClδa, Cnδa, CYδa = variation of rolling, yawing and side force coefficient with aileron angleClp, Cnp, CYp = variation of rolling, yawing and side force coefficient with roll rateClq, Cnq, CYq = variation of rolling, yawing and side force coefficient with pitch rateClr, Cnr, CYr = variation of rolling, yawing and side force coefficient with yaw rateih, iw = horizontal stabilizer and wing incidence angleIxx, Iyy, Izz = rolling, pitching, and yawing moments of inertiaL/D = lift-to-drag ratioN0 = neutral pointP = periodp, q, r = roll, pitch and yaw rateS = wing areaT1/2, N1/2 = time and cycle to damp-to-half amplitudeW = airplane maximum weightα = angle of attackβ = sideslip angle * Engineering Consultant. Address: Karliktepe Mah, Serap Sok, No 4/10, Kartal, Istanbul. E-mail: kxbiber@yahoo.com Senior member AIAA.

44th AIAA Aerospace Sciences Meeting and Exhibit9 - 12 January 2006, Reno, Nevada

AIAA 2006-255

Copyright © 2006 by Kasim Biber. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

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Fib)

δf, δe, δr, δa = flap, elevator, rudder and aileron deflection angleδal, δar = left and right aileron angle∆δ = change in control deflection∆α = change in angle of attack∆θ, ∆β, ∆φ = change in pitch, sideslip, and bank angle∆q, ∆q, ∆r = change in roll, pitch and yaw rate∆u, = change in horizontal velocityε = downwash angleλ = eigenvalueωn = undamped natural frequencyζ = damping ratioψ = yaw angleτ = roll time constantX, Y, Z = wind tunnel coordinate axis

I. IntroductionThere has been a growing interest in design and

development of a new cost-effective and relatively short-range cargo transport airplane. This airplane should carry 4LD-3 or 4 DEMI or mixed of these standard containershaving 3402-kg (7500-lb) revenue payload over 250 nauticalmiles. For a centerline thrust and reliability, it should also beequipped with a twin-pack engine driving a single-propellerthrough a unique combining gearbox.

Figure 1 shows the airplane 3-view having a high-wing,conventional-tail and fixed-nose and main landing gear.Maximum take-off weight is 8618-kg (19,000 lb), consideredas the certification limit for FAR23 commuter category.1Flight performance has been reported in companionpublications.2,3,4 Because of its rather unique design feature,two-phase wind tunnel tests were conducted on power-off andstick-fixed 1/12 scale model of this airplane. The testsincluded the investigation of flap, elevator, rudder and ailerondeflection on longitudinal and lateral-directionalaerodynamics.

The purpose of this paper is to report the first phase ofthese wind tunnel tests, and to provide static stability andcontrol derivatives. The derivative data was used to determinethe open loop dynamic stability and response characteristics,followed by an analysis to evaluate the airplane flyingqualities. Based on the analysis, suggestions are made forchanges in size and shape of the airplane components forimprovements in design. The suggested changes wereincorporated for the airplane configuration shown in Figure 1.The data presentation is made only for flaps up configurationconsidered as a baseline.

II. Experimental ProcA. Wind Tunnel

The experiments were conducted in the Wichita State Universihigh, 3.05 m (10 ft) wide and 3.66 m (12 ft) long test section. It section pressure. The tunnel is equipped with a pyramidal type extersystem for six-component force and moment data acquisition and red

a)

b

c

)

)

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g. 1 Airplane 3-view geometry, a) top, side and c) front views.

edure

ty low speed wind tunnel,5 having 2.13-m (7 ft)is a closed return tunnel with atmospheric testnal balance and Hewlett Packard 380- computeruction. The raw data is acquired from 6 balance

channels as average of 1024 samples of voltage readings and then converted to forces and moments. Tunnel wallcorrections are applied to the force and moment data. These corrections are namely buoyancy drag, solid and wakeblockage, and streamline curvature in three dimensions as described in Ref 6. The data reduction is made in windaxis system in which the test section centerline is considered as the horizontal. The test data can then be converted tothe body and stability-axis system, as desired. The tunnel coordinate axis consisted of X, Y and Z components andhad its origin at the model center of gravity. The center of gravity was located at the quarter-wing meanaerodynamic chord. The X-axis was in the plane of airplane symmetry and positive in the upstream direction. The Z-axis was also in the plane of symmetry and positive downwards. The Y-axis on the other hand was perpendicular tothe plane of symmetry and positive along the right wing. The resolution in the tunnel instrumentation is as follows:for lift, ±0.9N and ±0.001 (∆CL), for drag ±0.2N and ±0.0003 (∆CD), for pitching moment ±0.1N-m and ±0.0003(∆CM), for dynamic pressure ±4.8 N/m2, pressure transducers ±2.4 N/m2 and ±0.002 (∆CP), and for angle of attack±0.05 deg.

B. Test ModelThe test model was 1/12 scale of the cargo transport airplane. It had 1.83- m (6 ft) span in 3.05 m (10 ft) wide

test section. The fuselage and lifting surfaces were built all separate and then assembled together for the completemodel. The wing was made of solid aluminum in three pieces. For the present tests, it had NACA 4412 airfoil withconstant chord. The modified configuration (Fig 1) was however equipped with a custom design having maximumthickness 18%c root and 13%c tip airfoil. Flap, aileron, elevator and rudder were positioned by using differentbrackets for their angular setting. Tail surfaces were conventional design and made of solid aluminum with NACA0012 airfoil section. They were removed for tail-off wing-fuselage tests. The airplane is projected to have a fixedlanding gear, and therefore, the tricycle gear arrangement was maintained throughout the test program. The mainand nose landing gear was however removed from the fuselage at the last portion of tests to investigate gear effects.The model was installed in the test section by using three-point mount system.

C. Test ConditionsAll tests were made at a dynamic pressure of 268.5 kg/m2 (55 lb/ft2), imposed by the tunnel conditions and

model strength. This corresponds to a chord based Reynolds number of 0.92 million and Mach number of 0.2. In

3American Institute of Aeronautics and Astronautics

Fig. 2 Lift characteristics for flap anglesof 0, 10, 20 and 30 deg. Tail-off case isincluded.

order to improve the Reynolds number effects, boundary layer transition was fixed by two layers of 2.54-mm (0.1-inch) wide and 0.02-mm (0.0008-inch) thick strips at 5% fuselage length, wing chord, and horizontal and verticalstabilizer locations. Tufts and oil flow were used on the model surface to visualize the boundary layer flow patterns.

D. Test MatrixThe complete test program was performed in a series of 108 total tunnel runs. These runs were scheduled in

such a way that the minimum amount of time was spent for the model change. The pitch sweep was made at yawangles, ψ=0, 4, and 8 deg with angle of attack, α, ranging from –8 to 22 deg. The yaw sweep was made at α=0 and 6deg with ψ ranging from –4 to +16 deg. Wing flap had deflections of 10, 20 and 30 deg. The elevator, rudder andaileron powers were determined for both flaps up and down 30 deg cases. However, this paper presents the test datafor only flaps up baseline configuration. The derivatives in general represent the slopes of the best fit-linear data linefrom the origin of axis system. For pitch runs, they were obtained forthe range of angle of attack that corresponds to the linear lift curve.

III. Results and DiscussionA. Longitudinal Aerodynamics

Longitudinal aerodynamics was investigated from pitch runsconducted at zero-yaw. Figure 2 shows CL-α curves for flap angles of0, 10, 20 and 30 deg. Tail-off cases are also included for comparison.The lift coefficient at α=0 deg is 0.298 when δf=0 deg, and it becomes0.925 when δf=30 deg. From this CL-δf relation, the flap effectiveness,CLδf is obtained as 1.215/rad. The maximum lift coefficient is 1.398 forflaps up case having a stall angle 15.6 deg, and it becomes 1.775 forflaps down 30 deg case with a stall angle 11.65 deg. The flaps are

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apparently not effective in producing the amount of lift increment needed for high performance. Removing tailsurfaces results in a decrease of lift curve slope and CLmax. The CLmax contribution from the horizontal surface is0.152 (10.8% of CLmax) when δf=0 deg and 0.106 (5.8% of CLmax) when δf=30 deg.

Figure 3 shows the effect of gear and horizontal and vertical stabilizer components on lift, drag and pitchingmoment coefficient. Table 1 provides the pertinent CL and CD characteristics taken from the figure. Wing alone wasnot tested, but its CLα was estimated to be 5.10/rad, about 10% lower than that of the complete model, as expected.Horizontal stabilizer addition has an effect of increasing CLα, CLmax, and CD0. It changes the CM slope from positiveto negative for static stability, as expected. The CM curves have a difference in slope, CMCL, as much as −0.59,indicating the stability contribution from the horizontal. The model is trimmed when CL=0.311. Gear addition causesa substantial increase, as much as 25%, on CD0. For the complete model, the span efficiency factor, e was estimatedto be 0.81 from a plot of CL

2 with CD for tail-off case, as described in Ref 7. Maximum lift-to-drag ratio, L/D, is12.18.

The incidence for horizontal stabilizer, ih, varied over a range to determine its optimum setting and thecorresponding downwash angle. Figure 4 shows the CM variation with α for incidences from –4 to +4 deg, including

the tail-off. The equilibrium (CM=0) is obtainedwhen ih =0 deg, and therefore, the zero-incidence was used for the rest of horizontalsetting. This was for the convenience of tests,the horizontal tail incidence is normally setsuch that CM>0 at α=0 deg for positive staticstability. Downwash angle can be determinedfrom the CM curves. As described in Ref 6, theintersections of tail-on curve with the tail-offcurve are points where, for a given wing angleof attack, αw, tail-on and –off CM values areequal, that is, the tail is at zero-lift. Therefore,the horizontal angle of attack, αh =αw+ih–ε = 0.Since αh and ih are known from the intersectionpoints; ε may be determined and plotted againstαw. From this plot, the downwash derivativebecomes dε/dα=0.27. The downwash can havesignificant effect on the tail for the type ofhigh-wing configuration having a largepropeller disk diameter. This was evident fromthe behavior of tufts and oil flow attached onwing and fuselage surfaces. Vortices developedon wing and fuselage juncture shed

able 1 Configuration build up for CL and CD data

f α0 (deg) CLα (1/rad) CL0 CLmax CD0

−3.61 4.778 0.297 1.262 0.0344−3.58 4.784 0.296 1.248 0.0477

V −3.23 5.283 0.293 1.393 0.0393HV −3.24 5.283 0.297 1.402 0.0518

Fig. 3 Effect of gear and horizontal and vertical tail components on lift, drag andpitching moment coefficients. W-wing, B-body, G-gear, H-horizontal, V-vertical.

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4 CM variation with α at horizontal from −4º to including tail-off.

Fig. 6 CM variation with CL at elevator anglesfrom −25º to +10º, including tail-off.

downstream and joined with those on the upper corners of fuselage constant section. They apparently reduced theeffectiveness of tail and control elements.

The longitudinal stability was investigated from CM curves, obtained for various elevator angles. Figure 5shows the CM variation with α for elevator angles from –25 to +10 deg in 5 deg increments, including the tail-off.The elevator up, that is, negative deflection has the effect of increasing airplane CL. The elevator down, that is,positive deflection on the other hand has the effect of decreasing CL. The variation is almost linear up to the stall α.The slope of pitching moment coefficient, CMα is –1.66/rad, indicating a stabile airplane with flaps up. The CM

values at α=0 deg were used to determine the elevator power, which CMδe=–1.83/rad. The elevator effectiveness isreduced for deflections beyond –25 deg.

CM0.3dees

B.

moThdesidtaivedeanze

CnrumowiThoftwon

Fig. 5 CM variation with α at elevator angles from−25º to +10º, including tail-off.

5American Institute of Aeronautics an

Neutral point was determined by using the CM variation with CL as shown in Figure 6. The slope of CM curve,CL=–0.32. For the baseline-center of gravity at 0.25c, the neutral point is located at 0.57c. The slope becomes –7c for 0.20c and –0.17c for 0.40c c.g. locations. Power effect, that is, the running propeller would have a

stabilizing effect on the longitudinal stability. The effect reduces the static margin of airplane as much as 0.11c, astimated by the method of Ref 7. The power effect is however not included with the data presentation.

Lateral-Directional AerodynamicsYaw runs were conducted at α=0° to study the effect of rudder deflection on side force and yawing and rolling

ment. Figure 7 shows the variation of side force coefficient, CY with sideslip angle, β including the tail-off case.e rudder was deflected to the right at δr =0, −5, −10, −15, −20, and −25 deg. It was assumed that the left rudderflections would give the same results as the right deflections, due to the model symmetry. The model has positivee force with negative sideslip as expected. At β=−16 deg, the CY has a magnitude of 0.25 for tail-on and 0.1 forl-off configuration. The difference shows the significance ofrtical stabilizer. The side force coefficient due to sideslip has arivative CYβ = –0.86/rad. Side force variation with ruddergle was determined and had a derivative, CYδr =0.23/rad atro-sideslip condition.

Figure 8 shows the variation of yawing moment coefficient,, with β, including the tail-off case. The intersection of zero-dder with tail-off is offset from the origin, indicating somedel asymmetry. The airplane is however directionally stable

th a positive slope, Cnβ=0.132/rad for all rudder deflections.e change of Cn with rudder deflections produces a slope, Cnδr

around 0.132/rad, which is the rudder power. The ratio of theseo derivatives gives, dβ/dδr =1, the equilibrium value, meaninge-degree sideslip for one-degree rudder deflection. Roll

Fig. 7 CY variation with β at rudderangles from 0º to 25º including tail-off.

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stability is presented in Figure 9 including the tail-off case. The slope Clβ has a negative value of −0.115/rad,indicating an effective dihedral. Rolling moment coefficient Cl due to the rudder angle, Cδr, was determined to be0.026/rad.

Pileft ailedeflectiproduceaileron tunnel.6

FiCl, untivariatiolooses variatio

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loop dycalculatbaselinedata forpolar.

Fig. 8 Cn variation with β at rudderangles from 0º to 25º, including tail-off.

6American Institute of Aerona

tch runs were conducted at zero-yaw to investigate thron had positive-down deflections of 0, 5, 10, 15

ons of 0, −5, −10, −15, −20, and −25 deg. This setd in the right direction. The aileron tests were madeis carried away in flight due to helix angle, but it is b

gure 10 shows the aileron effects on rolling moment l δa=20 deg. The maximum Cl is about 0.064, consn with α is almost constant until the stall condition. Tits power gradually as its deflection increases to hign with α. Increase of aileron angle increases the slope

ngitudinal Motion and Responsee static stability and control data obtained from the namic stability and response characteristics. Tableed from the empirical methods.8,9,10,11 The analysis w center of gravity location at 0.25c. Table 3 contains similar airplanes.12 The CL1 value corresponds to the

Fig. 9 Cl variation with β at rudderangles from 0º to 25º including tail-off.

e effect of aileron on rolling and yawing moment. The, 20, and 25 deg and the right aileron negative-up up is meant to have a right roll due to adverse yaw with tail-off because the downwash produced by therought on the horizontal tail as extra load in the wind

coefficient, Cl. Increase of aileron angle, δa, increasesidered satisfactory for the test configuration. The Cl

he aileron power, Clδa is equal to 0.23/rad. The aileronh angles. Figure 11 shows the aileron effects on Cn

Cnα. The control derivative, Cnδa is −0.0115/rad.

Fig. 10 Cl variation with α at left and rightaileron angles from 0º to ±25º.

utics

wind 2 haas m

the a crui

Fig. 11 Cn variation with α at left andright aileron angles from 0º to ±25º.

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tunnel was used to determine the airplane opens a summary of the data in addition to thoseade for only cruise flight at 165 knots, with theirplane mass properties obtained from published

se level-flight, and CD1 is obtained from the drag

7American Institute of Aeronautics

T

−−−−

−−

=

01000545.7039.000142.007.27861.1246.0

2.320062.0031.0

longA

The airplane equation of motion is formulated in state-space model as, x′ = Ax+ηB, where x=[∆u, ∆α, ∆q, ∆θ]T isthe state vector, η=[∆δ] is the control vector, and thematrices A and B contain dimensional stability and controlderivatives, calculated using the corresponding values inTable 2. The matrix A, as defined in Ref 10, has thefollowing values for the longitudinal dynamics of airplane:

Expanding this matrix yields a forth order characteristicequation of the form: A1λ4 + B1λ3 + C1λ2 + D1λ + E1 = 0The coefficients of the characteristic equation areA1=281.6, B1=2565, C1=6421, D1=333.2, E1=107.4. Theeigenvalues for this characteristic equation describe themodes of motion: a) short period mode, λlong1,2 = −4.578 ±1.472I, b) phugiod mode, λlong2,3 = −0.015 ± 0.128i. Theeigenvalues are complex, and have negative real parts. Thismeans the airplane is dynamically stable. If the airplanewere given an initial disturbance, the disturbance woulddecay in time sinusoidally.

The eigenvalues are expressed in terms of dampingand frequency values; λ1,2= η ± iω; where, η=−ζωn andω=ωn(1−ζ2)1/2. The damping ratio, ζ and undamped naturalfrequency, ωn along with the time to half amplitude, T1/2, theperiod, P, and number of cycles of half amplitude, N1/2, arecalculated for the short-period and phugoid motions. Table 4contains the calculated values for the baseline configuration.Of these two modes, the short period mode is of moreimportance because of its relatively high frequency andheavy damping, for which airplane has a rapid respond to anelevator input without any undesirable overshoot. If thismode had light damping and low frequency values, then theairplane would be difficult to control and possiblydangerous to fly. The phugoid or long-period mode has sosmall frequency and light damping that the pilot can easilynegate the disturbances by small control movements. Itwould however cause fatigue on the pilot if the dampingwere too low.

The damping and frequency of both the short- andlong-period modes are in fact a function of aerodynamicstability derivatives. They can be controlled by changes inairplane geometric and aerodynamic characteristics. Forexample, increasing the tail size would increase both thestatic stability and damping of the short-period motion.However, the increased tail area would also increase theweight and drag of the airplane. This in turn reduces theairplane’s performance. There needs to be an optimumperformance that is both safe and easy to fly, and stabilityand control required for the pilot to consider the airplanesafe and flyable. This type of requirements from airplanes

able 2 The static stability and control data(Derivatives are given in 1/rad)

Wind tunnel data Estimated dataCL0 0.303 CLα

. 2.61CD0 0.0518 CLq 9.665CM0 0 CLu 0.027CLα 5.357 CDα 0.191CLδe 0.286 CTxu −0.158CMα −1.662 CMα

. −14.614CMδe −1.833 CMu 0CYβ −0.859 CMq −54.126CYδr 0.229 CYp 0CYδa 0 CYr 0.937Cnβ 0.132 Cnp −0.038Cnδr 0.132 Cnr −0.214Cnδa −0.011 Clp −0.893Clβ −0.108 Clr 0.127Clδr −0.0229Clδa 0.212

Table 3 The airplane data for cruise flight

Altitude, h (ft) 10,000Mach number, M 0.25True Air Speed, U1 (ft/s) 280c.g. location, fraction c 0.25Angle of attack, α1 (deg) 0Weight, W (lbs) 19,000Ixx (slug-ft2) 50,000Iyy (slug-ft2) 45,000Izz (slug-ft2) 90,000Ixz (slug-ft2) 0CL1 0.4CD1 0.0525CTX1 0.0525

Table 4 Longitudinal dynamic characteristicsshort period Phugoid

T1/2 (sec) 0.151 45.184P (sec) 4.267 49.022N1/2 (cycles) 0.035 0.922ζ 0.952 0.118ωn (cycles/s) 0.765 0.129

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8American Institute of Aeronautic

are regulated in flying qualities standards such as those given in MIL-F-8785C and MIL-HDBK-1797, Refs 13 and14. These documents contain a number of criteria to which the dynamic modes of an airplane can be compared topredict the expected flying-qualities levels.

There are four levels of flying qualities. Level 1 implies that flying qualities of an aircraft are clearlysatisfactory to perform a specific task with acceptable pilot workload at all times. At level 2, the aircraft still hasadequate flying qualities, but the pilot workload has increased, or achievable task performance is reduced. Level 3refers to the degradation of flying qualities such that the aircraft is controllable, but the task performance isinadequate, and the pilot workload is very high. Level 4 corresponds to situations where there is a high risk of lossof control. These levels of flying qualities are defined with reference to the Cooper-Harper rating scale.15 Cooper-Harper ratings of 1, 2, and 3 fall in level 1, while 4, 5, and 6are in level 2,and 7, 8, and 9 are in Level 4. References 9, and11 have these ratings expressed graphically for the short-period motion as a function of ωn and ζ values. Based onthose graphical displays, the present cargo transport airplanefor its cruise flight phase appears to achieve level 3 flyingqualities. With regard to the phugoid mode, the airplaneζ=0.118, greater than 0, qualifying for level 2 flying qualities.The airplane configuration apparently needs some changes toimprove its longitudinal flying qualities.

The sensitivity of short-period ωn and ζ values tochanges in stability derivatives was investigated. Thelongitudinal stability derivative, CMα is of importance,because of its dependence on the location of center of gravity.Figure 12 shows the effect of the CMα variation on dynamicstability characteristics. The baseline values correspond to theCMα value of present configuration. Increase of CMα (lessnegative) means moving the Xcg aft towards its neutral point.As a result, ωn decreases and ζ increases linearly for both theshort-period and phugoid modes. Figure 12 shows the effectof another important stability derivative, CMq, on ωn and ζparameters. As the CMq increases (becomes less negative)from the baseline value, the short period ζ decreasessignificantly. This shows the powerful effect of CMq on thedamping ratio of short-period mode.

An analysis was made to determine the free longitudinalresponse of airplane for given initial disturbance. For thisreason, the forth order system of equations of motion wasintegrated by using the classical Runge-Kutta integrationmethod. Figure 13 shows the response characteristics withinitial conditions ∆α=5 deg, ∆u=0.1 ft/s, ∆q=0 deg/s, and∆θ=0 deg. Disturbances in angle of attack and pitch ratedecay quickly and come to zero within 1-2 seconds. Thedisturbances in velocity and pitch angle on the other hand,persist for a while and decay slowly. In other words,disturbances in angle of attack and pitch rate decay rapidlyduring the short-period mode. During the phugoid mode,which continues after the decay of short-period mode, thevalue of angle of attack nearly remains constant, and the pitchrate is close to zero.

D. Lateral-Directional Motion and ResponseThe analysis was made similar to that for the

longitudinal motion. The equations given previously in thestate-space form has the space variables x=[∆β, ∆p, ∆r, ∆φ]T

Fig. 12 Sensitivity analysis for ωn and ζparameters with changes in stabilityderivatives, a) CMα, and b) CMq.

a)

b)

Fig. 13 Longitudinal response of theairplane with changes in a) velocity, b)angle of attack, c) pitch rate, and d) pitchangle.

a)

b)

c)

d)

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9American Institute of Aer

−−−−

−−

=

00100055.1186.0088.50126.1905.7964.7116.0964.00256.0

latA

and the state vector, η=[∆δa,∆δr]. The stability matrix A, as defined in Ref 10, has the following values for thelateral-directional dynamics of airplane:

Expanding this matrix yields another forth order characteristicequation of the form:A2λ4 + B2λ3 + C2λ2 + D2λ + E2 = 0The coefficients of the characteristic equation are A2=279,B2=2568, C2=4388, D2=12080, E2=86. The eigenvalues forthis characteristic equation describe the modes of motion as;

a) Dutch roll mode, λlat1,2= − 0.646 ± 2.246i ,b) roll mode, λlat3 = − 7.917, and c) spiral mode, λlat4 = − 0.00713. Apair of complex roots, having a damped oscillation with low frequency represents the Dutch-roll motion. The Dutchroll mode has a period of 2.798 sec, and is well-damped, requiring only 1.069 sec to halve the amplitude. The rootfor the roll mode is real and negative, indicating a stable and heavily damped rolling motion. The predicted time tohalf to the amplitude is only 0.087 sec. The root for thespiral mode is small and negative, indicating a slowlyconvergent spiral motion. It takes 96.7 sec to half theamplitude. Table 5 presents the characteristic valuesfor the lateral-directional motion.

Lateral-directional flying qualities of the airplanewere examined from the published specifications.9,10,11

Undamped natural frequency and damping ratio of thecharacteristic modes were calculated and included inTable 5. The Dutch roll mode has ωn=2.336 rad/s andζ=0.276 greater than the minimum required values forall flying quality level and flight phases. Thus, theairplane is not expected to encounter any problemfrom the Dutch roll mode. For the Roll mode, the timeconstant was calculated from τ =−1/λlat3 and found asτ=0.126 sec. This value is well within the maximumroll mode constant requirements for all of the flyingquality levels and flight phases. The spiral modealready has a time-to-half amplitude value of 96.7 sec,and so not included within the requirements.

The sensitivity of the lateral-directional ωn and ζvalues was determined on changes with the staticstability derivatives, CYβ, Clβ and Cnβ, as shown inFigure 14. The side-force due to sideslip derivative,CYβ, has an effect on only on the Dutch roll-dampingratio. This is because the side force opposes the lateralvelocity component, and thus it acts like a dampingforce. Yawing moment due to sideslip derivative, Cnβhas effect on the size and location of vertical tail. It isclear that Cnβ has a significant effect on Dutch rolldamping ratio, ζ_dr, and undamped natural frequency,ωn_dr, for values below the baseline, since theyapproach to the zero. Increasing the Cnβ has the effectof decreasing ζ_dr and increasing ωn_dr and ωn_smvalues. The roll mode frequency does not have anychange. Increasing the rolling moment coefficient dueto sideslip, Clβ, the so-called dihedral effect, increasesthe spiral stability, and decreases Dutch roll dampingratio, and roll time constant. The derivative Clβstrongly depends on wing dihedral angle and sweepangle. In gneral, some balance between Dutch roll

Table 5 Lateral-directional dynamic characteristics

Dutch Roll Roll SpiralT1/2 (sec) 1.069 0.087 96.7P (sec) 2.798 - -ζ 0.276 - -ωn (rad/s) 2.336 - -

ona

Fipab)

g. 14 Sensitivity analysis for ωn and ζrameters with changes in β derivatives, a) CYβ, Cnβ, and c) Clβ

a)

b)

c)

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Far

damping and spiral stability can be attained by appropriatechanges in the Clβ value.

The airplane free-response was also analyzed for thelateral –directional motion. The corresponding forth orderdifferential equations were integrated by using the Runge-Kutta method. Figure 15 shows the time history ofresponse characteristics for the initial conditions, ∆β=5deg, ∆p=0 deg/s, ∆r=0 deg/s, and ∆φ=0 deg. Thedisturbance in the sideslip angle decays to zero within 5 to6 six seconds. The disturbance induces rolling and yawingmotions. The rolling motion decays to the zero along withthe sideslip. However, the yawing motion does not go tozero. Instead, it assumes a non-zero steady-state value.This is due to the root becoming zero, which makes themotion involving yaw angle neutrally stable.

E. Suggested Geometric ChangesAs result of the wind tunnel tests, geometric changes

were made in airplane geometry to improve the flyingqualities. These changes are included in 3-view, shown inFigure 1. The wing originally had a rectangular planformwith constant NACA 4412 airfoil, adopted from anotherexisting airplane. It was changed to a taper planformhaving a taper ratio of 0.4, with custom design root and tip air13.5%, decreasing weight and parasite drag, and increasing improvement in airplane cruise efficiency, but requires a relrequirement. Wing fuselage juncture had some fairing to haveincreased 10% while having 15% reduction on its tail armhorizontal-tail volume coefficient. Vertical tail area was decrevolume coefficient. These changes in areas are expected to optithe amount of directional stability. The present test results yindicating a satisfactory stability for this type of cargo transporpropeller disk plane to the center of gravity was reduced by aalone would cause a direct reduction in the directional staderivative CMα, produced by the destabilizing effect of runninwas more rounded to alleviate the degradation effect of downwused for the wing was not effective in lift production. Thus, thethese suggested changes were incorporated with phase-two win

IV. ConclusStability and control characteristics of 1/12 scale model of

as they were obtained from Wichita State University wind tunnumber of 0.2. The tests were made for power-off and stick-fconclusions can be drawn:

1) Drag due to landing gear extended is considered signnumber above the test value, but still the gear setting needs impeffects.

2) Downwash effect at the conventional tail is consideredwing-fuselage juncture swirls downstream and joins the flowminimized by adding dorsal fin, vortilon or fairing parts, if not

ig. 15 Lateral –directional response of theirplane with changes in a) sideslip, b) rollate, c) yaw rate, and d) bank angle.

c)

d)

b)

a)

tics and Astronaut

foils for better pethe correspondingatively high pow a better downstr length. This chaased 16.2% caus

mize the amount oields a roll to yt, as mentioned ins much as 16% bbility derivative g propeller. Addiash flow on the ta flaps had a new d tunnel test mode

ions a high wing cargnel at a Reynoldsixed conditions. B

ificant. It might brovement to min

high. Flow visua on upper side

enough with some

ics

rformance. Wing area was reduced wing loading. This results in an

er input to meet the take-off fieldeam flow. Horizontal tail area wasnge resulted in 7.3% increase ining 9.34% decrease in vertical-tailf lateral stability as compared with

aw stability ratio, Clβ/Cnβ=−0.818, Ref 6. Also, the distance from the

y shortening the nose section. ThisCnβ and the longitudinal stabilitytionally, the fuselage cross sectionil surfaces. The simple slotted flap

design having a Fowler motion. Alll.

o transport airplane were presented, number of 0.92 million and Machased on the results, the following

e relatively low at some Reynoldsimize the interference and blockage

lizations reveals that the flow fromof fuselage. This effect might be changes on the fuselage shape.

11American Institute of Aeronautics and Astronautics

3) The airplane has the static stability about its all three axis. The pitch stability derivative produces a neutralpoint at 0.57c. Power effects would reduce the static margin of stability. There is a roll to yaw stability ratio of –0.818, considered satisfactory for this type of cargo transport.

4) Elevator, rudder and aileron controls produce satisfactory control power. Flap requires a better design toimprove take-off and landing performance. Fowler type slotted design is expected to provide relatively high liftperformance.

5) For its cruise plight phase, the airplane flying qualities are better than level 3 for longitudinal motion andlevel 2 for lateral-directional motion. Changes are suggested in lifting surfaces so that there is 7.3% increase inhorizontal-tail volume coefficient and 9.34% decrease in vertical-tail volume coefficient. These changes wereincorporated with the airplane model used for phase-two wind tunnel tests.

AcknowledgementsThe wind tunnel tests reported in this paper were conducted while the author was with Ayres Corporation of

Georgia in the United States. The author acknowledges Mr. Fred P. Ayres, CEO and President of AyresCorporation, for giving such a unique opportunity to work in design and testing of a new airplane. The author alsothanks his family in Istanbul, Turkey for the most needed support and encouragement he received during thecompletion of this research work.

References

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