Flightlab Ground School 4. Lateral/Directional...

Bill Crawford: WWW.FLIGHTLAB.NET 4.1

Flightlab Ground School4. Lateral/Directional Stability

Copyright Flight Emergency & Advanced Maneuvers Training, Inc. dba Flightlab, 2009. All rights reserved.For Training Purposes Only

Sideslips and Directional Stability, Cnβ

Most aerodynamics texts cover longitudinal(pitch axis stability) before tackling coupledlateral/directional behaviors. Since our flightprogram emphasizes those behaviors, we’ll dothings in our own order.

An aircraft is in a sideslip when its direction ofmotion (its velocity vector) does not lie on the x-z plane of symmetry. The top drawing in Figure1 defines the x-z plane, and in the bottomdrawing we’re looking down the z-axis. Theangle between the velocity vector, V, and the x-zplane is the sideslip angle, β (pronounced“beta”). In aerodynamics notation β is positive tothe right, negative to the left. (Just so there’s noconfusion, a -β sideslip to the left, for example,means that the nose is pointing to the right of theaircraft’s actual direction of motion.)

Rudder deflections, wind gusts, asymmetricthrust, adverse yaw, yaw due to roll, and bankangles in which the effective lift is less thanaircraft weight can all cause sideslips. Inresponse, sideslips typically create both yawingand rolling moments. A stable aircraft yawstoward the velocity vector, but rolls away. Thesemoments interact dynamically—playing out overtime, most notably in the form of thedisagreeable undulation called the Dutch roll.We cover the associated rolling moments a bitfarther on, but concentrate on yaw around the z-axis here, pretending for the time being that itoccurs in isolation.

The notation for the yawing moment coefficientis Cn (positive to the right, negative to the left).Remember that a moment produces a rotationabout a point or around an axis.

β is approximately equivalent to the AOA of the vertical tail. The actual sideslip angle at the tail depends on fuselage/tail interference effects, on fin offset and slipstream in the case of propeller-driven aircraft, and, especially at high angles of attack, on the influence of wing tip vortices or vortices shed by the forward part of the fuselage.

The side force produced by the tail, times the arm, generates an overall stabilizing yaw moment.

Fuselage center of pressure ahead of cg produces destabilizing yaw moment.

z-axis

X-Z plane is the surface of the paper.

x-axis

cg

arm

Right Sideslip

β

V

v

v is the Y-axis component of the aircraft’s velocity, V. v = V sin β

x

y-axis

Figure 1 Directional Stability

Lateral/Directional Stability

Bill Crawford: WWW.FLIGHTLAB.NET4.2

CNβ

Stable slope

+ β (sideslip to right)

+C n Nose-right yaw moment

-C n Nose-left yaw moment

Figure 2 Directional Stability Response

− β (sideslip to left)

An aircraft has static directional stability if ittends to respond to a sideslip by yawing aroundits z-axis back into alignment with the relativewind. Another way to put it is to say that adirectionally stable aircraft yaws toward thevelocity vector, returning it to the aircraft’s x-zplane of symmetry.

This is also called “weathercock” stability, inhonor of a much simpler invention. Figure 2shows that this stabilizing yaw moment is nottypically linear, but tends to decrease at high βangles. In the figure, a positive slope (rising tothe right) in the Cnβ curve indicates directionalstability. The steeper the slope the stronger is thetendency to weathercock.



Figure 4 World War I Fokker Dr1 rudder

Not all parts of the aircraft contribute todirectional stability. Alone, the fuselage isdestabilizing. In subsonic flight, the center ofpressure on a fuselage in a sideslip is usuallysomewhere forward of 25 percent of the fuselagelength. Since the aircraft’s center of gravity istypically aft of this point, the fuselage alonewould tend to turn broadside to the relative windin a sideslip. Notice in Figure 3 how thedestabilizing contribution from the fuselagelevels out as β increases.

Figure 3 breaks down the components ofdirectional stability. A sideslip to the right (+β)produces a nose-right, stabilizing yaw momentfor the entire airplane, but a destabilizing yaw tothe left (-Cn) for the fuselage alone.

Of course, the vertical tail contributes most todirectional stability. The yaw moment producedby the tail depends on the force its surfacegenerates and on the moment arm between thetail’s center of lift and the aircraft’s center ofgravity. (Therefore, a smaller tail needs a longerarm to produce a yaw moment equivalent to abigger tail on a shorter arm. That being said,changing the c.g. location for a given aircraft,within the envelope for longitudinal stability, haslittle effect on its directional stability.)

The rate of the increase in force generated by thetail as β increases depends on the tail’s lift curveslope (just as the rate of increase in CL withangle of attack depends on the slope of the liftcurve of a wing). Lift curve slope is itself afunction of aspect ratio. Higher aspect ratiosproduce steeper slopes. (See Figure 13, top.)

The Cnβ directional stability curve for thefuselage and tail together reaches its peak whenthe tail stalls. You can see in Figure 3 thatadding a dorsal fin increases the tail’seffectiveness (and without adding much weightor drag). Because of its higher aspect ratio andsteeper lift curve, the vertical tail properproduces strong and rapidly increasing yawmoments at lower sideslip angles, but soon stalls.But the dorsal fin, with its low aspect ratio andmore gradual lift curve, goes to a higher angle ofattack before stalling, and so helps the aircraftretain directional stability at higher sideslipangles. The dorsal fin can also generate a vortexthat delays the vertical tail’s stall.

The Fokker Dr1 triplane provides an extremeexample of a low-aspect-ratio tail (there’s arough approximation in Figure 4). Without afixed vertical fin, the aircraft had low directionalstability. The low-aspect-ratio rudder stalled atabout 30-degree deflection. The combinationgave the pilot the ability to yaw the nose aroundrapidly if necessary to get off a shot. But instraight-ahead flight the aircraft needed constantdirectional attention (a typical attribute of WW-Ifighters).

+β (sideslip to right)

+Cn Nose-right yaw moment

Tail alone

Fuselage alone

Fuselage and tail

Fuselage, tail, and dorsal fin

-Cn Nose-left yaw moment

Tail stalls here.

Figure 3 Contributions to Directional Stability

Dorsal fin

X

Z



Coming back to modern examples, it’sappropriate to note that the lift curve slope of thevertical tail tends to go down at high Machnumbers, taking directional stability with it. Thistendency is one reason why supersonic fightersneed to compensate with such apparently over-sized tails. Another reason is that the slope of theCnβ stability curve also tends to go down at highangles of attack as the fuselage begins tointerfere with the airflow over the tail. This isespecially so with swept-wing aircraft thatrequire higher angles of attack to achieve highlift coefficients. Directional stability is essentialto prevent asymmetries in lift caused by sideslipthat can lead one wing to stall before the otherand send the aircraft into a departure.

Propellers and Directional Stability

Propellers ahead of the aircraft c.g. aredirectionally destabilizing, mostly because ofslipstream effects and P-factor (Figure 5). OurAir Wolf is an example of an aircraft thatrequires lots of directional trimming (or justrudder pushing) to compensate for propellereffects as angle of attack and airspeed change. Inthis respect it’s quite unlike a jet, say, or anaircraft with counter-rotating propellers, whichtypically have no associated directional trimchanges.

Note that as an airplane slows down,asymmetrical propeller effects cause it to yaw. Ifthe pilot cancels the yaw rate, using rudder,while keeping the ball centered and the wingslevel, the aircraft will end up in a sideslip (to theleft to generate the side force required tocounteract the usual yawing effects due to aclockwise-turning propeller). Thus even a“straight-ahead” stall at idle power has a smallsideslip component that may affect its behavior.

Spiraling slipstream produces a side force at the tail. The resulting yaw moment is most apparent at low airspeeds and high power settings—for example, during a go-around or at the top of a loop.

Figure 5 Slipstream and P-factor

As aircraft α increases, P-factor causes the down-going blade to operate at a higher prop α than the up-going blade. The difference in thrust produces a yawing moment. A similar change in blade angle happens if the aircraft is in a sideslip, but produces a pitching moment. Left sideslip = pitch up; right sideslip = pitch down.

Slipstream

Prop cord

Plane of rotation

V∞

α

Down-going blade: higher prop α

Resultant

P-factor

Up-going blade Down-going blade

Thrust

V∞

α

Up-going blade: lower prop α

Moment

V∞



Dihedral Effect, Clβ

An aircraft with dihedral effect rolls away from asideslip (away from the velocity vector). Theterm describes a single behavior with more thana single cause. Dihedral effect was observed firstas resulting from actual geometric dihedral (wingtips higher than wing roots), but it’s alsoproduced by wing sweep, by a high winglocation on a fuselage, and by forces acting onthe vertical tail. For convenience, Figure 6 againillustrates sideslip angle, β, and sideslip velocity,v, velocity vector, V, plus the direction of roll.

During our flight program, we’ll do steady-heading sideslips to assess the presence ofdihedral effect. We’ll press on a rudder pedalwhile applying opposite aileron, so that theairplane will be banked but not turning. We’llnote the deflections necessary to keep the aircrafttracking on a steady heading, and we’ll see whathappens when we release the controls.

Steady-heading sideslips give test pilotsinformation about the rolling moments a slippingaircraft generates and its lateral/directionalhandling qualities. We use them to illustrate thenature of yaw/roll couple and to demonstrate theeffects of sideslip under various flapconfigurations, during aerobatic rollingmaneuvers, and during simulated controlfailures. As you’ll see, an aircraft can sideslip inany attitude—including upside-down.

The interaction between sideslip and dihedraleffect forms the basis of an aircraft’s lateralstability. Lateral stability can’t appear unless an

aircraft starts to sideslip first. An aircraft withpositive lateral stability rolls away from thesideslip (velocity vector) that results when awing drops, and that usually means back towardlevel flight (although an aircraft with dihedraleffect can go into a spiral dive if the bank angleis high and other moments prevail).

In the notation used in Figure 7, sideslip angle isβ (beta), and the rolling moment coefficient is Cl,so the slope of the curve of rolling moment dueto sideslip is Clβ (pronounced “C L beta”).Since it does roll off the tongue, if we lapse intothis terminology you’ll know what we mean. Thefigure shows that the slope must be negative(descending to the right) for stability when wefollow the standard sign conventions, whereaircraft right is positive, left is negative.

A laterally unstable aircraft tends to continue toroll toward the direction of sideslip (positiveslope). Sweeping the wings forward or mountingthem with a downward inclination so that the tipsare lower than the roots (anhedral) produces thistendency. Sometimes anhedral is used to correctswept-wing designs having too much positivelateral stability at high angles of attack. Toomuch lateral stability can cause sluggish rollresponse (especially if there’s also adverse yawpresent) and a tendency toward the coupledyaw/roll oscillation of Dutch roll.

β, Sideslip angle

Cl, Rolling moment coefficient

Left roll moment

Left

Right roll moment

Right

Unstable

Slightly stable

Stable slope Clβ

Figure 7 Lateral Stability

Left slip produces right roll.

Right slip produces left roll.

Figure 6 Sideslip Angle, β

V x-axis β

v is the y-axis component of the aircraft’s velocity, V. v = V sin β

v

y-axis

Roll Moment



Geometric dihedral effect is easy to understandbecause it’s easy to see how wing geometry andsideslip interact. Just stand on the flight line at adistance in front of an aircraft with geometricdihedral and pretend that you’re looking rightdown the path of the relative wind. You mayneed to stoop a little to approximate an in-flightangle of attack.

Maintain that eye height above the ground andmove back and forth in front of the aircraft,trying hard not to look too suspicious to possiblerepresentatives of the TSA. Notice how the angleof attack, α, of the near wing increases—you cansee more wing bottom—while that of the farwing decreases as you change your position, asillustrated at the top of Figure 8. With anhedral,you’d see just the opposite.

Figure 8 also presents the same idea in anotherway. In the lower figure, the y-axis componentof sideslip, v, is in turn broken down into twovector components projected onto the aircraft’sy-z plane, one parallel to and one perpendicularto the wing. On the upwind wing, theperpendicular component acts to increase theangle of attack. It does the opposite on thedownwind wing. The difference produces arolling moment. v

α decreasesα increases

v

y-axis

Dihedral angle, Γ

Rolling moment varies inapproximately a linear fashion withdihedral angle and sideslip angle.

Geometric dihedral, wing viewed from thedirection of a sideslip to the left (i.e., backdown the velocity vector)

z-axis

x-axis

v is the y-axiscomponent of thesideslip.

Figure 8Sideslip, DihedralAngle, and ResultingChange in α

Aircraft in a sideslipto its right



Again, dihedral effect can also result frominterference effects due to wing placement on thefuselage, from wing sweep, or from vertical tailheight. Flap geometry and angle of deploymentinfluence dihedral effect, as does propellerslipstream.

Figure 9 shows the contributions of wingposition, tail height, landing gear, and slipstreamangle to dihedral effect. Wing position guides thecross flow around the fuselage in a sideslip,altering the angles of attack on the near and farwings, and thus the relative lift. This isstabilizing on a high-wing aircraft. It’sdestabilizing on a low wing, which is why low-wing aircraft typically require more geometricdihedral. These fuselage effects are enhanced bysmooth airflow over the wing-body junction.They’re diminished by flow separation at thewing roots at the approach of a stall.

A vertical tail produces a side force during asideslip. If the tail is tall enough, so that itscenter of lift is a good distance above theaircraft’s center of gravity, the vertical momentarm can provoke a stabilizing roll response.Landing gear, below the c.g., is destabilizing.

The bottom illustration in Figure 9 shows howthe angle of the propwash during a sideslipcreates a destabilizing condition by increasingthe airflow, and thus the lift, over the downwindwing. This generates a rolling moment into thesideslip. The destabilizing effect increases withthe flaps down. It also increases at low airspeedsand high power settings, as the ratio of propwashvelocity to freestream velocity increases and thepropwash gains relatively more influence.

The propwash effect may vary somewhat,depending on the direction of the sideslip.Propeller swirl, as it’s sometimes called, createsan upwash on the left wing root and a downwashon the right, leading to a difference in angle ofattack between the wings and thus a rollingmoment. For the aircraft at the bottom of Figure9, clock-wise propeller swirl may initiallygenerate a rolling moment to the right, which cansuddenly reverse at high α, when the left wingstalls first because of its swirl-induced higherangle of attack. This is an important factor inspin departures, especially during the classic,career-ending skidding turn to final.

Stabilizing roll moment

+ AOA

- AOA

Destabilizing roll moment

+ AOA

- AOA

Figure 9 Sideslip-induced Roll

Propwash causes destabilizing roll moment toward sideslip.

v

v

Cross flow due to sideslip

v

Destabilizing roll moment caused by side force on landing gear



Figure 11 Geometric Dihedral Effect

Equal lift differences produce equal rolling moments.

Equal wing-to-wing α differences generated by a given sideslip angle at two different starting αs

α

CL

Left wing

Right wing

Propwash effects don’t occur in jets, but flapeffects do. Flaps shift the centers of lift inboardon the wings, as illustrated in Figure 10. Thisshortens the moment arms through which the liftchanges caused by sideslip act, and so sideslip-induced roll moments decrease.

We’ll explore this effect during steady-headingsideslips by raising and lowering the flaps andwatching the roll response. When the flaps godown, dihedral effect will diminish and theaircraft will start to roll in the direction of aileroninput. (This demonstration is important inunderstanding the concept of crossover speed.)

Propwash increases flap effects because of theadded airflow over the flap region of the up-going wing, but we can demonstrate with theprop at idle—it will just take more flapdeflection.

Because wing taper also shifts the centers of liftinboard on the wings, a high taper ratio (tipchord less than root chord) decreases lateralstability. High aspect ratios move the centers oflift outboard, increasing lateral stability.

Geometric Dihedral and Coefficient ofLift, CL

The strength of geometric dihedral effect doesnot depend directly on aircraft coefficient of lift(you’ll see the reason for the italic treatmentpresently). The CL/α curve for a cambered wingin Figure 11 is linear up to the stall, which meansthat for a given change in angle of attack(produced by a sideslip) there’s a givenincremental difference in coefficient, until theslope starts to decline near the stall. As a result, agiven sideslip angle combined with a givendihedral angle, will generate a given differencein CL. It doesn’t matter if you start at low orhigh CL, as long you stay on the straight line.That difference then produces a rolling momentthat varies directly with speed.

If you can tolerate even more confusion, imaginethat an aircraft with geometric dihedral is flyingat its zero lift angle of attack (maybe during apushover at the top of a zoom). If the airplanestarts to sideslip, it will begin to roll as the angleof attack changes on each wing and a spanwiseasymmetry in lift appears. Without geometric

dihedral, a purely swept-wing aircraft, at zerocoefficient of lift, won’t roll in the samesituation, because the sideslip has no influence iflift is not already being generated.

Centers of lift move inboard with flaps during a sideslip, reducing the moment arm through which dihedral effect operates. Roll moment decreases.

v

v

Wing center of lift Lift Distribution

Total lift is the same (lift=weight), but shifts inboard.

Resulting roll moment

Figure 10 Flap Effects



Swept-wing Dihedral Effect

Figure 12 shows the contribution of wing sweepangle (Λ) to dihedral effect. It’s almost enoughto say that in a sideslip, because of the angle ofintercept, the wing toward the sideslip “getsmore wind” across its span, while the oppositewing gets less. But we can gain a betterunderstanding of swept-wing characteristics byfirst breaking the airflow over the wing intonormal and spanwise vectors. It’s the normalvector (perpendicular to the leading edge on awing with no taper, or by conventionperpendicular to the 25% chord line on a wingwith taper) that does all the heavy lifting,because only the normal vector is accelerated bythe curve of the wing. There’s no accelerationand accompanying drop in static pressure in thespanwise direction, because there’s no spanwisecurve.

When a swept wing sideslips, the relativevelocities of the normal and spanwise vectorschange. The spanwise component decreases andthe normal component increases on the wingtoward the sideslip, and so lift goes up; just theopposite happens on the other wing, and therelift goes down. A roll moment results. Adirectionally stabilizing yaw moment alsoresults, because a difference in drag accompaniesthe difference in lift—but the effect is smallcompared to the stabilizing moment provided bythe tail.

For a swept wing, the roll moment coefficientdue to sideslip is directly proportional to thesideslip angle, to the sine of twice the sweepangle, and to the coefficient of lift.

The relationship between sideslip and sweepangles, and subsequent rolling moment can beanticipated just from looking at Figure 12, butthe variation in rolling moment with CL takesexplaining. The easiest approach is to think ofsideslip as changing the effective sweep angle ofeach wing, and thus the slope of their respectiveCL/α curves. Sweep angle and slope are relatedas shown at the top of Figure 13. In a sideslip, asshown on the bottom, a swept-wing aircraft hastwo CL/α curves: a steeper one than normal forthe wing into the wind, and a shallower one thannormal for the trailing wing. The differencebetween them creates the rolling moment. Notehow the difference at any given β increases withα, and therefore with CL.

Freestreamvector Normal

vector

Spanwisevector

Zero sideslip

Sideslip toright

Normal vectordecreases.

Normal vectorincreases.

Resulting dihedraleffect rollmoment to left

Stabilizing yaw momentcaused by unequal drag

25%cord

Λ

Less lift,less drag

More lift,more drag

β

Figure 12Wing Sweep

α

CL

Increasing the sweep angle (or decreasing the aspect ratio) decreases the slope.

CL

Aircraft in sideslip to the right

Normal, zero sideslip

Left wing—more sweep

Right wing—less sweep

α

Figure 13 Swept-wing Dihedral and CL

Greater lift difference at higher aircraft CL increases roll moment.



Back in Figure 12, right, note the difference inspanwise drag during a sideslip. That differenceis directionally stabilizing, and it’s the reasonwhy flying wing aircraft are swept.

Since wept-wing dihedral effect varies with liftcoefficient, so does lateral stability. Aircraft withhigh sweep angles can have acceptable dihedraleffect and lateral stability in normal cruise flightwhen CL is low, but excessive dihedral effect atlow speeds, or during aggressive turningmaneuvers, or at high altitudes, where in eachcase CL is necessarily high. Under thoseconditions, sideslips can produce strong rollingmoments. This can allow a pilot to accelerate aroll rate by forcing a sideslip with rudder, butalso increases the potential for Dutch rolloscillation and rudder misuse.

As mentioned, unlike a wing with geometricdihedral, a purely swept-wing will not roll inresponse to a sideslip unless it’s alreadygenerating lift. There’s no dihedral effectattributable to wing sweep at zero CL.

You can see that a wing possessing bothgeometric dihedral and sweep has a kind ofmultiple personality (and usually a yaw damper).

Straight Wings and Coefficient ofLift—Revisited

Despite the claim made earlier, straight-wingaircraft with geometric dihedral do exhibit aconnection between increased CL and increaseddihedral effect.1

If you go to the illustrations in our briefingmaterials on three-dimensional wings, you’lldiscover that the downwash caused by wing tipvortices alters the effective local angle of attackacross the span. The greater the downwash, thelower the local effective angle of attack on thewing ahead of the downwash. (The angle ofattack changes because the acceleration of airdownward by the vortices actually starts to occurahead of the wing. The air starts coming downeven before the wing arrives.)

In a sideslip the vortex flow shifts laterally, as inFigure 14. This changes the overall downwashdistribution, shifting it to the left in the case 1 Bernard Etkin, Dynamics of AtmosphericFlight, Wiley & Sons, 1972, p. 305-306.

illustrated, which in turn causes the averageeffective angle of attack of the left wing to belower than it would from dihedral geometryalone. The average effective angle of attack onthe right wing becomes higher. The result is arolling moment to the left (a moment that wouldtheoretically occur even if the wing had zerodihedral—as long as lift is being produced).

Since downwash strength is a function of CL,pulling or pushing on the stick will affect rollmoment due to sideslip in a manner similar tothe swept-wing example already described. (Ourtrainers’ rectangular planforms tend to promotestrong tip vortices. Other straight-wingplanforms with different lift distributions mightnot be as effective.)

Pushing and pulling on the stick during a sideslipalso causes the aircraft to pitch around its y windaxis (as opposed to body axis), which introducesa roll as described in Figure 19. The effect wouldbe in the same direction as the downwashphenomenon just mentioned, and the two mighteasily be confused.

From all the above, an under-appreciated yetnevertheless great truth of airmanship emerges:For a swept or a straight wing, pulling thestick back tends to increase rolling momentscaused by sideslip (and by yaw rate), pushingdecreases them.

β

Downwash shiftslaterally with β,increases with CL.

Downwash shiftcauses section anglesof attack to decrease.

Downwash shiftcauses section anglesof attack to increase.

Sideslip to right

Rolls left

Figure 14Vortex Effects



Sideslip and Roll Rate

With our particular emphasis on theaerodynamics of unusual-attitude recovery, hereare the behaviors we want to be sure youunderstand:

(1) Increasing CL (by pulling back on thecontrol) will increase rolling moment due tosideslip and yaw rate. Decreasing CL (by pushingforward) will decrease rolling moment due tosideslip and yaw rate. We’ll explore theimplications of this during our flight program.(See roll due to yaw rate, and y-wind-axis roll,farther on.)

(2) A laterally stable aircraft rolling with ailerontoward the direction of a sideslip/velocity vectorwill experience a decrease in roll rate inproportion to the opposing rolling moment thesideslip produces. An aircraft rolling with aileronaway from the direction of a sideslip/velocityvector will experience an increase in roll rate.You’ll discover this effect when we start rollingthe training aircraft through 360 degrees andbegin using rudder-controlled sideslips toaugment roll rates.

Figure 15 describes the link between sideslipdirection and roll rate at two points during a 360-degree roll to the left, and Figure 16 plots rollrate against time, given differences in rudder use,dihedral effect, and directional stability.

(When aircraft directional stability is greater than dihedral effect)

(When aircraft dihedral effect is greater than directional stability)

Coordinated rudder resulting in roll only

Insufficient rudder resulting in decreased roll moment caused by sideslip toward roll direction

Excess rudder resulting in increased roll moment caused by sideslip opposite roll direction

Rol

l Rat

e

Time

Figure 16 Dihedral Effect, Rudder Use, Roll Rate

Sideslip-induced roll momentopposes aileron roll momentand reduces roll rate.

Sideslip-induced rollmoment reinforces aileronroll moment and increasesroll rate.

Low directional stability,adverse yaw, or top ruddercould cause left sideslip.

Right sideslip could becaused by low directionalstability or by top rudder.

v

v

Aileronmoment

Figure 15Sideslip andRoll Rate

Sidewayscomponent ofrelative wind.



Aerobatic Aircraft and Dihedral Effect

High-performance aerobatic airplanes usuallyhave little or no geometric dihedral, and so verylittle lateral stability through dihedral effect. Onecan’t always know what the designer had inmind, but the absence of dihedral allows aircraftto roll faster in the presence of opposingsideslips, and makes them easier to fly tocompetition standards because roll rate andrudder deflection remain essentially independent.It’s possible to use the rudder to keep the nose upduring the last quarter of a slow roll (when anaircraft that’s rolling left, say, and going throughthe second knife edge is sideslipping to the right)without having to change aileron deflection tokeep the roll rate from accelerating.

These desirable characteristics for smoothaerobatic flying actually make an aircraft lesssuitable for unusual-attitude training. Mostaircraft do exhibit lateral stability, and theresulting characteristics are important tounderstand. For one thing, lateral stability allowsyou to roll an aircraft with rudder using normaldirectional input should you lose the primary rollcontrol—the ailerons.

Absent dihedral effect and unaccompanied byaileron, rudder deflection alone in someaerobatic aircraft will produce a roll opposite theexpected direction. For example, right rudder,instead of rolling the aircraft right by dihedraleffect (and roll due to yaw rate), slowly rolls it tothe left, as in Figure 17. Roll due to rudder iscaused by the vertical tail’s center of lift beingabove the aircraft’s center of gravity. A momentarm results. The effect could be particularlyevident in a zero-dihedral, low-wing aircraft,when a sideslip generated by rudder deflectionalso produces an accompanying, destabilizingroll due to cross flow. (Check back to Figure 9,top. Low wing is destabilizing.) The first timeyou try to unfold a map while using your feet tokeep the wings level in an aircraft that behaveslike this, you’re in for a surprise.

If you actually lost your ailerons you mightregain some positive dihedral effect and roll dueto yaw rate by slowing down and increasing thecoefficient of lift. Also, slowing down will raisethe nose, and so place the tail lower and decreasethe vertical distance between its center of lift andthe c.g., reducing the moment arm. Perhaps theaircraft would then respond in the normal way. Itmay be possible (as in the Giles G-200, for

example) to control an aircraft by using roll dueto rudder, but it’s not the sort of thing thathappens intuitively. Aileron failure is typicallycatastrophic in an aircraft without dihedral effect.That’s one reason why preflight inspection of thelateral control system in a zero-dihedralaerobatic aircraft (for integrity of the linkages,and for items that could cause jams like loosechange, nuts, bolts, screwdrivers, hotelpens—your mechanic has horror stories andprobably a collection of preserved examples) isso important. The same, of course, goes forelevator and rudder systems.

Here’s a related phenomenon: Next time you flythe swept-wing MiG-15, notice that rudderdeflection produces a roll in the expecteddirection until you get past about Mach 0.86, butthen the response reverses—left rudder causingthe right wing to drop, for example. A sideslip,as pointed out in Figures 12 and 13, reduces thesweep of one wing and increases the sweep ofthe other, relative to the free stream. Thereduction in the effective sweep of the rightwing, caused by pressing the left rudder, cansend the right wing past critical Mach number,causing shock airflow separation and a wingdrop. If you’re pulling g, the effect can happen ata lower speed because of the acceleration of theairflow over the wing caused by the higher angleof attack. Response to the rudder returns tonormal at about Mach 0.95.

Roll moment due torudder deflected to theright

c.g.

Verticaltail centerof liftabove c.g.

Figure 17Roll due toRudder, Cl

δr

No dihedral



Roll Due to Yaw Rate, Clr

When an aircraft yaws, the wing moving forwardhas higher local velocity than the wing movingback. The higher the yaw rate, or the longer thewingspan, the greater the velocity differencebecomes. Yaw rate produces a difference in liftand an accompanying roll moment, whichdisappears once yaw rate returns to zero. The rollmoment varies with the square of the differencein speeds across the span (since the lift producedby a wing varies with V2).

When you enter a sideslip by pressing therudder, some percentage of the roll momentgenerated is caused by dihedral effect, and someby roll due to yaw rate. Once a given sideslipangle is reached and held and yaw ratedisappears, dihedral effect provides theremaining rolling moment.

Like the dihedral effects described above, rolldue to yaw rate increases with coefficient of lift,CL. For rectangular wings, the value for therolling moment coefficient per unit of yaw rate,Clr, is about 0.25 times CL, on average. Wingtipwashout, and/or flap deployment, reduces Clr.

An aircraft in a banked turn has a yaw rate. Theoutside wing has to travel faster than the inside.This can create a destabilizing, “over-banking”tendency and force the pilot to hold outsideaileron during the turn. The situation gets worseas you slow down (or grow longer wings). For agiven bank angle, yaw rate varies inversely withairspeed. So as you slow down and increase CL,yaw rate also increases and roll due to yawbecomes more apparent. That’s why turning inslow-flight required so much opposite aileron tomaintain bank angle and felt so weird back inprimary training—and still does today.

An aircraft that requires lots of opposite aileronin response to yaw rate in a turn is likely to bespirally unstable if left to its free response. Whena wing goes down and an aircraft enters asideslip, dihedral effect will tend to decreasebank angle and roll the wing back up. But at thesame time the aircraft’s directional stability tendsto yaw the nose into the sideslip, generating ayaw rate and a rolling moment that increasesbank angle. If that moment wins the contest, aspiral begins.

x body axis

Figure 18Aircraft Yaw Around Z Wind Axis

Lift vector

z body axis

x wind axis

z wind axis

Aircraft yaw aroundtheir z wind axis. Arolling moment thatmay result occursaround the x windaxis.



Dutch Roll

Directional stability, dihedral effect, and roll dueto yaw rate all do battle in the dynamicphenomenon called Dutch roll. Dutch rolltendency appears in aircraft with high lateralstability as compared to directional stability. It’sparticularly a problem with swept-wing aircraft,in which lateral stability increases with angle ofattack (i.e. coefficient of lift), as alreadydescribed. Although not nearly as bad, ourstraight-wing Zlin has enough Dutch roll inturbulence to make the ride memorable.

In the Dutch roll, a disturbance in roll or yaw,whether pilot-induced or caused by turbulence,creates a sideslip. A sideslip shifting the velocityvector (relative wind) to the right, as in Figure20, for example, leads to an opposite rollingmoment to the left (through dihedral effect androll due to yaw rate). But the aircraft’sdirectional stability works to eliminate thesideslip by causing the nose to yaw to the right,back into the wind. However, momentum causesthe nose to yaw past center (past zero β), and thissets up a sideslip in the opposite direction, whichin turn sets up an opposite roll. The resulting out-

of-phase yawing and rolling motions woulddamp out more quickly if they occurredindependently. Instead, each motion drives theother. Note that Dutch roll is the result of thefundamental tendency of a stable aircraft to rollaway from but yaw toward the velocity vectorwhenever that vector leaves the aircraft’s planeof symmetry.

Without a yaw damper to do it for them, it’sdifficult for pilots to control a Dutch roll becauseits period is short. It’s hard to “jump in” with therequired damping input at the right time. Pilotsof swept-wing are frequently trained to keep offthe rudders, check the roll with temporary, quick,on-off applications of aileron, and then recoverto wings level. Another strategy is to use the

After initial disturbance, aircraft asshown wants to yaw right (directionalstability) but roll left (roll due tosideslip angle and dihedral effect). Asthe nose-right yaw rate increases, aright rolling moment due to yaw ratebuilds. Left-rolling dihedral effectdeclines as sideslip angle decreases.

Velocity vector

Yaw overshootsdecrease as motiondamps out. Rollsubsides.

Yaws past center and now wants toyaw left but roll right as sideslipangle changes sides. Yaw rate (andassociated roll moment) is highestas the nose passes through therelative wind. Roll moment due todihedral effect increases withsideslip angle, β.

Yaw

Roll

Yaw

Roll

Yaw

Roll

Figure 20Dutch Roll

Figure 19 Aircraft Pitch Around Y Wind Axis

V

x body axis

β

y body axis

y wind axis

Geometrically, pitching around the y wind axis also produces a roll. In a sideslip to the right, as above, pulling the control back will cause a roll to the left; pushing forward causes a roll to the right. This is easier to visualize if you try it with a hand aircraft model. Note that the rolling effect is consistent with (operates in the same direction as) the other sideslip/yaw-rate rolling moments described in the text.



rudder—not to combat yaw but to keep thewings level.

The tendency to Dutch roll increases at higherCL, because increasing the coefficient of liftincreases both dihedral effect (especially swept-wing) and roll due to yaw rate. Dutch rolltendency also increases at higher altitudes, whereaerodynamic damping effects diminish. Sinceaircraft must fly at high CL at high altitudes, theproblem compounds. Normally aspirated piston-engine aircraft upgraded with turbochargers forhigh-altitude flight sometimes end up needinglarger vertical tails for better damping.

Reducing dihedral effect will ease the Dutch rollproblem, but at the expense of reduced lateralstability.

Aircraft with greater directional than lateralstability tend to Dutch roll less, but also tend tobe spirally unstable. Traditionally, the designcompromise between Dutch roll tendency andspiral instability has been to suppress the formerand allow the latter, because spiral dives—whilepotentially deadly—begin slowly and are easierto control than Dutch roll.

Flightlab Ground School 4. Lateral/Directional...

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