Stick & Rudder

Test Pilotrt •*• .i '..

' "

A P R I L ' S "TEST P ILOT"discussed angle of attack(AOA), and we explainedhow your airplane's wingalways stalls at the sameangle of attack regardlessof its att i tude. We usedthe l i f t equation and thelift coefficient (CL) versusthe AOA curve to illustrate howairplane weight and acceleratedmaneuvering affect stall speedbut not the stall AOA.

Using a landing pattern ex-ample, we compared the stallprotection of an AOA-based fi-nal approach with a one-speed-fits-all shortcut or miscalcula-tion of a weight-based approachspeed. In short , we at tempted todemonstrate the simplicity of usingAOA for stall protection.

This month, we'll take the AOAdiscussion to another safety arena—maximum range glide. Yes, a singleAOA value will always yield the max-imum no-wind gl ide distance. Be-lieve it or not, that same AOA willalso provide the maximum cruiserange for your airplane.

Smaller Angle, Greater GlideGlide angle is the difference betweenyour airplane's f l ight path and thehor izonta l . I f your gl ide angle iszero, you're flying level. Your air-plane would never contact theground and would give you an infi-nite glide range. If your glide angle is90 degrees, your airplane is goingstraight down, and it has a zero gliderange. Reality is between these ex-tremes: The shallower the airplane'sglide angle, the farther it will glide.

During an engine-out glide, youcan fly an airplane at a variety ofglide angles. In Figure 1 both a i r -planes begin their glide at the same

Goin; the DistanceAngle of attack and lift/drag

ED KOLANO

Distance 1 Distance 2

Figure 1

altitude. The airplane on the righthas a shallower glide angle, or flightpath angle (y, Greek letter gamma),and therefore travels far ther thanthe other plane.

There's a technicalaviation term called

the pucker factor.It's a variable whoseintensity depends on

the nature of theevent that causes

its occurrence.Notice that we did not mention

glide speed. That's because how faran airplane glides depends only onits flight path angle. Yes, your air-

plane has an o p t i m u mglide speed that producesthe shallowest glide an-gle, but that speed de-pends on your plane'sweight. Gliding at a speedfaster or slower than theoptimum for that weightresults in a steeper f l ight

path angle and less range.In Figure 1, both airplanes

could be exactly the same butgliding at different speeds, andthe plane on the left could be ata speed faster or slower thanthe other plane. What's impor-tant is that there is only oneoptimum glide speed for a par-ticular a i rp lane weight , but

there is one AOA that ensures theoptimum glide speed and maximumrange for every airplane weight.

Last month's "Test Pilot" ex-plained how stall speed depends ona i rp lane weight because the s ta l lAOA doesn't change. The same ideaapplies to engine-out glide speed,but this time it's because the maxi-mum range AOA doesn't change.Here's why.

Let's start with the lift equation:

L is l if t , p (Greek letter rho) is airdensity. V is true airspeed. S is wingarea. CL is lift coefficient. Recall fromlast month that C| is uniquely re-lated to AOA. In other words, there isonly one CL that corresponds to aparticular AOA. There also is onlyone C| that will provide the maxi-mum lift-to-drag (L/D) ratio, which isthe L/D your airplane must be flownto achieve its maximum range.

Max L/DFigure 2 shows the forces acting onyour airplane dur ing a steady de-

98 MAY 2001

scent. Notice that Lift is perpen-dicular to both Thrust and Drag,but Weight points straightdown. For an easier force com-parison, we've shown theWeight components acting par-allel to Lift (W x cos y) and par-allel to Thrust and Drag (W xsin 7). Cos and sin are thetrigonometry functions cosineand sine.

During a steady descent, allthe forces are balanced. FromFigure 2 you can see that Lift equalsthe Weight component perpendicu-lar to the flight path (L = W x cos y),and Drag equals the sum of Thrustand the Weight component parallelto the flight path (D = T + W x sin y).But thrust is zero during an engine-out glide, so D = W x sin y. A littleequation manipulation:

L = W x cos(y)

D = W x sin(y)

= W

Lift (L)

Weight (W)

W x sin(y)

Figure 2W, so let's set them equal to eachother and do a little more manipu-lating.

L _ Dcos(y) sin(y)

glide range does not depend onits weight.

Okay, so far we know thatthe m a x i m u m glide range isachieved when your glide has

Thrust (T) tne smallest flight path angle,and that occurs when yourplane is flown at its maximumL/D. Now we'll show that themaximum L/D occurs at a sin-gle value of AOA.

If we look only at the l i f tequation, it might seem that

the biggest value of C| would pro-duce the biggest value of L, whichmight imply the greatest L/D, butthis is not the case. Take a look atthe drag equation:

1

cos(y)

Dsin(y) = W

We now have two expressions for

_L = cos(y) _D sin(y) tan(y)

L/D equals one over the tangentof the flight path angle. To ensurethe m a x i m u m L/D, we want thesmallest tan (y) possible, and thatmeans we want the smallest y possi-ble. This is our proof that the maxi-mum L/D occurs when the f l i gh tpath angle is as small as possible.Notice there's no W in the last equa-tion. That's because your airplane's

Notice the s imi lar i ty to the l i f tequation. CD is the drag coefficient,and it accounts for induced and par-asite drag. Figure 3 shows a genericrelationship between the lift curveand the drag curve versus AOA. No-tice how the increase in CD dramati-cally exceeds the increase in CL athigher values of AOA.

The maximum L/D, which is thesame as maximum CL/Cr> occurswhere the vertical distance betweenthe two curves is greatest — well be-

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Test Pilot

low the AOA for maximum CL.You can also see that there is onlyone AOA where this occurs. (Forthe purists , the l i f t and dragcurves in Figure 3 would normallybe vertically separated. They'reshown as they are to make the il-lustration more clear. The maxi-mum CL/CD AOA is the same.)

You already know from lastmonth's "'lest Pilot" that the liftcurve in Figure 3 applies to anyairplane weight at any altitude.The same is true for the dragcurve. The bottom line here is, thereis only one AOA that will give youthe farthest engine-out glide range,and this is why you can't stretch aglide. Your glide speed and descentrate will be fas ter when your air-

0>'o1ooO)2QT3cco

Max CL/CDoccurs at only

this AOA

Angle of AttackRgure 3

plane is heavier, but the range willremain the same.

If you change airplane configura-tion, like lower the flaps or leave theprop in Hat pitch, the lif t and dragcurves in Figure 3 wi l l change, but

there will still be just one AOA(probably d i f f e r e n t f rom theclean configuration AOA) foreach configuration that producesthe farthest glide distance.

There's a technical aviationterm called the pucker factor. It'sa var iab le whose in t ens i ty de-pends on the nature of the event

_ that causes its occurrence. Noone has yet derived a r e l i a b l eequation for the pucker factor,but empirical data and qualitativeevaluations allow us to conclude

that a sudden loss of engine poweryields an immense pucker factor.

Sizable pucker factors inhibit a pi-lot's math skills and recollectionacumen. What's my best glide speed?What airplane weight does it apply

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to? How much does my plane weigh right now? What'sthe speed adjustment I have to make to make sure I'mflying at the best glide speed? Wouldn't it be reassuringto know that little tick mark labeled "Max L/D" on yourAOA gauge guarantees the best glide?

Following an engine failure, most of us will probablytransition to some memorized glide speed as we attendto the other restart and forced landing procedures. Thisprocedure might be sufficient if your selected landingsite is nearby or if your restart is successful or if theweight variation of your plane is small enough that asingle glide speed guarantees 99 percent maximumrange for any weight. For all other conditions, that AOAgauge could be a lifesaver.

An AOA BonusBeyond the value of AOA as a stall margin indicator andmaximum glide range instrument, there's another bene-fit. Your airplane will cruise farthest when you fly at itsmaximum L/D. Your airplane's maximum L/D AOA isthe same for maximum cruise range as it is for maxi-mum glide distance, assuming the airplane configura-tion (landing gear, flaps, etc.) is the same.

Let's take a less technical, more intuitive approach tothis. Maximizing range, glide range, or cruise range isabout efficiency. The more efficiently you fly your air-plane, the farther it will glide given its available altitudeor fuel. Maximum lift and minimum drag would certainlybe ideal, but the laws of aerodynamics don't allow this.

Maximum lift occurs just as the wing stalls. Clearlythat won't get you very far. Even if you flew a couple ofknots below stall speed, you wouldn't get very far be-cause of the slow airspeed and high power (and fuelflow) requirements of slow flight.

Minimum drag seems like a good idea, but what yougain in endurance because of the lower power require-ment you lose in the resulting slow airspeed. Your fuelwould last longer, but you wouldn't travel as far.

There is some condition between minimum drag andmaximum lift where the tradeoff between less powerand more speed gives you the best deal. This occurs atthe maximum L/D, which occurs at only one AOA—thesame AOA as your airplane's maximum range glide AOA.

Why does weight affect speed and not AOA? As yourairplane burns fuel during a trip it becomes lighter. Ifyou fly a constant airspeed, you'd fly at a lower AOA asfuel burned and your cruise range would be less. If youcontinue to fly at your maximum range AOA, you'llhave to fly slower as fuel burned, but you would get themost mileage from your fuel.

Whether maximum efficiency is important dependson your needs. Most pilots cruise at a faster speed, andlower AOA, than maximum range AOA. These pilotstrade money (for the extra fuel speed costs) for a shorter

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flight (the result of speed).Someday, however, you may face

a diversion because of weather or anunexpectedly closed airport, and youmay not have enough fuel to reachyour new destination using yournormal cruise speed. Having the abil-ity to reference your "Max L/D" markon your AOA gauge could just giveyou those needed extra miles.

These last two "Test Pilots" haveunabashedly extolled the benefits ofangle of attack on safety and eff i-ciency. But if AOA is so wonderful,why doesn't the FAA require AOAindicators in airplanes?

Good question. Pilots can be justas safe and eff ic ient wi th properflight planning, solid piloting, anunderstanding of their airplane, andgood judgment without an AOAgauge. Having AOA at their disposalmakes it easier.

For small airplanes whose weightdoesn't vary much, a few airspeedreferences for maximum cruise andglide range and 1 G stall may be suf-f ic ient . For many homebuilt air-planes, however, where fuel andpayload weight can vary by a sub-stantial percentage of the airplane'soverall weight, there can be a con-siderable consequence in rangepenalties and stall margins.

The benefit of an AOA indicationduring maneuvering flight appliesacross the airplane spectrum andmay be particularly applicable tohomebuilt airplanes that don't ex-hibit a traditional stall warning.

Stepping off the soapbox, let'ssummarize. We've concluded ourdiscussion of AOA. Next month's"Test Pilot" tackles flight path stabil-ity. It's called stability, but it's reallyabout how changing your airspeedduring final approach affects yourglide path—and it's different for dif-ferent airplanes.

The address is Test Pilot, EAA Pub-lications, P.O. Box 3086, Oshkosh,WI 54903-3086 or eciitorial@eaa.orgwith TEST PILOT as the subject ofyour e-mail.102 MAY 2001