ppl_05_e2

CHAPTER 6: THE

If a pilot increases

speed and wishes to

maintain altitude, he must decrease angle of attack.

If a pilot decreases

speed and wishes to

maintain altitude, he must increase angle of attack.

Order: 6026

Customer: Oleg Ostapenko E-mail: ostapenko2002@yahoo.com

Customer: Oleg Ostapenko E-mail: ostapenko2002@yahoo.com

LIFT/DRAG RATIO

What the Graphs of CL and CD Against Angle Of Attack Teach Us.

The CL and CD curves are indicative of changes in the actual forces of lift and drag only if we assume constant airspeed and constant density. (However, even this latter statement is only of mathematical interest to us as, in real life, airspeed is itself directly related to angle of attack.)

However, if we bear in mind at all times the true nature of CL and CD, the CL and CD graphs give us some useful information. So, before we go on to examine the forces of lift and drag, considered in combination, let us take one more look at the CL and CD curves, separately, to see what they might have to teach us.

First of all, notice the difference in their shape.

The curve of CL against angle of attack (AoA) is almost a straight line, from a slightly negative AoA up to an AoA of about 10°. We can see, therefore, that a small increase in AoA , say of 1°, from 2° to 3°, has the same effect, in terms of augmenting the lift force (at constant airspeed and air density) as does a 1° AoA increase from 8° to 9°. CL continues to rise, less rapidly, beyond 10° AoA, reaching a maximum value, called CLMAX , just before the stalling angle (sometimes called the critical angle) of about 16°, beyond which lift decreases abruptly.

However, in terms of CD, for the same two increases in AoA, from 2° to 3° and from 8° to 9°, the effect is markedly different. A 1° increase in AoA from 2° to 3° makes no noticeable difference to the drag force (at constant airspeed and air density), while the

1° AoA increase from 8° to 9° produces a signifcant increase in drag. The increase in drag becomes even more rapid as the stalling angle of 16° is approached. CD continues to rise steeply beyond that angle as the airfow becomes more turbulent and erratic.

You will become aware of the importance of what these graphs are telling you, at appropriate phases in your fying training.

For instance, if we consider the information from the CL and CD graphs against AoA, along with the information that we can extract from the lift and drag equations,

Lift = CL ½ ρv2S and Drag = CD ½ ρv2S, we should easily be able to deduce the following piloting facts:

•If the airspeed, v, is increased while the angle of attack CL or CD remains constant, the magnitude of both the lift and the drag forces will increase, and the aircraft will begin to climb. (In fact, because lift and drag are proportional to v2, if the airspeed is doubled, the lift and drag increase fourfold.)

•If the pilot wishes to increase speed v in the cruise and to maintain altitude at the higher speed, he must hold lift constant by reducing angle of attack and thus CL.

•At constant air density and angle of attack, if Fowler Flaps are deployed (See Figure 10.12 in the Lift Augmentation Chapter), wing area, S, will increase; therefore, lift force (and, thus, altitude) will be able to be maintained at a lower airspeed.

Induced drag

is high at low airspeeds and

parasite drag is

high at high airspeed.

•Low airspeeds are related to high angles of attack.

•High airspeeds require low angles of attack.

•The total drag acting on an aircraft fying at low CD (say 0° angle of attack),

will still be high because although CD may be low, v in the equation Drag = CD ½ ρv2S will be high. Of course, drag varies directly, not with v, but with v2.

•At a higher all-up weight when no fap is selected, an aircraft needs to be fown at a higher angle of attack (higher CL) to maintain a given airspeed.

•The total drag acting on an aircraft fying at very high speeds and very low speeds is high in both cases. At high speed (small angle of attack and low CD), most of the drag

will be parasite drag, and, at low speed (large angle of attack and high CD), most of the drag will be induced drag.

(See Figure 6.2).

Total drag is high at both very high and very low speeds.

CL and CD are dimensionless

coefficients which takes

into account wing shape, configuration and angle of attack.

The lift-drag ratio varies

with angle of attack and,

therefore, also with airspeed.

When the liftdrag ratio is at

a maximum (at about 4° angle of attack), the wing is operating

at its most efficient.

•Because the indicated airspeed already takes into account the value of ρ, (the airspeed indicator (ASI) measures the dynamic pressure, ½ ρv2 ), an aircraft attempting to maintain steady, level fight at steadily increasing AoA will always stall at the same ASI reading.

The Lift-Drag Ratio.

In most (but not all) phases of fight, the generation of lift by the wing is a distinct beneft, while the generation of drag is a distinct disadvantage. When the aircraft is fying very fast at low angles of attack (low CD), we have seen that parasite drag is high, and when the aircraft is fying at low speeds and high angles of attack (high

CD), the induced drag is high. (See Figure 6.2). So at neither of these two extremes of high drag is the wing working at its most effcient. The wing will be working most effciently when it is generating maximum lift for minimum drag.

Consequently, a factor of greater signifcance to aircraft performance issues than lift and drag considered separately, is the lift-drag ratio. The lift-drag ratio is commonly expressed, using initial letters, as the L/D ratio.

Maximum lift for minimum drag occurs at the highest lift-drag ratio; that is at the highest value of the L/D ratio. From the values available from the two individual graphs of CL and CD against AoA, we can plot a further graph which shows how the lift-drag ratio (L/D ratio) varies with AoA. Such a graph is depicted in Figure 6.3.

You have already learnt that the values of lift and drag are not the same as the values of CL and CD because the actual lift and drag forces depend on other parameters such as airspeed, air density and wing area. But to obtain information on the lift to drag ratio, we may plot either Lift/Drag against AoA or CL/CD against AoA. The following

mathematical relationship illustrates why this is so.

The lift-drag ratio is at a

maximum where total

drag is at a minimum.

From Figure 6.3, then, you can see that the L/D ratio increases rapidly to a maximum value, at an AoA of around 4° and then falls away as AoA is increased further. Be aware that this does not mean that lift is greatest at 4° AoA. As the CL graph shows, lift carries on increasing well beyond an AoA of 4°. But, of course, from the CD graph you see that the drag goes on increasing beyond 4° AoA, too. Therefore, when we combine the data from the CL and CD curves, we see that the best L/D ratio (L/DMAX) occurs at 4° AoA.

In the chapter on drag, you learnt, that an AoA of 4° is the AoA for minimum drag. So minimum drag AoA is also the AoA for the L/DMAX.

Consequently, for the conventional aerofoil wing, greatest effciency is achieved at an AoA of 4°. This fact explains why the wing’s angle of incidence (rigger’s angle of incidence between the wing chord line and the aircraft’s longitudinal axis) is set so that, in level cruising fight, the relative airfow meets an aircraft’s wing at about 4°.

Of course, if it is the designer’s intention to design an aircraft for speed, the aircraft’s wing may meet the relative airfow at an AoA of less than 4°, in the cruise; but if economy and effciency of operation is the designer’s chief concern, the cruising AoA will be about 4°. The aircraft for which the L/D graph at Figure 6.3 was drawn has a maximum L/D ratio of 13 at an AoA of 4°. Let us assume that this aircraft is operated in steady cruising fight at an all-up weight of 2125 pounds (lbs). Because, in steady fight, lift must always equal weight (ignoring any downforce from the tailplane for this example), the lift generated by the aircraft would also have to be 2125 lbs (964 kg or about 9457 Newtons). If the aircraft is fown at an airspeed corresponding to the L/

DMAX AoA of 4°, the drag acting on the aircraft would have the value 163.5 lbs (74 kg or about 726 Newtons), which, of course, is one thirteenth of 2125 lbs. This would

be the minimum amount of drag generated to provide the lift necessary to support the weight of 2125 lbs. The weight could be supported at lower or higher airspeeds,

than the speed for L/DMAX, but, in that case, AoA would be higher or lower than the L/DMAX AoA of 4°, and drag would always be greater than 163.5 lbs.

Even if the aircraft were operated at a higher, or lower, all-up weight, the same maximum L/D ratio would be obtained at 4° AoA. However, as the lift and drag equations show, if the all-up weight were higher, lift would have to be higher and the maximum L/D ratio would be obtained at a higher airspeed. Similarly, if the all-up weight were lower, L/DMAX would be obtained at a lower airspeed.

Performance Criteria Related to Maximum Lift-Drag Ratio (L/DMAX).

In steady, level, cruising fight, the thrust developed by the propeller must equal drag; so, for fight at L/DMAX (that is, at minimum drag), the thrust required to maintain level fight is also a minimum.

Several important aspects of aircraft performance are related to an aircraft’s maximum achievable Lift-Drag ratio. The most relevant of these are: maximum power-off gliding range, maximum cruising range, and best rate of climb.

As you have learnt, L/DMAX corresponds to fight at 4°AoA, for a conventional aircraft.

Whilst light aircraft are not ftted with angle of attack indicators, you learnt in the

Chapter on lift that, at a given aircraft weight, a given angle of attack corresponds to a particular airspeed. Therefore, for a given aircraft, at an assumed normal operating weight, a speed will be published in the Pilot’s Operating Handbook (POH) for (amongst other performance criteria) best glide range, maximum cruising range and best rate of climb.

The following approximate speeds are given for the PA-28-161, Warrior, for an assumed maximum gross weight of 2440 lb (1107 kg or 10 860 Newtons):

Maximum range cruising speed = 105 knots.

Maximum rate of climb, without fap, = 75 knots.

Both these speeds will be achieved, with different power settings, of course, at an AoA of around 4°.

The greater the

aircraft’s weight, the higher the

airspeed at

which the lift-drag ratio is at a maximum.

An aircraft’s best glide

angle is not affected by the

aircraft’s weight. But a heavier aircraft will achieve its best glide angle at a higher airspeed than a lighter aircraft.

Figure 6.4 In still air, an aircraft’s glide performance (distance covered/height lost) is equal to the Lift-Drag ratio.

In the glide, you will notice that there are only three forces acting on the aircraft: lift, weight, and drag. In a steady glide, these three forces are in equilibrium, the weight of the aircraft being counterbalanced by the total reaction: the resultant of the lift and drag forces.

You can see, then, that an aircraft’s best glide range (minimum glide angle) is achieved at L/DMAX. The angle of attack (AoA) between the wing chord and the relative airfow will be, of course, about 4°. Without power, and at maximum all-up weight, this AoA will be achieved in the PA28 Warrior at an airspeed of about 74 knots.

An aircraft’s best glide angle is a function solely of the lift-drag ratio, and is not affected by the aircraft’s weight. However, the greater the weight, the higher will be the airspeed at which the best glide angle is achieved.

Glide performance will be covered in the Aircraft Performance section of this book.