Airfoils and Lift

As stated before, the lift of a wing is proportional to the amount of air diverted down times the vertical velocity of that air. As a plane increases speed, the scoop diverts more air. Since the load on the wing, which is the weight of the plane, does not increase the vertical speed of the diverted air must be decreased proportionately. Thus, the angle of attack is reduced to maintain a constant lift. When the plane goes higher, the air becomes less dense so the scoop diverts less air for the same speed. Thus, to compensate the angle of attack must be increased. The concepts of this section will be used to understand lift in a way not possible with the popular explanation.

Lift requires power

When a plane passes overhead the formerly still air ends up with a downward velocity. Thus, the air is left in motion after the plane leaves. The air has been given energy. Power is energy, or work, per time. So, lift must require power. This power is supplied by the airplane's engine (or by gravity and thermals for a sailplane).

How much power will we need to fly? The power needed for lift is the work (energy) per unit time and so is proportional to the amount of air diverted down times the velocity squared of that diverted air. We have already stated that the lift of a wing is proportional to the amount of air diverted down times the downward velocity of that air. Thus, the power needed to lift the airplane is proportional to the load (or weight) times the vertical velocity of the air. If the speed of the plane is doubled the amount of air diverted down doubles. Thus the angle of attack must be reduced to give a vertical velocity that is half the original to give the same lift. The power required for lift has been cut in half. This shows that the power required for lift becomes less as the airplane's speed increases. In fact, we have shown that this power to create lift is proportional to one over the speed of the plane.

But, we all know that to go faster (in cruise) we must apply more power. So there must be more to power than the power required for lift. The power associated with lift, described above, is often called the "induced" power. Power is also needed to overcome what is called "parasitic" drag, which is the drag associated with moving the wheels, struts, antenna, etc. through the air. The energy the airplane imparts to an air molecule on impact is proportional to the speed squared. The number of molecules struck per time is proportional to the speed. Thus the parasitic power required to overcome parasitic drag increases as the speed cubed.

Figure 11 shows the power curves for induced power, parasitic power, and total power which is the sum of induced power and parasitic power. Again, the induced power goes as one over the speed and the parasitic power goes as the speed cubed. At low speed the power requirements of flight are dominated by the induced power. The slower one flies the less air is diverted and thus the angle of attack must be increased to maintain lift. Pilots practice flying on the "backside of the power curve" so that they recognize that the angle of attack and the power required to stay in the air at very low speeds are considerable.

Fig 11 Power requirements versus speed.

At cruise, the power requirement is dominated by parasitic power. Since this goes as the speed cubed an increase in engine size gives one a faster rate of climb but does little to improve the cruise speed of the plane.

Since we now know how the power requirements vary with speed, we can understand drag, which is a force. Drag is simply power divided by speed. Figure 12 shows the induced, parasitic, and total drag as a function of speed. Here the induced drag varies as one over speed squared and parasitic drag varies as the speed squared. Taking a look at these curves one can deduce a few things about how airplanes are designed. Slower airplanes, such as gliders, are designed to minimize induced drag (or induced power), which dominates at lower speeds. Faster airplanes are more concerned with parasitic drag (or parasitic power).

Fig 12 Drag versus speed.

Wing efficiency

At cruise, a non-negligible amount of the drag of a modern wing is induced drag. Parasitic drag, which dominates at cruise, of a Boeing 747 wing is only equivalent to that of a 1/2-inch cable of the same length. One might ask what affects the efficiency of a wing. We saw that the induced power of a wing is proportional to the vertical velocity of the air. If the length of a wing were to be doubled, the size of our scoop would also double, diverting twice as much air. So, for the same lift the vertical velocity (and thus the angle of attack) would have to be halved. Since the induced power is proportional to the vertical velocity of the air, it too is reduced by half. Thus, the lifting efficiency of a wing is proportional to one over the length of the wing. The longer the wing the less induced power required to produce the same lift, though this is achieved with an increase in parasitic drag. Low speed airplanes are affected more by induced drag than fast airplanes and so have longer wings. That is why sailplanes, which fly at low speeds, have such long wings. High-speed fighters, on the other hand, feel the effects of parasitic drag more than our low speed trainers. Therefore, fast airplanes have shorter wings to lower parasite drag.

There is a misconception held by some that lift does not require power. This comes from aeronautics in the study of the idealized theory of wing sections (airfoils). When dealing with an airfoil, the picture is actually that of a wing with infinite span. Since we have seen that the power necessary for lift is proportional to one over the length of the wing, a wing of infinite span does not require power for lift. If lift did not require power airplanes would have the same range full as they do empty, and helicopters could hover at any altitude and load. Best of all, propellers (which are rotating wings) would not require power to produce thrust. Unfortunately, we live in the real world where both lift and propulsion require power.

Power and wing loading

Let us now consider the relationship between wing loading and power. Does it take more power to fly more passengers and cargo? And, does loading affect stall speed? At a constant speed, if the wing loading is increased the vertical velocity must be increased to compensate. This is done by increasing the angle of attack. If the total weight of the airplane were doubled (say, in a 2-g turn) the vertical velocity of the air is doubled to compensate for the increased wing loading. The induced power is proportional to the load times the vertical velocity of the diverted air, which have both doubled. Thus the induced power requirement has increased by a factor of four! The same thing would be true if the airplane's weight were doubled by adding more fuel, etc.

One way to measure the total power is to look at the rate of fuel consumption. Figure 13 shows the fuel consumption versus gross weight for a large transport airplane traveling at a constant speed (obtained from actual data). Since the speed is constant the change in fuel consumption is due to the change in induced power. The data are fitted by a constant (parasitic power) and a term that goes as the load squared. This second term is just what was predicted in our Newtonian discussion of the effect of load on induced power.

Fig 13 Fuel consumption versus load for a large transport airplane traveling at a constant speed.

The increase in the angle of attack with increased load has a downside other than just the need for more power. As shown in figure 9 a wing will eventually stall when the air can no longer follow the upper surface, that is, when the critical angle is reached. Figure 14 shows the angle of attack as a function of airspeed for a fixed load and for a 2-g turn. The angle of attack at which the plane stalls is constant and is not a function of wing loading. The stall speed increases as the square root of the load. Thus, increasing the load in a 2-g turn increases the speed at which the wing will stall by 40%. An increase in altitude will further increase the angle of attack in a 2-g turn. This is why pilots practice "accelerated stalls" which illustrate that an airplane can stall at any speed. For any speed there is a load that will induce a stall.

Fig 14 Angle of attack versus speed for straight and level flight and for a 2-g turn.

Wing vortices

One might ask what the downwash from a wing looks like. The downwash comes off the wing as a sheet and is related to the details of the load distribution on the wing. Figure 15 shows, through condensation, the distribution of lift on an airplane during a high-g maneuver. From the figure one can see that the distribution of load changes from the root of the wing to the tip. Thus, the amount of air in the downwash must also change along the wing. The wing near the root is "scooping" up much more air than the tip. Since the root is diverting so much air the net effect is that the downwash sheet will begin to curl outward around itself, just as the air bends around the top of the wing because of the change in the velocity of the air. This is the wing vortex. The tightness of the curling of the wing vortex is proportional to the rate of change in lift along the wing. At the wing tip the lift must rapidly become zero causing the tightest curl. This is the wing tip vortex and is just a small (though often most visible) part of the wing vortex. Returning to figure 6 one can clearly see the development of the wing vortices in the downwash as well as the wing tip vortices.

Fig 15 Condensation showing the distribution of lift along a wing. The wingtip vortices are also seen. (from Patterns in the Sky, J.F. Campbell and J.R. Chambers, NASA SP-514.)

Winglets (those small vertical extensions on the tips of some wings) are used to improve the efficiency of the wing by increasing the effective length of the wing. The lift of a normal wing must go to zero at the tip because the bottom and the top communicate around the end. The winglets blocks this communication so the lift can extend farther out on the wing. Since the efficiency of a wing increases with length, this gives increased efficiency. One caveat is that winglet design is tricky and winglets can actually be detrimental if not properly designed.

Ground effect

Another common phenomenon that is misunderstood is that of ground effect. That is the increased efficiency of a wing when flying within a wing length of the ground. A low-wing airplane will experience a reduction in drag by 50% just before it touches down. There is a great deal of confusion about ground effect. Many pilots (and the FAA VFR Exam-O-Gram No. 47) mistakenly believe that ground effect is the result of air being compressed between the wing and the ground.

To understand ground effect it is necessary to have an understanding of upwash. For the pressures involved in low speed flight, air is considered to be non-compressible. When the air is accelerated over the top of the wing and down, it must be replaced. So some air must shift around the wing (below and forward, and then up) to compensate, similar to the flow of water around a canoe paddle when rowing. This is the cause of upwash.

As stated earlier, upwash is accelerating air in the wrong direction for lift. Thus a greater amount of downwash is necessary to compensate for the upwash as well as to provide the necessary lift. Thus more work is done and more power required. Near the ground the upwash is reduced because the ground inhibits the circulation of the air under the wing. So less downwash is necessary to provide the lift. The angle of attack is reduced and so is the induced power, making the wing more efficient.

Earlier, we estimated that a Cessna 172 flying at 110 knots must divert about 2.5 ton/sec to provide lift. In our calculations we neglected the upwash. From the magnitude of ground effect, it is clear that the amount of air diverted is probably more like 5 ton/sec.

Conclusions

Let us review what we have learned and get some idea of how the physical description has given us a greater ability to understand flight. First what have we learned:

· The amount of air diverted by the wing is proportional to the speed of the wing and the air density.

· The vertical velocity of the diverted air is proportional to the speed of the wing and the angle of attack.

· The lift is proportional to the amount of air diverted times the vertical velocity of the air.

· The power needed for lift is proportional to the lift times the vertical velocity of the air.

Now let us look at some situations from the physical point of view and from the perspective of the popular explanation.

· The plane's speed is reduced. The physical view says that the amount of air diverted is reduced so the angle of attack is increased to compensate. The power needed for lift is also increased. The popular explanation cannot address this.

· The load of the plane is increased. The physical view says that the amount of air diverted is the same but the angle of attack must be increased to give additional lift. The power needed for lift has also increased. Again, the popular explanation cannot address this.

· A plane flies upside down. The physical view has no problem with this. The plane adjusts the angle of attack of the inverted wing to give the desired lift. The popular explanation implies that inverted flight is impossible.

As one can see, the popular explanation, which fixates on the shape of the wing, may satisfy many but it does not give one the tools to really understand flight. The physical description of lift is easy to understand and much more powerful.

Axis of Rotation

Axis of an Airplane in Flight.

An airplane may turn about three axes. Whenever the attitude of the airplane changes in flight (with respect to the ground or other fixed object), it will rotate about one or more of these axes. Think of these axes as imaginary axles around which the airplane turns like a wheel. The three axes intersect at the center of gravity and each one is perpendicular to the other two.

Longitudinal Axis: The imaginary line that extends lengthwise through the fuselage, from nose to tail, is the longitudinal axis. Motion about the longitudinal axis is roll and is produced by movement of the ailerons located at the trailing edges of the wings.

Lateral Axis: The imaginary line which extends crosswise, wing tip to wing tip, is the lateral axis. Motion about the lateral axis is pitch and is produced by movement of the elevators at the rear of the horizontal tail assembly.

Vertical Axis: The imaginary line which passes vertically through the center of gravity is the vertical axis. Motion about the vertical axis is yaw and is produced by movement of the rudder located at the rear of the vertical tail assembly.

DETAILS OF MODERN AIRSHIPS - 1927

Advantages of Rigid Type Airships--Airship Frame Construction--Large Airships Projected--Army Non-rigid Dirigibles--Requirements of Airships for Civilian Flying.

Advantages of Rigid Type Airship. Before describing typical lighter- than-air craft or airships that have received actual commercial as well as military usage, it may be well to briefly review some of the advantages of the rigid type, which is the one that lends itself most easily to large structures and which is also the safest of the three types we have previously reviewed in Chapter II which is devoted to a consideration of the elementary principles underlying airship construction and application. Rigid airships have made longer single flights than other types and have flown more hours and miles without refueling than any other form. The rigid airship is said to be the fastest large vehicle of transportation that engineering ability of man has yet evolved. The Navy Airship Los Angeles, shown near the mooring mast at Lakehurst, N. J. to which it may be anchored is depicted at Fig. 315. A design of the new 6,500,000 cubic foot capacity ship recently authorized by Congress is shown at Fig. 316 flying over a battleship at an elevation of about 1,500 feet. The rigid airship, owing to its large size and light weight can carry more load than any other type of aircraft. It is independent of topography as oceans and continents are but areas to fly over. Land vehicles must stop when they reach water, water transport must stop when the ship is docked.

Airship Frame Construction. The rigid airship, because of its bulkhead system, in which the lifting gas is carried in 16 to 20 cells, has a much greater safety factor than the types in which the gas is carried in only one or two containers. In event of damage to one or two cells, the ship can continue its journey and repairs can be made to a leaky gas cell while in flight.

The rigid ship has a complete metal framework. Girders extend from nose to tail, or in nautical parlance, from stem to stern. Ring girders set at intervals brace the longitudinals and are themselves internally reinforced by cross girders and tension wire bracing. The entire framework is enclosed by a network of wiring and the whole is streamlined or faired to minimize air resistance with a fabric covering.

The view of the crew's quarters on the Bodensee, a German air liner at Fig. 317, shows the triangular keel member with the cat-walk by which the crew can travel from one end of the ship to the other and gain access to the different gas bags. The character of the longitudinal duralumin girders and the way they are braced by the ring girders is clearly shown at Fig. 318. This depicts that portion of the hull where one set of fuel tanks are located. The view at Fig. 319 shows the interior with the deflated gas cells hanging from the top-most longitudinal ready for inflation.

The outer skin is in place and the large size and extreme lightness of the structure is clearly shown. The passenger cabin of the Deutschland, another rigid dirigible of the Zepellin series is shown at Fig. 320. Wicker chairs are used because of their light weight and the interior structure of the cabin can be determined by study of the illustration.

The control of a Zepellin type airship is not as simple as that of an airplane and no one man is at the controls. Special controls are provided for the elevators and still another set for the vertical rudders. The elevator control of the L59 with the instruments for altitude navigation is shown at Fig. 321. Control is by a large wheel similar to the steering wheel of a ship. Directional control is by a similar wheel at another part of the control car.

Large Airship Projected. The largest of the United States Navy airships, the Shenandoah was 600 feet long with a capacity of 2,115,000 cubic feet. The projected airship designed by the engineers of the Goodyear- Zepellin Company, while it has over three times the capacity of the Shenandoah will be only 100 feet longer and will be of such size that it may be housed in the Lakehurst hangar. The illustration at Fig. 322 shows how the new ships authorized by congress will compare with the Shenandoah. The control car will be built into the hull and streamlined. Engines of 4,800 horsepower, giving a speed of 90 miles per hour with fuel for from 5,000 to 8,000 miles will drive the ship. The air screws will be fitted in tilting mountings, which will turn in a 90 degree arc to help force the ship upward or downward as desired and greatly aid in controlling the huge vessel.

It will embody the proved structural advantages of some 135 ships built in the past.

(a) Multiple gas cells which function like bulk-heading on a steamship, so that if one or more cells fail the ship will still remain aloft: (b) The triple cover system, one cover to hold the lifting gas, one consisting of the shape-forming duralumin frame-work, and an outer cover to shed rain and snow, to reflect rather than to absorb heat, and to present a fair surface; (c) invulnerability against lightning; (d) accessibility to inspection and repair.

It will however present certain new features as well of far reaching importance: (a) A double or triple keel giving added longitudinal strength comparable to the breaking strength of one length of metal, as against two or three bolted together; (b) a new type of ring girder each internally braced and structurally self sufficient, which (c) will permit the control car and even the power cars to be built within the hull; (d) even fuller accessiblity to continuous inspection and permitting repairs to be made even in flight; (e) the use of new fuels to conserve helium and reduce weight.

Army Non-Rigid Dirigibles. The non-rigid dirigible is the smallest of the three types as the largest now being built in the United States for the Army and Navy service have a gas capacity of about one-tenth that of the Los Angeles. Under ordinary conditions a 230,000 cubic foot non-rigid has a cruising radius of from 500 to 1,000 miles and an air endurance of from 18 to 24 hours. Such airships are essentially motorized free balloons and the engines are carried in a car attached to the lower side or bottom of the bag. The Pilgrim, a small non-rigid previously described with a gas capacity of 50,000 cubic feet has a speed of 50 miles per hour and is propelled by a Wright "Gale" three-cylinder engine as shown at Fig. 323. This small ship was built to carry four passengers. The gas in non-rigid ships, as in the army TC types, as shown at Fig. 324 is contained in a single bag, but an inner two compartment bag, called the ballonet, is filled with air to keep the main container properly distended because the air pressure can be made to compensate for variations in gas pressure in the bag. These ships have a capacity of about 200,000 cubic feet, are 196 feet long overall and 47 feet in extreme height. The hull diameter is 33.5 feet. The fineness ratio is 4.4 to 1. The total lift is 11,584 pounds of which the useful lift is about 4,000 pounds. The gross weight per horsepower is 38.6 pounds. Two Wright Type I water-cooled engines of 150 horsepower each were provided on the first ships of this series but these have been replaced on later types with two Wright J1 engines, which are nine-cylinder radial air-cooled types driving tractor propellers 9 feet 10 inches in diameter. It is claimed that the saving of 400 pounds over the water-cooled installation permits an increase of speed from 54 to 60 miles per hour; with an increase in range of 10 per cent.

Flight Control Surfaces - Elevons

Delta winged aircraft use elevons as primary flight controls for

roll and pitch.

Elevon: Delta winged aircraft can not use conventional 3 axis flight control systems because of their unique delta shape. Therefore, it uses a device called an elevon. It is a combination of ailerons and elevators.

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