On improving take-off efficiency of airplanes

On improving take-off efficiency of airplanes

Arpan Dey

Abstract

In this paper, a special model for the airplane wing is proposed. The main aim of the model is to maximize take-off efficiency of airplanes and increase the effectiveness of in-flight maneuvers. The sudden movement of a leading-edge downward-movable control surface in the main wing could, if engineered cautiously and effectively, increase the lift force of an aircraft. This could work independently of the elevator. Finally, the pros and cons of the model is discussed from different perspectives.

Introduction

“Once you have tasted flight, you will forever walk the earth with your eyes turned skyward, for there you have been, and there you will always long to return..”[1] Leonardo da Vinci’s famous quote sums up humankind’s struggle to fly in the sky – from time immemorial. Today, that is no more a dream. The Wright brothers’ first flight could be done within the fuselage of modern airliners like the Airbus A380. Some would say flying has lost its charm. But every time you are in your seat – gripping your armrest as the plane rolls forward on the runway with flaps extended – you know that it hasn’t.

Poetry aside, the airline industry is a complex one – where boom-and-bust cycles are inevitable and can bring down companies from their pinnacles to a state of bankruptcy. A single crash can give rise to a long-standing saga, a single innovation can bring breakthroughs. On the whole, it is a much safer means of transportation, and undoubtedly the most convenient one. Some people are reminded of the old glory and luxury when asked about aviation. Some think of world wars. Many think of something similar to this.

Figure 1: Two Boeing 747s collided in Tenerife airport in Mach 1977. This remains the deadliest air crash in history.

Basics of flight

An airplane is not just a complex machine with millions of parts; it is also one of the most sensitive machines out there, with a lot of moving surfaces – a slight change in which can create a drastic outcome. An airplane flies by manipulating, with the help of movable control surfaces, the flow of air around it. The wing is designed such that the air above the wing would flow faster that the air below, and thus create a region of low air pressure above the wings – thus generating a lift force upward.

Four forces act on an airplane. The weight of the plane tends to bring it down. This is balanced by the lift force generated by the wings. The thrust of the engines tend to push the plane forward. This is balanced by air resistance, or drag.

Figure 2: A Boeing 787-8 Dreamliner in flight. Four forces act on an airplane.

Thus, all we need to do is generate more lift than weight and more thrust than drag, if we are to remain airborne and move forward. Thrust is easy to understand. The engines spin to create a region of low pressure just before them. This causes air to rush in, which is then passed through a compressor and ignited with the fuel in the combustion chamber. (Interestingly, part of this compressed air is circulated in the cabin, since air at high altitudes lack oxygen.) This air is then passed through the turbine station, causing the first-stage fan to spin faster and suck in more air. This incoming air will push the ignited air out from the exhaust. This backward push provides the forward thrust as a reaction force – which, though can be difficult to believe for beginners – pushes the huge aircraft at a speed of 170 knots on the runway. (1 knot is about 0.5 metres per second.)

Figure 3: A Boeing 777 jet engine nacelle. The jets are huge, and are most widely used today. Planes flying shorter distances, called turboprops, use different engines.

Figure 4: The above diagram shows the basic working of a typical jet engine.

What about the lift? We have the wings to generate them. Anyone who has travelled by air is aware of the huge surface area of the main wing. The wings are specially shaped to maximize lift force. The airfoil shape of the wing curves the air that is flowing on top of it, and slows down the air that is flowing below. This creates a difference in air pressure above and below the wing – with a greater pressure below. This is responsible for generating the force that pushes the wing upward.

Figure 5: Faster air molecules move, lower will their pressures be. This is exploited to generate the lift force.

Air is a fluid. When a fluid is in motion, it must move in such a way that mass is retained. Mass conservation places restrictions on the velocity field. Consider the steady flow of fluid through a duct (i.e., the inlet and outlet flows don’t vary with time). The inflow and outflow are one-dimensional, so that the velocity ν and density ρ are constant over the area Α.

Applying the principle of mass conservation, since there is no flow through the side walls of the duct, the mass that comes in over area Α₁ (area of inlet portion) goes out of Α₂ (area of outlet portion). The flow is steady so that mass is not accumulated. Over a short time-interval Δt,

Volume of inflow, Α₁ = Α₁ν₁Δt

where ν₁ is the velocity of the fluid when it is flowing through Α₁. Velocity times time gives distance (here, in the horizontal direction); which, when multiplied with the two-dimensional area of cross-section, gives the volume.

Similarly,

Volume of outflow, Α₂ = Α₂ν₂Δt

where ν₂ is the velocity of the fluid when it is flowing through Α₂.

We know that .

Mass in = ρΑ₁v₁∆t

Mass out = ρΑ₂v₂∆t

By the law of conservation of mass,

ρΑ₁v₁∆t = ρΑ₂v₂∆t → Α₁v₁ = Α₂v₂

This is the continuity equation for steady one-dimensional flow. The equation shows that the greater the area, the lower the velocity and vice-versa. This is precisely why water from a pipe rushes out at a greater velocity if the mouth of the pipe is pinched, thus decreasing the area of cross-section. This same principle is used by airplanes too.

However, it should be noted that the equal transit theory is flawed since the airflows above and below the wing need not meet at the trailing edge. Also, contrary to what is stated in the equal transit theory, velocity difference does not give rise to pressure difference, rather the opposite. Actually, as the streamline curvature theory suggests, the curvature of the wing is responsible for generating lift force. The key is to realize that if a streamline is curved, there must be a pressure gradient across the streamline, with the pressure increasing in the direction away from the centre of curvature.

The flow of a fluid is steady if at any given point, the velocity of each passing fluid particle remains constant in time. The path taken by a fluid particle under a steady flow is a streamline. Take a non-spinning ball moving relative to a fluid. The streamlines around this ball are symmetrical above and below the ball, and the velocity of the fluid above and below at corresponding points is the same. Thus, there is no pressure difference. The ball moves neither up nor down. Now, take a ball in a fluid which is moving and spinning clockwise. this ball drags the fluid with it. The ball is moving forward and relative to it, the fluid is moving backward. The velocity of the fluid above the ball relative to it is greater than that below the ball. The streamlines get crowded above and there is a pressure difference above and below the ball. The result is a net upward force. The airfoil shape is such that it can generate lift when it moves horizontally through a fluid (it need not spin).

First things first, let us look at the various parts of a typical modern airliner.

Figure 6: The various parts of an airplane. The undercarriage or the system of wheels that support the plane on ground is known as the landing gears. The above model is a Boeing 747.

Figure 7: The different control surfaces of an aircraft. The above model is an Airbus A380-800.

Figure 8: The different control surfaces on the main wing. The spoilers are moved upward to obstruct the airflow above the wing and slow down the airplane.

What about in-flight maneuvers? How does a plane bank, or change its altitude during flight? All that is done by some movable control surfaces. Ailerons are present near the end of the main wing, at either side. Alternate movements of ailerons cause the airplane to tilt. Now, the rudder is activated to turn sideways. The rudder is present at the end of the tail (the vertical stabilizer present at the back of an airplane). Sideways movement of the rudder diverts the airflow toward the left or right. The reaction force pushes the back portion of the plane in the opposite direction, thus making the plane turn in the desired direction.

Figure 9: Alternate movements of ailerons cause the airplane to bank sideways. Some of the lift acts sideways, and along with the lateral push provided by the rudder, pushes the airplane to one side.

Figure 10: Rudder helps in lateral turning. However, except in critical weather conditions, rudders alone are not used in turning. Rudders are activated along with ailerons for a smoother and more comfortable roll.

Take-off

Take-off is one of the most crucial phases of flight. After the V1 speed (the speed during the take-off roll after which the take-off can’t be cancelled), the elevators, located at the trailing edge of the horizontal stabilizers (the smaller set of wings present at the rear end of the airplane), are moved upward to divert airflow upward. The reaction force of the air pushes down the back of the airplane. This causes the airplane’s nose to tilt up during the ground run. The velocity at which this happens is known as VR or V-Rotate, since the body of the airplane rotates. After this, the plane lifts off. This is the V2 speed. (Interestingly, upward and downward movements of the elevator are also responsible for changing altitude en route.)

Figure 11: An American Airlines Airbus A320 at VR speed.

The wings are shaped and designed to generate lift force while kept in fluids. In older planes, the wings were positioned perpendicular to the body. In most modern planes however, the wings are slanted or swept backward. This design actually decreases the lift by a small amount, but increases the speed by a great extent, thus compensating for any decrease in lift.

Figure 12: Older aircrafts and some modern regional jets do not have swept wings. The wings are positioned perpendicular to the fuselage (body).

Figure 13: Modern airliners like the Airbus A350 have swept wings.

However, the lift generated by the main wing by itself is not sufficient to provide the energy needed to let the airplane break free of the ground. For this reason, the wings are equipped with certain movable control surfaces – the leading edge slats and the trailing edge flaps. Before take-off, these are extended downward – and the airfoil shape becomes more prominent. The low-hanging flaps also help to obstruct and slow down airflow below the main wing. Slower air is denser and is more high-pressured – and this generates the extra lift.

Figure 14: A “flaps-down” United Airlines Boeing 747-400 model.

Operating the flaps is complicated, and flaps are extended to different extents, depending on the weight, runway length, weather etc.. Flaps help to maximize the lift force at a particular angle of attack, without stalling the airplane and without airflow separation. [2] (Contrary to common misconception, flaps do not change the angle of attack – rather increases lift force at a given angle of attack.) Angle of attack is the angle between the oncoming air or relative wind and a reference line on the airplane or wing. The higher the angle of attack, the higher the lift force. However, there is a limit to this. If the angle of attack is too high, the airflows above and below the wing separate and create turbulent wind vortices. This kills lift and the airplane is unable to climb further. This condition is known as a stall.

Figure 15: The angle of attack is the angle between the direction of the flow of wind and the axis of the airplane.

Figure 16: For larger angles of attack, airflow separation takes place and the drag increases. This is when we say a plane has stalled.

Figure 17: After a certain angle of attack, the airflow above the wing separates from the airflow below and reduces lift.

Figure 18: Airflow separation gives rise to wind vortices and turbulence, thus increasing drag and killing lift.

Figure 19: Initially, the lift increases with the angle of attack. After the critical angle of attack, the lift begins to break down, with increasing drag.

It is clear that the main wing (and the entire airplane, for that matter) is very complex. Even slight design tweaks cost millions of dollars – but these are effective as long as they increase the fuel efficiency and safety of the airplane.

The “VR-Flap” design

Take-off is crucial since it is impossible to slow down from such velocities – and the length of the runway is not infinite. Larger planes can’t operate in shorter runways, heavier planes need more runway to take-off. Tailwinds and hot air also don’t help in the process. Improving take-off efficiency is, thus, always important.

From the beginnings of flight, we have devised ingenious ways of improving take-off efficiency of airplanes. Flaps are used for this reason. Increasing the surface area of the wing also helps. Modern planes also have raked wings and winglets. The wings are curved upward to increase efficiency.

Figure 20: The Boeing 777X is equipped with raked wingtips. The sweep of the wingtip is more that the sweep of the wing.

The design proposed in this paper has been referred to as the “VR-Flap” design. This indicates that it is an additional flap structure in the main wing that would help rotation at VR speeds during the take-off. Conventionally, this is done by the elevator. The “VR-Flap” design is basically a design tweak that could be introduced in airplanes to maximize take-off performance and/or pitch performance.

In this model, a proposed downward-movable control surface is added at the leading edge under the airplane’s main wing (the portion nearest to the fuselage). The VR-Flap should be added such that it can fold right inside the wing and does not, in the slightest, affect the smooth airfoil surface of the wing.

The VR-Flap essentially resembles a split flap [3], but set further forward. Split flaps are inefficient and increase drag. However, unlike split flaps, the VR-Flap is not meant to be activated for a long time. Thus, the resulting drag would be negligible.

Figure 21: The split flap.

The design is more efficient if the airplane has a wider wing surface. For instance, in this case, the Airbus A380 would stand a greater advantage than airplanes like the Boeing 737, which has relatively thinner wings as compared to the former. The VR-Flap need not be too thick, but should span a huge area. During the take-off roll, on reaching VR speed, the VR-Flap can be moved down to increase the lift under the leading edge of the wing. A cautiously-engineered sudden movement of the VR-Flap could, reasonably, provide enough lift force to the aircraft so that it can break ground without activating the elevators.

Figure 22: The lateral side view of the wing is shown, with the VR-Flap.

While the inconvenience and cost of installing such a structure in a commercial airplane seems formidable, it can come in handy in case of malfunctioning elevators, as well as helping in-flight maneuvers during rough weather conditions. However, the most important use of the VR-Flap design is of course that, if activated along with the elevators, it could decrease take-off space and/or increase maximum take-off weight of any airplane considerably. And at times, this becomes more economical, even if it means installing an entirely new structure in the wing.

Discussion

The major concern is that such a design would considerably affect the fuel capacity as the fuel, in most planes, is stored inside the main wing. However, though costly, the fuel could be stored inside the VR-Flap too, and the joining point between the main wings and the VR-Flap (that is, the pivot) could serve as the fuel pipe from the VR-Flap to the wings, and to the engines.

With the aid of the VR-Flap, in case of short runways or other emergency situations, the airplane, already at take-off roll, could easily take-off even below VR speed rather than abort the entire procedure (which at times becomes impossible). In this way, accidents like runway overruns during take-offs etc. could be avoided. It may prove effective in controlling turbulence, and with a balanced connection to the lift spoilers on the wings, the horizontal stabilizers may not need any movable surface at all. However, the horizontal stabilizers must be present anyway, for in-flight stability.

Other than the costs involved, there is no direct problem with the VR-Flap design. The question of airflow separation is also immaterial if the VR-Flap is moved down for a small instant of time. Admittedly, using both the elevator and the VR-Flap simultaneously increases the risk of tail strike (or the tail hitting the ground). Also, perhaps the most important question is the angle by which the VR-Flap needs to be moved down. In planes that sit low on the ground, this might be a problem – since the risk of the VR-Flap grazing the runway presents itself. Fortunately, modern airplanes usually have good ground clearance. Some airplanes like the Boeing 737 sit lower on the ground – but it still probably is high enough for the VR-Flap operations.

Figure 23: Boeing 737s were originally designed to operate in airfields and ramps without much advanced ground service equipment [2]. The planes were designed to sit low as that helped in loading and unloading.

Another problem with the VR-Flap design is that the jet engines in most modern airplanes are positioned in the leading edge of the main wings, which is also the proposed position for the VR-Flap. The VR-Flap could be designed in parts – and be accommodated under the wing with a gap for the engine pylons. Repositioning the engines is not always a valid option, since engines positioned at the leading edge of the main wings are more efficient and convenient than engines placed at the rear fuselage. Aft-mounted engines have some benefits, but wing-mounted engines are, on the whole, better and easier to maintain. Some older models, like the Boeing 727, have engines placed at the back of the fuselage. Setting up the VR-Flap would be more convenient in such models.

Figure 24: The Boeing 727 has three engines mounted not under the main wings, but at the rear fuselage. Setting up a structure under the main wings is easier in such airplanes, although this design is obsolete now.

The VR-Flap design would also be very convenient to install in high-wing airplanes. Most commercial airplanes are low-wing, that is, the body is placed over the wing. Some airplanes, like regional jets and/or cargo airplanes, have the main wing mounted over the body (high-wing).

Figure 25: Most modern airliners, like the Boeing 777X, are low-wing aircrafts.

Figure 26: The Antonov An-124 is a high-wing cargo aircraft.

The center of mass is beneath the center of lift in a high-wing airplane, thus causing it to be more inherently stable as compared to a low-wing airplane (whose center of lift is below the center of mass). [4] To improve the stability of a low-wing aircraft, designers compensate by angling the wingtips upward (dihedral) [2].

Figure 27: In most low-wing airplanes, the wings are curved upward (dihedral). When it comes to handling, the dihedral planes need to use more ailerons in a crosswind as compared to a flatter wing.

Figure 28: Most high-wing airplanes, like the Antonov An-225 cargo airplane (the world’s largest aircraft), have an anhedral design, that is, the wings literally “hang downward”.

Both high-wing configurations and low-wing ones have their own benefits, and none of the designs is better than the other. For instance, in an emergency water landing, passengers of an high-wing airplane can’t use the wing, while the wing is accessible in a low-wing airplane. While high-wing airplanes have more ground clearance, low-wing airplanes have enhanced ground performance. While low-wing airplanes have the wings to reduce the impact during a crash landing, the fuselage in high-wing airplanes have to handle the full impact. High-wing airplanes have less space for retracting the landing gears, low-wing airplanes can do so easily in the wings.

An important point to note here is that low-wing airplanes have reduced elevator and rudder effectiveness, since the main wing blocks some of the air that flows to the rear end of the plane. This justifies installing the VR-Flap structure to aid elevators and increase the effectiveness of maneuvers.

As an interesting endnote, the spoilers of the aircraft (that is to say, the lift spoilers and not the lift dumpers, for the latter would not be that much more efficient, its use being confined to the ground braking procedure after touchdown) could also be shaped as an Upside-Down (U-D) airfoil. This would increase the backward drag force if the wind is from upward direction, that is, downward and to some extent, if the wind is from downward, too. This little tweak in the design of the lift spoilers should not cost much, and neither would it be too inconvenient. The practical efficiency of such a design needs to be experimentally tested, however. To sum up, it is clear that slight design tweaks in the main wing can work wonders in increasing the efficiency of airplanes.

Conclusion

William Boeing said, “We are embarked as pioneers upon a new science and industry in which our problems are so new and unusual that it behooves no one to dismiss any novel idea with the statement that ‘It can’t be done!’”

It can be concluded that adding a downward-movable structure at the leading edge of the main wing in an airplane might help considerably in increasing take-off efficiency and the effectiveness of in-flight pitch control. It would also be very helpful in many emergency situations. Though costly, such a structure could help planes take-off below usual speeds, in short runways and adverse conditions. Things like ground clearance, wing configurations, engine positioning etc., need to be considered before installing such a structure. However, such a structure is possible to be installed in almost any airplane. It should be most convenient to install such a structure in low-wing or high-wing airplanes with good ground clearance, and preferably with aft-mounted engines. As of now, this idea could be experimentally tested on a cheaper model.

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[4] “High Wing vs Low Wing: What’s the Difference Between Them?” Pilot Mall. 2020. https://www.pilotmall.com/blogs/news/high-wing-vs-low-wing-what-s-the-difference-between-them

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About the Author

Arpan Dey, 16, is a high-school student from India who is deeply interested in physics, mathematics and the metaphysics of science. He has been working as an editor for the Young Scientists Journal and is involved in many STEM-related activities. He also enjoys reading, writing short stories (mainly sci-fi and detective) and listening to instrumental music. He is also an aviation enthusiast.