Editor | On 05, Apr 2010

By Prashant Y. Joglekar

Abstract

When it comes to airline businesses the world watches closely as airlines pass through rough waters. Operators have no control over the major costs incurred in running the business. For example, fuel accounts for nearly 30 to 40 percent of an airline’s total expenses. Using the Theory of Inventive Problem Solving (TRIZ) there are several ways fuel efficiency can be improved.

Introduction

Aircraft engineers could say that aerodynamics is a mature science. That was until NASA’s Richard T. Whitcomb invented vertical winglets, which could reduce the drag by nearly 20 percent. The problem explored in this article considers the trouble of drag reduction at an aircraft’s wingtips. This is one of the major contributors of problematic lift force, which adversely affects fuel efficiency.

The following includes what the problem is, where it occurs, what the contradictions are and how TRIZ principles could be used to create this concept. The proposed solution is tested and validated for improved fuel efficiency and includes several benefits.

Defining Broader Problems

It is a challenge to reduce fuel cost. The airline operator can try to do it by way of fuel hedging or by having a better business model, however, the aircraft manufacturer has to see profit growth from its customers.

This case study shows how the fuel cost reduction problem was tackled by the aircraft manufacturers. The broader problem, therefore, becomes “How to reduce fuel consumption.” The first step is to define “ideality” (i.e., maximum benefits / (zero cost + zero harm). The solution should include more good things than bad. When talking about a technical system it means maximization of a useful function performed by the system and reduction or elimination of the harmful function at no cost.

Defining Narrow Problems

First, look at the forces on an aircraft wing in cruise mode. Figure 1 illustrates how these forces are provided by the engine, the lift generated (due to the wings of the moving body), its own weight and the drag that is induced (by the stream of air as it passes through).

Figure 1: Forces Acting on the Wing of an Aircraft

The engine design can be examined for how to improve thrust per unit of fuel burnt. This involves mapping the engine system and maximizing useful functions with the elimination of harmful functions. Similarly, weight can be reduced by using knowledge from several fields where the similar problem of weight reduction is successfully solved. As a result, this is one of the directions that can be taken to tackle the fuel saving problem. The focus is on the reduction of harmful drag force, which will give better lift and will help get closer to an ideal solution.

Understanding Lift and Drag: Airfoil Components and Lift¹

An airfoil is the shape of a wing or blade (a propeller, rotor, turbine or sail) in the cross-section. Subsonic flight airfoils have a characteristic shape with a rounded leading edge, followed by a sharp trailing edge, often with an asymmetric camber, shown in Figure 2.

Figure 2: Air Foil Geometry (Side View)

Figure 3: Airflow Around the Air Foil

There is a flight theory called the Bernoulli Principle, which says the total pressure of an incompressible fluid is the sum of the static pressure and the dynamic pressure. If the fluid is air and the means for the fluid is accelerated as an airfoil, the side where the fluid travels the maximum distance will have the highest velocity and lowest static pressure. The difference in the velocity on each side of the airfoil determines the static pressure differential. That is what generates lift. The lift on an airfoil is primarily the result of its shape (in particular its camber line) and its angle of attack. When either or both are positive, the resulting flow field around the airfoil has a higher average velocity on the upper surface than on the lower surface. This velocity difference is accompanied by a pressure difference, which produces the lift force shown in Figure 3.

Designing a wing would have been simple if it were a two dimensional airfoil. But the wing has a finite length. The difference in air pressure between the lower and upper surfaces of a wing causes the air to escape around the wingtip, which reduces lift.

Drag²

Drag means the harmful forces acting on the wing that reduce available lift. There are two types of drag the first type is lift-induced drag. It accounts for 40 percent of the total drag and the other is parasitic drag.

Lift-induced Drag³

The lift-induced drag occurs as the result of the creation of lift on a three dimensional lifting body. Induced drag consists of primarily two components: the vortex drag and the viscous drag.

The motion of the air rushing around the wingtip coupled with the velocity of the airflow through the wing causes a vortex to form near the wingtip as shown in Figure 4. The vortex tip causes upwash and downwash air currents that alter the currents of the free stream flow around the wing, shown in Figure 5. The tip induces a decrease in the angle of attack from the average relative wind flowing around the wing. This results in two undesirable by-products. First, the wing generates lift perpendicular to the average relative wind. This diverts the lift vector away from the desired direction, which is perpendicular to the free steam. Diverting the lift vector causes a drag component to be generated that is parallel to the free stream airflow. The drag component varies as the cosine of the angle and the total lift vectors as shown in Figure 4.⁴

Figure 4: Three Dimensional Wing Flow and Drag Lift Vectors

The upwash / downwash effect (shown in Figure 5) of the tip vortices (shown in Figure 6) has its greatest influence on the wing section closest to the tip. The tip vortex has little effect on the average relative wind of the wing sections far from the wingtip.^4,6

Figure 5: Upwash / Downwash Effect

Figure 6: Vortex at the Wingtip

If the wingtips are pushed outboard, a smaller section of the wing will be affected by the tip vortex, which will reduce the upwash and downwash effect. In other words, if the span were infinite the induced drag would be zero because there would be no wingtip.

Parasitic Drag

Parasitic drag is caused by moving a solid object through fluid. This is around 60 percent of the drag. Parasitic drag is made up of multiple components including form drag, drag as a result of form from the object and skin drag (which occurs because of interaction with the object skins). A large, long wing with infinte span- to chord-ratio (shown in Figure 7) would have enormous parasitic drag. But by optimizing the wingspan, chord and airfoil from the drag can be controlled. The vortex drag remains and affects the wingtip by reducing the overall lift.

Figure 7: Wing Tip Geometry

Figure 8: Aspect Ratio and Lift Coefficient

No Further Optimization: The System Has Hit the Fundamental Limit

The vortex drag can be minimized by having an infinite span- to chord-ratio. If the designers optimize the aspect ratio for improvement in lift coefficient then the result shows that there is a marginal difference in the lift coefficient from a ratio of eight to infinity. For example, there is not a significant difference in the lift coefficient when the aspect ratio (wing length to width) is eight. The wing length is eight times the wing width or when it was increased to infinity where wing width is zero and wing length is infinite. This means the system has hit the limit and cannot be improved by further optimization, shown in Figure 8.⁴

When a System Hits its Fundamental Limit: A Contradiction Needs to be Solved

Plane wingtips create a drag by the vortices it generates. This drag causes more fuel burn increasing the operational cost of airline companies. Drag can be reduced by increasing the wingspan. Optimization tools can optimize the wingspan- to tip-ratio to reduce the drag, however, it needs a lot of experimentation. The wingspan cannot be increased as it cannot fit the airport gates. This causes a contradiction.

Formulating a Contradiction^6,7

A contradiction is recognized when two technical parameters are 180 degrees opposite. This means when an individual wants to improve one parameter the other side stops it from improving. In this case the parameter to improve is force (in order to reduce the drag, which is classified by TRIZ researchers under the parameter “force”) and the parameter that stops it from improving is the length of the wingspan.

There are two parameters that can worsen the wingspan (or length of the wing). The first one is the weight of the wing. If the wing is infinitely long then the structural weight would increase. This would increase the stress, which would lead to worsening the strength (as per the definition of contradiction parameters such as resistance to breaking or fatigue) as the wing structure will be subjected to cyclic stresses more than it is designed to accommodate. So the first sets of contradictions include the following:

Force (Improving Parameter), Strength (Worsening Parameter)

The inventive principles include:

Table 1: Force and Strength
Parameter being improved	Parameter that stops object from improving	Inventive principles used by other inventors to solve similar problems
Force (one of the equivalent meanings of force from several that are indicated in the Matrix 2003 is drag.) Parameter force is defined as: “Any interaction that is intended to change an object’s condition. Can be linear or rotational; the term applies equally well to torque. Applies to static and dynamic forces.” When talking about parameter force it means both increase or reduction in that parameter.	Strength (equivalent meaning: fatigue, creep, bond, join, muscle, droop, distortion, stiffness, rigidity, etc.) Parameter is defined as: “The extent to which an object is able to resist changing in response to force, resistance to breaking. Can mean elastic limit, plastic limit or ultimate strength, tensile or compressive; linear or rotational. Also includes toughness and hardness.	35 – Parameter changes 14 – Curvature 9 – Preliminary anti-action 3 – Local quality 17 – Another dimension 5 – Merging 27– Cheap, short-living objects 7 – Nested doll

Increasing the length of the wing will affect the weight of the wing, however, the plane cannot be accommodated at airport gates.

As per Matrix 2003, “length” is represented by two separate parameters. The first of those parameters is “length of a stationary object” and the second is “length of a moving object.” The task is to choose the right parameter for defining the contradiction.

For instance, consider the wingspan length under the parameter “length of the stationary object” as it seems that the length of the wingspan in the stationary condition (when the plane is grounded and about to stop in the parking lot) is the problem of its accommodation. What will be shown next is the effect of the cause that is making it longer.

The drag experienced by the wing, which affects the lift, is experienced in mid air because of the relative motion between the air and the wingspan; therefore, the parameter to select is “length of the moving object” and not the “length of the stationary object.”

• Contradiction is improving parameter = Force (reduction in drag)
  
• Worsening parameter = Length of the moving object (length of the wingspan)

The contradiction table and the corresponding inventive principles are summarized as follows:

Table 2: Contradiction Table and Inventive Principles
Parameter being improved	Parameter that stops object from improving	Inventive principles used by other inventors to solve similar problems
Force (one of the equivalent meanings of force from several others is drag). Parameter force is defined as: “Any interaction that is intended to change an object’s condition. Can be linear or rotational; the term applies equally well to torque. Applies to static and dynamic forces.” When talking about parameter force it means both increase or reduction in that parameter.	Length of the moving object. One of the equivalent meanings of length is span. Parameter “length of moving object” is defined as: “Any linear or angular dimension relating to a moving or mobile object.” Moving includes any situation where there is any degree of relative motion or mobility of two or more parts related to the problem. The relative motion may be a few microns or fractions of a degree – considerable amount.”	17 – Another dimension 35 – Parameter changes 9 – Preliminary anti-action 3 – Local quality 14 – Curvature 19 – Periodic action 28 – Mechanical substitution 36 – Phase transitions

Working of Winglets and the Effects^5,8

Before revealing how the inventive principles can be applied to the proposed solution, first an individual needs to see the developed solution.

By stretching wingspan or increasing aspect ratio it reduces induced drag. Designers, however, have to balance the benefits of less induced drag against the costs of structural weight increases, more parasitic drag or cost considerations. Winglets work because they efficiently produce aerodynamic side forces that divert the inflow of air from the tip vortex, therefore, the drag- to lift-ratio is not affected as it is with the normal wing and there is an improvement in lift-to drag-performance resulting in less fuel consumption.

Conventional and Blended Winglets

A blended winglet (as shown in Figure 9) is intended to reduce interference drag at the wing / winglet junction. A sharp interior angle in this region can interact with the boundary layer flow causing a drag inducing vortex, negating some of the benefits of the winglet. The blended winglet is joined to the wingtip in a constant radius curve, rather than a relatively sharp angle junction. According to Aviation Partner’s Inc. this smooth junction reduces shock interference between the winglet and the wing near the tip. This has achieved further improvement in the fuel consumption and has also moved the winglet forward eliminating problems with the roll up vortex. This reduces the drag. Figure 9 illustrates the design and the difference in the structure of conventional and blended winglets.

Figure 9: Conventional and Blended Winglets and the Aircraft with Winglets

Raked Wingtips

Raked wingtips (shown in Figure 10) are a feature on some Boeing airliners, where the tip of the wing has a higher degree of sweep than the rest of the wing. The stated purpose of this additional feature is to improve fuel efficiency, climb performance and to shorten takeoff field length. It has been found, however, that wingspan is generally more effective than a winglet of the same length, but may present difficulties in ground handling. For this reason, the short-range Boeing 787-3 design currently calls for winglets instead of the raked wingtips featured on all other 787 variants. Figure 10 uses principle 17, another dimension and principle 3, local quality.

Figure 10: Raked Wingtips

Figure 11 demonstrates the higher vortex intensity without a winglet (lefthand portion of the wing) and reduction of vortex intensity with a winglet (righthand portion of the wing).⁸

Figure 11: Reduction in Intensity of Tip Vortex

Principle 3: Local Quality

• Where an object or system is uniform or homogenous, make it non-uniform; blended winglet is a shorter extension of the wing, shown in Figure 9.
  
• Enable each part of the system or object to carry out different useful functions (possibly directly opposite); useful functions – wing is used to generate lift while the winglet reduces the vortex drag that adversely affects the lift, shown in Figure 9.

Principle 17: Another Dimension (Dimensionality Change; Move Into a New Dimension)

• If an object contains or moves in a straight line, consider the use of dimensions or movement outside the line; raked wingtip, shown in Figure 10.
  
• If an object contains or moves in a plane, consider the use of dimensions or movements outside the current plane; vertical portion of blended winglet, shown in Figure 9.

Principle 5: Merging (Combining, Consolidation, Integration)

• Physically join or merge identical or related objects; winglets on older planes are retrofitted while in the new aircrafts it is an integral part of the wing, shown in Figure 9.

Principle 14: Curvature (Spheroidality, Increase Curvature)

• Turn straight edges or flat surfaces into curves, the earlier winglet had a sharp angle at the junction of the wing and winglet, which created shock interference. The new winglets have a curve at the junction of the wing, which reduces shock interference, shown in Figure 9.

Benefits of the Improved Design⁹

1. Fuel consumption is reduced more than seven percent at speeds between 0.75 Mach to 0.80 Mach.
   
2. Typical 737 operators save 95,000 to 130,000 gallons per aircraft per year for the entire economic life of the aircraft.
   
3. It also has environmental benefits, which reduces carbon monoxide and nitrous oxide by four and five percent, respectively.⁹
   
4. An increase in the flight speed, improved stability and also has a faster climb to initial cruise altitude.
   
5. Reduction in the take off distance also benefits the airline operator to use airports with shorter runways.

Conclusion

The Theory of Inventive Problem Solving is a wonderful innovation science. Several of its problem formulations and solution generation tools have been validated through extensive research conducted over the past 50 years.

The contradiction of drag reduction versus length and weight is faced by several inventors in various fields and they have conquered it with a solution based on the inventive principles. If problem solving, strategy teams use TRIZ as their thinking methodology then the time to arrive at the best solution will be reduced. Interested readers can refer to reference seven to further augment any innovation efforts in a systematic manner.

One of the ways the author found to master its application is through reverse ideation (by working backwards to find out what the “general problem” is then applying the general solution to the specific problem). If a TRIZ facilitator is involved in system analysis, functional modeling, problem formulation or solution generation processes then it could help experts in the field to have access to knowledge of other fields for creation of new knowledge. In practice, after the design is frozen the next phase is to use optimization methods to arrive at the optimal design parameters.

“If the 20th century was of experts creating SILOS then the 21st century is of innovation generalist using systematic innovation to connect those experts and create a value which is truly ideal.”- Darrell Mann

References

1. Working of an Airfoil
   
2. Drag Physics
   
3. Understanding Lift Force
   
4. Understanding Winglet Technology
   
5. Mclean Doug; Wingtip Devices : What They Do and How They Do It, Boeing Aerodynamics, 2005.
   
6. Darrell Mann, Simon Dewulf, Boris Zlotin, Alla Zusman; Updating the TRIZ Contradiction Matrix, Creax Press, 2003.
   
7. Darrell Mann; Hands On Systematic Innovation, (Technical & Business Version) IFR Press, 2004.
   
8. Wingtip Devices
   
9. Flying Further For Less: Blended Winglets and Their Benefits; Airline Fleet and Network Management:March / April, 2006.