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AVEN 1920: INTRODUCTION TO

ENGINEERING

TITLE: AERODYNAMICS COMPARISON REPORT: B-52/F-111/C-130SUBMITTED TO: PROFESSOR N.A. AHMEDDATE: 2ND JUNE 2009AUTHOR: ALEX SCHRODER 3285832

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Contents

1. Introduction..................................................................................................................................3

2. B-52...............................................................................................................................................3

3. F-111.............................................................................................................................................5

4. C-130.............................................................................................................................................7

5. Conclusion ....................................................................................................................................8

6. Appendix.......................................................................................................................................9

6.1 Appendix Item A .....................................................................................................................9

6.2 Appendix Item B ...................................................................................................................12

6.3 Appendix Item C ...................................................................................................................15

7. Bibliography................................................................................................................................16

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1. Introduction

This report intends to examine the various designs of aircraft, with the B-52, F-111 and C-130 to be researched. Not only will the features of each wing be discussed, but also the reasons that the aircraft was designed in such a way. Design features that will be examined include wing length, aspect ratio, airfoil, aspect ratio and chord.

2. B-52

The B-52 bomber emerged following the end of World War II with the purpose of having

optimized aerodynamics in order to fly long distances and carry out bombing raids (Unknown

Author, 2004). The B-52B, the model with the most aircraft produced, had the following

wing specifications (Goebel G., 2009)

High mounted wings swept back 35°

15% (10.5m) chord at root, tapering to 8% at outer wing

Flex from 3m down to 6.7m up

Two “Fowler” type single slotted flaps that extended well beyond the trailing edge of

the wing, with an aileron between flaps

Row of 6 spoilers on top of each wing

Wingspan: 56.39m

Wing area: 371.

Airfoil: NACA 63A219.3 mod root, NACA 65A209.5 tip

Aspect ratio: 8.56

Root chord: 10.5m, mean chord 6.6m

Taper ration 0.37

Anhedral wing

Wonwinglo (2004) wrote that the most obvious reason for the B-52 having anhedral was

because it needed to have a castor on the end of the wing to support the aircraft’s weight and

provide stability. Wonwinglo also identifies the role of the B-52’s ailerons. When the aircraft

is banked, the low wing has far less lift than the higher wing. In order to reduce the bank, the

ailerons are used to increase the lift on the low wing and reduce the lift on the high wing.

This will stabilise the aircraft, and explains the purpose of the ailerons on the B-52.

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The 6 spoilers work in conjunction with the ailerons to provide lateral control (6) as well

as maintaining flight path control during landing. The purpose of the two fowler flaps,

positioned on the trailing edge of each wing is to control the increases in lift (6).

One of the B-52’s most distinctive features is its swept wings. In 1935 Buchmann

identified that a swept wing would delay the formation of shock waves encountered in a

transonic flow. Shock waves form when airflow reaches supersonic speeds, creating

acceleration in the airflow around curved surfaces such as the nose cone and wing, leading to

excess drag and reducing aerodynamic efficiency. The B-52 uses straight wings to avoid the

acceleration in airflow and subsequent increase in drag caused by curved wings. In

accordance with Buchmann’s theory, the B-52 has wings swept at 35° to delay the formation

of shock waves, as shown in Figure 1. Figure 2 demonstrates how increasingly swept wings

decrease drag.

Transonic drag is the name given to the drag that forms as a result of the shock waves.

One way to delay the onset of this drag, as identified by the US Centennial of Flight (USCF),

is to use long, thin airfoils. The USCF wrote that increases in transonic drag is roughly

proportional to the square of the thickness-chord ratio, so by reducing airfoil thickness and

increases the chord length, the transonic drag is reduced. The B-52 adapts this theory in its

airfoil, with a particularly long wing at 56.39m, whilst the thickness tapers from 15% chord at

root to 8% at the tip. This gives the airfoil a taper ratio of 0.37. Using the SNACK program, I

generated the airfoil of the B-52, shown in Figure 3

Fig. 1 (Wikipedia, 2009) Fig. 3

Fig. 2 (USCF, 2009)

35°

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The USCF also identified vortex generators as another strategy to reduce transonic drag.

This involves mounting small plates perpendicular to the wing surface, creating a strong tip

vortex. High energy is fed from the outside boundary layer into the slow moving air inside

the boundary layer, preventing the boundary layer from stalling and thus giving a small

increase in drag delay. Vortex generators are not used on the B-52.

The USCF also suggests the use of a supercritical wing to reduce transonic drag. A

supercritical wing is one that is flatter on top and rounder n the bottom, and was first put

forward by Whitcomb in the 1960s. Due to the flattened top lift is reduced, and therefore the

formation and strength of the shock waves are delayed at a point closer to the trailing edge.

The supercritical wing is not used by the B-52, however the USCF expects the concept to

grow in popularity.

3. F-111

The F-111 Aardvark began operation in 1967 as a low altitude strike fighter. In

accordance with this purpose, the aircraft must be able to function efficiently at low altitudes

and high speeds. As a result it has the following specifications:

Variable sweep wings ranging from 16° fully forward to 72.5° fully aft

Wingspan: 19m fully forward, 11.9m fully aft

Wing area: 61.07m2 fully forward, 48.77m2 fully aft

Aspect ratio: 7.56 fully forward, 1.95 fully aft

Full span flaps

Leading edge double slotted slats

Two sets of spoilers

Whilst the B-52 is distinguished by its long, swept wings, the F-111 can be identified by

its variable sweep wings, shown in Figure 4. The range is from 16° to 72.5°, which gives the

pilot capability to fly from slow approach speeds to the speed of sound, as well as flying at

over two times the speed of sound at high altitudes (Global Security, 2008). As the aircraft is

a strike fighter, during design it was foreseen that it may need to make emergency landings at

runways that weren’t of ideal length. The variable sweep accommodates for this, as when the

wings are fully swept the F-111 is able to take off and land within 2000ft (Global Security,

2008). This is possible as when the wings are fully forward they have more surface area,

giving maximum lift for short take off and landing. Furthermore, as a fighter airplane, the F-

111 was required to travel at extremely high speeds, which the variable sweep wings again

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cater for. When wings are fully swept back the F-11 can reach supersonic speeds at high and

low altitudes (Global Security, 2008).

Fig. 4 (Global Security, 2008)

Unlike the B-52, the F-111 does not have ailerons (Prahl V, 2000). The spoilers are used

for roll control, with the inboard pair locked down when wings are swept past 45°, and the

outboard pair locked when the wings are swept to 47°(Rotramel J, 2007). Buchmann’s theory

can be applied to the F-111 in the same way as it is to the B-52: by using swept wings, the

onset of shock waves is delayed and increases in drag are therefore reduced.

The spoilers also act to increase landing performance in a similar way to the B-52. The flaps

and slats on the aircraft, shown in Figure 5, are limited to wing sweep forward of 26°. They

also work in a similar way to that of the B-52: to control the lift. One property that the F-111

possesses that the B-52 doesn’t is “over-wing fairings”. These are large panels that cover the

top of the fuselage and are hinged to lift up during supersonic flight (Rotramel J., ). As a

result, air pressure between the fuselage and wing cavity is equalised to maintain stability.

Stability of the F-111 is further controlled when wings are spread as a result of a high aspect

ratio at 7.56 (Rotramel J, 2007).

Fig. 5 (Rotramel J, 2007)

The airfoil of the F-111 is NACA 64A210.86 at the root and NACA 64A209.80 at tip.

Using the SNACK program, I was able to generate Figure 6, the airfoil image.

From the airfoil digits I was able to interpret the following features of the F-111 airfoil:

At maximum thickness 40% back from the leading edge

Maximum efficiency and minimum drag is when coefficient of lift = 0.2

Thickness to length ratio of 10.68% at the maximum thickness

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“A” indicated that the curved shape has been replaced by a flat surface from about

80% up to the trailing edge

Fig. 6

The airfoil is of this shape in order to give a favourable coefficient lift that would allow

the F-111 to take off and land within restricted distances.

4. C-130

The Lockheed C-130 is the third aircraft to be analysed. This aircraft was created for a

role as a military transport vehicle, with its first flight in 1954 (Vogelaar, 2008). It also had a

purpose as a low level assault aircraft. The C-130 has the following specifications (Vogelaar,

2008)

Wingspan: 40.41m

Wing area: 161.m2

Aspect ratio: 10.09

Airfoil: NACA 64A318, 1.5% camber

Lockheed-Fowler flaps

The wings on the C-130 are high level full cantilever wings (Vogelaar, 2008; , Unknown

Author, 2007). From the airfoil digits, it can be determined that the airfoil is at maximum

thickness 40% of chord length from the leading edge, and is designed for a lift coefficient of

0.3. Furthermore, the airfoil has a thickness to length ratio of 18% at its maximum thickness.

These specifications are related to the aircraft’s purpose, in that the designers wanted to

achieve aerodynamic efficiency, similar to the aim when designing the F-111, with the result

being a lift coefficient of 0.3. The aspect ratio of the aircraft is very high (Vogelaar, 2008),

which provided the aircraft with additional roll stability. The purpose of such a high aspect

ratio was to give the aircraft extra maneuverability, a necessity for performing its duties in

transporting supplies and troops. The 1.5% camber assisted the aircraft in producing lift,

reducing the need for the C-130 to produce extra thrust and therefore making the aircraft

more aerodynamically and economically efficient.

The Lockheed-Fowler flaps on the aircraft wings work to provide the aircraft with

stability when rolling, which again increases its maneuverability and overall stability. Using

the airfoil value I was able to generate the following airfoil image, Figure 7. As Figure 8

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shows, the wings are not swept, and therefore do not benefit from Buchmann’s theory

outlined earlier. This leaves the aircraft susceptible to increases in shock waves forming, and

therefore contributes to the drag on the C-130 and reducing aerodynamic efficiency.

Fig. 7 Fig. 8

(Unknown author, 2007)

5. Conclusion

The main features of the wings of the B-52, F-111 and C-130 have now been identified.

The various sweep of wings is to be noted: the B-52 with its 35° sweep, the F-111 with a

sweep ranging from 16° to 72.5°, and the C-130 with no sweep. It is no coincidence that the

C-130 has a higher lift coefficient (0.3) than the B-52 and F-111 (0.2). The sweepback of the

latter wings contributes to the decrease in lift required as there is less drag on the aircraft

compared to the C-130.

Each of the aircraft employs different lift devices. The B-52 combines the use of ailerons,

flaps and spoilers, whilst the C-130 uses flaps. In contrast to the B-52, the F-111 uses flaps

and spoilers. These devices also assist in roll control.

The B-52, F-111 and C-130 together serve to demonstrate the various ways aircraft can

be designed to achieve optimum aerodynamic performance. They illustrate how devices can

be used in conjunction to ensure the aircraft is able to operate efficiently.

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6. Appendix

6.1 Appendix Item AUSCF, 2009http://www.centennialofflight.gov/essay/Theories_of_Flight/Transonic_Wings/TH20.htm

There are a number of ways of delaying the increase in drag encountered when an aircraft travels at high speeds, i.e., the transonic wave drag rise, or of increasing the drag-divergence Mach number (the free-stream Mach number at which drag rises precipitously) so that it is closer to 1. One way is by the use of thin airfoils: increase in drag associated with transonic flow is roughly proportional to the square of the thickness-chord ratio (t/c). If a thinner airfoil section is used, the airflow speeds around the airfoil will be less than those for the thicker airfoil. Thus, one may fly at a higher free-stream Mach number before a sonic point appears and before one reaches the drag-divergence Mach number. The disadvantages of using thin wings are that they are less effective (in terms of lift produced) in the subsonic speed range and they can accommodate less structure (wing fuel tanks, structural support members, armament stations, etc.) than a thicker wing.

In 1935, the German aerodynamicist Adolf Busemann proposed that a swept wing might delay and reduce the effects of compressibility. A swept wing would delay the formation of the shock waves encountered in transonic flow to a higher Mach number. Additionally, it would reduce the wave drag over all Mach numbers.

A swept wing would have virtually the same effect as a thinner airfoil section (the thickness-cord ratio (t/c) is reduced). The maximum ratio of thickness to chord for a swept wing is less than for a straight wing with the same airflow. One is effectively using a thinner airfoil section as the flow has more time in which to adjust to the high-speed situation. The critical Mach number (at which a sonic point appears) and the drag-divergence Mach number are delayed to higher values; Sweep forward or sweepback will accomplish these desired results. Forward sweep has disadvantages, however, in the stability and handling characteristics at low speeds.

A major disadvantage of swept wings is that there is a spanwise flow along the wing, and the boundary layer will thicken toward the wingtips for sweepback and toward the roots (the part of the wing closest to the fuselage) for sweep-forward. In the case of sweepback, there is an early separation and stall of the wingtip sections and the ailerons lose their roll control effectiveness. The spanwise flow may be reduced by the use of stall fences, which are thin plates parallel to the axis of symmetry of the airplane. In this manner a strong boundary layer buildup over the ailerons is prevented. Wing twist is another possible solution to this spanwise flow condition.

The wing's aspect ratio is another parameter that influences the critical Mach number and the transonic drag rise. Substantial increases in the critical Mach number (the subsonic Mach number at which sonic flow occurs at some point on the wing for the first time) occur when using an aspect ratio less than about four. However, low-aspect-ratio wings are at a disadvantage at subsonic speeds because of the higher induced drag.

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By bleeding off some of the boundary layer along an airfoil's surface, the drag-divergence Mach number can be increased. This increase results from the reduction or elimination of shock interactions between the subsonic boundary layer and the supersonic flow outside of it.

Vortex generators are small plates, mounted along the surface of a wing and protruding perpendicularly to the surface. They are basically small wings, and by creating a strong tip vortex, the vortex generators feed high-energy air from outside the boundary layer into the slow moving air inside the boundary layer. This condition reduces the adverse pressure gradients and prevents the boundary layer from stalling. A small increase in the drag-divergence Mach number can be achieved. This method is economically beneficial to airplanes designed for cruise at the highest possible drag-divergence Mach number.

A more recent development in transonic technology, and destined to be an important influence on future wing design, is the supercritical wing developed by Dr. Richard T. Whitcomb of NASA's Langley Research Center. With the supercritical wing, a substantial rise in the drag-divergence Mach number is realized and the critical Mach number is delayed even up to 0.99. This delay represents a major increase in commercial airplane performance.

The curvature of a wing gives the wing its lift. Because of the flattened upper surface of the supercritical airfoil, lift is reduced. However, to counteract this, the new supercritical wing has increased camber at the trailing edge.

There are two main advantages of the supercritical airfoil. First, by using the same thickness-chord ratio, the supercritical airfoil permits high subsonic cruise near Mach 1 before the transonic drag rise. Alternatively, at lower drag divergence Mach numbers, the supercritical airfoil permits a thicker wing section to be used without a drag penalty. This airfoil reduces structural weight and permits higher lift at lower speeds.

Coupled to supercritical technology is the "area-rule" concept also developed by Dr. Richard T. Whitcomb in the early 1950s for transonic airplanes and later applied to supersonic flight in general.

Basically, the area rule states that minimum transonic and supersonic drag is obtained when the cross-sectional area distribution of the airplane along the longitudinal axis can be projected into a body of revolution that is smooth and shows no abrupt changes in cross section along its length. Or, if a graph is made of the cross-sectional area against body position, the resulting curve is smooth. If it is not a smooth curve, then the cross section is changed accordingly.

The original Convair F-102A was simply a scaled-up version of the XF-92A with a pure delta wing. But early tests indicated that supersonic flight was beyond its capability because of excessive transonic drag and the project was about to be canceled. Area ruling, however, saved the airplane from this fate. In the original YF-102A, the curve of the cross-sectional area plotted against body station was not very smooth as there was a large increase in cross-sectional area when the wings were attached. The redesigned F-102A had a “coke-bottle”-waist-shaped fuselage and bulges added aft of the wing on each side of the tail to give a better area-rule distribution. The F-102A could then reach supersonic speeds because of the greatly reduced drag and entered military service in great numbers.

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Later, the area-rule concept was applied to design of a near-sonic transport capable of cruising at Mach numbers around 0.99. In addition to area ruling, a supercritical wing was used.

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6.2 Appendix Item B

Unknown Author, 2008http://www.aerospaceweb.org/question/airfoils/q0066.shtml

To get a general overview of the various NACA airfoil series, and the 6-Series in particular, check out a previous question on that subject. While earlier NACA series are relatively easy to generate based on geometric relationships and algebraic equations, the 6-Series uses complex conformal mapping techniques to produce the airfoil shape. This is not very easy for the novice to accomplish, but luckily there are a few computer programs out there that incorporate these advanced airfoil generation tools to automate the process. Probably the easiest to use of these programs is called SNACK, which can now be registered for free. We will discuss how this program can be used to accomplish your needs shortly.

First, a quick overview of the naming convention for the 6-Series airfoils. For this example, we will consider the 64-215, similar to one of the shapes mentioned in your question. The first digit simply represents the series name. The second indicates the location of the airfoil's maximum thickness (or minimum pressure) in tenths of chord (or length). In this case, the value 4 tells us that the airfoil is at its maximum thickness 40% back (or 0.4 chord) from the leading edge. The first digit after the dash is called the design lift coefficient, which is provided in tenths. What this means is that the airfoil was designed for maximum efficiency at a lift coefficient of approximately 0.2. At this operating condition, drag is minimized. The final two digits are the maximum airfoil thickness in percentage. Thus, this airfoil has a thickness-to-length ratio of 15% at the maximum point, which we already know is 40% back from the leading edge.

Now there are some slight differences between the class of airfoil we just discussed and and those you list in your question. First, you'll notice the capital A that appears in place of the dash (-). This indicates a modification to the basic geometry that eliminates much of the "cusped" shape on the lower surface towards the trailing edge of the airfoil. The purpose of this was entirely practical. Although the highly curved shapes were the result of the conformal mapping process, such shapes were impractical to build from an aircraft manufacturer's viewpoint. Therefore, the letter A simply indicates that the curved shape has been replaced by a flat surface from about 80% chord to the trailing edge. The other difference in the airfoil names is the decimal followed by two digits. All this indicates is a slight adjstment to the maximum thickness of the basic shape. While the 64A210 is 10% thick, the 64A210.68 is 10.68% thick and the entire thickness distribution along the airfoil length is scaled up to reflect this.

As for using SNACK to create these coordinates, download the software using the link above, install, and start the program. Airfoil coordinates are generated using the following method:

1. Select 'Airfoil' from the menu bar, then 'Creation,' and 'NACA 6 Series.' A screen will appear similar to that shown below.

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SNACK NACA 6 Series airoil generation window

2. Using the "clickable" geometery commands, change the geometry options for the airfoil you desire, the NACA 64A210 in this example:%Min Pressure Location = 40%Design Lift Coefficient = 0.2Eliminate Lower Cove = checked%Max Thickness = 10%While the Meanline Parameter (a) is an important value in defining the geometry, it is not specified in this case, so we will assume that it is equal to 1

3. Note that the airfoil number should now read 64A210 and the plot adjusts to the proper coordinates. If you like, you can also use the Number of Points and the Point Distribution to obtain more accurate coordinates for your application.

4. To actually see the coordinates, we need to export them in some format that can be read by another program. To do so, select 'File' from the menu bar and 'Save As...' and the following window will appear.

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Saving airfoil coordinates from SNACK

5. These file formats correspond to several airfoil aerodynamic analysis codes or CAD programs. If you wish to utilize your coordinates in one of these applications, select the appropriate bullet. If you simply want the coordinates, it makes little difference what format you choose, but I recommend RcCad (*.xy). You can then open this file with a text editor or a spreadheet program for further use. This format saves two columns of data corresponding to values of x (length) that start at the trailing edge (x=1) and go to the leading edge (x=0) along the upper surface (y greather than 0) and then repeats the process going back from the nose to the tail along the lower surface (y less than 0), y being the airfoil thickness above and below the x-axis.

6. The Save As... window also gives us the option of specifying an airfoil chord length. What this will do is scale the airfoil coordinates up (if entering a number greater than 1) or down (if entering a number less than 1) to match a desired case. For example, if we were generating the root airfoil section for an aircraft with a root chord length of 10 feet, we would enter 10. Nevertheless, I recommend leaving the chord at 1 to produce a generic set of coordinates. You can always scale the values yourself later on using a program like Microsoft Excel.

7. One limitation of SNACK is that it does not allow us to add the small thickness modifications called for in the F-111 airfoils (i.e. 10.68% and 9.80%). As with adjusting the chord length, you can add this small additional amount of thickness yourself in a spreadsheet program by simply scaling the y-coordinates up or down.

If you'd like to learn more about the mathematics of computing NACA airfoil coordinates, check out a NASA report, TM-4741, that covers each series. The report was written to

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6.3 Appendix Item C

Global Security, 2008http://www.globalsecurity.org/military/systems/aircraft/f-111.htm

F-111 Aardvark

Nicknamed 'Aardvark' because of its long, slightly upturned nose, the F-111 evolved in response to a joint services requirement in the 1960s for a long range interceptor (US Navy) and deep-strike interdictor (USAF). The F-111 was a multipurpose tactical fighter bomber capable of supersonic speeds. The aircraft was one of the more controversial aircraft ever to fly, yet it achieved one of the safest operational records of any aircraft in USAF history and became a highly effective all-weather interdiction aircraft. The F-111 provided many firsts among weapons systems. It was the first production aircraft with variable swing wings that could be swept back or brought forward to increase efficiency. It also had the first terrain-following radar, allowing it to fly at night at high speeds and low altitudes, as well as the first crew escape module. The aircraft was produced in seven different variants with the first production aircraft delivery in October 1967 and the last delivery in September 1976. F-111's are no longer in the Air Force inventory but were a major part of the fighter force for many years.

The Tactical Fighter Experimental (TFX) Program called for developing a single aircraft to fulfill a Navy fleet defense interceptor requirement and an Air Force supersonic strike aircraft requirement. The mission requirements were impossible to achieve, especially since planners placed priority upon the Air Force requirement, and then tried to tailor a heavy land-based aircraft to the demands of carrier-based naval aircraft. The naval version, the F-111B, was never placed into production. The Air Force aircraft was produced in a variety of models, including the F-111A, F-111D, F-111E, and F-111F fighter-bombers; the FB-111A strategic bomber; the F-111C for the Australian Air Force; and an EF-111 electronic warfare version. The US Air Force versions were retired in 1996, but the Australians plan to operate their fleet until well into the twenty-first century.

This aircraft was one of the more controversial aircraft ever to fly, yet it achieved one of the safest operational records of any aircraft in USAF history and became a highly effective all-weather interdiction aircraft. The last four F-111Fs in the United States Air Force returned to their birth-place for the F-111's retirement and naming ceremony 27 July 1996 at Lockheed Martin Tactical Aircraft Systems in Ft Worth, Texas, where the first F-111 rolled out of the (then) General Dynamic's mile-long plant Long known unofficially as the "Aardvark," the name became official at the ceremony.

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111.net/downloads/report/1_test_report.html>, viewed 27th May 2009

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