Friday, April 16, 2010

mechanical seminar hydrofoil ship design

1.Introduction

A Hydrofoil is a specially designed hydrodynamic surface that creates lift significantly exceeding drag. The main function of the hydrofoil is to lift the ships hull out side the water. At low speeds the ships hull sits on the water and the hydrofoils are totally submerged in water, but as the speed increases the hydrofoils create lift, bringing the hull outside the water surface.

The basic principle of the hydrofoil concept is simply to lift a ship's hull out of the water and support it dynamically on wing-like lifting surfaces, i.e. hydrofoils, to reduce the effect of waves on the ship and to reduce the power required to attain modestly high speeds. Engineers and naval architects have been intrigued with the possibilities of this concept for many years. A United States patent for a hydrofoil was defined in the late 1880s, about the same time as the early airplane and airfoil patents. The earliest record of a successful hydrofoil flight is 1894 when the Meacham brothers demonstrated their 14 foot test craft at Chicago, Illinois. This compares with the Wright brothers' first airplane flight in 1903. The early attempts to exploit the hydrofoil concept were frustrated by lack of suitable structural materials and power plants. However, advancement in these areas, much of it stemming from aircraft developments, has permitted development over the past 30 to 40 years of the technology necessary to achieve and demonstrate reliable and effective hydrofoil ships for both military and commercial below.

2.Hydrofoil Basics

Many people are familiar with airfoils. Foil is simply another word for the wing (such as the wing on an airplane). A hydrofoil is a wing that 'flies' in water. Hydrofoil is also used to refer to the boat to which the water wings are attached. A hydrofoil boat has two modes of operation:

(1) as a normal boat with a hull that displaces water and

(2) with the hull completely out of the water and only the foils submerged.

Hydrofoils let a boat go faster by getting the hull out of the water. When a normal boat moves forward, most of the energy expended goes into moving the water in front of the boat out of the way (by pushing the hull through it). Hydrofoils lift the hull out of the water so that you only have to overcome the drag on the foils instead of all of the drag on the hull.

The foils on a hydrofoil boat are much smaller than the wings (foils) on an airplane. This is because water is about 1000 times as dense as air. The higher density also means that the foils do not have to move anywhere near as fast as a plane before they generate enough lift to push the boat out of the water.

The hydrofoils generate lift only when they are in the water; if they leave the water, the boat will crash down onto the surface of the water (and thus submerge the foils) until the foils generate enough lift to lift it back out. Like an airplane, a hydrofoil must be controllable in terms of pitch, roll, and yaw. Unlike an airplane, a hydrofoil must also maintain a consistent depth. Whereas an airplane has a range of about 40,000 feet in which to maintain its altitude, a hydrofoil is limited to the length of the struts, which support the boat above the foils.

3.working

HOW DOES A HYDROFOIL(AEROFOIL, WING) WORK ?

MAIN FUNCTIONAL REQUIREMENT: Lift the boat’s hull outside the water.

DESIGN PARAMETER: Hydrofoil (It is a foil or wing under water used to lift the boat’s hull until it is totally outside the water.)

GEOMETRY/STRUCTURE:

hydrofoil-3.gif (4368 bytes)

Detail of Hydrofoil Geometry

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EXPLANATION OF HOW IT WORKS/ IS USED:

1. At low speeds the hull (body of ship) sits in the water and the hydrofoils are totally submerged in the water.

2. As the boat’s speed increases, the hydrofoils create lift.

3. At a certain speed, the lift produced by the hydrofoils equals the sum of of the boat and cargo weights. Therefore the hull comes out of the water.

4. Instead of having an increase in drag with increasing speed because the hull is lifted out of the water (contrary to what happens in traditional boats due to pressure drag), the hydrofoils provide a more efficient way of cruising. Decreasing the drag contributes to the better use of the power needed for the movement of the boat.

4.DOMINANT PHYSICS:

How is the lift produced - Fluid Dynamics.

Bernoulli’s Equation: Po = P1 + ½rv1² + rgy1 = P2 + ½rv2² + rgy2

Variables

Units

Po Stagnation Pressure

[Pa] or [lbf/ft2]

P Pressure

[Pa] or [lbf/ft2]

r Density

[kg/m3] or [lbf/ft3]

V Velocity

[m/s] or [ft/s]

g Gravitational-constant

[m/s2] or [ft/s2]

5.PRINCIPLE

This equation applies to flows along a streamline which can be modeled as: inviscid, incompressible, steady, irrotational and for which the body forces are conservative. Also the difference on the height of the foil (the distance from the bottom section to the upper one) is small enough so that the difference pgy2 - pgy1 is negligible compared to the difference of the rest of the terms. What is left is that the pressure plus one half the density times the velocity squared equals a constant (the stagnation pressure).

As the speed along these streamlines increases, the pressure drops (this will become important shortly). The fluid that moves over the upper surface of the foil moves faster than the fluid on the bottom. This is due in part to viscous effects, which lead to formation of vertices at the end of the foil. In order to conserve angular momentum caused by the counter-clockwise rotation of the vortices, there has to be an equal but opposite momentum exchange to the vortex at the trailing edge of the foil. This leads to circulation of the fluid around the foil. The vector summation of the velocities results on a higher speed on the top surface and a lower speed on the bottom surface. Applying this to Bernoulli’s it is observed that, as the foil cuts through fluid, the change in velocity produces the pressure drop needed for the lift. As it is presented in the diagram, the resulting or net force (force= (pressure)(area)) is upward.

This explanation can be enriched with the Principle of Conservation of Momentum. (Momentum = (mass)(velocity)) If the velocity of a particle with an initial momentum is increased, then there is a reactant momentum equal in magnitude and opposite in direction to the difference of the momentums. (See diagram).(Mi = Mf + M)

hydrofoil-1.gif (19235 bytes)

Detail of Hydrofoil:

a) Pressure Profile

b) Momentum Transfer

c) Circulation

d) Streamlines

6.FOIL LIFT AND DRAG

FOIL LIFT IS CALCULATED USING THE EQN:

Z=(1/2) p*V 2*Cl*S

FOIL DRAG IS CALCULATED USING THE EQN:

Z=(1/2) p*V 2*Cd*S

WHERE p=DENSITY, V=VELOCIYY, C=DRAG OR LIFT COEFF, S=PROFILE C.S.AREA


7.ANGLE OF ATTACK

As it has been presented, lift comes from the dynamics of the fluid in the area surrounding the foil. But the lift can be optimized by positioning the hydrofoil at an angle (relative to the incoming fluid flow) called the angle of attack (See diagram). The goal is to optimize the lift to drag ratio. This ratio depends on the shape of the foil, which in this case is considered to be a thin foil. With a small angle of attack, the lift increases rapidly while the drag increases at a small rate. After an angle of ~10° the lift increases slowly until ~15° where it reaches a maximum. After ~15° stall can set in. When the angle of attack is 3° to 4° the ratio of lift: drag is at it’s maximum. So the foil is more efficient at those angles (3°and 4°) with lift to drag ratios of ~ 20 to 25:1

8.LIMITING PHYSICS:

hydrofoil-5.gif (4136 bytes)

Detail of Hydrofoil Geometry

At first, people can think that stalling is likely to be a problem in hydrofoils as it is in airfoils, but surprisingly it is not. A steep angle of attack is not needed in the design of the hydrofoil. On the contrary, small angles of attack are used on hydrofoils to optimize the lift to drag ratio as explained before.

What is a primary concern is the design of the foil, the struts/supports, and their positioning. All these features have to be taken in consideration. So the features are designed to

produce a minimum speed that will lift the boat of certain weight and keep it foil borne.

One problem that a hydrofoil craft can experience is the height of the waves being greater than the struts. Also, if the craft is traveling faster than the waves, the foils could break to the surface and outside of the water, resulting in a loss of lift and a negative angle of attack when the foil dives into the next wave, making the craft crash into the sea. Engineers have designed hydrofoils to minimize these limitations and better the ship’s performance

There are two particularly persistent problems faced by designers of hydrofoils:

Cavitation and ventilation.

Ventilation occurs when part of a hydrofoil pierces the surface of the water and air gets sucked down the lifting surface of the foil. Since air is much less dense than water, the foil generates much less lift and the boat crashes down. Ventilation can occur at any air-water interface.

Ventilation occurs when air gets sucked down to the lifting surfaces. Although ventilation can occur on vertical struts, 'V' foils are particularly prone to this problem because of the shallow angle the foil makes with the water surface.

Cavitation occurs when the water pressure is lowered to the point where the water starts to boil. This frequently happens with propellers. When a propeller is turned fast enough, the blades generate so much lift (i.e. the pressure on the lifting surface of the blades goes down) that the water flowing over the propeller blades begins to boil. When cavitation occurs, the foil no longer generates enough lift and the boat crashed down onto the water.

Note that a hydrofoil is not a hovercraft. Hydrofoils fly on wings in the water that generate lift whereas hovercraft floats above the water on a layer of air. In both cases the boat's hull leaves the water, but the mechanisms by which this is achieved are completely different

9.configurations

Hydrofoil configurations can be divided into two general classifications, surface piercing and fully submerged which describe how the lifting surfaces are arranged and operate (see Figure 1). In the surface piercing concept, portions of the foils are designed to extend through the air/sea interface when foil borne. Struts connect the foils to the hull of the ship with sufficient length to support the hull free of the water surface when operating at design speeds. As speed is increased, the lifting force generated by the water flow over the submerged portion of the foils increases causing the ship to rise and the submerged area of the foils to decrease. For a given speed the ship will rise until the lifting force equals the weight carried by the foils. As indicated by the terminology, the foils of the fully submerged concept are designed...

Figure 1-- Surface-Piercing (Left) & Fully Submerged (Right) Foil Configurations

to operate at all times under the water surface. The struts which connect the foils to hull and support it when the ship is foilborne generally do not contribute to the total hydrofoil system lifting force. In this configuration, the hydrofoil system is not self-stabilizing. Means must be provided to vary the effective angle of attack of the foils to change the lifting force in response to changing conditions of ship speed, weight and sea conditions. The principal and unique operational capability of hydrofoils with fully-submerged foils is the ability to uncouple the ship to a substantial degree from the

effect of waves. This permits a relatively small hydrofoil ship to operate foilborne at high speed in sea conditions normally encountered while maintaining a comfortable motion environment for the crew and passengers and permitting effective employment of military equipment. It is this desirable characteristic which has caused the hydrofoil ship development in the United States to concentrate on the fully-submerged foil concept.

The basic choices in foil and strut arrangement are canard, conventional or tandem as shown in Figure 2. Generally ships are considered conventional or canard if 65% or more of the weight is supported on the front or the aft foil respectively. If the weight were distributed relatively evenly on the fore and aft foils, the configuration would be described as tandem.

SPLIT

NON-SPLIT

ARRANGEMENT

CONVENTIONAL

0.00 <>

CANARD

0.65 <>

TANDEM

0.35 <>

Figure 2 - Foil/Strut Arrangements

10.Features

10.1)Weight Limitations

Like the airplane designer, the hydrofoil designer must, at all times, be extremely conscious of weight. The hydrofoil type of craft is weight critical, and every pound of weight saved in structure, outfit, or machinery means weight available for payload and fuel.

The structural engineer, in designing hydrofoils to conserve weight, uses aircraft techniques. Relative to conventional ships, hydrofoil craft are subject to very high loadings, as caused by high operating speeds. Likewise, lightweight, high strength materials are used. He also must contend with fatigue and problems of hydroelasiticity, including both divergence and flutter.

10.2)Hull Considerations

The development of a satisfactory hull form for hydrofoil application represents a significant challenge to the designer. The hull should perform well in the hullborne mode but also during takeoff and during foilborne operation where impacts with waves are involved. In addition, the hull configuration of a hydrofoil ship must satisfy all of the requirements for strength, freeboard, and intact and damaged stability for any other ship.

Relatively high power requirements for high-speed operation, in common with other high performance systems, pay a high performance dividend for achieving a minimum weight structure. Therefore, hydrofoil ship hulls are generally constructed using high-grade aluminum alloys, 5000 series weldable alloy being typical. Structurally, the hull must have the strength to resist wave impact at high speed as well as distribute the concentrated load at the strut attachment points. Although hydrofoil hulls may appear quite conventional, the required compromises are more complex than for a monohull because of the many operating modes of the ship. An efficient hull form for a lower speed operation requires a narrow beam. However, a righting moment large enough to satisfy the stability criteria of reference [6] with the foils retracted generally dictates a wide beam. Cresting the tops of waves while foilborne points toward the use of a deep vee forward and high deadrise.

Another major consideration in hydrofoil hull design is the requirement for good seakeeping characteristics in a heavy sea. If hydrofoil craft are to operate unrestricted in open ocean, they must be capable of surviving storm seas in the hullborne condition. Furthermore, in certain missions, it may be expected that the hydrofoil ship will spend the greater portion of its operating lifetime in the hullborne mode. Thus, it is essential that close attention be given to the hull seakeeping characteristics. With the foils extended during hullborne operation, which is normal operation at sea, there is a significant reduction of craft motion in both the roll and pitch modes which is normally not heavily damped. Thus the strut/foil system gives hydrofoil craft hullborne motion characteristics of ships having much larger displacement.

10.3)Foil Systems

Foil variable lift is obtained by either trailing edge flaps or variable incidence of the entire foil as illustrated in Figure 5.

Figure 5 - Hydrodynamic Force Control

10.4)Weight Trend

A fundamental limitation is imposed by the so-called "square-cube" law, which impacts the growth potential of hydrofoil ships. The lift developed by the foils is proportional to their planform area (the square of a linear dimension), whereas the weight to be supported is proportional to a volume (the cube of a linear dimension). It follows that as size of the hydrofoil is increased, the foils tend to outgrow the hull. Aircraft solve this problem by increasing speed and wing loading as size is increased, but practical hydrofoil speeds are limited by cavitation.

In the early period of hydrofoil development it was felt that an increase in the foil and strut weight fraction by direct application of the square-cube law would inherently limit hydrofoil size. More detailed design studies show that foil system weight fractions increase only slightly with displacement, Figure 6.

Figure 6 - Strut and Foil System Weight Trend

The principal reasons why the weight fraction does not increase as might be expected is that required strut length varies with design sea state, not ship size, and larger foils are structurally more efficient. For hydrodynamic efficiency, it is desirable to use as high a foil aspect ratio (span/chord) as possible. The PHM aft foil extends almost 10 feet on either side of the hull. Thus, a camel is normally used to hold the ship away from the pier for mooring. When no camel is available the ship must be moored across the end of a pier or the transom of a larger ship with the stern overhanging. PHMs have occasionally nested bow to stern. As ship size increases and foils grow relative to the hull and in actual dimension, practical considerations dictate efforts to limit the span. The trend will be to move toward tandem foil configurations to divide the weight more evenly between the forward and aft foils.

11.Propulsion Systems

Modern hydrofoil ships have been made possible by the development of lightweight diesel engines and marinized gas turbine engines. Most of the European commercial ships using fixed surface-piercing foil systems have used lightweight diesel engines driving subcavitating propellers by means of an angled transmission system. This combination provides simplified construction, relative ease of maintenance and low cost. However, the comparatively high specific weight (6-8 pounds per horsepower) of the diesel engines and higher overall drag have resulted in practical design speeds of these ships of about 35 to 40 knots.

Existing aircraft gas turbine engines slightly modified and coupled with specially designed free powered turbines are available in sizes with power ratings up to about 30,000

horsepower and specific weights of around 0.5 pounds per horsepower. The newer large engines employing blade cooling techniques have specific fuel consumption rates at their design power about equal to diesel engines. Gas turbine engines have been used in all major U.S. military and commercial hydrofoil ships permitting practical design speeds greater than 40 knots. Propellers are the most efficient propulsion device available for operating over the subcavitating speed range of current hydrofoil ships. The power transmission systems required when using fully submerged foil systems consist of right angle bevel gears, flexible shafts and possibly a speed reduction gearbox in the propeller transmission pod. See Figure 7 as an example.

Figure 7 - PGH-1 FLAGSTAFF Propulsion System

Problems encountered with gear transmission systems in early hydrofoil ships led to interest in waterjet propulsion systems. While not entirely eliminating the need for gearboxes, these systems consist of underwater inlets, water ducts in the struts, a pump located in the machinery spaces and an above-water exhaust nozzle. The U.S. Navy's PHM waterjet system is shown on Figure 8. The price paid to achieve these less complex waterjet systems is a decrease in propulsive efficiency of about 20% at 45-50 knots and considerably more at takeoff speeds along with an increase in propulsion system weight due to the water carried in the system.

Figure 8 - PHM Waterjet System

12.Automatic Control System

As noted earlier, surface-piercing hydrofoil configurations are self-stabilizing in both pitch and roll and thus do not require an automatic control system. However, to reduce the inherent reaction to rough seas, a number of ships have added trailing-edge flaps to the surface-piercing foils and have used autopilots for ride improvement.

In the United States, full automatic control of submerged foils has been deemed necessary to attain the seaway performance desired for ocean-going hydrofoil ships. Typically, control is accomplished by positioning trailing-edge flaps on the forward and after foils and by rotating the swiveled forward strut (rudder), or by moving the entire foil surface and by using the power driven aft strut as a rudder. See Figures 9 and 10 for schematic and pictoral diagrams of a control system. The control surfaces are positioned by means of conventional electro- hydraulic servos. The control system motion sensors consist of: 1) a vertical gyro which measures craft pitch and roll angular motion, 2) a rate gyro which measures craft yaw rate, 3) three vertical accelerometers, one accelerometer being located approximately on top of each strut (the two aft accelerations work differentially to provide roll angular acceleration feedback, and they work in unison to provide pitch and heave acceleration feedback), and 4) a height sensor which measures the height of the bow above the water surface. The manual inputs consist of a foil depth command, which the helmsman uses to select any desired foil depth (or flying height), and the helm, which introduces the craft turning commands.

Figure 9 - Hydrofoil ACS Schematic

 
 
 
 

Figure 10 - Typical Hydrofoil Automatic Control System (ACS )

The ACS provides continuous control during takeoff, landing, and all foilborne operations. The pitch, roll, and height feedback loops provide automatic stabilization of the craft. The craft is automatically trimmed in pitch by the pitch feedback, and roll trim is accomplished by helm inputs. To steer the ship, the helmsman simply turns the helm, and the ACS automatically maintains a coordinated turn, with turn rate being proportional to helm deflection. ACS system requirements and operation are discussed in detail in References (7), (8), and (9).

13.Hydraulic System

The hydraulic and automatic control systems are worthy of mention because: 1) they have proven reliable and functionally well suited for a hydrofoil ship, 2) they combine proven aircraft system equipment applications, and 3) they are essential to all operations: foilborne, hullborne, and docking. Because the hydraulic systems are crucial to both foilborne and hullborne operation, the design should employ multiple levels of redundancy to assure continued operation in the event of system failures.

On the PHM, for instance, four separate systems supply the required power to the various hydraulic equipment users which include the foilborne and hullborne control actuators, strut retraction and lock actuators, bow thruster, anchor windlass, and emergency fuel pump. Systems No. 1 and No. 2 supply hydraulics to the forward part of the ship while systems No. 3 and No. 4 supply the aft part. Two separate supply systems feed each user with provisions included to transfer (shuttle) the user from its primary supply to its alternate supply in the event of loss of primary supply pressure. The hydraulic systems of the PHM operate at a standard 3,000 psi (20.68 MN/m2) constant pressure. Proven aircraft hardware, mostly from the Boeing 747 aircraft, was used where possible. The hydraulic pumps, tube fittings, tubing material, and filters were all taken directly from the 747. In the case of the foilborne and hullborne steering actuators, an automatic shuttle valve was specifically developed for the hydrofoil program which rapidly transfers the user actuator from a failed supply to the alternate, thus assuring continued safe foilborne operation. The hydraulic actuators on the PHM were for the most part specifically designed and developed for this program. The four foilborne control actuators, the hullborne steering actuator, two hullborne thrust reverser actuators and the strut retraction actuators all were designed, manufactured and qualified to military specifications including rigorous environmental and life testing.

The PHM hydrofoil program pioneered the use of a new hydraulic fluid, a synthetic hydrocarbon. This new fluid provides a much greater resistance to fire and explosion than its predecessor. At the same time it overcomes the serious shortcomings of phosphate ester base fluids which have proven to be incompatible with the saltwater environment.

14.Characteristics

14.1 Resistance and Powering

Although the major reason for the employment of hydrofoils is to lift the hull out of the water to reduce the effect of waves and to reduce the drag at high speed, a naval hydrofoil ship spends a considerable portion of its life hullborne and must have an efficient hull form to keep the drag low at low speed and through takeoff. Total drag just prior to takeoff is a significant factor in establishing the power requirement. Careful attention must be paid to the hull design to minimize this effect. Figure 3 shows a generalized smooth water drag curve for a hydrofoil craft with its significant "hump" prior to takeoff. Comparison is also made with a typical planing craft to illustrate the high-speed advantage of the hydrofoil even in smooth water. To overcome additional takeoff drag which results from rough water, a power margin

over the smooth-water takeoff drag is required. Since the magnitude of this margin is a prime factor in the sizing of the propulsion system, it is essential that it not be arbitrarily overspecified. Tests in design sea states on well-instrumented U.S. Navy hydrofoils show that 20 to 25 percent margin is ample to permit takeoff in rough water in any direction.

Figure 3 - Typical Calm Water Thrust

14.2 Seakeeping

Some of the principle advantages of hydrofoil ships, over all other monohull or alternative ship types are: (1) the ability of a ship, which is small by conventional ship standards, to operate effectively in nearly all sea environments, and (2) an improved ratio of power to displacement in the 30 to 50 knot speed range permitting economical operation at these higher speeds. The submerged-foil ship can maintain its speed and maneuverability in heavy seas while simultaneously providing a comfortable working environment for the crew. The ship's automatic control system (ACS) provides continuous dynamic control of the ship during takeoff, landing, and all foilborne operation. In addition to providing ship roll and pitch stability, the ACS controls the hull height above the water surface, provides the proper amount of banking in turns and all but eliminates ship motions caused by the orbital particle motion of waves. Foilborne operations only become limited as wave height exceeds the hydrofoil's strut length. Figure 4 shows operating data points for three submerged-foil hydrofoil ships in actual sea conditions. The data clearly show only a modest reduction in speed as wave heights increase. A hypothetical operating envelope is drawn to represent hydrofoils designed to have a 50-knot speed capability in calm water.

Figure 4 - Effect Of Sea State On Hydrofoil Speed and Drag Curves

 

14.3 Maneuvering

Besides a significant speed advantage, hydrofoils are more maneuverable and provide a more stable platform than conventional ships. Foilborne turns are accomplished in a banked (coordinated) fashion. This causes the centrifugal force required in turns to be provided predominantly by the reliable lift capability of the submerged foils rather than by the unpredictable side forces from the struts. Turn coordination enhances crew comfort during high-rate turns because the accelerations due to turning are felt primarily as slightly greater vertical forces rather than lateral forces. For example, a 0.4g turn is felt as only 0.08g vertical acceleration increase while the lateral acceleration is zero. Therefore, hydrofoil ships have design turn rates of 6 to 12 degrees per second, two to four times those of conventional ships, and they can maintain these rates in both calm and rough seas. This makes the hydrofoil ship a more difficult target for enemy missiles, guns, or torpedoes. The exceptional stability of the hydrofoil ship makes it a superior platform in which to mount surveillance equipment and weapons while maintaining crew comfort and proficiency.

15.Advantages

1) A hydrofoil requires only 50% of the power of a displacement vessel of comparable size, for a given speed

2) The hydrofoil due to their small size and maneuverability, are target less vulnerable to tactical military weapons like missiles

3) Greater platform stability and high speed

4) Can be maintained even in seaway due to better sea keeping ability

SOME HYDROFOILS AND THEIR USE: Hydrofoils have become very popular. They are used in various kind of sea traveling, from military use to water sports. The high speed, smooth cruise and better turns delivered by hydrofoils have been used in military ships. Sailing has also adopted the hydrofoils to gain more speed. They enable new inventions that can satisfy people’s desire to challenge danger, like the sky ski. It is a water ski with a hydrofoil attached, which permits people to fly above the water surface. Every day more hydrofoils are used, and in the future, they may be the dominate method of sea traveling

16.Summary

Although the basic concept of hydrofoils has been around for 85 years, it has only been in the last 35 years through advances in materials, light weight propulsion plants, and control theory, they have become a viable open ocean concept. Involved. The design of a hydrofoil demonstrates the very essence of engineering that is the trade-off and compromise among often-conflicting requirements of many disciplines to arrive at a good balanced design.

17.Conclusion

Although the basic concept of hydrofoils has been around for 85 years, it has only been in the last 35 years through advances in materials, light weight propulsion plants, and control theory, they have become a viable open ocean concept. Involved. The design of a hydrofoil demonstrates the very essence of engineering that is the trade-off and compromise among often-conflicting requirements of many disciplines to arrive at a good balanced design.

18.REFERENCES

www.foils.org

www.howstuffworks.com

www.

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