In general, the push of chopper is generated by its rotor blades. In hovering, the chopper will stay stationary at the land which means the push has the equal force with the entire weight of chopper. In axial mounting, extra push is generated to travel the chopper upward. Besides that, axial descent is another flight government which will hold opposite way with mounting. This flight government is more complicated because of the presence of both upward and downward flow in the rotor disc which can bring on important blade quiver. In the forward flight, the rotor disc is tilted in the flight way to make a thrust constituent in coveted way. The constituent of the push in the forward flight way must get the better of the retarding force. Sometimes, the chopper operation needs combination of two or more flight government. For illustration, set downing operation is a combination of forward flight and perpendicular descent.

The ideal state of affairs for a chopper is to accomplish a changeless lift throughout the rotor rhythm. However, since the rotor blades rotate in a individual way, in frontward flight there will be a force and minute instability. As the rotor blade moves in the same way as the forward flight velocity, the speed near the blade is big and since the lift is relative to the speed, the angle of onslaught demand non be big to accomplish sufficient lift. On the other manus, as the blade moves in a way antonym to the way of flight, the comparative speed is smaller and the angle of onslaught must therefore be larger to accomplish the same entire lift. Therefore, without a moment-balancing mechanism, the chopper would be given to turn over. To equilibrate the forces and minutes, we can utilize the rotor-tail chopper is used.

The chopper must run in a assortment of flight governments, for illustration, the hover, ascent, descent, or frontward flight. Besides that, chopper may consist of a combination of these few basic flight governments in order to finish their flight. Normally, choppers use their blades to command the flight governments such as make some angle difference on their blades.

Hovering is one of the chopper flight governments and it is considered as a really alone flight status because there has no frontward velocity every bit good as no perpendicular velocity for chopper.

By and large, in hovering, the lift force on chopper is produced by the rotor of chopper. In this instance, rotor of the chopper acts as a centrifugal axial pump, which is one of the turbomachinery applications, and causes the force per unit area difference between the top and the underside of the blade. This force per unit area difference will bring forth a lift force and do the chopper flight upward.

In order to make the analysis for the hovering of chopper, we may make some premises:

The flow through the rotor is incompressible

Flow belongingss at a point do non alter with clip

Flow is one dimensional

Inviscid flow or the flow of a fluid that is assumed to hold no viscousness.

In our premise, flow is one dimensional which means that the fluid belongingss across any plane analogue to the rotor plane are changeless. However it will alter merely with axial ( perpendicular ) place relation to the rotor. Besides that, we can see an ideal fluid which no syrupy shear between shear elements. As a consequence, the losingss in the fluid ensuing from the action of viscousness can be assumed as negligible.

Figure 1: Flow theoretical account used for analysis of a rotor in vibrating flight. Data beginning: Leishman ( 2000 ) .

Figure 1 shows that the chopper ‘s rotor in an axial ascent with speed Vc, for which the hovering status is obtained in the bound as Vc is closed to 0. The general equation of unstable mass, impulse, and energy preservation can be applied to the analysis of vibrating rotor. This corresponds to the status Vc 0 shown in Figure 1.

Harmonizing to Figure 1, cross subdivision 0 represent the plane far upstream of the rotor, where in the hovering instance the fluid is quiescent ( Vc V0 0 ) . Cross subdivision 1 and 2 are the planes merely above and below the rotor. Whereas airstream or downstream of the rotor is represented by cross subdivision ? shown in Figure 1. At the plane of rotor, we can presume that the induced speed in the control volume at the rotor phonograph record is Vi..The speed at the airstream is represented by tungsten and eventually the country of rotor phonograph record is A.

By utilizing the rule of preservation of mass and the premise of flow belongingss in the flow is changeless with clip, we known that the mass flow rate, , must be changeless within the boundary of the rotor aftermath ( control volume ) . Wake is the part of re-circulating flow instantly behind or below a traveling solid organic structure. Besides that, from one dimensional incompressible flow premise we can compose down:

Mass go throughing through component in unit clip, =

…………………………………………………………………… . ( 1 )

By utilizing the rule of preservation of fluid impulse, we found the relationship between the rotor push, T and the rate of alteration of impulse out of the control volume ( Newton ‘s 2nd jurisprudence ) . The rotor push is equal and opposite the force on the fluid, which is given by

Since in vibrating flight the speed good upriver of the rotor is quiescent, the 2nd term of the right-hand side of above equation can be consider as nothing ( Hence, for the rotor push can be written as the equation:

…………………………………………………………………………………… ( 2 )

From the rule of preservation of energy, the work done on the rotor is equal to the addition in energy of the fluid per unit clip. The work done per unit clip, or the power consumed by the rotor is TVi and this consequence in the equation

Power = TVi = addition in energy of the fluid per unit clip

Again, in hover, the 2nd term on the right-hand side of the above equation is zero so that:

……………………………………………………………………………… . ( 3 )

From the Equation ( 2 ) and ( 3 ) , we will hold

………..……………………………………………………………………………… ( 4 )

Therefore, we already have the relationship between the induced speed in the plane of rotor and the airstream speed. From this relationship, we have known that the flow speed additions in the aftermath below the rotor, continuity consideration require that the country of the airstream must diminish. This is followed from the preservation of unstable mass between the rotor and from continuity of flow we have,

Mass of fluid come ining per unit clip

Mass of fluid go forthing per unit clip

Increase of mass of fluid in the control volume per unit clip

Since the fluid flow around the control volume of rotor is assumed as steady flow, hence,

Mass of fluid come ining per unit clip = Mass of fluid go forthing per unit clip

Therefore another equation is formed:

From the Equation ( 4 ) we have,

So that in hover, the ratio of the cross-sectional country of the to the full developed far aftermath to the country of the rotor disc is

………………………………………………………………………………….…… . ( 5 )

In the other word, based on ideal fluid flow premise, the vein contracta is an country that is precisely half of the rotor disc country. Vena contracta is an country in a fluid watercourse where the diameter of the watercourse is the least, for illustration, when the fluid come out from a nose or opening. Alternatively, by sing the radius of the far rotor aftermath r? , comparative to that of the rotor, R,

Since A = 2 & A ; deg ; r2

……………………………………………………………………………………… ( 6 )

Therefore, the ratio of the radius of the aftermath to the radius of the rotor is = 0.0707. This is called the aftermath contraction ratio. In pattern, it has been found by experimentation that the aftermath contraction ratio is non every bit much as the theoretical value given by the impulse theory. However, it is merely approximately 0.78 compared to 0.0707. This is because of some ground like a effect of the viscousness of the fluid, the world that a non-uniform influx will be produced over the disc and a little swirl constituent of speed in the rotor aftermath induced by whirling rotor blades. These effects serve to cut down alteration of the fluid impulse in the perpendicular way, and they decrease the rotor push for a given shaft torsion which is power supplied. In the other word, it will cut down the efficiency of the chopper.

It has been shown antecedently utilizing Equation ( 2 ) that preservation of impulse theory can be used to associate the rotor push to the induced speed at the rotor disc by utilizing the equation

…………………………………………………………………………….. ( 7 )

Rearranging this equation and work outing for the induced speed at the plane of the rotor disc, Vh gives

………………………………………………………………………… . ( 8 )

In order to happen the power required to vibrate, we can utilize

……………………………………………………………………..…………… ( 9 )

This power is besides called ideal power, from the Equation ( 9 ) , we known that the higher rotor power will bring forth more push and bigger country of the blade of chopper will bring forth the higher push if the rotor power is changeless.

We besides can happen the relationship between the induced speed and the rotor power by utilizing P = Tvi and besides Equation ( 4 ) :

………………………………………….…………………………………….. ( 10 )

From Equation ( 10 ) , it is shown that the power required to vibrate will increase with the regular hexahedron of the induced speed ( or inflow ) at the disc. Obviously, to do a rotor hover at a given push with lower limit induced power, the induced speed at the disc must be little. Therefore, the mass flow through the disc must be big and this accordingly requires a big rotor disc country. This is a cardinal design characteristic of all choppers.

The force per unit area fluctuation through the rotor flow field in the hover province can be found from the application of Bernoulli ‘s equation along a streamline above the rotor phonograph record. Since there is a force per unit area leap across the phonograph record, and this will bring forth add-on energy by the rotor, so that Bernoulli ‘s equation can non be applied between points in the flow across the disc. However, the force per unit area leap is unvarying over the rotor disc so the Bernoulli ‘s equation can be applied to all streamline contained within the control volume alternatively of the energy equation. For incompressible flow, the Bernoulli ‘s equation is an alternate to the energy equation. Applying Bernoulli ‘s equation up to the disc between subdivision 0 and 1 in Figure 1 green goodss

…………………………………………………………………… ( 11 )

Below the disc, between subdivision 2 and ? in Figure 1, the application of Bernoulli ‘s equation gives:

………………………………………………………………… ( 12 )

Since the force per unit area difference is unvarying, as a consequence, the value must be equal to the disc lading T/A. Hence,

and

……………………………………………………………………………… . ( 13 )

It is seen that the rotor disc burden is equal to the dynamic force per unit area in the rotor airstream. One can besides find the force per unit area merely above the disc and merely below the disc in term of the disc burden. Then, we use the Bernoulli ‘s equation:

Above the disc

…………………………………………………………………………….. ( 14 )

Below the disc

……………………………………………………………………….…….. ( 15 )

Therefore, the inactive force per unit area is reduced by ? ( T/A ) above the rotor disc and addition by ? ( T/A ) below the disc. As a consequence, this lift force ( push ) will be produced because of the force per unit area difference between the above and below the disc will do a alteration in flow way viz. from the higher force per unit area ( below the disc ) to take down force per unit area ( above the disc ) .

Climbing flight public presentation is an of import operation because sufficient power must be design to the rotor blade chopper to execute this type operation.

In mounting battle, we can utilize the same premise every bit good as use the three preservation Torahs in vibrating. In contrast to the hover instance, the comparative speed far upstream relation to the rotor now will be Vc. At the plane of the rotor, the speed will be, and the airstream ( vena contracta ) speed is. By the preservation of mass, the mass flow rate is changeless within the boundaries of the aftermath and so

By the rule of preservation of impulse and

……………………………………………………………………….. ( 16 )

This equation is same as Equation ( 2 ) which obtains for the rotor push in the hovering.

However, the work done by the mounting rotor push is now

……………………………………………………… ( 17 )

From Equation ( 16 ) and ( 17 ) , we can acquire the relationship between the tungsten and Vi:

W= 2Vi

From Equation ( 16 ) :

Therefore, from Equation ( 8 ) ,

………………………………………………………… ( 18 )

Equation ( 18 ) is a quadratic equation in, and this equation has the solution of

Since the value of must be positive hence,

………………………………………………………….. ( 19 )

The Equation ( 19 ) shows that when the ascent speed additions, the induced speed at the rotor will diminish.

The hover and ascent theoretical account can non be used for descent because the Vc is straight upward and so the airstream will be above the rotor. In add-on, the magnitude for the Vc must be twice of the norm induced speed at the disc or we can compose mathematically the scope of Vc:

Figure 2: The false flow theoretical account and control volume environing of falling rotor. Data beginning: Leishman ( 2000 ) .

Form Figure 2, we found that the slipsteam will ever be above the rotor and embracing the rotor disc. The speed at the far upstream the rotor is equal to Vc. In order to do thing easier, we assumed that Vc is positive when the way is downward.

By preservation of mass, the fluid mass flow rate through the disc is,

By preservation of fluid impulse give in this instance

……………………………………………………………………….. ( 20 )

In the Equation ( 20 ) , the negative mark originating because the flow way is opposite to the ascent instance. In steady descent, the speed far upstream of the rotor must be finite.

The work done by the rotor in descending is

…………………………………………………………… . ( 21 )

The Equation ( 21 ) shows the negative value. This shows that the rotor is now pull outing power from the airstream and this operation status is known as windmill province. By utilizing equation ( 20 ) and ( 21 ) , we can acquire the relationship between the tungsten and Vi:

w= 2Vi

Since the net speed in the airstream is less than Vc and so from the continuity considerations the aftermath boundary expands above the falling rotor disc. For the descending rotor

Therefore, from Equation ( 8 ) ,

………………………………………………………… ( 21 )

Equation ( 21 ) is a quadratic equation in, and this equation has the solution of

Since the value of must be more than 1 hence,

………………………………………………………….. ( 22 )

The Equation ( 22 ) is merely valid for, and this equation shows that when the descent speed additions, the induced speed at the rotor will diminish asymptotes swimmingly to zero at high descent rate.

The production of bulk chopper in this epoch is chiefly built in with a individual chief rotor with tail rotor constellation. The chief intent of the tail rotor is twofold. The torque reaction produced by the chief rotor on the fuselage is foremost countered by the tail rotor. The tail rotor besides provides swerve stableness which allows the pilot have directional control over the yaw axis. The aeromechanicss of the tail rotor provides the chopper with important weathercock stableness. For illustration, if the aircraft is yawed nose-left, so the tail rotor will see an effectual ascent. If the corporate pitch is held changeless, so this will ensue in a lessening of push ( a consequence of higher influx ) and reconstructing minute about the yawing axis. Similarly, if the chopper yaws nose-right, the tail rotor experience an effectual descent, with an addition in push, and once more, a restoring minute is produced. The weathercock stableness is a utile characteristic, but it can besides do choppers less manoeuvrable.

The tail rotor has to run in a comparatively complex aerodynamic environment and must bring forth push with the comparative flow coming from basically any way. For illustration, the tail rotor must run decently in side air currents and during yaw manoeuvres. In a yawing manoeuvre, the tail rotor operates either in an effectual ascent manner or in descent, depending on the yaw way. The gaping way that produces an effectual descending status is the most critical because it is possible for the tail rotor to come in the whirl pealing province. This can ensue in a loss of tail rotor authorization, and possibly even loss of control under the incorrect combination of conditions. These effects are carefully examined during enfranchisement of the chopper to guarantee that there is a minimum opportunity that the machine will unwittingly exhibit unwanted flight feature.

As seen above, the tail rotor is besides placed closely to a perpendicular five or other tail assembly, and the aerodynamic interactions will consequence chase rotor operation. In add-on, the operation of the tail rotor will be affected by turbulent separated flow generated by the chief rotor hub a fuselage aftermaths and the energetic chief rotor aftermath itself. This rough environment shows that tail rotor design for aerodynamic intent will be different from the chief rotor. For these grounds, it is known to be hard to plan a tail rotor that will run into all the aerodynamic, control, stableness, weight, and structural demands.

The primary intent of the tail rotor is to supply a sideward force in a way and of sufficient magnitude to counter the chief rotor torsion reaction. The tail rotor besides provides yaw control. Roughly, the tail rotor consumes up to about 10 % of the sum aircraft power. This is power that is wholly lost, because unless the tail rotor is canted, as on the UH-60 Blackhawk, it provides no utile raising force. The intent of the atilt tail design is to widen the allowable centre gravitation of the aircraft. This, nevertheless, introduces an inauspicious yoke between swerve and pitch, but this consequence can be minimized by a flight control system.

The way of the anti-torque force depends on the way of the rotary motion of the chief rotor. For a rotor turning in the conventional way ( anticlockwise way when viewed from above ) , the tail rotor push is to the right ( starboard ) . The magnitude of this push every bit good as the power ingestion depends on the location of the tail rotor from the centre of gravitation ( i.e. , the minute arm ) . The chief rotor torsion reaction consequence, , is cancelled when the tail rotor minute is equal to the yaw reaction torsion, that is, , where is the yaw acceleration and is the mass minute of inactiveness about the swerve axis.

The tail rotor push is controlled by the pilot ‘s pess by forcing on a set of floor mounted pedals. For illustration, for a rotor turning in the conventional way, forcing on the left pedal increases tail rotor push ( positive to starboard ) and the chopper will gape nose left. The tail rotor must besides supply the specified swerve acceleration in the maximal specified crosswind conditions, taking into consideration possible losingss on efficiency because of aeromechanicss interference effects between the tail rotor and the perpendicular five. Keep in head that when the chief rotor push or power is increased, for illustration to mount, the reaction torsion, , on the fuselage is increased. This means that the tail rotor push must besides increase to equilibrate this torque reaction, hence, when the pilot increases the corporate to mount, he or she must besides apple pes force per unit area to the appropriate pedal to maintain the nose pointed heterosexual in the way of the flight.

The chief considerations in planing a chopper are the ability to run expeditiously for long periods of clip in hover, high cruising efficiency and velocity, scope, and warhead. All of these considerations are influenced greatly by the aeromechanicss of the rotor blades and by other interactions between assorted constituents. Unlike fixed-wing aircraft, the chopper frequently operates in an unsteady environment ; whether in hover or in forward flight, the chopper operates in, or really nears, its ain aftermath which is 3-dimensional and extremely unsteady.

In hover, theoretically, spare and flap are non required to equilibrate forces on an stray rotor. However, non-uniformities and the presence of the fuselage make them necessary. In add-on, rotor blades are twisted and frequently tapered. A distorted blade is one in which the local geometric pitch angle varies along the span. To supply spare capableness and for aeroelastic emphasis alleviation, chopper rotors are frequently hinged in the sense that the rotor blades must be permitted to flex out of the rotor disc plane every bit good as pitch to fulfill spare demands. Rotor blades have a big span-to-chord ratio and therefore terrible emphasiss can be communicated to the hub if the blades are non permitted to roll. However, if the blades are aeroelastically soft, so hub emphasiss can be kept to a lower limit and flexible joints can be eliminated. In such instances, the rotor is said to be hingeless.