__DRAG__

__DRAG__

Each part of an aircraft in flight produces an aerodynamic force. Total drag is the sum of all the components of the aerodynamic forces, which act parallel and opposite to the direction of flight. Each part of total drag represents a value of resistance of the aircraft’s movement, that is, lost energy.

__Components of Total Drag__

There are three points to be borne in mind when considering total drag:

- An aircraft in flight will have drag even when it is not producing lift.

- In producing lift the whole aircraft produces additional drag and some of this will be increment in those components which make up zero lift drag.

** Zero Lift Drag. **When an aircraft is flying at zero lift angle of attack the resultant of all the aerodynamic forces acts parallel and opposite to the direction of flight. This is known as Zero Lift Drag (referred to as Profile Drag or Boundary Layer Drag) and is composed of:

- Surface friction drag.

- Form drag (boundary layer normal pressure drag).

- Interference drag.

** Lift Dependent Drag. **In producing lift the whole aircraft will produce additional drag composed of:

- Induced drag (vortex drag).

- Increments of:

- Surface friction drag.

- Form drag.

- Interference drag.

__ZERO LIFT DRAG__

__ZERO LIFT DRAG__

__The Boundary Layer__

Although it is convenient to ignore the effects of viscosity whenever possible, certain aspects of aerodynamics cannot be explained if viscosity is disregarded.

Because air is viscous, any object moving through it collects a group of air particles which it pulls along. A particle directly adjacent to the object’s surface will, because of viscous adhesion, be pulled along at approximately the speed of the object. A particle slightly further away from the surface will also be pulled along, however its velocity will be slightly less than the object’s velocity. As we move further and further away from the surface, the particles of air are affected less and less, until a point is reached where the movement of the body does not cause any parallel motion of air particles whatsoever.

**The layer of air extending from the surface to the point where no dragging effect is discernable is known as the boundary layer**. In flight, **the nature of the boundary layer determines the maximum lift coefficient, stalling characteristics of a wing, value of form drag, and to some extent the high speed characteristics of an aircraft.**

The viscous drag force within the boundary layer is not sensitive to pressure and density variations and is therefore unaffected by the variations in pressures at right angles (normal) to the surface of the body. The coefficient of viscosity of air is directly proportional to temperature and therefore decreases with altitude.

__Surface Friction Drag__

The surface friction drag is determined by:

- The total surface area of the aircraft.

- The coefficient of viscosity of air.

- The rate of change of velocity across the flow.

** Surface Area. **The whole surface area of the aircraft has a boundary layer and therefore has surface friction drag.

** Coefficient of Viscosity. **The absolute coefficient of viscosity (µ) is a direct measure of the viscosity of a fluid. The greater the viscosity of air, the greater the dragging effect on the aircraft’s surface.

**Rate of Change of Velocity.** Consider the flow of air moving across a thin flat plate, as in Fig below. The boundary layer is normally defined as that region of flow in which the speed is less than 99% of the free stream flow, and usually exists in two forms, laminar and turbulent. In general, the flow at the front of a body is laminar and becomes turbulent at a point some distance along the surface, known as the transition point. From the Fig it can be seen that the rate of change of velocity is greater at the surface in the turbulent flow than in the laminar. This higher rate of change of velocity results in greater surface friction drag. The velocity profile for the turbulent layer shows the effect of mixing with the faster moving air above the boundary layer. This is an important characteristic of the turbulent flow since it indicates a higher level of kinetic energy. Even when the boundary layer is turbulent, a very thin layer exists immediately adjacent to the surface in which random velocities are smoothed out. This very thin layer (perhaps 1% of the total thickness of the turbulent layer) remains in the laminar state and is called the laminar sub-layer. Though extremely thin, the presence of this layer is important when considering the surface friction drag of a body and the reduction that can be obtained in the drag of a body as a result of smoothing the surface.

Fig Boundary Layer

**Transition to Turbulence **

The forward movement of the transition point increases the surface friction drag. The position of the transition point depends upon:

(a) Surface condition.

(b) Speed of the flow.

(c) Size of the object.

(d) Adverse pressure gradient.

**Surface Condition**. Both the laminar and turbulent boundary layers thicken downstream, the average thickness varying from approximately 2 mm at a point 1 m downstream of the leading

edge, to 20 mm at a point 1 m downstream of the transition point. Generally, the turbulent layer is about ten times thicker than the laminar layer but exact values vary from surface to surface. The thin laminar layer is extremely sensitive to surface irregularities. Any roughness which can be felt by the hand, on the skin of the aircraft, will cause transition to turbulence at that point, and the thickening boundary layer will spread out fanwise down-stream causing a marked increase in surface friction drag.

** Speed and Size. ** In a fluid flow of given density and viscosity, the flow changes from streamline to turbulent when the velocity reaches a value that is inversely proportional to the thickness of a body in the flow. That is, thicker the body, lower is the speed at which transition occurs. Applied to an aerofoil of given thickness it follows that an increase of flow velocity will cause the transition point to move forward towards the leading edge. Earlier transition means that a greater part of the surface is covered by a turbulent boundary layer, creating greater surface friction drag. However, it should be remembered that the turbulent layer has greater kinetic energy than the laminar, the effect of which is to delay separation, thereby increasing the maximum value of C

_{L}, as explained in the chapter on Lift.

** Adverse Pressure Gradient.** A laminar boundary layer cannot be maintained, without mechanical assistance, when the pressure is rising in the direction of flow, i.e. in an adverse pressure gradient. Thus on the on the curved surfaces of an aircraft the transition point is usually beneath, or near to, the point of minimum pressure and this is normally found to be at the point of

maximum thickness. Fig below illustrates the comparison between a flat plate and a curved surface.

**Effect of Adverse Pressure Gradient**

__Form Drag (Boundary Layer Normal Pressure Drag)__

The difference between surface friction and form drag can be easily appreciated if a flat plate is considered in two attitudes, first at zero angle of attack when all the drag is friction drag, and second at 90° angle of attack when all the drag is form drag due to the separation.

** Separation **The effect of surface friction is to reduce the velocity, and therefore the kinetic energy of the air within the boundary layer. On a curved surface the effect of the adverse pressure gradient is to reduce further the kinetic energy of the boundary layer. Eventually, at a point close to the trailing edge of the surface, a finite amount of the boundary layer stops moving, resulting in eddies within the turbulent wake. Fig below shows the separation point and the flow reversal, which occurs behind that point. Aft of the transition point, the faster moving air above mixes with the turbulent boundary layer and therefore has greater kinetic energy than the laminar layer. The turbulent layer will now separate as readily under the influence of the adverse pressure as would the laminar layer.

**Boundary Layer Separation**

**Streamlining** When a boundary layer separates some distance forward of the trailing edge, the pressure existing at the separation point will be something less than at the forward stagnation point. Each part of the aircraft will therefore be subject to a drag force due to the differences in pressure between its fore and aft surface areas. This pressure drag (boundary layer normal pressure drag) can be a large part of the total drag and it is therefore necessary to delay separation for as long as possible. The streamlining of any object is a means of increasing the fineness ratio to reduce the curvature of the surfaces and thus the adverse pressure gradient (fineness ratio of an aerofoil is Chord / Thickness).

** Interference Drag. **On a complete aircraft the total drag is greater than the sum of the values of drag for the separate parts of the aircraft. The additional drag is the result of flow interference at wing / fuselage, wing / nacelle and other such junctions leading to modification of the boundary layers. Further turbulence in the wake causes a greater pressure difference between fore and aft surface areas and therefore additional resistance to movement. For subsonic flight this component of total drag can be reduced by the addition of fairings at the junctions, e.g. at the trailing edge wing roots.

** Effect of Configuration, Altitude and Speed.** Inferring from the above explained factors, changes in configuration, altitude and speed will cause the Zero Lift Drag to vary as follows:

The zero lift drag is unaffected by the lift but is affected by the dynamic pressure and the effective frontal area. With changes in configuration the effective frontal area changes which causes the form drag and the interference drag to change in the same ratio as the change in effective frontal area.__Effect of Configuration.__

For a given aircraft, flying at the same TAS and configuration, an increase in altitude will reduce the dynamic pressure acting upon it and thus the zero lift drag will reduce. The reduction in dynamic pressure will be directly proportional to the change in relative density. However, if the ac is flying at the same IAS, the dynamic pressure and therefore the zero lift drag will not change.__Effect of Altitude.__

The effect of speed alone on the zero lift drag is the most If all the other factors like altitude, configuration, weight etc. are kept constant, the zero lift drag is directly proportional to the square of EAS.__Effect of Speed.__

__LIFT DEPENDENT DRAG__

__LIFT DEPENDENT DRAG__

All of the drag which arises because the aircraft is producing lift is called lift dependent drag. It comprises mainly of induced drag, but also contains increments of the types of drag which make up zero lift drag. The latter are more apparent at high angles of attack.

** Wing Tip Vortices. **If a finite rectangular wing at a positive angle of attack is considered, the spanwise pressure distribution will be as shown in Fig below. On the underside of the wing, the pressure is higher than that of the surrounding atmosphere so the air spills around the wing tips, causing an outward airflow towards them. On the upper surface, the pressure is low, and the air flows inwards. This pattern of airflow results in a twisting motion in the air as it leaves the trailing edge. Viewed from just downstream of the wing, the air rotates and forms a series of vortices along the trailing edge, and near the wing tips the air forms into a concentrated vortex. Further downstream all of the vortices collect into trailing vortices . The wing tip vortices intensify under high lift conditions, e.g. during manoeuvre, and the drop in pressure at the core may be sufficient to cause vapour trails to form.

Spanwise Flow

__Induced Downwash__

The main consequence of these vortices is that the air in the immediate vicinity of the wing, and behind it, acquires a downward velocity component. This phenomenon is known as induced downwash, though the adjective ‘induced’ is often omitted. It may be measured in terms of either downwash velocity, usually denoted by “w”, or downwash angel, denoted by “ε”. These two parameters are, of course, related, as shown by the velocity triangle in Fig Below. It is clear from the diagram that tan ε = w / V. But w is always small compared with V, so that ε is a small angle, and tan ε = ε. We therefore use the relationship ε = w/V

Where ε is measured in radians.

In general, the downwash angle varies across the span. However, there are some cases in which the downwash is constant across the span, and this is commonly assumed to be approximately true for most wings of conventional planform, i.e., straight and moderately tapered. The downwash also varies in the stream-wise direction. It reaches its ultimate value little more than a chord length behind the trailing edge and its mean value at the wing itself can be shown to be one half of this ultimate value. The downwash is particularly important for two reasons:

- It reduces the effective angle of attack of the wing. This affects both the lift and drag characteristics of the wing adversely.

- In a conventional aircraft design, downwash affects the flow over the tailplane. This has important consequences in connection with the stability of the aircraft.

__Lift and Downwash__

The lift produced by a wing is imparted to it through the variations in pressure over its surface. This lift force has its reaction in the downward momentum, which is imparted to the air, as it flows over the wing. Thus the lift of the wing is equal to the rate of transport of downward momentum of this air. This downward momentum is measured in terms of the induced downwash described above.

__Induced Drag__

__Induced Drag__

The trailing vortices which are shed from near the tips of a finite wing contain energy associated with the rotational velocities. This energy is abstracted from the airflow, so that some power must be provided to maintain the airflow at a given velocity. This power must equal the rate of flow of energy associated with the trailing vortices. This is equivalent to saying that there is now a further drag force of the wing, to be added to its profile drag. This is known as induced drag, and it forms a very important part of the total drag of a finite wing.

Coefficient of Induced drag is given by

CDi = K CL²/ π A

Consider a section of a wing of infinite span which is producing lift but has no trailing edge vortices. Fig below (a) a shows a total aerodynamic reaction (TR), which is divided into lift (L) and drag (D). The lift component, being equal and opposite to weight, is at right angles to the direction of flight, and the drag component is parallel and opposite to the direction of flight. The angle at which the total reaction lies to the relative airflow is determined only by the angle of attack of the aerofoil as the total reaction is considered to be perpendicular to the RAF.

Fig (b) shows the same section, but of a wing of finite span and therefore having trailing edge vortices. The effect of the induced downwash, due to the vortices, is to tilt downwards the effective relative airflow, thereby reducing the effective angle of attack. To regain the consequent loss of lift the aerofoil must be raised until the original lift value is restored

Fig (c). The total reaction now lies at the original angle, but relative to the effective airflow, the component parallel to the direction of flight is longer. This additional value of the drag, resulting from the presence of wing vortices, is known as induced drag or vortex drag.

__Factors Affecting Induced Drag__

The main factors affecting vortex formation and therefore induced drag are:

(a) Planform.

(b) Aspect ratio.

(c) Lift and weight.

(d) Speed.

** Planform.** Induced drag is greatest where the vortices are greatest, that is, at the wing tips and so, to reduce the induced drag the aim must be to achieve an even spanwise pressure distribution. An elliptical planform has unique properties due to elliptic spanwise lift distribution, viz:

- The downwash is constant along the span.

- For a given lift, span and velocity, this planform creates the minimum induced drag. An elliptical wing poses manufacturing difficulties, fortunately a careful combination of taper and washout, or section change at the tips can approximate to the elliptic ideal.

** Aspect Ratio (AR). ** If the AR is infinite then the induced drag is zero. The nearer we can get to this impossible configuration, the lesser induced drag is produced. Induced drag is inversely proportional to the AR, e.g. if the AR is doubled, then the induced drag is halved.

** Effect of Lift and Weight. **The induced downwash angle and therefore the induced drag depends upon the difference in pressure between the upper and lower surfaces of the wing, and this pressure difference is the lift produced by the wing. It follows then that an increase in C

_{L}(e.g. during manoeuvres or with increased weight) will increase the induced drag at that speed. In fact, the induced drag varies as C

_{L}

^{2}or the lift

^{2}and therefore as weight

^{2}, at a given speed.

** Effect of Speed and Altitude. **If, while maintaining level flight, the speed is reduced to say, half the original, then the dynamic pressure producing the lift (½ρV

^{2}) is reduced four times. To restore the lift to its original value, the value of C

_{L}must be increased four-fold. The increased angle of attack necessary to do this inclines the lift vector to the rear, increasing the contribution to the induced drag. In addition, the vortices are affected, since the top and bottom aerofoil pressures are altered with the angle of attack. If an ac is flown at a constant TAS, keeping all other factors like weight, surface area and aspect ratio etc. constant, then with a change in altitude, for the same TAS, the IAS will reduce, which will therefore cause the induced drag to increase. However if the aircraft is flying at the same IAS, the induced drag at the two levels will remain unchanged.

** High Angles of Attack.** Induced drag at high angles of attack, such as that occurs at take-off, can account for nearly three-quarters of the total drag, falling to an almost insignificant figure at high speed.

__TOTAL DRAG__

Total drag can be considered in terms of zero lift drag and lift dependent drag and Fig below a graph showing variations of total drag with EAS. This curve is valid for one particular aircraft for one weight only in level flight and is the most important factor in performance theory. Speeds of particular interest are indicated on the graph

(a) __Minimum Power Required Speed (V___{MP}** ). **On the drag curve in Fig consider a point A and construct ordinates to the two axes. The area of the rectangle so formed is the product of drag and speed.

Drag X Speed = Force X Velocity = Work done in unit time = Power.

Therefore the area under A is a measure of the power required to fly the aircraft in level flight, at that speed. The smallest possible area under the graph will be found to the left of the minimum drag speed and will therefore represent the minimum value of drag x speed for level flight. The shaded area is the minimum product of drag and velocity and is therefore the minimum power required speed (V_{MP}).

__Minimum Drag Speed (V___{IMD}The graph shows the variation of total drag with speed in level flight, and lift is therefore constant. The maximum value of L/D is at the lowest drag speed and it coincides with where the drag is minimum, i.e. at V__).___{IMD}.

__Maximum EAS / Drag Ratio Speed (1.32 V___{IMD}If in the figure, a line is drawn from the origin to the curve, the angle subtended by the line with the horizontal axis is a measure of the ratio of EAS/Drag. In particular, cot θ = EAS/Drag. The ratio of EAS / Drag is maximum where the angle θ is minimum. The only point which satisfies this condition is C on the tangent to the drag curve, drawn through the origin. This is the main aerodynamic consideration for best range and is usually expressed as a fraction of min drag speed. It has the value of 1.32 V__).___{IMD}.

** Effect of Weight. ** when the weight is changed and therefore the C

_{L}, to maintain level flight, there is a corresponding change in the lift dependent drag. Since this component of total drag varies as C

_{L}

^{2}(or Weight

^{2}), it follows that the difference in total drag will be greatest at high angles of attacks and least at the lower angles. Furthermore, a change in weight will alter the point at which the lift dependent and zero lift drag curves cross, and so change the minimum drag speed, e.g., an increase in weight will increase the V

_{IMD}as well as the total drag.

__Effect of High Drag Devices.____ It is sometimes necessary to decrease the V___{IMD}. This is achieved by deliberately increasing the zero lift drag. This is done by using airbrakes, flaps, drag parachutes etc., which have the effect of increasing the zero lift drag and will also increase the total drag.

Coefficient of total drag is dependent upon the following factors:

- Angle of attack.
- Shape i.e. section and planform.
- Surface condition.
- Reynolds Number.
- Speed of sound (Mach number).

Minimum drag speed (V_{IMD}) gives the following:

- Endurance speed for turbo jets.

- Range speed for propeller aircraft.

- Maximum angle of climb for turbo jets.

- Maximum gliding range for both types.

Minimum power speed (V_{IMP}) gives the following:

- Endurance speed for propeller aircraft.
- Maximum gliding endurance for both types.
- Maximum TAS / Drag speed gives best range speed for turbo jets.

__Summary __

The drag created when an aircraft is not producing lift, e.g. in a truly vertical flight path, is called zero lift drag and it comprises of:

- Surface friction drag.

- Form drag (boundary layer normal pressure drag).

- Interference drag.

Surface friction drag is dependent upon:

- Total wetted area.

- Viscosity of air.

- Rate of change of velocity across the flow which is dependent upon:

- Transition point.

- Surface condition.

- Speed and size.

- Adverse pressure gradient.

Form drag is dependent upon:

- Separation point:

- Transition point.

- Adverse pressure gradient.

Interference drag is caused by the mixing of airflows at airframe junctions.

Zero lift drag varies as the square of the equivalent air speed (EAS).

Lift dependent drag comprises:

- Induced drag (vortex drag).

- Increments of:

- Surface friction drag.

- Form drag.

- Interference drag.