Drag curve

633618 airfoil. Full curves are lift, dashed drag; red curves have = 3·106, blue 9·106. , parasitic drag and total drag as a function of airspeed. 633618 airfoil, colour-coded as opposite plot. The significant aerodynamic properties of aircraft wings are summarised by two dimensionless quantities, the lift and drag coefficients and . Like other such aerodynamic quantities, they are functions only of the angle of attack , the Reynolds number and the Mach number . and can be plotted against , or can be plotted against each other. however drag curves are rarely plotted today using polar coordinates. Depending on the aircraft type, it may be necessary to plot drag curves at different Reynolds and Mach numbers. The design of a fighter will require drag curves for different Mach numbers, whereas gliders, which spend their time either flying slowly in thermals or rapidly between them, may require curves at different Reynolds numbers but are unaffected by compressibility effects. During the evolution of the design the drag curve will be refined. A particular aircraft may have different curves even at the same and values, depending for example on whether undercarriage and flaps are deployed. The accompanying diagram shows against for a typical light aircraft. The minimum point is at the left-most point on the plot. One component of drag on three-dimensional wings is induced drag (an inevitable side-effect of producing lift, which can be reduced by increasing the indicated airspeed). This is proportional to . The other drag mechanisms, parasitic and wave drag, have both constant components, totalling , and lift-dependent contributions that increase in proportion to . In total, then :: The effect of is to shift the curve up the graph; physically this is caused by some vertical asymmetry, such as a cambered wing or a finite angle of incidence, which ensures the minimum drag attitude produces lift and increases the maximum lift-to-drag ratio. ==Power required curves==

One example of the way the curve is used in the design process is the calculation of the power required () curve, which plots the power needed for steady, level flight over the operating speed range. The forces involved are obtained from the coefficients by multiplication with , where ρ is the density of the atmosphere at the flight altitude, is the wing area and is the speed. In level flight, lift equals weight and thrust equals drag, so :::::::::: and ::::::::::. The extra factor of /η, with η the propeller efficiency, in the second equation enters because = (required thrust)×/η. Power rather than thrust is appropriate for a propeller driven aircraft, since it is roughly independent of speed; jet engines produce constant thrust. Since the weight is constant, the first of these equations determines how falls with increasing speed. Putting these values into the second equation with from the drag curve produces the power curve. The low speed region shows a fall in lift induced drag, through a minimum followed by an increase in profile drag at higher speeds. The minimum power required, at a speed of 195 km/h  (121 mph) is about 86 kW (115 hp); 135 kW (181 hp) is required for a maximum speed of 300 km/h (186 mph). Flight at the power minimum will provide maximum endurance; the speed for greatest range is where the tangent to the power curve passes through the origin, about 240 km/h (150 mph). (sometimes "back of the drag curve") where more thrust is required to sustain flight at lower speeds. It is an inefficient region of flight because a decrease in speed requires increased thrust and a resultant increase in fuel consumption. It is regarded as a "speed unstable" region of flight, because unlike normal circumstances, a decrease in airspeed due to a nose-up pitch control input will not correct itself if the controls are returned to their previous position. Instead, airspeed will remain low and drag will progressively accumulate as airspeed and altitude continue to decay, and this condition will persist until thrust is increased, angle of attack is reduced (which will also shed altitude), or drag is otherwise reduced (such as by retracting the landing gear). Sustained flight behind the power curve requires alert piloting because inadequate thrust will cause a steady decrease in airspeed and a corresponding steady increase in descent rate, which may go unnoticed, and can be difficult to correct close to the ground. A not-infrequent result is the aircraft "mushing" and crashing short of the intended landing site because the pilot did not decrease angle of attack or increase thrust in time, or because adequate thrust is not available; the latter is a particular hazard during a forced landing after an engine failure. Failure to control airspeed and descent rate while flying behind the power curve has been implicated in a number of prominent aviation accidents, such as Asiana Airlines Flight 214. Rate of climb For an aircraft to climb at an angle θ and at speed its engine must be developing more power in excess of power required to balance the drag experienced at that speed in level flight and shown on the power required plot. In level flight = but in the climb there is the additional weight component to include, that is :::::::::: = + .sin θ = + . Hence the climb rate .sin θ = . Supposing the 135 kW engine required for a maximum speed at 300 km/h is fitted, the maximum excess power is 135 - 87 = 48 Kw at the minimum of and the rate of climb 2.4 m/s. ==Fuel efficiency==

For propeller aircraft (including turboprops), maximum range and therefore maximum fuel efficiency is achieved by flying at the speed for maximum lift-to-drag ratio. This is the speed which covers the greatest distance for a given amount of fuel. Maximum endurance (time in the air) is achieved at a lower speed, when drag is minimised. For jet aircraft, maximum endurance occurs when the lift-to-drag ratio is maximised. Maximum range occurs at a higher speed. This is because jet engines are thrust-producing, not power-producing. Turboprop aircraft do produce some thrust through the turbine exhaust gases, however most of their output is as power through the propeller. "Long-range cruise" speed (LRC) is typically chosen to give 1% less fuel efficiency than maximum range speed, because this results in a 3-5% increase in speed. However, fuel is not the only marginal cost in airline operations, so the speed for most economical operation (ECON) is chosen based on the cost index (CI), which is the ratio of time cost to fuel cost. ==Gliders==

Without power, a gliding aircraft has only gravity to propel it. At a glide angle of \theta, the weight has two components, W\cos(\theta) at right angles to the flight line and W\sin(\theta) parallel to it. These are balanced by the force and lift components respectively, so W\cos(\theta) = \frac{1}{2}\rho V^2SC_L and W\sin(\theta) = \frac{1}{2}\rho V^2SC_D Dividing one equation by the other shows that the glide angle is given by \tan(\theta) =C_D/C_L. The performance characteristics of most interest in unpowered flight are the speed across the ground, V_g say, and the sink speed V_s; these are displayed by plotting V\sin(\theta) = V_s against V\cos(\theta) = V_g. Such plots are generally termed polars, and to produce them the glide angle as a function of V is required. Polar curves are used to compute the glider's minimum sink speed, best lift over drag (L/D), and speed to fly. The polar curve of a glider is derived from theoretical calculations, or by measuring the rate of sink at various airspeeds. These data points are then connected by a line to form the curve. Each type of glider has a unique polar curve, and individual gliders vary somewhat depending on the smoothness of the wing, control surface drag, or the presence of bugs, dirt, and rain on the wing. Different glider configurations will have different polar curves, for example, solo versus dual flight, with and without water ballast, different flap settings, or with and without wing-tip extensions. For racing, glider pilots will often use water ballast to increase the weight of their glider. This increases the optimum speed, at a cost of low speed performance and a reduced climb rate in thermals. Ballast can also be used to adjust the centre of gravity of the glider, which can improve performance. ==See also==