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 θ, the weight has two components, at right angles to the flight line and parallel to it. These are balanced by the force and lift components respectively, so and . Dividing one equation by the other shows that the glide angle is given by tan θ = /. The performance characteristics of most interest in unpowered flight are the speed across the ground, say, and the sink speed ; these are displayed by plotting .sin θ = against .cos θ = . Such plots are generally termed polars, and to produce them the glide angle as a function of is required. One way of finding solutions to the two force equations is to square them both then add together; this shows the possible , values lie on a circle of radius / . When this is plotted on the drag polar, the intersection of the two curves locates the solution and its θ value read off. Alternatively, bearing in mind that glides are usually shallow, the approximation cos θ ≃ 1, good for θ less than 10°, can be used in the lift equation and the value of for a chosen calculated, finding from the drag polar and then calculating θ. The example polar here shows the gliding performance of the aircraft analysed above, assuming its drag polar is not much altered by the stationary propeller. A straight line from the origin to some point on the curve has a gradient equal to the glide angle at that speed, so the corresponding tangent shows the best glide angle ≃ 3.3°. This is not the lowest rate of sink but provides the greatest range, requiring a speed of 240 km/h (149 mph); the minimum sink rate of about 3.5 m/s is at 180 km/h (112 mph), speeds seen in the previous, powered plots. Sink rate A graph showing the sink rate of an aircraft (typically a glider) against its airspeed is known as a polar curve. Polar curves are used to compute the glider's minimum sink speed, best lift over drag