Editing Lift-induced drag (section)

==Combined effect with other drag sources==
[[File:Drag curves for aircraft in flight.svg|thumb|Total drag is [[parasitic drag]] plus induced drag]]

In 1891, [[Samuel Langley]] published the results of his experiments on various flat plates. At the same airspeed and the same angle of attack, plates with higher [[Aspect ratio (aeronautics)|aspect ratio]] produced greater [[Lift (force)|lift]] and experienced lower drag than those with lower aspect ratio.<ref name="Fehrm"/>

His experiments were carried out at relatively low airspeeds, slower than the speed for minimum drag.<ref name="Hallion">{{cite book |last1=Hallion |first1=Richard |title=Taking Flight: Inventing the Aerial Age, from Antiquity Through the First World War |date=8 May 2003 |publisher=Oxford University Press, USA |isbn=978-0-19-516035-2 |page=147 |url=https://books.google.com/books?id=YRqV_PayIKIC |access-date=13 April 2022 |language=en}}</ref> He observed that, at these low airspeeds, increasing speed required reducing power.<ref name="Hansen">{{cite book |last1=Hansen |first1=James R. |title=The Bird Is on the Wing: Aerodynamics and the Progress of the American Airplane |date=2004 |publisher=Texas A&M University Press |location=College Station |isbn=978-1-58544-243-0 |page=23 |url=https://books.google.com/books?id=GDDQ8jQmPTEC |access-date=13 April 2022 |language=en}}</ref> (At higher airspeeds, [[parasitic drag]] came to dominate, causing the power required to increase with increasing airspeed.)

Induced drag must be added to the parasitic drag to find the total drag. Since induced drag is inversely proportional to the square of the airspeed (at a given lift) whereas parasitic drag is proportional to the square of the airspeed, the combined overall [[drag curve]] shows a minimum at some airspeed - the minimum drag speed (V<sub>MD</sub>). An aircraft flying at this speed is operating at its optimal aerodynamic efficiency. According to the above equations, the speed for minimum drag occurs at the speed where the induced drag is equal to the parasitic drag.<ref name="Clancy"/>{{rp|Section 5.25}} This is the speed at which for unpowered aircraft, optimum glide angle is achieved. This is also the speed for greatest range (although V<sub>MD</sub> will decrease as the plane consumes fuel and becomes lighter). The speed for greatest range (i.e. distance travelled) is the speed at which a straight line from the origin is tangent to the fuel flow rate curve.

The curve of range versus airspeed is normally very shallow and it is customary to operate at the speed for [[Cruise (aeronautics)#Cruise speed|99% best range]] since this gives 3-5% greater speed for only 1% less range. Flying higher where the air is thinner will raise the speed at which minimum drag occurs, and so permits a faster voyage for the same amount of fuel. If the plane is flying at the maximum permissible speed, then there is an altitude at which the air density will be sufficient to keep it aloft while flying at the angle of attack that minimizes the drag. The optimum altitude will increase during the flight as the plane becomes lighter.

The speed for maximum endurance (i.e. time in the air) is the speed for minimum fuel flow rate, and is always less than the speed for greatest range. The fuel flow rate is calculated as the product of the power required and the engine specific fuel consumption (fuel flow rate per unit of power{{efn|The engine specific fuel consumption is normally expressed in units of fuel flow rate per unit of thrust or per unit of power depending on whether the engine output is measured in thrust, as for a jet engine, or shaft horsepower, as for a propeller engine. To convert fuel rate per unit thrust to fuel rate per unit power one must divide by the speed.}}). The power required is equal to the drag times the speed.