Three Forces on a Paper Glider


Three principal forces act on aircraft and animals when gliding:

  • weight – gravity acts in the downwards direction
  • lift – acts perpendicularly to the vector representing airspeed
  • drag – acts parallel to the vector representing the airspeed

As the aircraft or animal descends, the air moving over the wings generates lift. The lift force acts slightly forward of vertical because it is created at right angles to the airflow which comes from slightly below as the glider descends, see angle of attack. This horizontal component of lift is enough to overcome drag and allows the glider to accelerate forward. Even though the weight causes the aircraft to descend, if the air is rising faster than the sink rate, there will be a gain of altitude.

Lift to drag ratio

The lift-to-drag ratio, or L/D ratio (“ell-over-dee” in the US, “ell-dee” in the UK), is the amount of lift generated by a wing or vehicle, divided by the drag it creates by moving through the air. A higher or more favourable L/D ratio is typically one of the major goals in aircraft design; since a particular aircraft’s needed lift is set by its weight, delivering that lift with lower drag leads directly to better fuel economy and climb performance.


Airplane forces


The term is calculated for any particular airspeed by dividing the measured lift by the measured drag at that speed. When measured against speed, the results can be plotted on a 2D graph. The lift curve proceeds in a straight line towards the critical angle, where it sharply drops off, and the drag curve forms a parabolic or U shape, the symmetry and shape depending on the effect of two main components of drag. The L/D curve normally forms a lopsided upside down U shape which peaks around the point of minimum drag.

As lift and drag are both proportional to the coefficient or Lift and Drag respectively multiplied by the same factor (1/2mv2S), the L/D ratio can be simplified to the Coefficient of lift divided by the coefficient of drag or Cl/Cd, and since both are proportional to the airspeed, the ratio of L/D or Cl/Cd is then typically plotted against angle of attack.


Induced drag is caused by the generation of lift by the wing. Lift generated by a wing is perpendicular to the wing, but since wings typically fly at some small angle of attack, this means that a component of the force is directed to the rear. The rearward component of this force is seen as drag. At low speeds an aircraft has to generate lift with a higher angle of attack, thereby leading to greater induced drag. This term dominates the low-speed side of the drag graph, the left side of the U.

Profile drag is caused by air hitting the wing, and other parts of the aircraft. This form of drag, also known as wind resistance, varies with the square of speed (see drag equation). For this reason profile drag is more pronounced at higher speeds, forming the right side of the drag graph’s U shape. Profile drag is lowered primarily by reducing cross section and streamlining.

As lift increases steadily until the critical angle, it is normally the point where the combined drag is at its lowest, that the wing or aircraft is performing at its best L/D.

Designers will typically select a wing design which produces an L/D peak at the chosen cruising speed for a powered fixed-wing aircraft, thereby maximizing economy. Like all things in aeronautical engineering, the lift-to-drag ratio is not the only consideration for wing design. Performance at high angle of attack and a gentle stall are also important.

Minimising drag is of particular interest in the design and operation of high performance glider (sailplane)s, the largest of which can have glide ratios approaching 60 to 1, though many others have a lower performance; 25:1 being considered adequate for training use.

Glide ratio

When flown at a constant speed in still air a glider moves forwards a certain distance for a certain distance downwards. The ratio of the distance forwards to downwards is called the glide ratio. The glide ratio is numerically equal to the Lift-to-drag ratio under these conditions; but is not necessarily equal during other manoeuvres, especially if speed is not constant. A glider’s glide ratio varies with airspeed, but there is a maximum value which is frequently quoted. Glide ratio usually varies little with vehicle loading however, a heavier vehicle glides faster, but maintains its glide ratio.

Glide ratio is also known as glide number, finesse and is the cotangent of the downward angle- the glide angle. Alternatively it is also the forward speed divided by sink speed (unpowered aircraft):

Importance of the glide ratio in gliding flight

Although the best glide ratio is important when measuring the performance of a gliding aircraft, its glide ratio at a range of speeds also determines its success (see article on gliding).

Pilots sometimes fly at the aircraft’s best L/D by precisely controlling airspeed and smoothly operating the controls to reduce drag. However the strength of the likely next lift and the strength of the wind also affects the optimal speed to fly. To achieve higher speed across country, gliders (sailplanes) are often loaded with water ballast to increase the airspeed and so reach the next area of lift sooner. This has little effect on the glide angle but increases rate of sink (and speed over ground in proportion) because the heavier aircraft achieves optimal L/D at a higher airspeed.

If the air is rising faster than the rate of sink, the aircraft will climb. At lower speeds an aircraft may have a worse glide ratio but it will also have a lower rate of sink. A low airspeed also improves its ability to turn tightly in centre of the rising air where the rate of ascent is greatest. A sink rate of approximately 1.0 m/s is the most that a practical hang glider or paraglider could have before it would limit the occasions that a climb was possible to only when there was strongly rising air. Gliders (sailplanes) have minimum sink rates of between 0.4 and 0.6 m/s depending on the class. Aircraft such as airliners may have a better glide ratio than a hang glider, but would rarely be able to thermal because of their much higher forward speed and their much higher sink rate. (Note that the Boeing 767 in the Gimli Glider incident achieved a glide ratio of only 12:1.)

During landing, a high lift/drag ratio is desirable. Some aircraft therefore employ flaps, to increase their performance at lower speeds. Experiments with lifting bodies show that a lift/drag ratio below about 2 makes landing very difficult because of the high rate of descent.

The loss of height can be measured at several speeds and plotted on a “polar curve” to calculate the best speed to fly in various conditions, such as when flying into wind or when in sinking air. Other polar curves can be measured after loading the glider with water ballast. As mass increases, the best glide ratio is achieved at higher speeds. (The glide ratio is not increased.)


Soaring animals and aircraft may alternate glides with periods of soaring in rising air. Five principal types of lift are used: thermals,ridge lift, lee waves, convergences and dynamic soaring. Dynamic soaring is used predominately by birds, and some model aircraft, though it has also been achieved on rare occasions by piloted aircraft.

Examples of soaring flight by birds are the use of:

  • Thermals and convergences by raptors such as vultures
  • Ridge lift by gulls near cliffs
  • Wave lift by migrating birds
  • Dynamic effects near the surface of the sea by albatrosses

For humans, soaring is the basis for three air sports: gliding, hang gliding and paragliding.

Originally posted 2012-04-07 21:29:49.

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