Aerodynamics basics: How an airplane flies
| Abstract | This article wants to present a comprehensive and practical introduction to aerodynamics mainly for pilots, either model RC or full size airplanes. |
| Author | Joan C. Abelaira |
| Literature |
Deeper information can be found in these text books:
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The basic four forces
For an airplane to be in the air, there must be some force upwards to cancel gravity action, weight. This force is called lift and is generated by the wing(s) as airplane moves. Airplanes (other than gliders and alike) have some kind of propulsion (propeller or jet) creating a force in the forward direction, called thrust, necessary for the airplane to move. Finally, as elementary physics tells us, if a plane keeps its speed constant (no acceleration) and there is a forward force there must be another force equal in magnitude but in the opposite direction, called drag. Drag can be seen as the resistance force, as when we take out our hand out of the car window, but most of the drag is generated by the wing to create lift.
| These are the forces in horizontal, steady flight (no acceleration). Thrust equals drag and Lift equals weight. If thrust were greater than drag, the airplane will speed up, and if lift were greater than weight the aircraft will ascend but keeping itself horizontal. |
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In a climb, as airplane axes change their orientation, lift, thrust and drag also do, as they depend on geometry. But weight vector remains pointing earth's center and tilts with respect to aircraft axes. Following elementary physics, weight is decomposed into aircraft axes. A part of weight is added to drag and therefore more thrust is needed, and less list is needed to balance the aircraft. |
Axes and turns
A car or a ship moves (most of the times) on a plane (the road or the sea surface) and can only turn around one axis. This is called a 3 degrees of freedom movement (two linear speed components plus a rotation). But with an airplane there are three speed components plus three possible turns and it's called a 6 degrees of freedom movement.
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Standard convention about axes is:
Turns around these axes are called:
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Control surfaces
For an airplane to generate lift only the main wing is needed. But for purposes of stability and control, the empennage (the tail) is also necessary. In a conventional airplane, there are two planes at the tail, a vertical one (the fin) and an horizontal pair, like small wings (called stabilizer).
The fin has the effect of a weathercock, avoiding the aircraft to yaw to one side. The stabilizer helps keeping the desired pitch angle of the nose for horizontal flight, climb or dive.
All planes (wings, fin and stabilizer) have movable parts (control surfaces), controlled by the pilot (or autopilot) to control the desired flight condition and making maneuvers. Picture below shows almost all control surfaces in a commercial airliner (Boeing 737).
Fortunately, the basic control surfaces are less:
- Ailerons: located at the trailing edge of the wings. They move opposite each other (if the one in the left wing raises, the other lowers). Ailerons cause banking (roll) to make turns. In small sport airplanes is controlled with the lateral movement of the stick.
- Flaps: there are many kinds of flaps, being the most common in the trailing edge of wings. They resemble ailerons, but their function is completely different. Flaps are always closer to the fuselage than ailerons. They move only downwards and in the same way with respect each other. They are used to create more lift and being able to takeoff and land at reduced speed.
- Rudder: it's in the vertical fin and its movement creates a yaw. But an airplane turn is not usually made with the rudder. Rudder is used to cancel a cross wind drift and to coordinate banking in turns. In small airplanes, rudder is controlled with two pedals.
- Elevator: they are in the stabilizer planes and move up and down and also both in the same direction. Elevator is used to change and control pitch angle, and is controlled with the forward-backward movement of the stick.
Lift and drag of airfoils
If we look at an airplane wing from the tip, we observe a more or less curved shape, round at the leading edge and sharp at the trailing edge. That shape is called airfoil and has the magic of creating lift and drag. There is (or can be) a difference between a wing and an airfoil. Usually, a wing is tapered (the root is wider than the tip) and there is something called twist (the tips are slightly turned down). This makes the actual wing a mix of a range of airfoils, but we still can think of the whole wing as an airfoil.
There are whole thick books devoted to explain how a wing moving through a fluid creates lift. But in this article I skipped all the science and just present the facts. A wing has a reference line from the leading edge to the trailing edge but the movement will make a certain small angle with this reference line. This angle is called angle of attack and is the main variable that tells us how much lift and drag will the wing produce.
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Lift and drag forces are actually distributed all along the airfoil, but they can be mathematically concentrated at one point (its position also depends on the angle of attack) called CP (Center of Pressure). |
There are thousands of different airfoils. Different research institutes and administrations (NACA, Göttingen, Eppler, Benedek, etc.) keep catalogues with airfoil shapes and data for designers. Airfoil data basically contains two coefficients, called CL and CD (coefficient of lift and coefficient of drag, respectively). They are usually presented in graphs like the one below. X axis is attack angle.
Note that lift coefficient increases linearly with increasing angle of atack but there is a point that suddenly decreases (with some airfoils really abruptly). This point is very important, even for pilots. It's called the stall of the wing. Drag coefficient, as all bad things, always increases with attack angle and somehow in a quadratic way. The graph on the right shows just the ratio CL/CD which is important to choose an economical speed to fly and also for gliders.
But these coefficients aren't yet the lift and drag force. There are three factors in between. One is constant and is the wing area. the bigger the wing the more lift with the same CL. The second one is air density and can be considered constant for small airplanes (there is a slight variation of a few percent with temperature and pressure). The third factor is very important and is the square of the speed. As the pilot can control the airplane speed can also modify lift with it.
For those loving maths, equations are:
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L, D : Lift and drag forces (N) CL, CD : Lift and drag coefficients (no units) ρ : air density (kg/m3) S : wing surface (m2) V : speed (m/s) |
The stall
The stall is the sudden drop in lift because of the disruption of the airflow through the airfoil. Air moving through the upper part of the wing is deflected down by the wing curvature. When all is ok, air moves all the way along the airfoil to the trailing edge. As the attack angle increases, when air stream loses its energy, stops moving downwards and a turbulence is set. Theory, practice and accidents prove that a stalled wing has much less lift. Pictures below show the airflow in three conditions (last one is stalled).
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Pilots know the stall speed of the aircraft and, specially when landing, always keep a safety margin (for example 1,3 Vs where Vs is the stall speed).
Longitudinal control. Elevator and thrust
With this controls the pilot make the airplane to ascend, flight level or descend. There is a common misconception which is thinking the airplane goes where the nose points to. Forget this and you will see it clear. Elevator just sets the nose pitch angle by lowering or raising the tail. Pitch angle is controlled just to have more or less lift coefficient, not only to look at the sky or the ground. Then (or before), engine power is set according to the the speed and vertical speed desired.
For example, when approaching an airport, speed is low and nose points up to have the maximum lift coefficient and be able to fly at low speed. But the engine is set at such a power that actually the plane descends. Concorde's famous nose moving down for the pilots to see the runway when landing shows how a plane can descend while having the nose pointing up.
Another misconception is to think attack angle is the angle the wing form with the horizontal plane. If a plane descends at an angle of 15º and pitch angle is 5º, then attack angle is 20º. If a plane climbs at 15º a pitch angle of 30º means an attack angle of 15º and the wings are not stalled.
Lateral stability. Ailerons
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Ailerons are used to bank the airplane to one side and make a turn, a little bit the way people do in a bicycle. Ailerons always move in opposite directions, the wing with the aileron lowered will have more lift (and drag) and the other, with the aileron rised, will have less lift. The reason why a banked plane turns can be explained again with some physics. As lift makes a right angle to the wings, lift force splits in two components. The horizontal lift component is that makes the plane to turn (remember that force creates acceleration that is just speed change, not only in magnitude but also in direction). It is important to note here that the vertical component of lift is reduced. This means that in a turn, the plane tends to descend unless corrected with elevator and/or throttle. |
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There are two more subtleties about banks and turns: adverse yaw and turn coordination.
Adverse yaw
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In a turn, even if the bank angle is constant and ailerons remain flat, the wing coefficients are the same but the outer wing travels faster and creates more lift and drag. This difference in drag force makes the plane to yaw opposite to the intended turn. Pilots always apply some rudder to the turn side just to compensate adverse yaw. Some airplanes have a compensation system that applies some rudder when turning. |
Turn coordination
When an airplane turns, as in a car, we feel two forces: gravity, always downwards to mother Earth and the reaction force of centripetal force, the centrifugal force (a fictitious force according to Physics, but a force that push people and things out of the turns). The resultant force is not vertical but makes an angle to one side. Turns in roads are sloped for the passengers in cars still feel the tilted force right into the pavement.
In a plane, when the resultant force of gravity (lift) and centrifugal force goes right to the plane's floor, there is a feeling of 'nice, safe' turning. This is a coordinated turn and is done by applying the right amount of rudder. If there is a mismatch in these forces, either a skid (feeling forces outside the turn) or a slip (feeling forces into the turn) happens. First one can be funny, second one is a little bit squeary.
Directional stability. Rudder
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Rudder effect is to create a yaw. As it is not used for turning, it's almost a secondary control (despite some RC model airplanes use rudder for turning and have no ailerons). Main use of rudder is to cancel a cross wind drift, as well as to coordinate turns. For propeller driven airplanes, because of some effects of the propeller and airstream, an airplane can have a tendency to yaw that is compensated with the rudder. If only rudder is applied to yaw an airplane, as it turns flat and the outer wing goes faster it has more lift and raises, thus creating a bank that increases the turn rate. That's the way of turning for model airplanes without ailerons. |
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