Aerodynamics is the study of forces and motion of objects through the air. Basic knowledge of the aerodynamic principles is highly recommended before getting involved in building and/or flying model aircraft.

      A model aircraft that is hanging still in air during strong winds may be subject to the same aerodynamic forces as a model aircraft that is flying fast during calm weather. The aerodynamic forces depend much on the air density.

      For example, if a glider glides 25 meters from a given altitude during low atmospheric pressure, it may glide 40 meters during high pressure. The air density depends on the atmospheric pressure and on the air temperature.

      The air density decreases with increasing of the air temperature and/or with decreasing of the atmospheric pressure. The air density increases with decreasing of the air temperature and/or with increasing of the atmospheric pressure.

      A flying aircraft is subject to a pressure depending on the airspeed and the air density. This pressure increases exponentially with increasing of the airspeed. The aircraft’s resistance to the airflow (drag) depends on the shape of the fuselage and flying surfaces. An aircraft that is intended to fly fast has a thinner and different wing profile than one that is intended to fly slower. That’s why many aircraft change their wing profile’s on landing approach by lowering the flaps located at the wings’ trailing edge and the slats at the leading edge in order to keep a reasonable lifting force during the much lower landing speed.

      The wings’ profile of a slower aircraft is usually asymmetric, this causes the airspeed on the wings upper side to be higher than the underside, which in turn makes the pressure on the upper side to be lower than the underside, thereby a lift force is created. The lift force of a symmetric profile is based on the airspeed and on a positive angle of attack to on-coming flow.

      The following picture shows the airflow through two wing profiles.

      The uppermost profile has a lower angle of attack than the lowest one. When the air flows evenly through the surface is called a laminar flow. A too high angle of attack causes turbulence on the upper surface and dramatically increases the air resistance (drag) this may result in an abrupt loss of lift, which is known as stall. The aircraft generates lift by moving through the air. The wings have airfoil shaped profiles that create a pressure difference between upper and lower wing surfaces, with a high pressure region underneath and a low pressure region on top.

      The lift produced will be proportional to the size of the wings, the square of airspeed, the density of the surrounding air and the wing’s angle of attack to on-coming flow before reaching the stall angle. How does a glider generate the velocity needed for flight? The simple answer is that a glider trades altitude for velocity. It trades the potential energy difference from a higher altitude to a lower altitude to produce kinetic energy, which means velocity. Gliders are always descending relative to the air in which they are flying.

      How do gliders stay aloft for hours if they constantly descend? The gliders are designed to descend very slowly. If the pilot can locate a pocket of air that is rising faster than the glider is descending, the glider can actually gain altitude, increasing its potential energy. Pockets of rising air are called updrafts. Updrafts are found when the wind blowing at a hill or mountain rises to climb over it. (However, there may be a downdraft on the other side!) Updrafts can also be found over dark land masses that absorb more heat from the sun than light land masses. The heat from the ground heats the surrounding air, which causes the air to rise. The rising pockets of hot air are called thermals.

      Large gliding birds, such as owls

      and hawks,

      are often seen circling inside a thermal to gain altitude without flapping their wings. Gliders can do exactly the same thing.

      Wing Geometry

      A cut through the wing perpendicular to the leading and trailing edges will show the cross-section of the wing.

      This side view (profile) is called an Airfoil, and it has some geometry definitions of its own as shown on the picture below. The longest straight line that can be drawn from the leading to trailing edge of the airfoil is called the Chord Line. The Chord Line cuts the airfoil into an upper surface and a lower surface. If we plot the points that lie halfway between the upper and lower surfaces, we obtain a curve called the Mean Camber Line.

      For a symmetric airfoil (upper surface the same shape as the lower surface) the Mean Camber Line will fall on top of the Chord Line. But in most cases, these are two separate lines. The maximum distance between these two lines is called the Camber, which is a measure of the curvature of the airfoil (high camber means high curvature). The maximum distance between the upper and lower surfaces is called the thickness. Often you will see these values divided by the chord length to produce a non-dimensional or “percent” type of number. Airfoils can come with all kinds of combinations of camber and thickness distributions. NACA (the precursor of NASA) established a method of designating classes of airfoils and then wind tunnel tested the airfoils in order to provide lift coefficients and drag coefficients for designers.

      Aspect Ratio is a measure of how long and slender a wing is from tip to tip. The Aspect Ratio of a wing is defined to be the square of the span divided by the wing area and is given the symbol AR. The formula is simplified for a rectangular wing, as being the ratio of the span to the chord length as shown on the figure below.

      Wing Dihedral refers to the angle of wing panels as seen in the aircraft’s front view. Dihedral is added to the wings for roll stability; a wing with some Dihedral will naturally return to its original position if it is subject to a briefly slight roll displacement. Most large airliner wings are designed with Dihedral. On the contrary the highly maneuverable fighter planes have no Dihedral. In fact, some fighter aircraft have the wing tips lower than the roots, giving the aircraft a high roll rate.

       A negative Dihedral angle is called Anhedral.

      Forces in Flight (Gravity, Lift, Thrust and Drag).

      Gravity is a force that is always directed toward the centre of the earth. The magnitude of the force depends on the mass of all the aircraft parts. The gravity is also called weight and is distributed throughout the aircraft.

      We can think of it as collected and acting through a single point called the centre of gravity. In flight, the aircraft rotates about its centre of gravity, but the direction of the weight force always remains toward the centre of the earth.

      Lift is the force generated in order to overcome the weight, which makes the aircraft fly. This force is obtained by the motion of the aircraft through the air.

      Factors that affect lift: 

      Thrust is the force generated by some kind of propulsion system. The magnitude of the thrust depends on many factors associated with the propulsion system used:

                1. Type of engine 

                2. Number of engines 

                3. Throttle setting 

                4. Speed 

      The direction of the force depends on how the engines are attached to
the aircraft. The glider, however, has no engine to generate thrust. It uses the potential energy difference from a higher altitude to a lower altitude to produce kinetic energy, which means velocity. Gliders are always descending relative to the air in which they are flying.

      Drag is the aerodynamic force that opposes an aircraft’s motion through the air.  Drag is generated by every part of the aircraft (even the engines).

      There are several sources of drag: One of them is the skin friction between the molecules of the air and the surface of the aircraft. The skin friction causes the air near the wing’s surface to slow down.

      This slowed down layer of air is called the boundary layer. The boundary layer builds up thicker when moving from the front of the airfoil toward the wing trailing edge.

      Another factor is called the Reynolds effect, which means that the slower we fly, the thicker the boundary layer becomes.

      Form drag is another source of drag. This one depends on the shape of the aircraft. As the air flows around the surfaces, the local velocity and pressure changes. The component of the aerodynamic force on the wings that is opposed to the motion is the wing’s drag, while the component perpendicular to the motion is the wing’s lift. Both the lift and drag force act through the centre of pressure of the wing.

      Induced drag is a further sort of drag caused by the wing’s generation of lift. This drag occurs because the flow near the wing tips is distorted as a result of the pressure difference between the top and the bottom of the wing, which results in swirling vortices being formed at the wing tips. The induced drag is an indication of the amount of energy lost to the tip vortices.

      The swirling vortices cause downwash near the wing tips, which reduces the overall lift coefficient of the wing. The magnitude of induced drag depends on the amount of lift being generated by the wing and on the wing geometry.

      Long wing with a small chord (high aspect ratio) has low induced drag, whereas a short wing with a large chord has high-induced drag.

      The pictures below show the downwash caused by an aircraft. The downwash from the wing has pushed a trough into the cloud deck. The swirling flow from the tip vortices is also evident.

      In order to minimize tip vortices some aircraft designers design a special shape for the wing tips.

      With drooped or raised wing tips, the vortex is forced further out. 

      However this method causes an increase in weight since they need to be added to the wing tip.

      An easier and lighter method is by cutting the wing tip at 45-degrees. With a small radius at the bottom and a relatively sharp top corner, the air from the secondary flow travels around the rounded bottom but can’t go around the sharp top corner and is pushed outward. 

      There’s also the Interference drag, which is generated by the mixing of streamlines between one or more components, it accounts for 5 to 10% of the drag on an airplane. It may be reduced by proper fairing and filleting which allows the streamlines to meet gradually rather than abruptly.

      All drag that is not associated with the production of lift is defined as Parasite drag.

      Stability Concepts

      The aircraft’s response to momentary disturbance is associated with its inherent degree of stability built in by the designer, in each of the three axes, and occurring without any reaction from the pilot. There is another condition affecting flight, which is the aircraft’s state of trim or equilibrium (where the net sum of all forces equals zero). Some aircraft can be trimmed by the pilot to fly ‘hands off’ for straight and level flight, for climb or for descent. Free flight models generally have to rely on the state of trim built in by the designer and adjusted by the rigger, while the remote controlled models have some form of trim devices which are adjustable during the flight.

      An aircraft’s stability is expressed in relation to each axis: 

      Lateral stability (stability in roll), 

       Directional stability (stability in yaw)

      And longitudinal stability (stability in pitch).

      Lateral and directional stability are inter-dependent.

      Stability may be defined as follows:

• Positive stability – tends to return to original condition after a disturbance.

• Negative stability – tends to increase the disturbance.

• Neutral stability – remains at the new condition.

• Static stability – refers to the aircraft’s initial response to a disturbance.

• Dynamic stability – refers to the aircraft response over time to a disturbance.

      A totally stable aircraft will return, more or less immediately, to its trimmed state without pilot intervention. However, such an aircraft is rare and not much desirable. We usually want an aircraft just to be reasonably stable so it is easy to fly. If it is too stable, it tends to be sluggish in maneuvering, exhibiting too slow response on the controls. Too much instability is also an undesirable characteristic, except where an extremely maneuverable aircraft is needed and the instability can be continually corrected by on-board ‘fly-by-wire’ computers rather than the pilot, such as a supersonic air superiority fighter.

      Lateral stability is achieved through dihedral, sweepback, keel effect and proper distribution of weight. The dihedral angle is the angle that each wing makes with the horizontal (see Wing Geometry). If a disturbance causes one wing to drop, the lower wing will receive more lift and the aircraft will roll back into the horizontal level. A sweptback wing is one in which the leading edge slopes backward. When a disturbance causes an aircraft with sweepback to slip or drop a wing, the low wing presents its leading edge at an angle more perpendicular to the relative airflow. As a result, the low wing acquires more lift and rises, restoring the aircraft to its original flight attitude.

      The keel effect occurs with high wing aircraft. These are laterally stable simply because the wings are attached in a high position on the fuselage, making the fuselage behave like a keel. When the aircraft is disturbed and one wing dips, the fuselage weight acts like a pendulum returning the aircraft to the horizontal level.

      The tail fin determines the directional stability. If a gust of wind strikes the aircraft from the right it will be in a slip and the fin will get an angle of attack causing the aircraft to yaw until the slip is eliminated.

      Longitudinal stability depends on the location of the centre of gravity, the stabilizer area and how far the stabilizer is placed from the main wing. Most aircraft would be completely unstable without the horizontal stabilizer. The stabilizer provides the same function in longitudinal stability as the fin does in directional stability. It is of crucial importance that the aircraft’s Centre of Gravity (CG) is located at the right point, so that a stable and controllable flight can be achieved. In order to achieve a good longitudinal stability, the CG should be ahead of the Neutral Point (NP), which is the Aerodynamic Centre of the whole aircraft.

      NP is the position through which all the net lift increments act for a change in angle of attack. The major contributors are the main wing, stabilizer surfaces and fuselage.

      The bigger the stabilizer area in relationship to the wing area and the longer the tail moment arm relative to the wing chord, the farther aft the NP will be and the farther aft the CG may be, provided it’s kept ahead of the NP for stability.

      The angle of the fuselage to the direction of flight affects its drag, but has little effect on the pitch trim unless both the projected area of the fuselage and its angle to the direction of flight are quite large. A tail-heavy aircraft will be more unstable and susceptible to stall at low speed e. g. during the landing approach.

      A nose-heavy aircraft will be more difficult to takeoff from the ground and to gain altitude and will tend to drop its nose when the throttle is reduced. It also requires higher speed in order to land safely.

      The angle between the wing chord line and the stabilizer chord line is called the Longitudinal Dihedral (LD) or decalage. For a given centre of gravity, there is a LD angle that results in a certain trimmed flight speed and pitch attitude. If the LD angle is increased the plane will take on a more nose up pitch attitude, whereas with a decreased LD angle the plane will take on a more nose down pitch attitude. There is also the Angle of Incidence, which is the angle of a flying surface related to a common reference line drawn along the fuselage. The purpose of this line is to make it easier to set up the relationships among the thrust, the wing and the stabilizer incidence angles. Thus, the Longitudinal Dihedral and the Angle of Incidence are interdependent.

      Longitudinal stability is also improved if the stabilizer is situated so that it lies outside the influence of the main wing downwash. Stabilizers are therefore often staggered and mounted at a different height in order to improve their stabilizing effectiveness. It has been found both experimentally and theoretically that, if the aerodynamic force is applied at a location 1/4 from the leading edge of a rectangular wing at subsonic speed, the magnitude of the aerodynamic moment remains nearly constant even when the angle of attack changes. This location is called the wing’s Aerodynamic Centre AC. (At supersonic speed, the aerodynamic centre is near 1/2 of the chord).

      In order to obtain a good Longitudinal Stability the Centre of Gravity CG should be close to the main wings’ Aerodynamic Centre AC. For wings with other than rectangular form (such as triangular, trapezoidal, compound, etc.) we have to find the Mean Aerodynamic Chord (MAC) which is the average for the whole wing as the drawings below: 

      For a delta wing the CG should be located 10% ahead of the geometrically calculated point as shown above. For conventional designs (with main wing and horizontal stab) the CG location range is usually between 28% and 33% from the leading edge of the main wing’s MAC, which means between about 5% and 15% ahead of the aircraft’s Neutral Point NP. This is called the Static Margin, which is expressed as a percentage of MAC. When the static margin is zero (CG coincident with NP) the aircraft is considered “neutrally stable”. However, for conventional designs the static margin should be between 5% and 15% of the MAC ahead of the NP.

      The CG location as described above is pretty close to the wing’s Aerodynamic Center AC because the lift due to the horizontal stab has only a slightly effect on the conventional R/C models. However, those figures may vary with other designs, as the NP location depends on the size of the main wing vs. the stab size and the distance between the main wing’s AC and the stab’s AC. The simplest way of locating the aircraft’s NP is by using the areas of the two horizontal lifting surfaces (main wing and stab) and locate the NP proportionately along the distance between the main wing’s AC point and the stab’s AC point. For example, the NP distance to the main wing’s AC point is: D = L · (stab area) / (main wing area + stab area) as shown on the picture below:

      There are other factors, however, that make the simple formula above inaccurate. In case the two wings have different aspect ratios (different dCL/d-alpha) the NP will be closer to the one that has higher aspect ratio. Also, since the stab operates in disturbed air, the NP will be more forward than the simple formula predicts. The figure below shows a somewhat more complex formula to locate the NP but would give a more accurate result for conventional monoplanes with wings’ AR between 4 and 9. This formula gives the NP position as a percentage (%) of the wing’s MAC aft of its leading edge.

      Stall & Spin

      One of the first questions a pilot might ask, when converting to a new aircraft type, is “What’s the stall speed?” The reason for the enquiry is that usually, but not always, the approach speed chosen for landing is 1.3 times the stall speed. Stall is an undesirable phenomenon in which the aircraft wings produce an increased air resistance and decreased lift, which may cause an aircraft to crash. The stall of the wing occurs when the airflow no longer can go around the airfoil’s nose (leading edge) and separates from the upper wing surface. It happens when a plane is under too great an angle of attack (the angle of attack is the angle between the airfoil chord line and the direction of flight). For light aircraft, without high-lift devices, is this critical angle usually around 16°. The picture below shows a stalled airfoil:

      The stall may occur during take-off or landing, just when the flight speed is low. At low speed the aerodynamic forces are smaller and if a non-experienced pilot tries to lift the aircraft at a too low speed, it may exceed the critical angle of attack and stall occurs. The rapid reduction in speed after passing the critical angle of attack means the wing is now unable to provide sufficient lift to totally balance weight and, in a normal stall, the aircraft starts to sink, but if one wing stalls before the other, that wing will drop, the plane falls out of the air. The ground waits below. Stalls may also occur at high airspeeds. If at max airspeed and full throttle the pilot suddenly applies excessive up elevator, the aircraft will rotate upwards, however, due to aircraft’s inertia, it may continue flying in the same direction but with the wings at an angle of attack that may exceed the stall angle. Stalling at high-speed gives a more dramatic effect than at low speed. This because the strong propeller wash causes one of the wings to stall first that combined with the high speed produces a snap roll followed by a spiral dive. This happens very fast causing the aircraft to dive at full throttle and unless there’s enough height for recovery, the crash will be inevitable.

      An aircraft with relatively low wing loading has a lower stall speed (wing loading is the aircraft’s weight divided by the wing area).

      The airfoil also affects the stall speed and the max angle of attack. Many aircraft are equipped with flaps (on the wing trailing edge), and a few designs use slats (on the wing leading edge), which further lowers the stall speed and allow higher angle of attack. Another factor that affects the aircraft’s stall characteristics is the location of its centre of gravity CG. A tail-heavy aircraft is likely to stall at higher airspeed than one with the CG at the right location. Aircraft that are designed for Short Take-Off and Landing (STOL) use slots on the wing’s leading edge together with flaps on the trailing edge, which gives high lift coefficient and remarkable slow flying capabilities by allowing greater angle of attack without stalling.

      The leading edge slots prevent the stall up to approximately 30 degrees angle of attack by picking up a lot of air from below, accelerating the air in the funnel shaped slot (venturi effect) and forcing the air around the leading edge onto the upper wing surface.

      The disadvantage of the slots and flaps is that they produce higher drag. Since the high lift is only needed when flying slowly (take-off, initial climb, and final approach and landing) some designers use retractable devices, which closes at higher speeds to reduce drag.

      Such devices are seldom used in model aircraft (especially the smaller ones), mainly due to its complexity and also the increasing of wing loading, which may counter-act the increased lift obtained. Another method to improve an aircraft’s stall characteristics is by using wing washout, which refers to wings designed so that the outboard sections have a lower angle of attack than the inboard sections in all flight conditions.

      The outboard sections (toward the wing tips) will reach the stalling angle after the inboard sections, thus allowing effective aileron control as the stall progresses. This is usually achieved by building a twist into the wing structure or by using a different airfoil in the outboard section. A similar effect is achieved by the use of flaps.

      The aileron drag is a further factor that may cause an aircraft to stall. When the pilot applies aileron to roll upright during low speed, the downward movement of the aileron on the lower wing might take an angle on that part of the wing past the critical stall angle.

      Thus that section of wing, rather than increasing lift and making the wing rise, will stall, lose lift and the aircraft < instead of straightening up, will roll into a steeper bank and descend quickly. Also the wing with the down aileron often produces a larger drag, which may create a yaw motion in the opposite direction of the roll. This yaw motion partially counteracts the desired roll motion and is called the adverse yaw.

      Following configurations are often used to reduce aileron drag:

• Differential ailerons where the down-going aileron moves through a smaller angle than the up-going.

• Frise ailerons, where the leading edge of the up-going aileron protrudes below the wing’s under surface, increasing the drag on the down-going wing.

• And the wing washout.

     Stall due to aileron drag is more likely to occur with flat bottom wings. Since differential ailerons will have the opposite effect when flying inverted, some aircraft with symmetrical airfoils designed for aerobatics don’t use this system.

      The picture below illustrates an example of a Frise aileron combined with differential up/down movement.

      Recovering from a stall.

      In order to recover from a stall, the pilot has to reduce the angle of attack back to a low value. Despite the aircraft is already falling toward the ground, the pilot has to push the stick forward to get the nose even further down. This reduces the angle of attack and the drag, which increases the speed.

      After the aircraft gained speed and the airflow incidence on the wing becomes favorable, the pilot may pull back on his stick to increase the angle of attack again (within allowable range) restoring the lift. Since recovering from a stall involves some loss of height, the stall is most dangerous at low altitudes. Engine power can help reduce the loss of height, by increasing the velocity more quickly and also by helping to reattach the flow over the wing. How difficult it is to recover from a stall depends on the plane. Some full-size aircraft that are difficult to recover have stick shakers: the shaking stick alerts the pilot that a stall is imminent.

      Spin

      A worse version of a stall is called spin, in which the plane spirals down. A stall can develop into a spin through the exertion of a sidewise moment. Depending on the plane, (and where its CG is located) it may be more difficult or impossible to recover from a spin. Recovery requires good efficiency from the tail surfaces of the plane. Typically recovery involves the use of the rudder to stop the spinning motion, in addition to the elevator to break the stall.

      However the wings might block the airflow to the tail. If the centre of gravity of the plane is too far back, it tends to make recovery much more difficult.

      Another circumstance that may cause loss of control is when a hinged control surface starts to flutter. Such flutter is harmless if it just vibrates slightly at certain airspeed (possibly giving a kind of buzzing sound), but ceases as soon as the airspeed drops. In some cases however, the flutter increases rapidly so that the model is no longer controllable. The pilot may not be aware of the cause and suspect radio interference instead. To reduce the flutter, the control linkages should not be loosely fitted and the push rods should be stiff. In some difficult cases, the control surface has to be balanced so that its centre of mass (gravity) is ahead of the hinge line: