Last Updated: Monday, November 10, 2003
Parts of this document were taken from "Model Aircraft Aerodynamics" by Martin Simons
For those of you that don’t know my background, let me introduce myself. My name is Jeff Weiss. I am the owner of Air-Kill products, a small manufacturing company in Sacramento Ca. My company was started almost 3 years ago when I became interested in small scale R/C aircraft. The 704 or 1/12 scale aircraft are of particular interest to me in that they are easy to build and do not cost a small fortune to produce. I was getting increasingly disenchanted with the "large" scale need for bigger, better and more expensive. As a child I built plastic models from the age of 6. I was also involved in a model club in High School as a control line scale model builder. Upon my enlistment in the Air Force as a heavy aircraft mechanic on B-52’s and Kc-135 aircraft, I was finally able to get into the R/C aircraft hobby. After learning to fly, in 1981, with a old broken down Carl Goldberg "Sky lark" that I found in a trash can, I was hooked for life. When I became interested in combat aircraft I did what the average Joe does when he wants to get into some thing new. I when out and got my hands on a commercially available 1/12 scale kit from my local hobby shop and started to build. When I was done I had a model of a plane that was kind of like a brick that looked like a sad excuse for a P-51. After my first launch and 2 second flight I realized that some thing was wrong. After looking over the sad state of affairs I decided that there must be a better way to do this. After all I was able to build scale looking .049 models for control line and free flight in the past that would fly without to much difficulty.
I am the guy that is not content with the accepted norm, I must be different. Some say that is a fault, but I prefer to consider it an asset. So 3 years ago I decided to go against the flow and start scratch building my combat aircraft using what ever experience that I had and what ever plans I could get my hands on. What I found was that the majority of the 704 design available at the time for balsa construction were not very scale. I was delighted to discover Gus Morfis designs because he had a wide variety of unusual aircraft. Being partial to smaller that usual aircraft My first plan that I bought from Gus was the Lavochkin La-5/7. This little aircraft was probably the worst possible choice for a new combat builder and flyer, but it was "cool". After reviewing the plans I discovered that on the whole it was a fairly good representation of the real aircraft, but it was not very scale in respect to the cowl or canopy. I realized that if I wanted a scale looking airplane I had to make my own plastic parts. After 4 or 5 plans worth of molds for parts I realized that there are other guys out there that were of the same mind as myself and wanted "scale" looking aircraft. So Air-Kill products was born. We started the company by making scale looking plastic parts for 1/12 scale models.
After networking with the 704 builders around the country, I found that many people had the impression that Gus Morfis Designed aircraft did not fly well. I had not found this to be true and needed to find out why the other pilots felt this way. I had talked with Mr. Morfis on a number of occasions and found him to very knowledgeable about aerodynamics. I guess that goes with him being a retired advanced aerodynamic engineer from Northrop. He was involved with the design of the Northrop F5E "Freedom Fighter". After about 2 years worth of R&D work and about 25 combat aircraft I think I have a good grasp of the dynamics that make a good 704 model. Now I am not an expert on aerodynamic theory by any stretch of the imagination, but what I have learned has been proven out time and time again both by myself and others who build these small aircraft with an eye trained to the details. The solutions that I put forth here are by no means the only answer to the questions that we are presented with, but again, they work. The most challenging aircraft that I have come across so far is the Bf-109F. This happens to be one of my personal favorites and when my first prototype from the Gus Morfis design failed miserably, I needed to find out why. Those of you that were at the Billings event in July, 1997 may have seen my yellow nose Bf-109G. I flew it at the event with a off brand of engine that was not much more powerful that a sick OS .15 FP and it flew good. It was not good enough to compete with, but I proved out my aircraft design principals in the most challenging environment, at a high altitude. Well any way, lets get started.
1) Fundamentals
There are laws of motion that effect aerodynamic theory. The first of these is Equilibrium. If a body is in equilibrium, then its tend to remain so. A model standing still on a table is in equilibrium unless something disturbs it by accelerating it in some direction. A moving model flying straight and level in calm air, at a constant speed and not turning is in a balanced state , or equilibrium and will have a tendency to stay that way if it is trimmed properly. The same could be said for a model that is climbing or diving at a constant speed. Equilibrium is a condition of steady motion or rest, in contrast to states of unsteady motion involving acceleration negative acceleration or deceleration.
Changing the speed or direction of flight in any way, disturbs equilibrium. It order to cause this condition a force variation is required to bring about an acceleration in the appropriate sense. The second law of motion requires that the strength of force required for any given acceleration depends on the mass of the model. Mass is not the same as weight. Weight is the force exerted by mass. A model of large mass would require greater force to disturb equilibrium to any given extent than that of a small model. But the larger mass also requires a larger force to accelerate it to flying speed, and more force to change the flight attitude. Whenever there is a disturbance of equilibrium, an acceleration or deceleration, change in direction, this mass, called inertia, opposes the change. When turning a model, inertia tends to cause the model to return to straight flight. Turning flight is a form of lateral inertia. Pulling out of a dive involves a change of direction in the vertical plane, and mass resists this change. This Inertia tends to cause the dive to continue.
The third law of motion establishes that action and reaction are equal and opposite. If a model is at equilibrium then the action and reaction forces are set as equal. Any imbalance of these forces will produce an acceleration in a given direction. When a aircraft starts it take off roll the plane is not at equilibrium, that is to say that thrust is greater than drag. The model will continue to accelerate in the forward direction until the drag of the wheels on the ground or the aerodynamic drag on the aircraft in flight causes it to fly at a constant speed. The thrust is the action force and the drag is the reaction force. In level flight the weight force acting vertically in the downward direction is opposed by the vertical upward reaction generated by the lift of the wing and other possible surfaces. If the upward reaction against the weight fails, or is reduced, the model accelerates downward. To stop the acceleration it is necessary to restore an upward reaction to equal the weight. This brings equilibrium but will not stop the descent. To do this an additional force must bring about deceleration or acceleration in the positive direction, up. All such acceleration and deceleration will be resisted by the mass of the model in the form of inertia.
A model under power and in level flight is under the influence of many forces acting on every part of it. These forces may all be added and sorted out into four general forces arranged in action - reaction pairs. These pairs are Lift (action) - Weight (reaction), Thrust (action) - Drag (reaction). In order for a model to achieve equilibrium, these actions and reaction forces must be equal. That is to say we must have a resolution of forces to gain equilibrium.
2) Factors affecting Lift and Drag
The air forces that act upon a model, arise from the properties of the air, which is said to have mass. To have a wing work, the wing must move through the air, disturbing it. In addition to the wing , all other parts of the aircraft also disturb the air and add to the total amount of energy needed for flight, but may not add any lift. The greater the expediter of energy required to generate a given amount of lift force, the less efficient the model is. The mass of the air available for a model to work on is dependent on three factors: 1) the amount of air in a given space, or the mass density of air where the model operates. 2) The size of the model and 3) The speed, or velocity of its flight.
At the fundamental level, air is a combination of gases. These gases are regarded as consisting of enormous numbers of separate molecules that are violently in motion. The temperature of a gas is the measure of this molecular motion; low temperatures are states of less molecular motion than high temperatures. It is the impact of the moving particles which creates gas pressure on objects immersed in gas. Density is the measure of the number of molecules in a given space. In low speed aerodynamics that 704 aircraft are forces to operate, it is not necessary to consider the molecular structure of the air. The medium in which models fly is a fluid. This is not to say that air is a liquid. Liquids are fluids which are almost totally incompressible, gases are compressible fluids. Model aircraft do not (as yet) fly at such speeds that the compressibility of the air needs to be allowed for. For modeling purposes, fortunately, the air may always be regarded as an incompressible fluid. Even so, significant variations of density occur. They are related to altitude and weather. At high altitudes and in hot weather, the air is less dense than near sea level when cold. Modelers operating at the higher elevations find air density does make a difference since to achieve the same air mass reactions to gain lift, their models have to fly faster. Engines and propellers may also be adversely affected.
A large model, flying through air of standard density, must create more disturbance and hence generates more air reaction, both lift and drag, than a small model, at similar speed. The wing span in relation to the model weight, or span loading, is of some importance. A large span wing at a given speed sweeps through a larger mass of air than a short wing. To gain the same reactive forces, with a larger total mass to work on, smaller accelerations are needed. Model size is most conveniently expressed in terms of wing area as opposed to span loading. Units of wing area are usually expressed in terms of square inches and wing loading in terms of ounces per sq. foot. With a model of given span and area, a larger mass of air will be disturbed if speed is high than if low. However large and fast a model may be, its ability to gain lift will depend almost entirely on the form of the wing and its angle of attack relative to the airflow. The angle of attack is measured in degrees from some more or less arbitrary reference line, usually the straight line through the extreme leading and trailing edges of the wing airfoil section or profile. In some cases, especially for an airfoil with a flat underside, such as the Clark Y, a line tangential to the under surface may be used. The angle between the reference line and the airflow at a distance from the wing is the geometric angle of attack. The aerodynamic angle of attack, i.e., the angle at which the air actually meets the wing, is almost always different. The angle of attack (both geometric and aerodynamic) of the main wing is governed in orthodox models by the relative setting of wing and tail plane. The tail plane is a small wing which may or may not contribute lift to the total, but whose main function is to trim the main plane to the desired angle of attack and hold it there. The angle of incidence of tail and wing to the fuselage must be distinguished from the angle of attack to the air. The fuselage itself may not be aligned with the airflow. The term angle of attack is reserved for the angle of wing or tail airflow, and angle of incidence refers only to the rigging angle of such surfaces relative to some datum line on the drawing board. This convention is not always observed.
Almost all ordinary combat airplanes are 'tandems' in that they have two wing-like surfaces disposed one behind the other and set at different rigging angles relative to one another. The relative areas and spans of these surfaces are matters of the designer's choice. Whether one wing or the other carries most of the load or all of it is a matter of trim and center of gravity position. If one of the pair of wings carries no load or very little, it functions only as a stabilizer and control surface and may then be very small relative to the main load-carrying wing.
The efficiency of a wing is influenced greatly by its airfoil section or profile, which has some degree and type of camber and some thickness . Fuselages and other similar-shaped components of a model also produce some lift force, depending again on their shape and angle of attack. However, a fuselage does produce forces analogous to lift which affect the stability of the model, almost invariably in ways that oppose the efforts of the stabilizer to hold the mainplane at a fixed angle of attack. For level flight,
the total lift force generated by a model must equal the total weight, so it is possible to write:
Total Lift = Total Weight, or L = W (Action = Reaction).
This will not apply exactly if the model is descending or climbing. The factors affecting lift force are model size or area, speed of flight, air mass density and the airfoil-plus-trim factor, and the lift coefficient or CL. For convenience, designers adopt a convention which allows all of the very complex factors of wing trim and shape to be summed up in one figure, the coefficient of lift. This tells how much the model as a whole, or any part of it taken separately, is working as a lift producer. In every case, an increase in one of these factors, greater area, more speed, increased density or higher lift coefficient, will produce a larger lift force. It is to be expected that when a formula for lift is worked out, it will include all these factors. In mathematical language,
Lift = some function of p, V, S and CL p = Area S = Air density
V = Speed CL = Lift coefficient
The standard formula for lift, which arises out of the basic principles of mechanics and the pioneer work of Daniel Bernoulli in the eighteenth century, is
L = 1/2 x p x V2 x S x CL
It is not particularly important for modelers to know this formula but it is necessary to see how the various factors in the lift equation are interdependent. For a model to be capable of level flight, the lift must equal the weight. If the model's weight increases (as when it Tums out heavier than expected), a larger lift force will be needed to support it. Some item on the right hand side of the equation, or more than one of them, must be increased. The modeler has no control of air density, p. That is to say, we can’t control the elevation we fly at. The model could be re-trimmed, increasing the wing's angle of attack to get a higher CL . More wing area might be added, although this would add mass and increase the speed of flight and possibly increasing the stall speed.
Since V is squared in the formula (multiplied by itself), a relatively small increase in V yields a large increase in lift force other things being equal. This is the most compelling factor for the use of higher performance engines. The faster the plane accelerates the faster lift is generated to support the weight and mass of the model. It follows from this that a heavy model (of given area, trim, ) has to fly faster than a light one. However, to increase V takes energy and in an extreme case the engine of the model may be incapable of giving sufficient power to sustain flight. In such a case, if launched from a height the model would descend at some angle even with engine at full power. Here also is a good argument against low power type engines.
The preceding speaks loudly to the set up of a 704 combat model. Take note that when we talk about the CL of a airfoil, I am referring to the properties of the airfoil used on the Air-Kill designs. All airfoil designs have very different CL characteristics. A semi symmetrical airfoil is an airfoil with some measure of camber, that is to say that the bottom of the airfoil aft of the center of pressure is not the same as the top of the airfoil. This is referred to as camber. In order to get an acceptable CLfrom our airfoil a main wing incidence of 2 to 3 degrees is necessary for proper flight. The NACA 64A series airfoil we use is of a laminar design and is quite efficient in the area of CL.
The importance of weight relative to wing area is apparent from the above. The wing loading, often written W/S and expressed in (ounces per sq. ft.), is the easiest way of portraying this relationship. The weight of model, neglecting small changes caused by fuel consumption, is constant during on flight. The speed at a given trim (angle of attack) will depend entirely on the wing loading.
When the air meets any body, such as a wing, it is deflected over the surfaces. Above and below a wing there is a complex variation of velocity and pressure. For positive reaction, which is the basis of lift, there must be a positive difference in total pressures on top and bottom surfaces. The air over the upper surface is therefore made to flow over a longer route, so that it moves faster than that taking a shorter route below. These effects are felt both ahead of and behind the wing. The pressure difference
between the two surfaces may be increased up to a point by increasing the angle of attack, or increasing the camber or both. There is a very definite limit to this. If either the angle of attack or the camber is increased too much, the streamlining breaks down and the flow separates from the wing. Flow separation not only creates a great deal of drag, but also changes markedly the pressure difference between upper and lower surfaces. The lift force is drastically reduced, the wing is stalled. Flow separation on a smaller scale is common.
It is hardly ever necessary to calculate the actual drag of model components. The main thing is to know how drag is caused and how to reduce it. Modelers quite often speak of increasing lift by changing the trim or using a different wing section. In level flight the lift force equals the weight and this remains true after the trim or airfoil change just as before. Hence although the lift coefficient, may have been increased, the lift force remains equal to the weight in level flight. Every change of this kind however, does change the drag of the aircraft. If the drag is regarded as the inevitable price paid for keeping a given model in the air, reducing the drag price always makes for a more efficient flight.
Induced drag is now called Vortex drag because it is associated with the rotating vortices which trail behind any wing, or any surface, which is yielding aerodynamic lift. The appearance of the vortices is directly associated with the lift: the higher the lift coefficient of a given wing, the more significant is the effect of the vortices. Since when flight speed, V, is low, a given model must work at a higher lift coefficient than when V is high, the induced drag increases as the velocity decreases. (Mathematically, vortex induced drag is proportional to L/V .) This is the major, though not the only cause of the reduction of lift to drag ratio at low speeds.
Form or pressure drag is caused by the total of all the pressure variations over a body as the air flows round it, and skin friction or viscous drag is caused by the contact of the air with the model's surfaces. Although it is useful to separate these different types of drag for purposes of study, it is clear that they almost always occur together. For instance, wings will produce both form drag and skin friction in addition to vortex drag. The relationship between skin drag and form drag is particularly close: the two affect one another. For example, skin friction is very much governed by the speed of the air flow, and the speed of the local flow next to the skin is mainly determined by the shape of the body as a whole. For this reason, particularly when wings are concerned, skin friction and form drag are commonly taken together and termed profile drag. In contrast to induced drag, skin friction and form drag are both directly proportional to V . Thus, as the induced drag falls with rising speed, the form drag and skin drag rise, and vice versa.
3) Scale effect and the boundary layer
The most important differences between model and full-sized aircraft aerodynamics can be attributed to the boundary layer, the thin layer of air close to the surface of a wing or any solid body over which the air flows. Two properties of air, its mass and its viscosity, determine the behavior of the boundary layer. Viscosity may be roughly described as the stickiness of any fluid. Treacle and glycerin are highly viscous at normal temperatures. Cream and water are less viscous, air and other gases are less viscous still. The viscosity, like the density of air, is beyond control for practical purposes in model aerodynamics. Like air density, it does vary with temperature and air pressure. Inertia opposes change of direction or velocity. Viscosity resists shearing flows and tends to keep the fluid in contact with surfaces. In situations where fluid in the boundary layer over a surface is accelerating or decelerating, forces arising from mass and from viscosity interact, sometimes reinforcing one another, sometimes in mutual opposition. With model wings, at low speeds, viscous forces become relatively more important. A very small wing operates in a fluid which seems relatively much more viscous than the air does to the wing of a larger wing. It cannot be expected that a model wing, even one made to exact scale from a full-sized prototype, will behave in exactly the same way as its larger counterpart. Unfortunately such scale effects almost invariably work to the disadvantage of the smaller aircraft.
Experimental work shows that there are two distinct types of flow, laminar and turbulent. These may change from one to the other according to particular conditions. Which type of flow prevails in the boundary layer at any point depends on the form, waviness and roughness of the surface, the speed of the mainstream measured at a distance from the surface itself, the distance over which the flow has passed on the surface, and the ratio of density to viscosity of the fluid. A variation in any of these factors can bring about a change in the boundary layer. Combining all these variables except surface condition, into one figure, yields the Reynolds number. The formula for Reynolds number is:
Reynolds Number = Re = Density/ Viscosity x Velocity x Length
or
for our use in models : Re = 6363 x V x L
where 6363 is equal to the complex equation
and V and L are in units of ft/sec and feet
It is important to remember that the chord of a wing tip is usually smaller than the root, so the Re is less. For the example model with Re average about 68000, the tip chord might be 0.08 meters and the root 0. 12. so the Re at each would be about 48000 and 81000. This is of special importance for the phenomenon of wing tip stalling in models. No model flies at constant speed for long. Each change of speed alters the Re, in simple proportion. The faster the flight, the higher the Reynolds number. If the tailplane has smaller chord than the wing, the operating Re will be less for the tail.
Reynolds numbers applied to a wing chord is not the same as the Re inside the boundary layer itself. As the airflow meets the wing near the leading edge, there is a point, called the stagnation point where the flow divides, some to pass above and some
below the wing. The Re in the boundary layer at this point is zero, since the distance covered over the surface is nil. The boundary layer flow moves from the stagnation point along the skin of the wing and the Reynolds number at each point is based on the
distance of that point measured round the airfoil profile, from the stagnation point. Hence the Re in the boundary layer increases as the distance from the stagnation point increases. By the time the boundary layer reaches the trailing edge its Re will be higher,
because of the greater distance covered, than the average worked out crudely using the wing chord, which is the straight line distance from leading edge to trailing edge. Since most airfoils have different contours on upper and lower surfaces, and the wing is
normally operating at some angle of attack, the boundary layer Re at opposite stations on top and bottom will differ a little. In what follows it is important to distinguish the so-called 'critical Re' of an airfoil profile from the 'critical Re' in the boundary layer itself.
Laminar flow causes considerably less skin friction than turbulent. In a laminar boundary layer the air moves in very smooth fashion, as if each tiny layer of the fluid was a separate sheet, or lamina, sliding past the others with only slight stickiness
or viscous stress between. There is no movement of particles of air up or down from layer to layer. The lowest lamina is stuck to the surface. The layer above it slides smoothly over this immobile layer, and the next above smoothly over that and so on until at the outermost limit of the boundary layer, the last lamina of all is moving almost at the speed of the main stream. The total thickness of the whole boundary layer may be a few hundredths of a centimeter. It is found that the velocity increases fairly steadily from bottom to top. The laminae near the surface are creeping along, those next above move only slightly faster. It is this slow, smooth movement of the layers near the surface that reduces the skin friction. But because these layers are so slow, and receive little traction from the main stream, they are all too easily brought to a standstill.
Small surface imperfections such as rough spots, blobs of paint, unsanded foam cut surface, flaws in covering, or bumps caused by protruding spars; etc., tend to disturb the laminar boundary layer, but at low boundary layer Reynolds numbers (i.e., near
the leading edge of the wing), viscosity tends to damp down the disturbances and the laminar flow successfully over-rides them. Low flying speeds and small dimensions encourage the formation of laminar boundary layers on the leading edges of model wings. This is a good quality for our 1/12 scale models. Even when the surface is not perfect, and no surface ever is, the boundary layer will initially be laminar. As the flow continues to move over the surface, the boundary layer Re rises with distance covered, and the damping effect of the viscosity becomes progressively less. Somewhere a critical point will be reached at which the small air ripples caused by surface irregularities just manage to maintain themselves without being damped out, and a small distance behind this point any minute disturbance will overcome the damping effect altogether. A distinctly wavy or rough surface will cause this sooner, i.e., at a lower Re.
The laminae break up rather sharply and the flow makes a transition to turbulence point or narrow zone on the surface where this occurs is the transition zone, and it is associated with a critical boundary layer Reynolds Number. At higher b.l. Re (that is,behind this zone on the wing) the boundary layer will be turbulent. This condition is undesirable in that it is what causes the wing to stall, or the lift coefficient is reduced. Because the Re is small at launch and also the CL is low, an irregular wing shin surface can cause poor stall characteristics and may promote tip stalling of the wing.
In a turbulent boundary layer there is no tidy system of sliding layers. Instead air particles move with a good deal of freedom, up and down as well as in the general direction of the main flow. A very smooth surface, free from dirt, waves and other flaws, may delay transition. Transition on such surfaces moves aft, the critical Re in the boundary layer is high. A rough surface, or one with relatively large waves or bumps, brings transition forward, reducing the critical Re. For each type of surface there is a critical boundary layer Reynolds Number which for a given speed of mainstream flow is reached at some particular point. If the mainstream flow speeds up, the critical Re remains the same but it is reached earlier; i.e. the transition point or zone moves forward as speed rises, and back as speed is reduced. With full-sized aircraft transition usually takes place quite near the leading edge of wings, unless special airfoils and very smooth surfaces, or other devices such as boundary layer suction, to remove the turbulent layers as it forms, are used. With models laminar flow tends to persist, which at first seems to give such small wings an advantage in terms of drag. Unfortunately other factors arise because of changes of pressure associated with the generation of lift by the wing. The fact that when the Re is higher when the transition point is farther back on the wing, has caused Air-Kill to develop a laminar flow type airfoil. Our experimentation has shown that higher angles of attack can be maintained at lower speeds with out the danger of tips stalls being increased. That is not to say that we have eliminated them by any means, just reduced them.
When a wing is operated at a angle of attack that will cause the critical Re to be low, the laminar flow will lift from the skin of the wing. The area under the laminar flow and above the wing skin is referred to as a separation bubble. Within the separation bubble there is a local, detached circulation of flow with the layers of air nearest the skin flowing forwards. A very flattened vortex forms, extending spanwise. It has also been found that cross-vortices develop in the boundary layer behind the bubble, aligning themselves more or less chordwise. Laminar separation bubbles are almost always present on model aircraft wings, often despite efforts to prevent their appearance by use of turbulators. They occur also on full-sized sailplanes and other small, slow-flying aircraft, though with less serious effects. The lower the Reynolds number, the larger the effect of the separation bubble on the total drag of the wing. Sometimes the separation bubble may be 40% of the wing chord in extent, the flow separates over the whole middle part of the upper surface, but re-attaches before the trailing edge. At high angles of attack the minimum pressure point on many airfoils moves forward and the bubble follows close behind, sometimes becoming shorter. The turbulent boundary layer after the bubble may then not have sufficient energy to enable it to remain attached completely, and it may separate somewhere before the trailing edge.
As the angle of attack increases further, the separation point moves almost to the leading edge, and eventually the 'bubble' bursts. This is how most model wings stall . The direct result of the low Reynolds number is an early stall.
4) Basic model performance problems
Aspect ratio is by far the most important factor in reducing vortex drag, but some model aircraft designers throw away part of the advantage gained from high a.r. by carelessness in detail. The aerodynamic or effective span of any wing is always slightly less than the physical length of the surface, because the tip vortex leaves the wing slightly in-board of the tip. A bad choice of tip shape, or a bad planform, or a wing with too much or too little twist (variation of rigging angle from place to place), reduces the effective wing span: the wing will behave as if it were smaller in both area and aspect ratio. The factor 'k' in the induced drag equation will enlarge.
THE RECTANGULAR WING
The easiest type of wing to build is one with rectangular plan. All the ribs are identical and there are no awkward joints in leading or trailing edge members. Such a planform is not the best aerodynamically, the basic reason being that some parts of such a wing are underemployed, not carrying their fair share of the model's weight. The circulation of air and vortex strength over one part of a wing influences the direction of flow over the adjacent parts and changes the local angle of attack. With a rectangular wing the tip vortex is strong and hence the downwash near the tip large. The closer a segment lies to the tip, the more it is influenced by the vortex. The section angle of attack near the tip, is reduced and almost zero. Thus, although the wing chord is constant, the load carried by each chordwise section falls off sharply towards the tips. The wing, even with no geometric twist, or washout, works at reducing aerodynamic angles of attack over the whole outer span, with the result that the load distribution resembles that sketched in Figure 6.1a. Assuming the wing is of constant airfoil section throughout, the maximum possible section , at each point is the same. Since, however, the tips are at a lower angle of attack, they are still well below the stalling angle when the roots reach it. The rectangular wing thus has an inherently safe stalling characteristics, the wing in the center stalls while the tips are still lifting. There is no tendency for a tip to drop first. If the model is radio controlled, the ailerons remain effective over the outer sections even when the center is on the verge of stalling. Such wings need no geometric washout, but this is at a cost in terms of effective wing loading. If some of the area were taken from the tips and distributed over the central portions of the wing, the wing as a whole would stall later.
THE STRONGLY TAPERED WING
The converse of a rectangular wing is one such as that shown in Figure 6.1b, strongly tapered with tips almost pointed. This is not only very inefficient but dangerous. The strength of downwash over the various parts of such a wing is such that the local angle of attack increases towards the tips, where the area is smaller. There is an aerodynamic 'wash-in', the tips are over-loaded and stall first, indeed, with a wing like that sketched, they would be almost permanently stalled.
The narrow outer panels are called upon to provide far more lift than their section c max. permits, while the roots contribute little. The model would fly better if its ends were cut off altogether, squaring the tips.
WASHOUT
The strongly tapered wing does possess one advantage. Because it has a very broad and thick root, it may be very lightly built without loss of strength. The tip stalling problems were avoided by giving the whole wing a marked twist or wash-out to reduce the geometric angle of attack over the outer panels by approximately the amount needed to equalize the downwash across the span. This tended to distribute the load more in proportion to the area and so reduced the vortex drag. The result was an efficient wing, but at only one airspeed.
At the designed speed, the whole wing works at roughly constant aerodynamic angle of attack, but at any other speed the distribution changes. In particular, as speed increases, the wing tips reach their local zero angle of attack quite soon as the average angle of attack of the whole wing decreased. At any higher speed than this, the outer wing panels actually operate at negative angles of attack to the local airflow, and begin to 'lift' downwards. Although this lift force is directed down, the resolved drag component is still directed aft. Thus, not only will the tips of these highly twisted wings throw extra down loads onto the rest of the wing, but they will add vortex drag. More importantly, as the speed is increased, the profile drag at the tips, operating at negative angles of attack, will rise rapidly. Too much wing twist, introduced to cure a bad choice of planform, results in a 'one speed' wing. This is not for any type that needs to fly at varying speeds. Wing twist renders the model more sensitive to slight trimming errors. A small departure from the idea airspeed causes a disproportionate rise of drag. Washout often proves very useful in preventing dangerous tip stalling on all models, particularly for scale types where the wing of the prototype is strongly tapered. Washout also aids aileron control at low speeds.
THE ELLIPTICAL WING
Mathematical analysis and experiment show that the only type of wing that will produce, at all speeds, constant down wash and a load distribution exactly matching the area is one with elliptical planform distribution.The effective angle of attack everywhere is the same and reached simultaneously along the entire span. This follows from the equal distribution of load, area for area, of the wing. In practice, such a simultaneous stall is rarely achieved, since the wing is usually slightly yawed or one wingis low prior to the stall, and the elliptical planform will then appear to cause tip stalling of a mild kind.
Tip stalling is also encouraged by the lower Re of the outer wing. To prevent this an increase of outer chord above that of the pure ellipse is needed. With all tapered wings on models, the tip chord should error on the generous side to avoid tip stalling
caused by scale effects and laminar separation.
The airfoil section at the tip should normally be thinner than at the root, for the same reason. Whatever the planform of the model, serious losses occur if there are gaps through the wing at any point. These often do appear in flight, particularly on large sailplanes, where the wings flex and work slightly apart at rigging joints. Through such gaps the air flows from the high to the low pressure side of the wing, creating turbulence and reducing lift. Control gaps have similar effects. All such leakage's should be carefully sealed.
5) Airfoil sections and camber
Quite often modelers draw out their own airfoils freehand or with the aid of the simplest drawing instruments. Such apparently casual methods can yield good results if informed by a good deal of experienced judgement. The airfoils produced in these ways are very orthodox. They resemble forms that have been in widespread use for many years, and these prototypes were originally designed under sound theoretical principles. Modelers frequently modify airfoils in rather arbitrary ways. Sometimes the upper surface of some well-known profile is used, but with a flat undersurface to make the wing easy to build. This has unpredictable effects on the profile; it is changed in both camber and thickness form. Less-intentional changes occur on the drawing board or in the workshop. Profiles may be inaccurately enlarged from drawings in magazines; a commercially produced leading edge member may be used, although it does not quite fit the profile as designed, a moment's too much rubbing with a sanding block can alter the shape of wing ribs quite a lot, and so on. For these reasons modelers are rightly doubtful of theories which seem to demand a wholly unrealistic standard of craftsmanship. However, while for the smallest and slowest-flying models, traditional structures with flimsy covering sagging between ribs and stretched over protruding spars seem likely to be best both aerodynamically and structurally, theory does suggest the possibility of considerable improvements for larger and faster models, if attention is given to greater accuracy of wing surfaces.In designing airfoils it is usual to consider the effects of camber and thickness form separately. This is justifiable only up to a point. The detailed airflow over the wing is affected equally by both camber and thickness, so both need to be considered simultaneously. Modelers sometimes have mistaken ideas about camber. The so called semi- symmetrical profile is a cambered section and the camber may vary greatly from one such airfoil to another, depending on the shape of the camber line itself in combination with the thickness form. If a symmetrical airfoil is at zero angle of attack, it yields no lift, whereas a cambered one will lift when its chord line, i.e. the straight line from extreme leading edge to trailing edge, is parallel to the general airflow.
Assuming a nearly elliptical planform, the wing roots, because of the greater camber there, will reach their stalling angle before the tips. This is good in the sense that it prevents tip stalling. At high speeds, however, when the roots are still lifting, the tips will already be close to their aerodynamic zero. The lift distribution will not be elliptical, and at some speed the tips will begin to bend downwards like a wing with marked geometrical washout . To restore elliptical lift distribution, the tips should really be twisted the other way (wash-in), which will unfortunately cause tip stalling because the less-cambered profile has a lower c maximum. Many models have been built with reduced camber at the tips plus a few degrees of washout.
This combines both aerodynamic and geometric washout; the total effect may be as much as six or seven degrees of aerodynamic twist. The tip stall is controlled, but the efficiency suffers. If, instead of camber decreasing at the tips, it is increased, or decreased at the roots, the tips will tend to stall first, which is highly undesirable. However, if the aerodynamic twist or 'wash-in' caused by the in creased tip camber is counteracted by an equal geometric twist or washout in the opposite direction, the result is excellent. If, for example, the difference in absolute zero of the airfoil at the wing root and that at the tip is two degrees, with the more cambered form at the tip the geometric twist should be two degrees washout or, to be on the safe side, a little more. The whole wing then reaches its aerodynamic zero at the same angle. There is no tip stall, because the more cambered profile has a higher lift measured from the aerodynamic zero and stalls later. Hence the root reaches stalling angle first. Ok after all of this what did we say. The end result is that we want to have a combat aircraft with the following characteristics:
Airfoil = Laminar flow type with 2 to 3 degrees of incidence at the root
Washout = Should equal in angle the amount of incidence.
Horizontal tail = Set at a positive incidence of 1 to 2 degrees to maintain the main wing at the proper angle of attack when the fuse is at its minimum drag angle. This will vary do to wing and stab relationships in span, cord and tail moment length.
Engine = Should have the power level to accelerate the airframe above stall as soon as possible.
Control movement = Should be kept to an absolute minimum to retard over controlling possible stall at launch and during high speed maneuvering. Recommend 1/4" to 1/8" on elevators and 3/16" to 1/4" on ailerons.
Balance point = The balance point should be a little farther forward that the normal convention of 33%. The nose heavy model is less likely to tip stall and will be more stable under conditions likely to occur during combat. A noticeable node heavy trim will be relaxed in inverted flight, but how long can you fly inverted in a combat match?