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REMOTE CONTROL By BOB YOUNG Model aircraft aerodynamics Last month we dealt with the three main axes of flight and the interaction between them, and we noted that scale aircraft do not behave like full size aircraft. This month we continue with a discussion on aerodynamics. Coping with the interaction between axes has been the prime mover in the quest for computerised model encoders, but the story does not end there. Other reasons include overcoming non linearity in electronic components, non linearity in airframes, convenience, the good old fashioned (or is it new fashioned) love of "gingerbread", and the dreaded sales gimmick. The importance of this last factor must not be underestimated in the development of sophisticated equipment. At the very heart of aerodynamics lie several very simple mathematical statements and Newton's three laws of motion: The fuselage of the Grumman Panther provides about 30% of the total lift which means that the centre of gravity must be located forward of the leading edge of the wing to produce a controllable model. 88 SILCON CHIP (1). Bernoulli's Theorem. This states quite simply that the sum of the static and dynamic pressures in air must remain a constant. This is the factor that makes flight possible. (2). The "Velocity Squared" factor. This simply means that if you travel twice as fast you will generate four times as much force; four times as fast, 16 times the force. All of the major forces in aerodynamics have a velocity squared component: lift, drag, kinetic energy, centrifugal and centripetal forces. This is the factor that makes high speed flight difficult and expensive. (3). Newton's First Law. This states that if a body is in equilibrium it tends to remain so. All of the forces acting on that body are in balance and there is no tendency for it to change state or accelerate or decelerate in any direction. (4). Newton's Second Law. This states that the force required to br- ing about a change of state in the motion of any body is directly related to the mass of that body. Mass is not the same as weight. Weight is the force of gravity applied to a mass here on Earth. On Mars the weight would be less but the mass remains the same. (5). Newton's Third Law. The third law of motion establishes that action and reaction are equal and opposite. A model in level flight, which is not climbing, diving, accelerating, decelerating or turning, may be said to be in equilibrium. Thus, lift equals weight and thrust equals drag (see Fig.1). Any change in one of these factors will cause a change in state. Thus, a change in thrust will cause acceleration until the increase in drag brings the system back into equilibrium. Control interaction It is here that we first begin to see the highly interactive nature of the aircraft and the usefulness of the computer encoder. An increase in thrust will increase speed which will increase lift which will either make the aircraft climb or call for Fig.1: these diagrams show the forces acting on an aircraft in (a) level flight; (b) gliding; (c) climbing; (d) diving; (e) vertical climb; and (f) • vertical dive. When the aircraft is flying straight and level, the lift equals the weight and the thrust equals the drag. LIFT TOTAL LIFT= TOTAL WEIGHT TOTAL THRUST = TOTAL DRAG FLIGHT PATH DRAG THRUST WEIGHT (a) POWER MODEL IN LEVEL FLIGHT LIFT = WEIGHT x COSINEC\' 0 DRAG = WEIGHT x SINEO'" TOTAL AIR REACTION WEIGHT WEIGHT COMPONENT OPPOSING LIFT (b) GLIDING THRUST LIFT = WEIGHT X COSINEU0 ORAG + (WEIGHT x SINEU = THRUST WEIGHT 0 ) WEIGHT (c) CLIMBING DRAG ORAG LIFT the pilot to alter the elevator trim to maintain level flight. A computer coupled to the throttle could automatically apply the correct amount of down elevator trim required to maintain level flight, thereby making the flyer 's life just that much easier. There is a ea tch here, however. What if the pilot wants to climb and the increase of thrust was applied to achieve just that? No problem, for the control stick still has ample overriding movement for the pilot to apply the correct amount of up elevator trim required for the climb. In this example, we merely encounter the big problem with all computerised devices. They are just dumb machines which must be given every instruction very carefully indeed. I am never very happy about electronic gimmickry in any field. The real art in any endeavour is mastering the manual dexterity required to wring the very best out of · your machine. The prime example of this situation is the electronic organ. Where does playing the electronic organ stop and playing a CD begin? Certainly they are great fun but do they really teach you anything of real substance in the end? ANGLE OF DIVEC\'' DRAG = THRUST + W.SINEO'' LIFT = w.cosa· WEIGHT WEIGHT (d) DIVING DRAG THRUST DRAG = THRUST + WEIGHT LIFT= 0 THRUST = WEIGHT + ORAG LIFT= 0 ANGLE OF DIVEC\' 0 = 90° 0 ANGLE OF CLIMB // = 90' WEIGHT WEIGHT DRAG WEIGHT + DRAG (e) VERTICAL CLIMB THRUST WEIGHT + THRUST (n VERTICAL DIVE Model helicopters The best example I ever experienced was in regard to flying aerobatics. When I was in Pennsylvania in 1971 I saw the first public demonstration of model helicopters, by Dieter Schluter and a friend, who not content with flying one helicopter, flew TWO in formation. I was stunned and knew I just had to have one of these fascinating toys. I subsequently purchased one of Oki's (the Japanese licence builder of the Schluter helicopter) Kalt Huey Cobras and in due course was taught to fly helicopters by Oki himself. This was in 1972 and I APRIL 1990 89 F·Low SEPARATION LOW PRESSURE -----------==== OEc:c~~TES c'") HIGH P R E S S ~ ~ IJow. '-.J ;yW.q FLOW ACCELERATES Sf! THE ORIGIN OF LIFT STALLING Fig.2: a wing generates lift because air flowing over the top surface is made to take a longer route. It thus flows faster than the air taking the shorter route below and this creates a pressure differential. Fig.4: when a wing is in a stalled condition, the air no longer follows a streamlined path and the flow separates from the wing. This creates a great deal of drag and also drastically reduces the lift. CD 0.32 o· I I - I ORDINARY ANGLES OF FLIGHT 15 ' I I I I 0.24 ,.._ i ~, ,.._ ~l O.F., t:: ::l l1 0.2 Ii z w "' 51 i ~I ~ 0.16 "' ~I 0.12 0.4 .08 / 0.2 .04 0 .___.,__~_ _...___ -4 · o· 4• __.__ __,__--'--'_ __. 5• 12 · 16 ° 20 · __,.. ........ SILICON CHIP ~I "" :;;1 / I I 0 - 4· o· 4• 8' 12 · 15 • 20 ° ANGLE OF ATTACK Fig.3: this graph plots the lift of a wing against the angle of attack. Note that lift falls away rapidly for angles of attack greater than 15°, at which point the wing is in a stalled condition. 90 / 1~::1 I ANGLE OF ATTACK believe that I was one of the first to achieve solo status on helicopters in this country. Oki was a wild man and we flew that helicopter inside my factory and over the roof. As a grand finale, Oki flew it at the Easter show in 1973 and during that show he also flew a Jet Rang.er around the Clock Tower at the Showground. I was his caller that day and he kept asking me was it time to turn yet. It was the longest pylon course I have ever called on, as the chopper was half a mile away before he finally turned. I had these awful visions of it running smack into the tower as it is very difficult to judge perspective at those distances. However, he made it safely and the crowd roared. I made myself scarce. Now the real point is that for about two years I was totally engrossed in flying helicopters and this was in the days before they had I I 0.8 15 u I --i I 0.28 Fig.5: drag coefficient vs. angle of attack. Note how the drag coefficient increases rapidly for angles of attack greater than about 8°. The stalling angle is 15°, at which point the aircraft falls like a stone. gyros on the tail rotor. This meant I had to learn to coordinate my left thumb, as the tail rotor on a model helicopter needs constant attention, as indeed do all the controls. This is why model helicopters need such large flight batteries. When I returned to pattern flying I was suddenly a good flyer. Slow rolls, 4-point and 8-point rolls, indeed all manoeuvres that I had had great difficulty with previously, were suddenly a breeze and a friend asked on seeing me fly for the first time in many years, "where did you learn to fly like that?" It took me awhile to realise that the dexterity developed while flying helicopters was vital to my aerobatic flying. The key was the use of the left thumb which is pivotal to good rolling manoeuvres and which prior to 1972 was useless to me. I tend to feel that modern helicopter flyers miss out on this training, using gyros as they do and special helicopter encoders fitted with all kinds of mixing programs and gadgets. The same trend is developing in model aircraft with programmable manoeuvres being built into radio transmitters. Is this real flying? Here there is room for endless debate. The aerofoil However, to return to the beginning. From Bernoulli's Theorem comes the basis of the curved lifting surface or aerofoil. Fig.2 illustrates this quite clearly. In order for the split airstreams flowing over the aerofoil shown to arrive simultaneously at the trailing edge, as they must, the upper stream speeds up because it is following a longer path and for the opposite reason, the lower stream slows down. This results in an increase in dynamic pressure and a reduction of the static pressure on the upper wing surface and an increase in static pressure and a reduction of the dynamic pressure on the lower surface. The result is a nett upward force which follows the formula below: L = ½p.V 2 .S.C1 For level flight then: L = total weight of the aircraft; p = air density; V = velocity; S = lifting surface area. The term S can include fuselage and tailplane lift and C1 is the coeffici~t of lift of either the wing, tailplane or complete airframe, depending upon which unit is under examination. It is an expression of the ability of the surface to create lift. Thus, a body with a C1 of 1.3 will generate more lift than a body with a C1 of 0.8. Note also that C1 is dependent upon the angle of attack for its final value (see Fig.3). The concept of the fuselage providing lift may come as a surprise to some but I have seen figures as high as 30% of the lift coming from the fuselage. The Grumman Panther, a 1950's fighter, gave a figure similar to this and anyone who builds a model of this fighter is in for an awful surprise if he locates the centre of gravity more rearward than 3cm in front of the leading edge of the wing. (Normally it would be 3-Scm behind the leading edge). I did and found out to my horror that fuselage lift played a major role in determining the location of the centre of gravity on that particular aircraft. As stated previously, an aircraft is a highly interactive device. Fig.3 shows the relationship of the angle of attack to the lift coefficient, C1, Note here that C1 is the coefficient of lift of the practical surface while C1 is that of the wing section as determined in wind tunnel testing. The two are not the same for reasons too complex to explain in this series of articles. Note that C1 increases to about 12° then begins to level off until at about 15° the lift falls away rapidly. At this point the wing is said to be in a stalled condition. Fig.4 shows the airflow separation over a stalled wing. In effect, the air can no longer follow a streamlined path and breaks down into a turbulent flow. At this point virtually all lift is lost and the aircraft falls like a stone. Fig.5 shows the drag coefficient of the wing section at all angles of attack. Note the rapid increase in drag from about S 0 onwards. Fig.6 shows the relationship between lift and drag and is a most important graph. Note that the curve peaks at 4° and so this is the most efficient angle for this particular section to operate at. The LID ratio is a most important relationship as we shall soon see. WANT A REALLY LOUD SIREN FOR YOUR ALARM? Then have a look at this READY MADE and TESTED UNIT. 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The others must not be underestimated however, for on a hot day the subsequent reduction in air density will affect take off performance quite noticeably, through both loss of engine performance and lift. Now there is a point here which is vital to the safety of any aircraft, full size or model. Notice that total lift depends upon C1 for one of its components. As C1 is dependent upon the angle of attack for its final value, in practice what can happen is as follows. On a hot day, air density falls and engine power falls, so we have a double reduction in the total lift available for take off. The most important is loss of engine power which results in loss of forward speed and the old vz reduction in lift. Thus the pilot (full size or model) has only one immediate fix at his disposal. This is to increase lift by increasing the angle of attack, by pulling back harder on the elevator control than usual. 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The prudent pilot knows when to abort a take off. 14 Loss of engine power A really dangerous situation arises in a twin engine aircraft which loses one engine just after take off. All of the above factors are valid but to these must be added a further drag increase in the form of asymmetric drag. This arises because the thrust line is suddenly moved off centre towards the active engine. The result is an immediate turn in the direction of the dead engine. Countering this turn calls for large applications of rudder which puts the entire airframe in a yaw and increases the drag on every component of the airframe. One safety rule to keep in mind here is never turn into the dead engine, always turn away from the dead engine. It is very easy for the forces generated in a turn into the dead engine to exceed the control forces available for recovery. The result will be a spiral dive and a certain crash. Flying twin engined models is a tricky business and calls for some study into the problems involved. There is a further compounding factor in this scenario. The propeller is only another aerofoil subject to the same LID formula. In model aircraft, the pitch of the prop (angle of attack) is fixed. Thus it is designed to operate at the best forward speed (when flying straight and level). As the forward speed of the aircraft increases in a dive there is an effective reduction in 92 SILICON CHIP the pitch and a subsequent loss of thrust. If the aircraft slows down, as is the case at take off, the pitch angle is usually too high and therefore the prop operates inefficiently and loads the motor heavily. For this reason, full size aircraft use variable pitch propellers. The pitch angle can be matched to the forward speed. Any aircraft with a fixed pitch prop that is caught in the above "drag bucket" scenario is in double trouble. The wing drag and prop drag will load the motor and the prop will not develop anything like full thrust. Sometimes the only way out of this situation is to trade every centimetre of height available for forward speed by diving, thus unloading the prop and motor and reducing the angle of attack of the airframe. This calls for a cool head and steady hand, but one centimetre of altitude is all that is required to keep the aircraft flying. Once the speed begins to build, thrust and lift will increase and drag will reduce. This is easy for a model pilot safely on the ground but unnerving for a full size pilot who knows full well that a mistake will see him thump into the ground with a force related to the square of the increased velocity achieved in the dive. Also in the foregoing, we arrived at a mathematical analysis of a very serious argument in aerodynamics. There is and always has been a tendency for people to underpower aircraft, particularly in the model field. There are many reasons for this, including cost and lack of suitable engines, but one reason often put forward is that overpowered aircraft are dangerous. This may be so but underpowered aircraft are lethal. There are many situations in which any degradation of any of the above factors can be made good by a small increase in velocity. This increase is so easily obtained if sufficient reserve power is available. You do not have to use full power but it is nice to have it if needed. The big problem with this approach is that it is very easy to o· 4• 15' I I I I I I 12 ( 10 II " ~ I I \ I I '\ \i ;;iz ... C I .I... I ;;i~ ~, i\ "'~ ....., c:, ;;;!f :E I I I I D -4' I 4' a· 12' 16' ANGLE OF ATTACK Fig.5: the graph shows the lift to drag ratio for increasing angles of attack. Note that the curve peaks at 4° and so this the most efficient angle to operate at. become caught in an upward power/weight spiral, particularly in view of the fact that the v2 component gives rise to increased forces which must be taken into account in the aircraft structure. Compromise, always compromise. Unfortunately, the formula for drag also follows a similar square law and the maths involved are as follows: D = ½p.V 2 .S.Co As before, p = air density, V = velocity, S = the same surface area as used in the lift calculation, and Co is the drag coefficient of the body under examination. Basically, Co is an expression of the "aerodynamic cleanness" of the body in question. The interactive relationship between lift, drag and thrust have some interesting ramifications. If we wish to travel twice as fast we must use four times as much power. We will, however, have an increase in engine weight. This in turn will require an increase in structural strength (and thus weight) to hold this engine in place and to cope with the increased aerodynamic and "G" forces generated by the higher speed. These interactions will be examined in detail next month. ~ 20'