Helicopter Flight Theory

1. Helicopter Flight

The motion of the blades of a helicopter in flight conjures up the ancient vision of the airscrew: lifting surfaces rotating about a vertical axis and inclined at an angle so, as they turn, a lifting force is obtained from the resistance of the air. This recurring theme in the history of aeronautics was crystallized in the writings of Leonardo Da Vinci. Centuries later, but still many years before the perfection of the helicopter, master storyteller Jules Verne wrote a novel Robur le conquerant in which his hero explained the functioning of the huge vertical take-off aircraft in which he cruises over the earth by comparing its propellers with the screws of a steamship. Historically, much of the early helicopter experimentation developed from this concept of lifting surfaces operated as a kind of airscrew. Even today it is not too wide of the mark to use this term, especially if we take note of the screwlike spiral path made by the rotor blades when a helicopter rises straight up. But this is not the way it really works; for an understanding of what makes a helicopter fly it is necessary to take a different approach and consider the key phrase, "rotating-wing". For a helicopter flies as does an airplane, by the movement of its wings through the air. These wings, of course, are whirling rotor blades. This is the essence of helicopter flight — "wings" rotating around a central shaft. A fuller understanding of rotating-wing aircraft really begins with the workings of the fixed-wing airplane. Here lies the similarity — and, paradoxically, the difference — between the two types of aircraft. In the most basic terms, a wing is a fixed surface that will produce a lifting force when it is moved through the air with enough speed or, as an engineer would put it, with sufficient velocity. To appreciate why a wing has this property, we need to consider the substance called air. Air is a fluid that behaves just as do wet fluids such as water or oil. If you move through a fluid slowly it will resist — but give way — as the water in a swimming pool clings and then flows around you as you walk or swim through it. If you speed up your movement, the resistance (drag) will increase out of all proportion to the increase in speed. For example, if you move through it twice as fast as before, the drag will be four times as much (an engineer would say that the resistance is going up by the square of the speed — multiplied by itself). And consequently, this property has resulted in the art of streamlining, the creation of shapes that offer the least resistance so that movement through fluids can be accomplished with the least expenditure of power. The trick in making a heavier-than-air machine fly is to take the resistance, which is trying to hold you back, and put it to work so that it provides a lifting force. The means for accomplishing this was known for hundreds, even thousands of years before the first aircraft were flown. The lesson was learned from the ordinary kite: if a lightweight, flat surface was inclined at a slight angle to a constant airflow (the wind), a lifting force resulted and the surface rose and flew. In more precise aeronautical terminology, the front or leading edge of the lifting surface had to be raised higher, relative to the air flowing against it, than the rear edge. In the same way, a lifting force results as air is pushed down by the slanting under-surface of a wing or rotor blade. The faster the movement through the air, the stronger the reaction and the greater the lifting force. What is happening is that the surface is being supported by "planing", sliding along on a mass of piled-up fluid. The name that has been accepted for the fixed-wing flying machine, "airplane", is in itself a substantial clue to the workings of a wing in flight. One way actually to feel this lifting force is to hold your hand stiffly, at a slight angle, in a steady blast of air. The kite, so much a classic example of why an airplane flies that at least one aeronautical authority refers to all airplanes as basically "kitecraft", is still useful today for illustrating this principle of flight. When held at the correct angle of attack to the wind by the balance between its rag tail and the kite string, it will maintain itself steadily in the air; it is a lifting surface that is supported by the pressure of the stream of air. This stream is the relative airflow — that is, a flow of air relative to the inclined angle of the lifting surface. This flow can be created by holding the surface still in a moving airflow, or the air can be at rest with the lifting surface being moved through it rapidly, as with the wing of an airplane or the rotor blades of a helicopter. In both cases the effect is exactly the same: a constant airflow against a lifting surface. For example, a kite that was being pulled along at a steady 10 miles an hour in still air would be lifting in exactly the same manner, with the same force, as a kite riding in a constant 10-mile-an-hour wind. If we were to install an engine and propeller on our kite, and tail surfaces to balance it and hold the right angle of attack, it could be made to create its own relative airflow simply by moving through the air. Of course, the self-propelled kite, that we have imagined here is actually an airplane, basically nothing more than a powered kite that planes through the air, and the transition we have made here from kite to free-flying aircraft actually parallels the historical development of the airplane; before they flew the world's first powered plane at Kitty Hawk in 1903 the Wright brothers spent years testing man-carrying kites. An illustration of the force produced by an airfoil operating at a positive angle of attack to an airflow; normally this force is inclined upward and slightly to the rear. The airfoil shown here is symmetrical: the curves on the upper and lower surfaces are identical Yet, though the term "planing" is helpful in creating a visual image of the action of a lifting surface, it must be said that this does nothing to explain how the actual lift forces are produced or show the real effect on the air mass. The theoretical aspects cannot be adequately explained here; however, several important points are plain enough and can be described. One concept is that the moving wing creates a vortex system (air moving in a circular pattern) which deflects the air downward. This in turn produces a reaction on the wing in the opposite direction, the lift force that supports the aircraft. A useful and interesting description of the ultimate effect, not only on the air mass but on the earth below as well, is furnished in a U.S. Air Force textbook, Foundations of Airpower. It is quoted in part as follows: The wing produces lift by driving air downward. The more rapidly and efficiently it does this, the more lift it will produce. A wing is therefore the same, in this respect at least, as a helicopter rotor, a ducted fan, or other lift-creating devices. But it is not the air that ultimately supports the airplane. Consider a tub of water weighing 50 pounds. If you float a 5-pound toy boat in it, the combination must weigh 55 pounds. The boat does not cease to have weight merely because it is floating; its weight, too, must be supported by the scale. Ultimately it is the earth that provides the reaction upward against the air directly beneath the aircraft. The air merely transmits the weight of the aircraft down to the ground. But since the air pressures decrease with the square of the height of the aircraft, they are extremely small by the time they reach any particular point on the ground (unless the plane is only a few feet up). There are other factors that are also at work in the creation of lift by an airfoil. One that is frequently mentioned in older textbooks is the "Bernoulli effect", which relates to the flow of air over the upper surface of the wing as well as against the lower surface. Basically, this theory says that because of the angle of attack at which the airflow strikes the leading edge (and also because of the thick curve found on the upper surface of many airfoils), the air traveling over the top of the wing is forced to travel a greater distance than the air going under the bottom. In order to avoid creating a vacuum behind the trailing edge, the theory says, the airflow over the top has to speed up to a velocity greater than that of the flow on the bottom. This difference in velocity is the key to the lifting effect; the theorem expounded by the eighteenth-century scientist Daniel Bernoulli states that as the velocity of the airflow over a surface increases, the direct atmospheric pressure on the surface decreases. Therefore, the difference in the speed of the flow between the upper and lower surfaces causes a difference in atmospheric pressure; specifically, there is more pressure on the lower surface of the wing than on the upper, and a lifting force results. Interestingly, the vortex or circulation theory that we mentioned earlier is frequently considered to be an extension of the Bernoulli theorem. Without getting the reader too involved in, and confused with, the theory of lift it must be said that both of the explanations provided here (there are still more) are really oversimplifications of a very complex airflow system and do not correspond with all of the realities of the situation. In any case, to move on to a safer subject, the effectiveness of a lifting surface depends greatly on the shape of its airfoil; this is the shape that you would see if you could imagine slicing across a wing or a rotor blade from the leading to the trailing edge, at right angles to the span. It can be thought of as two curves, the one on the top surface and the one on the bottom, joined together to form a streamlined shape. With many of the older standard airfoils this takes the form of a kind of arched-out teardrop curve on top that goes down to a knife edge at the rear, combined with a bottom surface that is nearly flat. Basically, the airfoil shape serves two closely interrelated functions. The first, obviously, is to obtain the maximum lifting force. Secondly, the shape of the airfoil is intended to permit the wing to move through the air with as little resistance as possible: it is the best shape for the work it has to do. In the language of the aeronautical engineer the efficiency of an airfoil, with regard to these two functions, is expressed in terms of the "lift-drag ratio". An airfoil with the best lift-drag ratio for a particular aircraft is simply the one that furnishes the greatest lift with the least resistance (drag) to the airflow. Surprisingly, this very special airfoil shape, as well as many of the other aerodynamic shapes used in aircraft design, have frequently been determined more by trial and error than anything else. This helps to explain why elaborate wind tunnels and extremely accurate scale models are so important to aerodynamic research. Obviously, if it is necessary to test endless combinations of shapes and curves you must have some way to duplicate the interaction between the airflow and the shape without building a whole new wing or rotor for every experiment. One type has exactly the same amount of curvature on the bottom as on the top: this is often referred to as a "symmetrical" airfoil. Many helicopter rotor blades have this shape — a stretched-out teardrop curve from the leading edge to the trailing edge that is exactly the same on both the top and the bottom. In comparison with the more conventionally shaped airfoils the symmetrical airfoil offers several advantages, particularly for the rotor blades of a helicopter. One of the most important of these is a highly desirable aerodynamic characteristic: very little center-of-pressure change under different angles of attack (the center of pressure is generally considered to be the center of the lift force acting on the wing). (With conventional airfoils that have a full curve only on top, as the angle of attack is increased the center of pressure moves forward considerably, and this complicates the problem of stabilizing and controlling the lifting surface.) Other desirable features of a rotor blade designed with a symmetrical airfoil are structural rather than aerodynamic. For one thing they are generally easier to manufacture, since the top and bottom skins are identical and other parts may be as well. C.Gablehouse "Helicopters and Autogiros", 1969

1. Helicopter Flight | 2. Flight Controls | 3. Autorotation | 4. Rotor Mechanism