Airfoils and Lift — страница 3

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not address acrobatic airplanes, with symmetric wings (the top and bottom surfaces are the same shape), or how a wing adjusts for the great changes in load such as when pulling out of a dive or in a steep turn. So, why has the popular explanation prevailed for so long? One answer is that the Bernoulli principle is easy to understand. There is nothing wrong with the Bernoulli principle, or with the statement that the air goes faster over the top of the wing. But, as the above discussion suggests, our understanding is not complete with this explanation. The problem is that we are missing a vital piece when we apply Bernoulli’s principle. We can calculate the pressures around the wing if we know the speed of the air over and under the wing, but how do we determine the speed?

Another fundamental shortcoming of the popular explanation is that it ignores the work that is done. Lift requires power (which is work per time). As will be seen later, an understanding of power is key to the understanding of many of the interesting phenomena of lift. Newton’s laws and lift So, how does a wing generate lift? To begin to understand lift we must return to high school physics and review Newton’s first and third laws. (We will introduce Newton’s second law a little later.) Newton’s first law states a body at rest will remain at rest, and a body in motion will continue in straight-line motion unless subjected to an external applied force. That means, if one sees a bend in the flow of air, or if air originally at rest is accelerated into motion, there is a

force acting on it. Newton’s third law states that for every action there is an equal and opposite reaction. As an example, an object sitting on a table exerts a force on the table (its weight) and the table puts an equal and opposite force on the object to hold it up. In order to generate lift a wing must do something to the air. What the wing does to the air is the action while lift is the reaction. Let’s compare two figures used to show streams of air (streamlines) over a wing. In figure 3 the air comes straight at the wing, bends around it, and then leaves straight behind the wing. We have all seen similar pictures, even in flight manuals. But, the air leaves the wing exactly as it appeared ahead of the wing. There is no net action on the air so there can be no lift!

Figure 4 shows the streamlines, as they should be drawn. The air passes over the wing and is bent down. The bending of the air is the action. The reaction is the lift on the wing. Fig 3 Common depiction of airflow over a wing. This wing has no lift. Fig 4 True airflow over a wing with lift, showing upwash and downwash. The wing as a pump As Newton’s laws suggest, the wing must change something of the air to get lift. Changes in the air’s momentum will result in forces on the wing. To generate lift a wing must divert air down, lots of air. The lift of a wing is equal to the change in momentum of the air it diverts down. Momentum is the product of mass and velocity. The lift of a wing is proportional to the amount of air diverted down times the downward velocity of that air.

Its that simple. (Here we have used an alternate form of Newton’s second law that relates the acceleration of an object to its mass and to the force on it, F=ma) For more lift the wing can either divert more air (mass) or increase its downward velocity. This downward velocity behind the wing is called "downwash". Figure 5 shows how the downwash appears to the pilot (or in a wind tunnel). The figure also shows how the downwash appears to an observer on the ground watching the wing go by. To the pilot the air is coming off the wing at roughly the angle of attack. To the observer on the ground, if he or she could see the air, it would be coming off the wing almost vertically. The greater the angle of attack, the greater the vertical velocity. Likewise, for the same angle

of attack, the greater the speed of the wing the greater the vertical velocity. Both the increase in the speed and the increase of the angle of attack increase the length of the vertical arrow. It is this vertical velocity that gives the wing lift. Fig 5 How downwash appears to a pilot and to an observer on the ground. As stated, an observer on the ground would see the air going almost straight down behind the plane. This can be demonstrated by observing the tight column of air behind a propeller, a household fan, or under the rotors of a helicopter, all of which are rotating wings. If the air were coming off the blades at an angle the air would produce a cone rather than a tight column. If a plane were to fly over a very large scale, the scale would register the weight of the