Paul V. Cochrane
In this work its assumed that a suitable power source plant is in place and functioning.
A properly designed airfoil when angled into the airstream creates a maximum amount of downwash (and therefore a maximum amount of lift) while at the same time creating the least amount of turbulence (drag) on its surface. The airfoil’s top surface should be cambered (slight curvature) to encourage the air flow flowing over its surface to travel a greater distance. This would cause a flow differential (top, fast-bottom, slow) which would result in a pressure differential, (low on the top, high on the bottom), or an enactment of the laws stated by Daniel Bernoulli (1700-1782) which in effect said that when the velocity of a fluid is increased the pressure it exerts is decreased. In layman’s terms the wing will experience “lift”.
Before we tackle any more questions it would be useful to look at our own encounters with air flow. We can wait for a hurricane or get into the family car to gather first hand encounters with the wind. Accelerate the car to 55 m.p.h. and put your hand out the open window, it may be presented to the air in one of three basic positions. First hold your hand parallel to the ground. The air should stream past in an even flow. Next tilt your hand up at about a 20 degree angle and your hand will rise quickly. You’re experiencing Newton’s law—action equals reaction. Your palm is hit by the air, which in turn “downwashes” and your hand rises for you have exposed more of its area to wind. You experience lift and an increased drag at the same time. The last position, hold your hand at right angles to the wind. Your hand is hard to control for it wants to move with the air stream to the rear, your getting a lot of drag, for you have exposed a maximum amount of area (palm) to the moving air.
We want an airfoil which will rise into the air and then level off into smooth flight. If we wanted to increase our rate of fall or had to stop quickly then we would present a lot of drag surface (palm) to the air stream. What we are discussing here are angles of attack (AOA). Angles at which an airfoil is presented to the airstream. An airfoil which is angled to the airstream would flip back causing a rotation along its longitudinal axis This prevented by the fuselage (which acts a a lever) and the tail wing. The tail wing falls in response to the rotation and becomes an air foil with a positive angle of attack so it rises, gets lift, and levels out the nose of the plane and settles back into a zero angle with respect to the oncoming stream of air. The plane then stabilizes itself into a level flight.
The next part of the discussion has to do the “boundary layer” which is best seen as part of visual example. Place a large telephone book on a table. Place one finger on the cut edge which is parallel to its spine and apply a gentle but firm pressure. The upper pages will slide quickly, the pages in the middle will move less rapidly and the bottom will stick to the desk top. According to Ludwig Prandtl (1875-1953) air on airfoil does much the same thing. The first layer which is in contact with the wing sticks there and does not move, except with the plane. About this first layer are a series of layers which make up a boundary layer. In this boundary layer air moves across the wing first in a laminar flow (steady) and finally as it proceeds across the wing changes into a turbulent flow. As each layer, which is within the boundary layer, gets further from the wing’s surface its speed accelerates until it matches the velocity of the airstream above. This laminar region thickness ranges from one tenth of an inch, at the leading edge, up to a few inches at the trailing edge. As air streams over this boundary layer it first encounters the region over the laminar part of the boundary layer where there is no friction. This changes when this air must stream over the turbulent part of the boundary layer where it encounters friction or drag. When a wing’s angle of attack is too great this boundary layer can no longer adhere to the wing, the wing loses its lift capability and the craft falls.
The trick is to design an airfoil which encourages laminar flow. In John Anderson’s
Introduction To Flight
airfoils standard and laminar are compared on pages 139-140 figures 4.34. The lift capability of the laminar design is clearly shown.
(figure available in print form)
We next look at the Magnus effect. If a cylinder is placed in an ideal air flow (one in which there is no viscosity) air will pass around the cylinder as in an uninterrupted flow. If we take a rotating cylinder and observe in a real fluid, we will see that a portion of the surrounding liquid will swirl in the same direction as the cylinder is rotating. This we refer to as a bound vortex. Now if we take this experiment and place it in an airstream, the bound vortex of the spinning cylinder will cause a few things to happen. First take the air stream as coming from the left through to the right. Secondly the cylinder is rotating in a clockwise manner. The bound vortex downwashes onto the streamline below, slowing them and causing pressure, as it passes up over the front of the cylinder it enhances the stream lines accelerating them, causing a drop in pressure (Bernoulli’s law) and the cylinder rises. This demonstration can be done in any class room as shown in the demonstration sheet which is included at the end of this paper.
The Magnus effect was included to help us visualize the next theory on lift which is referred to as the circulation theory. The theory takes the Magnus effect and connects it to an airfoil, and mathematically it works. If the air flow is from the left, the circulation theory says that there is a closed curve which has a clockwise flow and moves with and around the airfoil. The clockwise flow moves down from the trailing edge compressing the air below causing pressure, continues on its way up over the leading edge, accelerating the on coming air, causing an enhanced lift. This, circulation, combined with an angle of attack and Bernoulli law is what causes lift and leads to flight.
This is an attempt to introduce the reader to some of the underlying ideas of flight, and the men who made it possible.
(figure available in print form)
