Fluid Dynamics (1999)
Air effects are used to drive sailboats. In combination with water effects, sailboats can be made to head partly toward the direction of the wind. Golf balls are hit with a low angle of launch but with backspin so that the ball rises to a great height and with long hang time to get a large distance. The curve in baseball is a tactical weapon to keep the batters guessing and less able to hit the ball. We will study the air and water effects on various sports. We will start with the curve ball in baseball. The range of a ball launched at 40 degrees elevation and a speed of 90 mi/hr in air is about 1/2 the range of a similar ball launched in vacuum. Air resistance is a drag force which acts opposite to the direction of the ball's flight. For a thrown ball, the direction of the ball's velocity and hence the vector force changes continuously.The air resistance also changes it's magnitude. A ball standing still in the air has no air resistance. At high speed, the air resistance is quite large [think of the force on your hand in the airstream when you are driving fast]. The precise calculation of air resistance affects is beyond the scope of this course but we will look at some approximate caculations. We have studied collisions in Volume 2. We can think of air resistance as the collision between air molecules and the ball. The collision transfers momentum to the air molecules and the reaction force acts on the ball to slow it down. Since there are so many air molecules, the molecules collide amongst themselves as well as with the ball so that a rather large scale coherent motion of the air results from this interaction. We will describe the lift phenomenom in the familar terms of momentum transfer and Newton's laws of motion. The only new thing is the idea that air and water are viscous. They will stick to a surface and drag the fluid along with its motion. You can see that old fan blades have dust stuck to the blades when intuition tells you that the rushing air should have blown it away. It won't because the air next to the blade does not move.