Transcript ch9spin
EFFECT OF SPIN EFFECT OF SPIN Spin develops lift force because: Velocity higher on top; Separation delayed on top; Wake is deflected downward. SEPARATION POINTS Visualization of the flow on a counter-rotating (left) and non-rotating Wheel. Re = 0.53 x 106. From Race Car Aerodynamics by J. Katz Separation Flow from left to right, spin is clockwise, visualization via smoke Separation EFFECT OF SPIN Magnus force mostly affected by spin ratio, D/(2V). Reynolds number less Important. At low spin ratios, Magnus force is in the opposite direction. WHY? Gustav Magnus discovered Magnus effect in 1852 What’s wrong with one of these illustrations? Sport Science – Peter Brancazio Do Curve Balls Really Curve? “A curve ball,” says Baltimore Orioles pitch hitter Terry Cowley, “comes straight in, then about four of five feet from home plate, it breaks straight down”. “it is not only theoretically practically impossible for any such impetus to be conveyed to a moving body as would be required … to control the movement of what is termed a curve ball.” Professor Stoddard of Worcester University “ It is not necessary to waste space to prove that the ball can be made to change is course to right or left. The only real question is, whether the change in direction is instantaneous or gradual – that is, whether it is an angle or a curve.” – 1877 Spauldings Baseball Guide Do Curve Balls Really Curve? The fact that tennis balls curve because of the spin imparted on them was noted as early as 1671 by Sir Isaac Newton. In 1877 Lord Rayleigh in a paper also describing the irregular flight of a tennis ball, credited G. Magnus with the first explanation of the lateral deflection of a spinning ball in 1853. A similar explanation was given by Robins, a century before. v v U increases, P decreases U decreases, P increases Magnus and Robins explained phenomenon by invoking (improperly) Bernoulli’s Equation Curve ball Screw ball Pictures from 1941 LIFE magazine by Gjon Mili “showing” that curve balls really do not curve, only an illusion. Pitches were thrown by Carl Hubbell of the New York Giants. Curve do to spin alone ~ 1 foot Curve due to gravity alone Thick streamtube v Narrow streamtube v It is the shifted wake that leads to a lateral force on the ball. Note, this could not happen in an inviscid fluid. The existence of a wake creates a drag force. If the wake is symmetrical the drag will simply slow the ball down. If the wake is not symmetrical, then by Newton’s 3rd Law the ball will be deflected in the opposite direction. Flow over a sphere. Trip Bottom: Re = 15,000 (laminar separation) Trip: Re = 30,000 (with trip wire turbulent separation) From Van Dyke, Album of Fluid Motion Parabolic Press, 1982 Original photographs by Werle, ONERA, 1980 Smooth Drag coefficient as a function of Reynolds number for spheres with different degrees of roughness. K is the equivalent roughness height, and D is the sphere diameter. From Munson, Young, & Okiishi, Fundamentals of Fluid Mechanics, John Wiley & Sons, 1998 Drag coef. for various spheres the size of a baseball. When drag force = weight of ball then terminal velocity ~ 95 mph. FLOW AROUND A SPINLESS BALL Laminar flow over Smooth surface Some base ball facts ~ In air terminal velocity of baseball ~ 95 mph (42.5 m/s) A 450 ft drive requires launch velocity of about 110 mph Max pitching speed recorded is 100.9 mph (Nolan Ryan) Baseball may spin at 1800 rpm i.e. about 15 rev before reaching home plate Weight and diameter of major league baseball is 5-5.25 oz and 2.86-2.94 inches. Time for 85 mph pitch to reach home plate, about 60 feet, is 0.48 s Briggs (Am. J. Phys., Vol. 27, 1959, pg 232-240) report that an 80 mph curve ball rotating at 1800 rpm can curve as much as 17.5 inches, force is about ½ the weight of the ball. Will a dimpled bat hit a grand slam? FLETTNER ROTOR SHIP 9 ft 50 ft What will be the force parallel and perpendicular to ship centerline? Describe how you would estimate the power to drive the rotors? 100 ft long (displaced 800 tons) (wetted area = 3500 ft2) = 750 rpm CD = 4; CL = 10 L/b = U = 2a a CL = L/(1/2 U2A) = U2a2b ------------------(1/2U22ab) = 2a/U 2a b = SPIN RATIO Theoretical and experimental lift and drag coefficients of a rotating cylinder (large difference –50%, account of flow separation). FD / FL = (CD ½ U2 AP) / (CL ½ U2 AP)