SPIN

EFFECT OF SPIN

NOLIFT

LIFTUO

EFFECT OF SPIN

A B

C D

EFFECT OF SPIN

A

B

C

D

Sport Science – Peter Brancazio

Gustav Magnus discovered Magnus effect in 1852

What’s wrong with one of these illustrations?

EFFECT OF SPIN

SEPARATION POINTS

Spin develops lift force because:Velocity higher on top;

Separation delayed on top;Wake is deflected downward.

V + r

V - r

Visualization of the flow on a counter-rotating (left) and non-rotatingWheel. Re = 0.53 x 106. From Race Car Aerodynamics by J. Katz

SEPARATION SEPARATION

Separation

Separation

WHICH WAY

IS BALL

SPINNING?

Separation

Separation

Flow from left to right,

spin is clockwise,

visualization via smoke

Magnus force mostly affected by spin ratio,

D/(2V).

At low spin ratios,Magnus force is in the

opposite direction.WHY?

Reynolds number lessimportant.

Spin Ratio for Sphere, D/(2V)

SPHERE

Curve Balls

“it is 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

“A curve ball,” says Baltimore Orioles pitch hitter Terry Cowley,“comes straight in, then about four of five feet from home plate, then it breaks straight down”.

Do Curve Balls Really Curve?

“ It is not necessary to waste space to prove that the ball can be madeto 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

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.

The fact that tennis balls curve because of the spin imparted on them was noted as early as 1671 by Sir Isaac Newton.

Do Curve Balls Really Curve?

v v

Magnus and Robins explained phenomenonby invoking Bernoulli’s Equation

U increases, P decreases

U decreases, P increases

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 ball Screw ball

~ 1 foot

Curve do to spin alone

Curve due to gravity alone

v

v

Narrow streamtube

Thick streamtube

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.

It is the shifted wake that leadsto a lateral force on the ball.

Note, this could not happen in an inviscid fluid.

Laminar flow overSmooth surface

FLOW AROUND A SPINLESS BALL

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 mphMax 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 about½ the weight of the ball.

Will a dimpled bathit a grand slam?

FLETTNER ROTOR SHIP

100 ft long(displaced 800 tons)

(wetted area = 3500 ft2)

50 ft

9 ft

= 750 rpm

CD = 4; CL = 10

What will be the force parallel and perpendicular

to ship centerline?

Describe how you would estimate the power

to drive the rotors?

FD / FL = (CD ½ U2 AP) / (CL ½ U2 AP)

= SPIN RATIO

Lift Coefficient for rotating cylinder is significantly higher than that associated with wing at standard conditions

Theoretical and experimental lift and drag coefficients of a rotating cylinder (large difference –50%, account of flow separation).

L/b = U = 2a aCL = L/(1/2 U2A)

U2a2b= ------------------- (1/2U22ab)

= 2a/U = SPIN RATIO

.

.

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.POTENTIALFLOW

THEORY

THE END