Ping Pong Ball Flight Mathematical Modeling Garren Plemmons and Kevin Kotecki Enka High School and Wakefield High School 2008

Outline Introduction Problem Goals Background Information Equations Collected Data Conclusion Bibliography Acknowledgements

Problem? How is the flight of a ping pong ball effected through the parameters of drag, lift, initial angle of the ball and velocity of the ball?

Goals Prove the input of drag, lift, angle, and speed to create a different output when changed in different situations. Model the flight of the ball through V-Python and collect informative and testable data. Learn the effects of aerodynamics in spherical objects.

Background Information Equipment: Ball (40 mm) Hardtop table (9’x5’) 6” net Paddles http://salzburgacademyusa.files.wordpress.com/2007/06/l-ping-pong-ball-and-paddle_7506.jpg http://www.recreationcentral.com/ping-pong/images/200-ping-pong-table.jpg

Background Information Rules: Two to four player. A players must allow a ball played towards them only one bounce on their side of the table Then must return it so that it bounces on the opposite side of the playing surface. A point is scored when the opponent fails to return the ball.

Mathematical Values and Meanings F = lift force V = velocity of the ball A = cross-sectional area of ball C = lift coefficient a= acceleration = theta http://farm1.static.flickr.com/189/509787527_cda2ba774c_m.jpg

Equations Newton’s Second Law of Motion F=force M=mass A=acceleration http://www.union.edu/PUBLIC/PHYDEPT/jonesc/images/Scientific/ping%20pong%20ball%20bouncing.jpg

Mathematical Equations g=gravity 9.8 meters per second c= drag coefficient V=velocity of the y component K=lift coefficient

Mathematical Equations a = acceleration dt = change in time

Mathematical Equations a = acceleration dt = change in time

Mathematical Equations g=gravity 9.8 meters per second c= drag coefficient V=velocity of the y component K=lift coefficient

Bernoulli’s Principle Due to the conservation of energy the wing is not able to separate and settle the circulation predicament. This creates a higher pressure are beneath the wing than above it. The pressure difference causes the wing to push upwards and lift is created. http://www.hiflykites.co.za/kite-online-shop/x-zylo-flying-principles-3.gif

Mechanical and Airfoil lift similarities The overall behavior of Mechanical lift is similar to that around an aerofoil with a circulation which is generated by the mechanical rotation, rather than by aerofoil action. http://www.furball.warbirdsiii.com/krod/images/airfoil.jpg http://upload.wikimedia.org/wikipedia/en/thumb/1/15/Magnus_effect.svg/644px-Magnus_effect.svg.png

Forces Affecting the Flight of a Ping Pong Ball Magnus Force/Effect: Perpendicular axis High Pressure pushes the ball Spin causes high pressure due to the pushed air http://www.symscape.com/files/images/curveball_1.img_assist_custom.jpg

Force Diagram

Magnus Forces Rotation axis-the axis in which the ball spins Pressure Topspin Backspin Pressure The low and high pressure areas are on opposite sides of the ball. The Magnus force is described as the low pressure area during the flight of the spinning ball.

Magnus Forces Velocity in Direction The direction in which the ball is traveling Perpendicular to the Magnus force and the rotational axis of the ball Effects how radical the ball flies according to lift, drag, and spin.

Life Like Table Bouncing table Bouncing net Limited bouncing

Variable Pitch Changed the initial angle only Started at 0 and went to 75 by 15 increments All other settings were at ‘default’

Variable Pitch

Variable Drag Changed drag coefficient only Started at 0.0 drag co. and went to 2.0 drag co. Increments of 0.5 All other settings at ‘default’

Variable Drag

Variable Lift Changed lift coefficient only Started at 0.0 lift co. and went to 2.0 lift co. Increments of 0.5 All other settings at ‘default’

Variable Lift

Variable Speed Changed the initial speed All other settings set at ‘default’

Variable Speed

Variable Pitch with Drag Changed initial pitch only Started at 0 and went to 75 by 15 increments Added drag coefficient of 0.5

Variable Pitch with Drag

Variable Pitch with Lift Changed initial pitch only Started at 0 and went to 75 by 15 increments Added a lift coefficient at 0.5

Variable Pitch with Lift

Variable Speed with Lift Changed initial speed Started at 0.5 lift co.

Variable Speed with Lift

Variable Speed with Drag Changed initial speed Set 0.5 drag co.

Variable Speed with Drag

Variable Speed with Lift and Drag Altered the initial speed only Added a lift co. of 0.5 Added a drag co. of 0.5

Variable Speed with Lift and Drag

Variable Pitch with Lift and Drag Changed the pitch from 0 to 75 Increments of 15 Added lift co. and drag co. of 0.5

Variable Pitch with Lift and Drag

Summary The drag and lift coefficients on a flying ping pong ball was tested through trial and recording, finding the effects of angle, pitch, drag, and lift on a spherical object.

Conclusion When experimenting with angle, speed, lift and drag we found that the parameters effect the flight of the ball to a considerable amount. Drag decreases the efficiency of flight Lift can increase the efficiency of flight but not always Angle and speed create a variable flight path due to conditions

Bibliography http://library.thinkquest.org/2819/bernoull.htm http://en.wikipedia.org/wiki/Table_tennis http://en.wikipedia.org/wiki/Bernoulli%27s_principle http://tabletennis.about.com/od/beginnersguide/a/physics_mathsTT_2.htm http://www.grc.nasa.gov/WWW/K-12/baseball/index.html http://ffden-2.phys.uaf.edu/211_fall2002.web.dir/Jon_Drobnis/Curveball.html http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=150

Acknowledgements Dr.Russell Herman and Mr. David Glasier SVSM Staff UNC Wilmington Mr. and Mrs. Cavender