The Pitch
The Magnus Force Activity

Drag Simulation Activity
The Magnus Force Activity
Pitch Trajectory Activity
Graphing Calculator Activity

Overview of Lesson

This lesson will focus on the Magnus force. Students will create an apparatus and perform an experiment to answer the central question: How does spin affect the trajectory of a thrown ball?

Goal

Students will investigate and develop an understanding of the Magnus force.

Objectives

• The students will construct an apparatus to throw a ball with significant spin.

• The students will conduct an experiment to answer the central question.

• The students will list the variables that contribute to the calculation of the Magnus force.

• The students will predict the effect of changing variables within the investigation.

• The students will summarize the findings from their experimentation.

• The students will discuss the limitations of their experiment.

Ohio Academic Content Standards

Materials

• Assortment of lightweight balls: Styrofoam craft balls (1- to 2-inch diameter), ping-pong balls, practice golf balls, Wiffle balls, etc.

• Assortment of tubes: cardboard shipping tubes, paper towel tubes, wrapping paper tubes, plastic golf club tubes, PVC pipe, etc.

• Assortment of materials to add friction: sand paper, thin craft foam rubber, bicycle inner tube scraps, etc.

• Glue

• Tape

• Scissors

• Markers

• 2-foot-square white boards and dry erase markers for use in the reporting-out phase (optional)

Procedure

1. Split your students into groups of two to four students and introduce them to the central question that will guide them in their investigation: How does spin affect the trajectory of a ball?

2. Ask students to make a workable apparatus that allows the ball to spin. Show the groups the assortment of materials they have to work with, mention the safety precautions of using scissors and turn them loose.
   
   A workable apparatus is simply a tube with a short sandpaper or rubber strip affixed to the inside of one side of the tube, near one end. The tube may also be cut in half lengthwise to form a throwing scoop.

3. As the activity progresses the teacher's job is to give helpful hints and ask focusing questions only when groups seem to be sputtering. Resist the natural instinct to show them how to construct a workable apparatus.

   Examples of helpful hints and focusing questions:

   • Can the tube be used somehow to throw the ball?

   • How can you tell in which direction the ball is spinning?

   • What could you do to get the ball to spin faster?

   • What is the relationship between spin direction and the curve of the ball?

   • What is the relationship between spin speed and the amount of curve?

   • If a pitcher wants to throw a ball that breaks to the right, which way does the ball need to be spinning?

   • Is there a simple way to summarize your results?

4. When all groups have completed their investigation and summarized their findings (use 2-foot-square white boards or chart paper for this part of the process), bring the class back together and ask each group to report out what they discovered and how they discovered it. Most groups will have discovered the correct relationships, but it is good for them see how various groups constructed their apparatus and performed their investigations. It is also important to discuss how the results can best be simplified into a simple set of relationships. (For example, the amount of break is proportional to the rate of spin, and the direction of the break is the same as the direction that the leading edge of the ball is turning. A more subtle relationship also exists between the linear speed at which the ball is thrown and the amount of break that occurs over a given distance, like the 60 feet 6 inches from the pitcher's mound to home plate. If the students did not think of this during their initial investigation it can be posed and assigned as a follow-up investigation.)

5. As a follow-up to the ball and tube activity, the teacher may ask students to do some research on the topic of the Magnus force and/or give a short lecture introducing them to the concept of the Magnus force and the equation that physicists use to calculate it. Below is an outline of the basics:

   • Historical Information: The effects of spin on a ball's trajectory have been studied since the time of Newton, who in 1671 wrote a paper concerning the spin effects on the flight of lawn tennis balls. In 1852 the German physicist Gustav Magnus performed experiments confirming that a spinning ball experiences a "sideways" force; this force is now known as the Magnus force and is the fundamental principle behind the curved flight of any spinning ball.

   • Results should show that the Magnus force acts in the direction that the front of the ball is turning toward, i.e., a ball thrown with backspin will experience an upward Magnus force, causing it to rise somewhat from its normal trajectory.

   • Variables: velocity, roughness (orientation of seams), air density (atmospheric conditions), drag, rate of spin.

   • F_m = kfvC_d Where F_m is the Magnus force, k is a constant, f is the spin rate, v is the velocity, and C_d is the drag coefficient.

   • Explanation: As a spinning ball moves through the air, the boundary layer separates from the ball at different points on opposite sides of the ball: farther upstream on the side of the ball that is turning into the airflow, and farther downstream on the side turning backward. The result is an asymmetric wake behind the ball and a pressure difference across the ball, creating a lateral force component at right angles to the motion of the ball.

   • By properly orienting the spin direction, the pitcher can orient the Magnus force in any direction he chooses.

   • The rates of spin for a major league pitcher can approach 2000 rpm and the Magnus force can be equal to about half of the weight of the ball. This means that a curve ball thrown with topspin experiences a downward force 1.5 times that of gravity alone; therefore, it will drop 1.5 times as far as it would without spin.

Note: Be sure to have enough materials on hand to allow groups to make several modifications and reengineering steps along the way.

Evaluation

The evaluation for this activity is informal. The questions posed in the process by the teacher and fellow students will allow the teacher to gauge the level of understanding during the experimental phase. The reporting of group findings will allow the teacher to see how well each group answered the central question. The concepts investigated here will be recalled and applied in the graphing lesson.

Note

• This activity may be changed to include a more traditional lab write-up.

• There is a toy from the good old days called Tracball by Wham-O. It is a curved throwing scoop with sharp teeth that grips the ball and gives it incredible spin. The old commercials had kids playing catch around a tree. Sets have been found on eBay for about $10.