The Pitch
Drag Simulation Activity

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

Overview of Lesson

The focus of this lesson is air drag. Students will role-play the part of an object (baseball) fighting its way through the air molecules.

Goal

Students will get a feel for the mechanism responsible for air drag and for the variables that factor in.

Objectives

• The students will simulate the complex processes associated with air drag.

• The students will list the variables that contribute to the calculation of air drag.

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

• The students will be able to discuss the limitations of simulations.

Ohio Academic Content Standards

Materials

A large, open area in a classroom or gymnasium.

Procedure

1. Clear as large an area as possible in your classroom or, better yet, take the students to the gymnasium or outside.

2. Explain to the students that they are going to be role-players in a simulation that will give them a feel for the mechanism and variables associated with the phenomenon of air drag as it relates to the flight of a baseball.

3. Simulation Stage 1: Assign two or three students to hold hands in a small circle. They will act as the "ball" in the simulation. Ask the remaining students to stand to one side and just observe for the time being. Ask the "ball" to walk from one side of the room to the other. Tell the class that this represents a baseball thrown in a vacuum with nothing to affect it along the way.

4. Simulation Stage 2: Now ask the remaining students, or a portion of them, to act as molecules of air. Have them spread out at least arms-length apart and randomly scattered around the open area of the floor. Have the "air molecules" begin milling around in a sort of slow-motion slam dance. Now have the "ball" walk from one side of the room to the other again. Let students observe and describe the fact that the "ball's" progress is now impeded by collisions with the air molecules. Explain that in a rough way this simulates the flight of a baseball pitched through the air on its way to home plate.

5. Simulation Stage 3: Through a series of "What if?" questions posed by the teacher and/or coaxed out of the students, the simulation can be modified to investigate all of the variables that factor into the calculation of air drag.

   a. What if the density of the air were to change due to a change in temperature or humidity? Simulate an increase in air density by adding more "air molecules" into the group and/or having them move closer together.

   b. What if the size of the ball changed, from a baseball to a softball? Simulate this by adding a few more students to the "ball," making a larger circle. They should see that this larger "ball" will interact with more "air molecules."

   c. What if the shape of the ball were to change? Simulate the effect of aerodynamic properties by having the "ball" flatten out or become more streamlined like the nose cone of a rocket. The overall aerodynamics of an object are expressed as its drag coefficient.

   d. What if the ball were thrown faster? Simulate this by having the "ball" move faster across the room. Students should see that if the ball moves faster it will collide with "air molecules" more often and more violently, slowing it down even more.

6. After the group has acted out all of the "What if?" scenarios, the teacher can introduce the equation that physicists use to calculate the air drag force on objects such as baseballs.
   
   
   
   
   The equation states the drag force (F_d) is directly proportional to the drag coefficient (C_d), the cross sectional area of the object (A), the air density (r), and one-half of the square of the velocity (V) of the object. Have the students relate their experiences in the simulation to each of the variables.
   
   *One aspect that is not so obvious to deduce from the simulation is the proportionality with the square of the velocity; just explain that it is a result of empirical data. Another factor mentioned in the videos that is very counterintuitive for students is the fact that a rough ball (like a baseball with its 108 stitches or a golf ball with its dimples) is actually aerodynamically superior (having a lower C_d value) to a smooth ball. To explain this apparent discrepancy one must look at the idea of a boundary-layer of air being pushed ahead of a smooth object, effectively increasing its cross-sectional area (A). Ask the students how you might adjust your simulation to include the boundary-layer variable.

7. As a follow-up, the teacher can lead a discussion of the limitations of this simulation and simulations in general. The obvious points to emphasize are the relative size and number of the objects involved, and the simplification of the interactions. More accurate computer simulations can be found online and viewed to add to the discussion.

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. The concepts investigated here will be recalled and applied in the graphing lesson.

Note

Although a simulation such as this may seem grossly oversimplified and somewhat juvenile, the kinesthetic aspect provides a strong memory hook of the concepts, which makes the process very worthwhile.