Getting a ball (e.g. a cricket ball, soccer ball, tennis ball, or baseball) to move laterally is somewhat difficult (though I find it all too easy with a golf ball). The fluid mechanics of this phenomenon is quite interesting and provides insight in to how boundary layer separation influences both drag and lift. Here is a simple demonstration for showing how to get a ball to move upward after release by putting backspin on it.
- A ping-pong ball
- Some sort of track. I used a 30 inch wall mounted shelving frame piece that you can get at a hardware store (I used this one http://www.lowes.com/ProductDisplay?productId=3006188)
Figure 1. Equipment.
- Hold the bottom of the track and rest the ball on top of your hand (see figure 2 below).
- Rotate your wrist rapidly so that the ball is forced up the track and forwards (see figure 3 below)
With a bit of practice you can get the ball to fly off the end of the track roughly horizontally and then rise up due to the lift force
Figure 2. Initial setup.
Figure 3. Launching the ball by rapidly rotating the track.
The key to the explanation is that the rotation of the ball leads to asymmetric boundary layer separation. As you flick your wrist and rotate the track the ball is accelerated and forced up the track. Friction with the track imparts a backspin to the ball such that, as the ball leaves the end of the track, it is rotating in a clockwise direction as shown in figure 3. The backspin on the ball means that the lower side of the ball is moving faster than the upper part of the ball (see figure 4 below). As a result, provided you are in the right Reynolds number regime such that the separation point is Re dependent, the boundary layer on the top of the ball will stay attached over a greater distance than the boundary layer on the lower side (see figure 4 below). As a result the airflow will be deflected downward by the ball.
Figure 4. The rotation of the ball causes the underside to move faster and the underside boundary layer to separate further upstream than on the top.
If you draw a control volume around the ball with the control volume moving with the ball then the C. V. inflow is in the direction of flight and the outflow is deflected downward. Therefore, the ball must be applying a downward force on the airflow to create the downward component of the outflow momentum. As a result, the airflow must be applying a force vertically upward in reaction. This lift force drives the ball upward.
Figure 5. Control volume moving with the ball showing the inflow, the deflected outflow and the force that the ball applies to the flow to generate the downward momentum.
The demonstration requires very little equipment but is a little fiddly. You need to use a ping-pong ball as it is light enough that the lift force can overcome the balls weight and move it upward. An alternate way to do this is to spin it sideways and get it to move laterally. The implications of this physics are discussed with actual numbers in “The physics of baseball” by R. K. Adir. The origin of this particular demonstration is unknown though I have seen basic descriptions of it in a few different books.
An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (firstname.lastname@example.org). I also welcome comments (through the comments section or via email) on improving the demonstrations.