Many science museums have demonstrations in which a ball is levitated by an air jet. Typically the ball is quite light and the air jet quite broad. These setups can produce reasonably stable results with the ball staying supported by the air jet. They even work when the air jet is inclined. There are occasionally explanations associated with the demonstration talking about how the drag from the air jet supports the weight of the ball and as it moves off-center then Bernoulli means that there is a low pressure on the jet side of the ball that draws it back in. This is often unsatisfying as an explanation. It also ignores the fact that, when the air jet is inclined, the ball typically rotates. To get at this in a little more detail I tried it with a golf ball.
- Shop-vac that can blow air
- golf ball
- a steady hand or some sort of mount for the hose outlet. I had a spare trolley that I could have a mount built on. See figure 1 below for the setup.
Figure 1. image of the shop-vac and adjustable mount for the hose outlet
The mount shown is adjustable so that one can change the outlet flow angle. The shop-vac I used has an outlet nozzle diameter of 2.5 cm and the air speed, measured 25 cm downstream of the outlet, was 36 m/s. The main downsides of this are that it is quite noisy and also it can be tricky getting the ball to sit in the air stream.
- turn on the shop-vac and place the ball in the air stream
- release the ball such that it remains supported by the flow (This is a lot easier said than done).
- observe the behavior
- slowly adjust the angle of the air jet (I started at vertical and adjusted from there).
Animated gifs of this demonstration for three different jet angles are shown in figure 2.
Figure 2. Animated gifs of the demonstration for three different jet angles showing the different behavior for each angle. the uninterrupted outlet velocity is the same for each case.
- when the air stream is vertical the ball is quite unstable and, after bouncing around for a while, it falls out of the stream. This differs from many museum exhibits where the ball is lighter and is able to change rotational direction more rapidly.
- when the air jet is not vertical the ball is more stable. It rotates rapidly and oscillates backward and forward along the line of the air jet.
The rotation of the ball is key here. The balls rotation deflects the air jet changing the momentum of the flow (see figure 3). To do this the ball must apply a force normal to the direction of the incoming air jet. The reaction to this is a lift force on the ball normal to the direction of the incoming air stream (see figure 4). This is the same process used to throw curve balls (see Lift, Boundary layer separation, and curve balls).
The vertical components of the drag and lift both act upward and together balance the weight of the ball.
Figure 3. Schematic diagram showing the incoming air stream, the ball rotation, and the resulting wake deflection.
Figure 4. (Left) free body diagram of the ball showing the drag, lift, and weight forces. (Right) force triangle showing the force balance when the ball is stable.
The rotation of the ball is established by the air stream. When the ball is placed in the air stream, if it is not rotating, it will fall out. As it does, the air flow across the top of the ball is substantially faster than across the bottom. This drives the ball to rotate which in turn deflects the wake downward and generates the lift force. This is also why it can take a few goes to get the demonstration to work as the rotational inertia of the golf ball limits the rotational acceleration.
Back of the envelope calculation
A standard golf ball has a mass of 46 grams and a diameter of 43 mm. I assumed the density of air to be 1.25 kg/m3 and the measured air velocity from my set up was 36 m/s and I took the jet angle to be 45 degrees. In this case the sum of the forces in the vertical direction becomes
mg=0.5ρu2A sin45 (CD+CL) (1)
Substituting values into (1) leads to CD+CL=0.54. The Reynolds number is approximately 105 which is in the region of the drag crisis for a golf ball (Link) so the coefficient sum would appear to be reasonable.
There are lots of circumstances in which the rotation of a compact object causes a lift force. The most obvious is the in-flight curve of a golf ball when not hit perfectly. One application I am working on is the lift-off and flight of compact debris in severe storms. In particular I am interested in the conditions under which loose-laid roof gravel is removed during hurricanes and tornadoes. On possible mechanism is that the wind shear on the gravel surface pushes a gravel piece to roll over its downwind neighbor. If it is deflected up during this process then the large velocity gradient (wind shear) near the surface could generate the rotation required to generate a lift force and launch the gravel up into the wind field. My student and I will be doing testing on this, and other potential mechanisms, at the Florida International University Wall of Wind Experimental Facility over the next few years.
The research and outreach project (including this post) are based upon work supported by the National Science Foundation under Grant No. 1760999. Any opinions, findings, and conclusions or recommendations expressed in the material are those of the author and do not necessarily reflect the views of the NSF.
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.