# How to make, read, and calibrate a ping-pong ball anemometer?

I'd like to make a ping-pong ball anemometer to make estimates or approximate measurements of wind and surface air currents at low to moderate speeds. I don't own an anemometer now, but I'd estimate the speeds of interest to be between zero and a maximum of order of 10 or 15 mph (feels similar to riding a (non-racing) bicycle down hill on an otherwise windless day).

If I understand correctly, a ping-pong ball anemometer probably refers to the use of a ping-pong ball or other tell-tale normally used to indicate wind direction to also try to use it to estimate the speed of the wind.

If this were a problem on a test, I'd set up the equations for force and balance the vertical and horizontal forces separately, assuming the wind is horizontal. For the horizontal force, I'd use a simple equation for drag force as a function of velocity from Wikipedia:

$$F_D(v)= \frac{1}{2} \rho v^2 C_D A$$

where the density of air at low elevations and moderate temperature is roughly 1.2 kg/m^3, $$A$$ is the cross-sectional area of the ping-pong ball $$\pi R_{p-pb}^2$$ and $$C_D$$ would be the drag coefficient, which is where all of the reality and the complications of aerodynamics are actually hidden in practice. $$C_D$$ is not really a constant, and is often plotted against velocity and other parameters. However, for some range of Reynolds numbers, a perfect sphere would have a roughly constant $$C_D$$ of about 0.47.

But a 2.7 gram, 40mm diameter ping-pong ball anemometer, or similar device is a real-world device. Maybe I should use a heavier ball, but I think the smoothness of the ball is critical if I want to use a theoretical $$C_D$$ and estimate speeds using equations rather than doing a real calibration against a known anemometer or riding in/on a vehicle at a known speed.

Are there any instructions for how to build, use, and calibrate or interpret results for this kind of simple anemometer? Ideally some dimensions and a suggested scale would be great! Or if this has been actually measured for a pingpong ball or another object, that would also be a great answer as well.

If the concept is good enough for a Mars lander weather station, then it's good enough for me! above: GIF from images transmitted from Mars. From the The Telltale project page on the Mars Simulation Laboratory. Also archived here. above: Instrument as delivered to NASA. From the The Telltale project page on the Mars Simulation Laboratory. Also archived here. That's a 45 degree mirror below the telltale providing a simultaneous view from below.

• This is probably more suited to engineering, but I can understand why it's being asked here: maybe someone knowledgeable about meteorology knows how these devices are made. To get the best calibration you'd need a wind tunnel, which most likely wouldn't be an option. With the device on Mars wind blowing parallel to the support arm will affect the results because of interference. Best results will be for wind perpendicular to the support arm. To make it light weight & more responsive to winds, I'd try to connect the ball fine light fishing line.
– Fred
Jun 18 '17 at 11:59
• @Fred yep you are right. If I wanted an engineering answer I'd have answered it already. I'm looking for someone who has perhaps already made estimates or approximate measurements of wind and surface air currents perhaps as part of a class instruction or a field measurement. It could be in a basic Earth Science text book perhaps. I only added the math to introduce the concept of the drag coefficient to make sure that it's clear that the smoothness of the ball matters. If 10 degrees = 15 mph for a smooth ball, then it might mean 20 mph for a dimpled ball or 10 mph for a ball with holes.
– uhoh
Jun 18 '17 at 12:15
• @uhoh, it's definitely not mentioned in basic earth science text books, and don't believe it's in meteorological books generally either. I'd have to check my meteorological measurements textbook when I'm near it, but not sure we're going to have a lot to help, as generally the instrument focus is on more precise, standardized equipment. That said, interesting topic. Jun 19 '17 at 17:23
• @JeopardyTempest thanks for checking! I suppose I could try to make a simple hot wire anemometer with a battery and a volt meter but I think that would get messy and have repeatability problems. The smooth ping-pong ball, piece of thread, and bit of wax(?) to stick it together seems so simple. I may just try it and calibrate by riding a bike at different speeds and having someone record a video.
– uhoh
Jun 20 '17 at 2:28
• @uhoh that sounds like a creative idea! It'll be a few days until I'm back home where textbooks are. Jun 20 '17 at 17:39

The drag coefficient varies with Reynolds number and hence with wind speed. Most fluid-dynamics textbooks have a graph of the drag coefficient of a sphere versus Reynolds number. Hopefully that could help. (A sphere such as a ping-pong ball is the best shape since its shape is the same in all orientations --- only a sphere has complete omnidirectional symmetry.) Because wind is rarely steady but usually includes gusts and lulls, it may be necessary to account for overshooting. A sudden gust can cause the ping-pong ball to temporarily overshoot to a higher angle than in a steady wind at the same speed as the gust.

• For Reynolds numbers corresponding to wind speeds in the range of say 1 mph to "10 to 15 mph", ($R_e$ about 1,200 to 18,000 at ~20°C & sea level) isn't the $C_D$ of a smooth 4cm sphere almost constant? At least compared to all the other sources of error? I'm just trying "to make estimates or approximate measurements" here.
– uhoh
Jun 20 '17 at 8:13
• If CD doesn't vary much of course it can be approximated as constant. Overshooting due to gusts and lulls, may be a bigger source of error. Of course for measuring wind speed from steady sources such as fans overshooting doesn't occur. Jun 21 '17 at 0:07
• A really good point, and makes it more interesting!!. If the wind is not steady, then this becomes a nonlinear dynamical system (pendulum is given as an example there) and interaction with the time-dependent wind will be complicated. In this case even the average angle of the pendulum would not correspond to the average wind speed. A cup anemometer on the other hand has no restoring force to produce oscillations, but has a big moment of inertia that would be better at averaging. Plenty here to think about, thank you!!
– uhoh
Jun 21 '17 at 4:44
• Propeller-type anemometers are probably the most accurate for both sustained winds and gusts. Kestrel makes good ones. Jun 21 '17 at 6:48
• I'll do some reading and then ask a follow up. I didn't expect anemometry to be so interesting, thanks!
– uhoh
Jun 21 '17 at 7:18