<p>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.</p>

CC BY-SA 3.0
2017-06-20T08:13:35.367Z
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](https://commons.wikimedia.org/wiki/File:Drag_coefficient_on_a_sphere_vs._Reynolds_number_-_main_trends.svg)? At least compared to all the other sources of error? I'm just trying "to make estimates or approximate measurements" here.
uhoh
CC BY-SA 3.0
2017-06-21T00:07:44.773Z
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.
Jack Denur
CC BY-SA 3.0
2017-06-21T04:44:26.277Z
A really good point, and makes it more interesting!!. If the wind is not steady, then this becomes a nonlinear [dynamical system](https://en.wikipedia.org/wiki/Dynamical_systems_theory#Dynamical_systems) (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
CC BY-SA 3.0
2017-06-21T06:48:44.840Z
Propeller-type anemometers are probably the most accurate for both sustained winds and gusts. Kestrel makes good ones.
Jack Denur
CC BY-SA 3.0
2017-06-21T07:18:31.780Z
I'll do some reading and then ask a follow up. I didn't expect anemometry to be so interesting, thanks!
uhoh
CC BY-SA 3.0
2017-06-20T07:54:04.203Z
2017-06-20T07:54:04.203Z
Jack Denur
<p>I'd like to make a <a href="https://en.wikipedia.org/wiki/Anemometer#Ping-pong_ball_anemometers" rel="nofollow noreferrer">ping-pong ball anemometer</a> 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).</p>

<p>If I understand correctly, a ping-pong ball anemometer probably refers to the use of a ping-pong ball or other <a href="https://en.wikipedia.org/wiki/Tell-tale" rel="nofollow noreferrer">tell-tale</a> normally used to indicate wind direction to <em>also try to use it</em> to estimate the speed of the wind.</p>

<p>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 <a href="https://en.wikipedia.org/wiki/Drag_(physics)" rel="nofollow noreferrer">Wikipedia</a>:</p>

<p><span class="math-container">$$F_D(v)= \frac{1}{2} \rho v^2 C_D A$$</span></p>

<p>where the <a href="https://en.wikipedia.org/wiki/Density_of_air" rel="nofollow noreferrer">density of air at low elevations and moderate temperature</a> is roughly 1.2 kg/m^3, <span class="math-container">$A$</span> is the cross-sectional area of the ping-pong ball <span class="math-container">$\pi R_{p-pb}^2$</span> and <span class="math-container">$C_D$</span> would be the <a href="https://en.wikipedia.org/wiki/Drag_coefficient" rel="nofollow noreferrer">drag coefficient</a>, which is where all of the reality and the complications of aerodynamics are actually hidden in practice. <span class="math-container">$C_D$</span> is not really a constant, and is often <a href="https://commons.wikimedia.org/wiki/File:Drag_coefficient_on_a_sphere_vs._Reynolds_number_-_main_trends.svg" rel="nofollow noreferrer">plotted against velocity</a> and other parameters. However, for some range of <a href="https://en.wikipedia.org/wiki/Reynolds_number" rel="nofollow noreferrer">Reynolds numbers</a>, a perfect sphere would have a roughly constant <span class="math-container">$C_D$</span> <a href="https://en.wikipedia.org/wiki/Drag_coefficient" rel="nofollow noreferrer">of about 0.47</a>.</p>

<p>But a <a href="https://en.wikipedia.org/wiki/Table_tennis#Ball" rel="nofollow noreferrer">2.7 gram, 40mm diameter ping-pong ball</a> 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 <span class="math-container">$C_D$</span> 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. </p>

<p>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.</p>

<hr>

<hr>

<p>If <a href="https://en.wikipedia.org/wiki/Tell-tale#Space" rel="nofollow noreferrer">the concept</a> is good enough for a <a href="https://space.stackexchange.com/q/21680/12102">Mars lander weather station</a>, then it's good enough for me!</p>

<p><a href="https://i.sstatic.net/FJbPa.gif" rel="nofollow noreferrer"><img src="https://i.sstatic.net/FJbPa.gif" alt="enter image description here"></a></p>

<p><strong>above:</strong> GIF from images transmitted from Mars. From the <a href="http://marslab.au.dk/research/instrument-development/the-telltale-project/" rel="nofollow noreferrer">The Telltale project</a> page on the <a href="http://marslab.au.dk/" rel="nofollow noreferrer">Mars Simulation Laboratory</a>. Also <a href="https://web.archive.org/web/20120220080017/http://www.marslab.dk/TelltaleProject.html" rel="nofollow noreferrer">archived here</a>.</p>

<p><a href="https://i.sstatic.net/xCWAk.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/xCWAk.jpg" alt="enter image description here"></a></p>

<p><strong>above:</strong> Instrument as delivered to NASA. From the <a href="http://marslab.au.dk/research/instrument-development/the-telltale-project/" rel="nofollow noreferrer">The Telltale project</a> page on the <a href="http://marslab.au.dk/" rel="nofollow noreferrer">Mars Simulation Laboratory</a>. Also <a href="https://web.archive.org/web/20120220080017/http://www.marslab.dk/TelltaleProject.html" rel="nofollow noreferrer">archived here</a>. That's a 45 degree mirror below the telltale providing a simultaneous view from below.</p>

CC BY-SA 3.0
2017-06-18T11:59:05.247Z
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
CC BY-SA 3.0
2017-06-18T12:15:20.600Z
@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
CC BY-SA 3.0
2017-06-19T17:23:35.093Z
@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.
JeopardyTempest
CC BY-SA 3.0
2017-06-20T02:28:52.650Z
@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
CC BY-SA 3.0
2017-06-20T17:39:07.530Z
@uhoh that sounds like a creative idea!  It'll be a few days until I'm back home where textbooks are.
JeopardyTempest
<measurements><wind><field-measurements>
How to make, read, and calibrate a ping-pong ball anemometer?
uhoh
# How to make, read, and calibrate a ping-pong ball anemometer?

(Asked by: username_0 on 2017-06-18)

I'd like to make a [ping-pong ball anemometer](https://en.wikipedia.org/wiki/Anemometer#Ping-pong_ball_anemometers) 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](https://en.wikipedia.org/wiki/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](https://en.wikipedia.org/wiki/Drag_(physics)):

$$F\_D(v)= \frac{1}{2} \rho v^2 C\_D A$$

where the [density of air at low elevations and moderate temperature](https://en.wikipedia.org/wiki/Density_of_air) 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](https://en.wikipedia.org/wiki/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](https://commons.wikimedia.org/wiki/File:Drag_coefficient_on_a_sphere_vs._Reynolds_number_-_main_trends.svg) and other parameters. However, for some range of [Reynolds numbers](https://en.wikipedia.org/wiki/Reynolds_number), a perfect sphere would have a roughly constant $C\_D$ [of about 0.47](https://en.wikipedia.org/wiki/Drag_coefficient).

But a [2.7 gram, 40mm diameter ping-pong ball](https://en.wikipedia.org/wiki/Table_tennis#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](https://en.wikipedia.org/wiki/Tell-tale#Space) is good enough for a [Mars lander weather station](https://space.stackexchange.com/q/21680/12102), then it's good enough for me!

[![enter image description here](https://i.sstatic.net/FJbPa.gif)](https://i.sstatic.net/FJbPa.gif)

**above:** GIF from images transmitted from Mars. From the [The Telltale project](http://marslab.au.dk/research/instrument-development/the-telltale-project/) page on the [Mars Simulation Laboratory](http://marslab.au.dk/). Also [archived here](https://web.archive.org/web/20120220080017/http://www.marslab.dk/TelltaleProject.html).

[![enter image description here](https://i.sstatic.net/xCWAk.jpg)](https://i.sstatic.net/xCWAk.jpg)

**above:** Instrument as delivered to NASA. From the [The Telltale project](http://marslab.au.dk/research/instrument-development/the-telltale-project/) page on the [Mars Simulation Laboratory](http://marslab.au.dk/). Also [archived here](https://web.archive.org/web/20120220080017/http://www.marslab.dk/TelltaleProject.html). That's a 45 degree mirror below the telltale providing a simultaneous view from below.

**Tags:** measurements, wind, field-measurements

> **Comments:**
> **username_1**: 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.  
> **username_0**: @username_1 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.  
> **username_2**: @username_0, 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.  
> **username_0**: @username_2 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.  
> **username_2**: @username_0 that sounds like a creative idea!  It'll be a few days until I'm back home where textbooks are.  

---

## 1 answers

### Answer by username_3 on 2017-06-20. Score: 3 | Accepted answer

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.

> **Comments:**
> **username_0**: 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](https://commons.wikimedia.org/wiki/File:Drag_coefficient_on_a_sphere_vs._Reynolds_number_-_main_trends.svg)? At least compared to all the other sources of error? I'm just trying "to make estimates or approximate measurements" here.  
> **username_3**: 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.  
> **username_0**: A really good point, and makes it more interesting!!. If the wind is not steady, then this becomes a nonlinear [dynamical system](https://en.wikipedia.org/wiki/Dynamical_systems_theory#Dynamical_systems) (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!!  
> **username_3**: Propeller-type anemometers are probably the most accurate for both sustained winds and gusts. Kestrel makes good ones.  
> **username_0**: I'll do some reading and then ask a follow up. I didn't expect anemometry to be so interesting, thanks!  

---

