Measuring the Wind with Hot Metal

Supplemental Information to "The Amateur Scientist"
(Scientific American, November 1995)

by Shawn Carlson

HOT BALL ANEMOMETRY

Thermal anemometry measures wind speed by finding the rate at which flowing air cools a hot piece of metal. The method has been around for a long time. References to the technique go back as far as the 1840's. Today, researchers use micro-fine platinum wires and sophisticated electronics to monitor how turbulent processes at a million times a second. Unfortunately, such complex and delicate equipment are not well suited for most amateur projects. The devices are quite expensive and the probes break often.

Cup anemometers (what you normally see on a weather station) are bulky and depend on a difference in dynamic pressure to determine the wind speed. Their sensitivity scales as the square of the wind speed and this makes them quite sensitive at large wind speeds but horribly insensitive at low wind speeds. As a rule of thumb, cup anemometer should not be trusted below 5 meters per second, unless they have been independently calibrated. Thermal anemometers, on the other hand, are most sensitive at low wind speeds and lose sensitivity at higher speeds. The anemometer described in "The Amateur Scientist" (Scientific American, Nov, 1995) is quite accurate starting below 0.1 meters per second and running all the up to at least 22 meters per second.

The anemometer described in "The Amateur Scientist" is ideal for amateur use. It will respond to changing wind speeds in about 5 seconds-- fast enough for many applications. It's small enough to fit inside a peanut butter jar. It's inexpensive and durable. And it will perform under a variety of environmental conditions from direct sunlight to the damp darkness of a bat's cave.

AIR FLOW OVER THE BALLS-- LAMINAR VS TURBULENCE

A hot object cools in three different ways: radiation, conduction and convection. Heat "radiates" from all objects as inferred light. But so little of the hot ball's energy escapes in this way that we don't need to worry about it.

Now let's assume that the ball sits in still air. At first some heat will be conducted away from the ball through the thermocouple wire. This can be a significant source of heat loss early on, but since the wires and the resistor are insulated, once the wire warms up very little heat escapes through this path.

More important is the heat loss directly to the air. The ball will impart heat into the air molecules that strike its surface. The air that touches the ball is heated just a little bit, and, since hot air rises, it carries this heat upward away from the ball. Cooler air then flows in from all sides to fill the void. This new air is in turn warmed by the ball and rises away to carry off additional energy. In this way, the hot ball sets up a continuous air current that carries away heat. We call this process "convection."

Of course, the hotter the ball is, the faster this will happen. A very hot ball will heat the air around it very quickly, causing a sizable air current to flow. A slightly warm ball will also be cooled in this way, but at a much slower rate. The resister dumps heat energy into the ball causing its temperature to rise until the energy leaving the ball equals the energy being dumped into it.

As this self-generated current of air flows over the ball, different parts of the ball achieve slightly different temperatures. Heat is most efficiently conducted from the equator of the ball, and less so from the polls. You can actually see this with your anemometer as follows: Turn on your resistor and let the ball heat up until it reaches it's maximum temperature. Then, very gently rotate the hot ball 90 degrees about the horizontal in place by twisting the insulated thermocouple lead. You'll see your voltage readings change as the heat flows around the ball to establish a new equilibrium.

A slight breeze flowing over the ball will conduct heat away. At slow wind speeds, conduction and convection compete, but much above about 0.1 meter/second, the conductive losses to the wind dominate. This means that the physical mechanism of heat loss changes between 0 and 0.1 meter/second wind speed and this is important to keep in mind. It's tempting to calibrate the anemometer at wind speeds above 0.1 meter per second and simply extrapolate below that speed. This will not lead to reliable results because the physical mechanism for the heat loss, and thereby the calibration curve, changes below about 0.1 meter per second. If you want to make meaningful measurements in this region, you'll need to take some measurements at wind speeds below 0.1 meter per second.

Above 0.1 meter per second conduction dominates. The balls aren't perfect spheres because of the wires sticking out of them which interfere with how the wind flows. If the wind speed isn't too fast, the air currents flow in smooth continuous lines around the balls. We call such smooth flow "laminar flow." As the wind speed increases, more air molecules are brought against the ball per unit time and so more heat is taken away. If the flow remains laminar, the temperature of the ball will fall exponentially with wind speed.

Eventually, as the wind speed is increased ever faster, the air will rush over so fast that smooth laminar flow is not longer possible. Eddies and backwash develop behind the ball. The air flow becomes broken or "turbulent." Turbulent flow removes heat much faster than laminar flow. If you take your data carefully, you'll see the onset of turbulence in your calibration curve. More about that later.

CALIBRATION

By far the simplest way to get your anemometer calibrated is to place it in a wind tunnel. So, before using the method described in The Amateur Scientist, TRY TO GET ACCESS TO A WIND TUNNEL!

This may be easier than you think. Call your local universities and see if any physics or engineering department has one has one. Tell the people in charge of it what you're doing and you may very well get an hour on the machine to calibrate your anemometer. Are there any aircraft or auto-makers near you? Any engineering firms? Ask around. Only after you've exhausted these options should you build your own calibration system.

You may calibrate the anemometer by comparing it to another anemometer. However, if you have a standard cup anemometer, watch out! These anemometers are notoriously inaccurate. Calibration errors as large as 200 percent are common. The biggest errors for cup anemometers occur at the lowest wind speeds because that is where they are least sensitive. Never trust a cup anemometer that hasn't been independently calibrated. And even then, never use a cup anemometer to calibrate a hot ball anemometer at speeds below about 3 meters per second.

Professionals sometimes lay out a section of model railroad track down a long hallway and affix their anemometer to a railroad car. They run a string from the car to a tin can which they rotate with a very slow (1 revolution per minute or so) electric motor. As the can rotates it pulls the car along the rack at a known rate. (v = 2 PI x rf where is the radius of the can, PI is 3.14159, r is the distance from the center of motion, and f is the frequency of rotation or the number of revolutions the can makes per unit time.) By using cans of different radius and rotating the cans at different frequencies one can measure the anemometer's performance at a number of different velocities.

A better way to do this is described in "The Amateur Scientist" and involves using a ceiling fan motor to rotate the anemometer through the air at a number of known speeds. The Scientific American article describes strapping a digital voltmeter to the rotating armature, and reading this with a strobe light. This technique works fine. But if you want to do a detailed calibration, you may want a better way of reading the voltage.

GETTING THE SIGNAL OFF THE PLATFORM

I do this using ultrasound. The method is easy and inexpensive but you have to know what you are doing. Ultrasound may sound exotic, but it's actually really easy (if you know a little electronics) to generate, detect and use. Just feed the signal into a voltage controlled oscillator (VCO, also known as a "voltage to frequency converter") and use that to drive a piezoelectric speaker at about 5 kHz. The VCO is a standard chip that's produced by many different companies that only requires a capacitor and a resistor to set the central frequency. The speaker can be purchased from Radio Shack for a few dollars.

Put the speaker just above the center of the fan motor. I use a $3 microphone from Radio Shack to pick up the signal. The microphone rests some distance above the rotating platform. The output of the microphone goes into an integrator circuit. Every time the microphone output goes high, the integrator circuit puts a small but constant unit of change onto a capacitor. The capacitor is part of an RC circuit with a time constant large compared to the frequency of the sound pulses, but short compared to the time it takes for the anemometer to respond to changing air speeds. The voltage across the resistor is proportional to the frequency of the sound being recorded by the microphone.

GENERAL CONSTRUCTION TIPS

Here are some useful tips to keep in mind while you're building the anemometer.

TIP: Cover Balls With Candle Wax To Avoid Splashing Them With Epoxy

Aluminized epoxy on the surface of the balls will alter their thermal properties and lower the air speed at which turbulence becomes a problem. It is vital that you do not have any excess epoxy marring the surfaces.

To avoid this problem, coat the balls with a layer of candle wax. I plugged the holes with a dollop of silly putty and dipped the balls in melted paraffin. You could, no doubt, drip candle wax onto the surfaces and spread it around with your finger. Assemble the unit as described below. After the epoxy has firmed up (about 30-45 minutes), but before it sets completely, break off the wax and, using a sharp knife, scrap off any epoxy that may be sticking up out of the holes.

TIP: Expose the Epoxy to Vacuum to Eliminate Air Bubbles

Mixing the resin with the hardener invariably adds many small air bubbles. If allowed to cure, these air bubbles will weaken the bonds. Also, like the air gap between the glass sheets inside a storm window, these bubbles will reduce heat conduction through the epoxy, lengthening the time it takes the ball to come to equilibrium. Neither problem is serious, but they can be easily avoided if you have access to a vacuum pump and a bell jar.

Pumping down on the freshly mixed epoxy causes the air bubbles to expand and break out of the surface. The result is a nearly bubble-free mixture. To avoid splatter, make sure to mix only small quantities in a disposable Dixie cup. (Keep this tip in mind whenever you use epoxy.)

Of course, you'll add more bubbles when you insert the epoxy into balls to glue the components in place. These can also be removed by placing the whole assembly in a vacuum chamber just after it's put together but before the epoxy has had a chance to set. Make sure to wipe off any splatter. In fact, some of the material may bubble out and so you may have to repeat this process a couple of times to fill the whole.

TIP: Mount the Hot Ball Above the Cold Ball

You should mount the hot ball above the cold ball. Otherwise, in still air, air warmed by the hot ball will convect up over the cold ball and warm it.

TIP: Color Code Your Wires

If you color code your wires by function, you'll find your circuits are much easier to build and debug. For instance, you might make your ground wires all black, your single wires red and your connection wires green.

TIP: Continuity Checks

Use the continuity tester on your voltmeter to verify the following connections:

A) Check the copper wire leads from the thermocouple as soon as they are tapped for the signal leads. Make sure you have already doped the twisted junctions with enamel but that you have not yet inserted them into the balls. You should get continuity. If you don't, you'll need to remove the enamel and rebuild the junction. If you do not get continuity, the device will not work!

b) As soon as you insert the thermocouple junctions into the balls, but before the epoxy sets, be sure that you have no continuity between the copper lead wires and either of the balls. The thermocouple wires should be electrically insulated from the spheres. If they are not, remove them, remove the epoxy and the enamel and re-enamel the connections. The trick is to make the junctions electrically insulated, but not thermally insulated.

c) After inserting the resistor inside the hot ball but before the epoxy sets, make sure the resistor leads show no continuity between with the hot ball. If there is continuity, you'll have to remove the resistor, remove the epoxy and re-coat the resistor leads with enamel. Make certain you only enamel up to the surface where the wire enters the resistor. Do not get any enamel on the cylindrical surface of the resistor's body! You want to let heat easily conduct out of the resistor into the ball.

TESTING THE CIRCUIT

After you've built the circuit described in The Amateur Scientist, here are some easy checks to make sure everything is working correctly.

CHECK 1: PRESS AN ICE CUBE AGAINST THE COLD BALL
The voltage should go down. If the voltage goes up, you've got the signal leads reversed into the inputs on the op amp. Recheck the schematic. Make sure the lead from the cold ball is inserted into ground and that the lead from the hot ball is inserted into pin 3 of the Op Amp.

CHECK 2: PUT HOT BALL IN CUP OF HOT WATER
The voltage should go up. Ditto for check 1.

IF THE VOLTAGE DOES NOT CHANGE...
If the voltage does not change and is several volts positive or negative, the op amp is probably saturated. One or more of your batteries may be low. Check them with your voltmeter. Then check to make sure the battery voltage is getting to everywhere in the circuit it's suppose to. Make sure all of the parts of the circuit are at ground that should be at ground, and that all the positive and negative connections are also correct. If all that checks out, then perform continuity checks and make sure all the closed circuit paths are closed. If you're still having problem, recheck the wiring very carefully and make sure it exactly matches the schematic.

FIRST EXPERIMENT:

The first experiment you should do is monitor the voltage output as the hot ball heats up. To do this, measure the voltage just before you connect the resistor to power and then again the instant after. The instant current flows into the resistor you'll see the voltage jump by quite a few millivolts. This is NOT due to the ball warming, because the jump occurs too fast for the resistor to transfer a measurable amount of heat to the ball. Rather, it occurs because the thermocouple is capacitively coupled to the ball.

You should note this jump in your log book. Or better yet, record all your data in a spread sheet program running on your home computer! Data recorded on a personal computer can be processed so much faster and easier than possible by hand. If you have access to a computer, use it!

The voltage you should use as your reference, that is the voltage before the ball begins to warm, is the voltage you measure the instant AFTER the resistor's power is turned on.

Then, record the voltmeter reading every 10 seconds. It's best to have a colleague write down the numbers in a column in your laboratory notebook or type them into a computerized spread sheet as you call them off.

You need an absolute commitment to honesty in data taking. Keep your eyes rigidly fixed on the second hand of your timepiece. Wait until exactly 10 seconds has counted off. Then instantly snap your eyes to the voltmeter. Write down or call out whatever number you see there the moment your eyes focus. Often, the number fluctuates in the instant between the time you see it and the time you look to the notebook. Always, ALWAYS, record the very first number you see.

If you don't do this you may get yourself into trouble. Once you get into the swing of things, it's impossible not to anticipate what number you'll see when next you look at the voltmeter. Sometimes you'll see a different number when you first look, but then before you look away to record the datum the number will change into the number you expected. It's human nature, but bad science, to write down the number you expected.

The battle between human nature and good science subtly creeps into every scientific experiment you'll ever do. Sadly, many researchers, professional and amateur, succumb to human nature and produce unreliable results. The first defense against this is a deep appreciation for how easily we can fool ourselves and bias our results. The second defense is to always establish exactly what protocol, down to the very last detail, you will follow every single time you record data and scrupulously follow through to the point of obsession. This unwavering commitment to eliminating all human bias from your experiments is very difficult to maintain but it is essential to produce reliable data. Perfection in this matter must always be your goal.

Keep taking data until the voltage measured remains constant for at least 2 minutes. For my apparatus, this took about 12 minutes.

When you've got all your data, make a second column and fill in the voltage read minus the initial voltage, that is, subtract the voltage you measured when the ball was cold from each voltage you measured. (See why it's nice to have a computerized spread sheet?) Now graph the result.

This data should fit the following function:

V(t) = Vh(1 - exp(-t/t0)) + V0

V0 is the voltage your first measure before beginning the resistor begins to heat. Vh is how much the voltage increased. It's easy to get from the graph. Just subtract the initial voltage from the final voltage. Vh will depend on how much power you're dumping into the ball and how effective the atmosphere is at taking that energy away. If you insulated the ball so very little heat escaped, this voltage would be quite high. If you did the experiment in a tank of water, where the energy could be conducted away very quickly, this voltage would be quite low. Also, if you dumped a great deal of power into the ball this voltage would be high because the ball would run hotter. If you lowered the power, the temperature, and therefore this voltage, would drop.

t0 measures how fast the voltage rises. It depends on how much heat it takes to raise the ball's temperature (the ball's heat capacity) and on how much power the resistor dumps into it. If the ball's heat capacity is large (if it takes a lot of heat to raise the ball's temperature 1 degree) then it will take a long time for the resistor to supply enough energy to do that. If the resistor delivers a lot of power, the ball's temperature will rise quickly. t0 is also easy to find. Multiply Vh by 0.368 and add that to V0. Clearly, the result will be about one third of the way up the curve. Find the time it took for the voltage to reach that value. That time is t0.

V0, Vh and t0 can tell you a lot about the heat capacity and thermal conductivity of the system.

TIP: ALWAYS WAIT FOR THE BALL TO HEAT UP BEFORE MAKING MEASUREMENTS.

Now you know how long it takes for the ball to heat once the current is turned on. Always make sure to wait at least that long before starting to take data.

MORE ABOUT FOR CALIBRATING THE DEVICE

The Amateur Scientist column described a method to calibrate the anemometer using a ceiling fan motor to swing the anemometer about at a known speed. Here are some important fine points you will need to consider to do this calibration correctly.

First: If you live in an area with a lot of radio noise, you may well pick up excess voltage in the lead wires running from the anemometer to the amplifier. This problem can be so severe that rotating the meter stick 90 degrees can cause fluctuations in the voltage by 30 millivolts or more! You could place the device inside a Faraday cage (basically a box with metal wire mesh on all sides) to absorb all the radio energy. Low pass filters DO NOT solve the problem. The best thing to do is to avoid the noise all together and take the device to a location where the noise is less. You don't necessary have to head for the mountains. I was able to find locations within 20 yards of my residence where the metal in the surrounding structures blocked the radio signals enough to substantially reduce the noise.

Even if you can find a place where this effect is small, the ionosphere may cause you problems. Once while calibrating the device I noted a slow steady drift in the signal voltage even though the device was isolated from any air movement. Investigations showed that the drift was likely due to radio energy bounced from the ionosphere.

These radio problems arise because the long signal leads between the anemometer and the electronics box act as radio antenna and couple the radio energy into the system. The best way to eliminate this problem is to mount the anemometer directly to the electronics box, then move the entire electronics box to change the wind speed.

CALIBRATION BETWEEN V to VCO and Vout.

One problem... If you attach the anemometer to the electronics box, the box will create turbulent air as it whips around. The anemometer will then run into the box's wake on the next pass. To reduce this problem, I use a cardboard spoiler which I place in both and in front and behind the box to make sure the air flow around the box is "smooth" (or more correctly, "laminar"). If you go this route, make the electronics box as small as possible.

EXPLORING TURBULENCE

Here's how to use your calibration set up to explore the onset of turbulence.

The further out a point rests along the rotating arm, the faster it travels. That means that the outer surface of the anemometer balls travel faster than their inner surface. At some speed, the outer surface will just begin to create turbulent flow around the outer edge of the ball. When that happens, the temperature will take a sudden drop because turbulent flow removes heat substantially faster than laminar flow. At a slightly higher speed the inner surface will also create turbulence. Above this speed the ball's temperature vs. speed will follow a different curve. With sufficient care, you may be able to see this in your data.

Here are some issues you may want to explore:

• At what speed does the onset of turbulence occur?
• What can you say about heat conduction between the speeds where the inner and outer rim of the ball create turbulence?
• If you attach irregularities onto the surface, how does that affect the speed at which turbulence becomes important?
• Try getting balls of different size and materials. What effect does shape, substance and size have on the onset of turbulence?

Researchers with SAS are beginning to explore this issue. I would be delighted to see any results you obtain.

ONCE CALIBRATED...

your hot ball anemometer is a useful and sensitive device. It is best used for measuring low to medium wind speed (less than about 30 meters/second), and it can be placed in all sorts of places where a conventional anemometer just won't fit.

If you're looking for interesting science projects, here are just a few:

• Measure how effectively a bird's nest cuts the chill of a winter storm. You can do this by putting a bird's nest in a constant source of wind and then measuring the wind speed at several locations above and inside the nest.
  
• Measure how effectively a thicket protects it's inhabitants from wind. First, measure the wind speed at different distances in front of a strong fan. Then place the fan in front of the thicket (you may need a portable generator to power the fan) and measure the wind speed a several different heights and distances inside the thicket.
  
• Measure how a fan's efficiency changes as it's speed is increased. To do this you'll need to measure the wind speed coming out of the fan for several different fan settings. You'll also need to measure the power consumed by the fan. You can get that by measuring the current being fed into the fan, and the voltage across the fan's terminals. The power is just the product of these two numbers. Working with electricity is always potentially hazardous so be absolutely certain you know how to measure the current and voltages safely. If you are under 18, be sure to conduct these measurements under the supervision of an adult who understands electricity and it's hazards.
  
• Measure the wind speed at different, but connected, gopher holes. Figure out how to measure the speed of the air moving somewhere deep inside the burrow. Can you think of a way to also measure the wind's direction (up the shaft or down)? How do these subterranean burrows get ventilated?
  
• How much wind must an ant contend with while it's on an ant trail? How much work (force x distance) must it do to move itself against the wind? How does this affect how often it must eat?
  
• Measure the wind speed at different heights in a forest. How does the tree cover protect the life that inhabits different strata in different kinds of forests? How can you quantify the density of plant life in the forest?
  
• Develop a way to measure the wind speeds at different places around a bird in flight. Think about using a wind tunnel to provide the wind for the bird to fly against.
  
• Study the updrafts near cliffs. Compare with what you get for similar studies near the top of a tall building.
  
• Map out the air flow patterns between large buildings. Can you relate the speed and direction to physical features of the buildings?
  
• Identify a microclimate that interests you and use the hot ball anemometer to measure the wind speed under various conditions of importance to the animals who live there.
  

Also, please do share your results of your experiments. If you use any of these ideas in a science fair, or if this inspires you to do other explorations, please let me know!

Shawn Carlson
scarlson@sas.org

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