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Cooling Some Thermal Superstitions


by Peter Gray


"I swear by tractor thermals," my friend Scott Rutledge, ace Chelan XC pilot, said two years ago, "I just fly from tractor to tractor. It works every time."
"Every time?"
"Well, maybe not every time, but."
A few days later, I had my longest open-distance Chelan flight to that date, naturally the day after the XC Classic ended.
"Scott, I flew almost to Davenport yesterday. Eighty-three miles, alone, and I didn't use a single tractor thermal."
"Of course not, silly." Scott scoffed, "It was Sunday and all the tractors were in their barns!"


Silly Rabbit, Wicks are for Candles

Scott has plenty of good company. The idea of "thermal triggers" is widely accepted, with several recent accounts in the USHPA magazines. My old friend and respected colleague, Dennis Pagen, wrote about them in his excellent 1992 book, Understanding the Sky. In "Bird Man," an April 2001 Paragliding article about famous instructor Dixon White, Tom Harpole wrote that thermals can be "released mechanically by something as small as a rabbit running through them." In "Thermals: Collectors, Wicks and Triggers" (Dec. 2000 Paragliding, Jan. 2001 Hang Gliding), Will Gadd describes similar "active triggers," as well as passive ones such as ditches, hedges, and power lines that supposedly "trip" thermals loose or "wick" them into the sky. After many lively discussions and lots of research and calculation, here's my conclusion: tractors, cars, gliders, animals, power lines, and assorted objects on the ground are effective at breaking thermals loose. just as effective as rain dances are at producing thunderstorms.


Physics for Fun and Distance

Why do I say this? For a sense of scale, let's start with a brief tour of the math and physics. How big is a thermal large enough for us to soar in? In theory, the minimum practical turning radius for a hang glider is about 40 feet, at stall speed and a 45-degree bank, and a paraglider could reduce that radius to about 22 feet. A steeper bank is rarely profitable, as it swaps a heavy sink rate toll for slight reductions in radius. In reality, a paraglider's inside wingtip in such a small turn would be far below stall speed. More realistic minimum thermaling radii are on the order of 13 m (40ft) for a paraglider, 20 m (60ft) for a hang glider. The best climb rates are typically found by circling at about half the radius of the entire thermal, and workable small thermals are usually at least five times taller than their diameters. I've measured thermaling circles with my GPS tracklog interval set at one second, map page at highest resolution, and have rarely found myself circling at smaller than a 70 m (200ft) diameter on a hang glider. The reader might enjoy trying the same experiment. Walking a 30 m (100ft) and a 70 m (200ft) circle on the ground before flight can be good for getting familiar with the display scale.

For illustration, let's define a "small hang glider thermal" as being 70 m (200ft) in diameter and 300 m (1,000ft) tall, while a small paraglider-workable one is 50 m (140ft) by 230 m (700ft). Note: I emphatically do not suggest that real thermals are shaped like tennis ball cans, or that they have sharply defined edges. With that caveat, it can be enlightening to model them as simple cylinders. Using well-known values for air density, the paraglider thermal, at sea level on a warm day, will have a mass of about 400 tons, while the hang glider thermal weighs 1,200 tons (in my experience flying both aircraft, the discrepancy in workable thermal volume seems less than 3:1, but that's only a personal impression).

A common large thermal would be 330 m (1,000ft) in diameter, 3300 m (10,000ft) tall. That one has a mass of 300,000 tons. For comparison, a high-end nuclear aircraft carrier weighs some 91,000 tons. Toward the extreme but plausible end is a thermal of 700 m (2,000ft) by 6,000 m (17,000ft), weighing two million tons, equivalent to more than five Empire State Buildings (due to the net effects of pressure drop and cooling, such a thermal would expand to about a 800 m (2,300ft) diameter at its top). We can expect to encounter thermals in a mass range of several thousand to more than 100,000 tons.

If these numbers sound, well, inflated, it's because we're accustomed to thinking of air as wispy, insubstantial stuff, partly because it is invisible. For another angle, compare a glider/pilot combo weighing 113 kg (250 pounds), which I'll refer to as a Standard Glider (a medium-sized pilot on a high-performance hang glider, or a heavy pilot on a paraglider). Under typical conditions, one SG weighs the same as a sphere of air 6-7 m (18 -20ft) in diameter.

We all know that thermals, and weather in general, are solar-powered, but what does this mean in practical terms? Air under atmospheric conditions obeys the Ideal Gas Laws of physics to a very close approximation, so estimating the energy requirements for lift production is a matter of looking up standard values, converting units, and applying simple math, most of which I will spare the reader (for background and discussion, see here). Let's refer back to our Standard Glider. To produce buoyancy to balance one SG, we must heat a volume of air by adding 8.2 million calories. Within a reasonable range, the volume is irrelevant. With the same energy input, we can get 113 kg (250 pounds) of buoyancy by raising the temperature of 8909 cubic meter (314,000ft3) of air (one percent of a small HG thermal) from 26.7C (80F) to 27.3C (81.2F), or by heating 92 m3 (3,245ft3) (the 3 meter-diameter sea level SG-equivalent) to 326C (620F).

That example is for illustration, and I am not suggesting that every time the ground absorbs 8.2 million calories of sunlight, a usable thermal will be formed. Instead, this energy (when conducted to air) creates one SG worth of buoyancy. If we could contain the warm air in a perfectly insulated, weightless bag, it would be just enough to suspend one glider and pilot. In reality, we can only utilize a small fraction of a thermal's lifting power. On the other hand, in sufficiently unstable air, a relatively small amount of warm air could evolve into a thermal capable of lifting a larger load than the raw energy input would indicate. But without solar heating, such a good lapse rate cannot last for long. The essential point: 8.2 million calories is a bare minimum for simply balancing one glider and pilot.

How much solar energy might be available? At maximum, during June and July in the southwestern United States, about one kilowatt of sunlight per square meter reaches horizontal ground at mid-day. At 0.86 million calories per kilowatt-hour, that translates to 3.5 billion calories per acre-hour (1.4 billion calories per hectar-hour). If we assume that half of this energy heats the overlying air rather than reflecting into space or conducting deep into the ground, one acre will produce almost four SGs of buoyancy per minute.

This raw buoyancy does not tell us how large or frequent the resulting thermals will be or how quickly they will ascend. To make such predictions would require a sophisticated fluid dynamics analysis beyond the scope of this article, but we can make some observations:

- Each 3 C (5.4F) temperature increase will expand a volume of air by one percent, making it one percent less dense than the surrounding air. For example, heating 3,000 tons of air by 6 C (10.8F) will produce a modest-sized thermal (or say, 80 m diameter and 700 m height) with 60 tons (480 SGs) of buoyancy. This requires four billion calories, roughly the output of four acres in a half-hour under ideal conditions.

- For the same temperature change, a larger thermal will have a higher buoyancy-to-drag ratio and will therefore accelerate more quickly and reach a higher terminal velocity.

- For the same total buoyancy, a smaller, hotter thermal will have less drag than a bigger one, and will ascend faster.

In light of the physical dimensions of thermals, how could tiny objects such as tractors, gliders, or rabbits have any effect on them? Only if thermals are somehow stuck to the ground, yearning for the open sky, but tethered like hot air balloons. What kind of force could restrain a thermal with buoyancy in the tens of tons? Dixon White, according to "Bird Man," describes thermals in terms of surface tension: ".surface bubbles of warm air [that] eventually exceed their inherent ability to swell, then they burst and rise." So does Gadd, who writes that rocks are ".good wicks and passive triggers, as they tend to pierce the surface tension." In his book, Pagen implicitly accepts the surface tension idea by describing a thermal as "a bubble.that remains on the ground for a period of time before it releases in a sudden rush."


Bubble Theory

Sorry to burst all these bubbles, but.surface tension is strictly a liquid phenomenon! It cannot occur within or between gasses. When I mention this, some people say, "Maybe it's not really surface tension, but it's something like surface tension." That's an unsatisfying explanation and it is quite an understatement. Water has relatively strong surface tension, but it cannot support a drop of condensation weighing more than about 0.15 gram, or 1/200 ounce. A force capable of holding down a thermal would need to be some 10,000 times stronger than the surface tension of water. Anyone who demonstrates the existence of such a novel effect can earn a slam-dunk PhD, if not a Nobel Prize, in physics. But research efforts are probably better spent in pursuit of cold fusion.

What supports the Bubble Model of thermals? First, the analogy of air or steam bubbles on the bottom of a heated pan of water is appealing because it occurs for similar reasons; it's neat and clear; and we can see it happen! Second, we want to explain the cyclical nature of thermals. Discrete bubbles seem to behave the same way. As they grow, first they stick to the surface, then they pop loose and float upward. While a bubble is stuck to the pan, in unstable equilibrium, perhaps a tractor the size of a grain of salt could bump it loose.

A fundamental principle of science says that we should only look for novel explanations when established theory fails to explain a phenomenon. Surface tension between masses of air certainly qualifies as a novel hypothesis, previously unknown to science, so the burden of proof should be on those who propose it. On the other hand, can we explain our experience with thermals in terms of conventional fluid dynamics and thermodynamics?

While some thermal sources produce lift more or less continuously for hours at a stretch, most of them are periodic, with bursts of lift alternating with lulls. Something must hold the air close to the ground while it warms and gains buoyancy, but surface tension is not required. The more prosaic forces of time and inertia can do the job.

Let's look at two models in parallel sequences of snapshots. In the Bubble Model, pools of air form above thermal generators or collectors. The pools evolve into domes and then spheres of warm air that is trapped or stuck to the ground by surface tension. If a "triggering" object or event comes along, it can break loose the bubble, which will suddenly "bloop up into the atmosphere," according to "Bird Man." If tractors, rabbits, and power lines are unavailable, the bubbles will "eventually exceed their inherent ability to swell, then they burst and rise."

In the Realistic Model, thermals are not so neatly defined. Air above heated ground gradually warms, expands, and begins to rise. Meanwhile, it mixes to some extent with surrounding air, and it might be diluted by wind. As the air slowly rises, it forms an indistinct dome. Near the surface, cooler ambient air moves in to replace the rising air, and is in turn heated by the ground. This process continues in a gradually accelerating manner. When the rising, fuzzy blob of air attains a sufficient vertical speed, the heated ground below it cannot produce warm air fast enough for a continuous supply. The incoming air also ventilates and cools the warm ground. At this point, which might be a few minutes to as long as 30 or so minutes after the beginning of the sequence, the thermal cycle ends, and we go back to Frame 1.

What provides this leisurely cycle time? Remember that significant heating (in the 2-3 C range) of a modest-sized thermal produces lifting power on the order of 30 to 60 tons. We can call this the thermal's absolute buoyancy. However, the same thermal's relative buoyancy, compared to an equal volume of surrounding air, is only one or two percent. If we hold a chunk of wood, waterlogged so that only two percent of it shows above water when it floats, on the bottom of a pool, it will rise slowly at first. The same applies to our several-thousand-ton thermal. It's in no hurry. Here's one place where the bubble analogy falls down. An air bubble in a pan of hot water has a relative buoyancy of about 78,000 percent! A far better-but more difficult to see-analogue is the warm water that forms actual thermals in a heated pan, visible against shiny metal in good light. That water makes indistinct, turbulent columns that climb far more slowly than the nearby frantic bubbles.

Consider Frame 3 in both sequences, and imagine that the heat is switched off by a dense cloud shadow. In the bubble model, the thermal will stick to the ground indefinitely if nothing triggers it. After all, the surface tension that holds it to the ground also isolates it from the surroundings, so it can only lose heat slowly through conduction. In the realistic model, the thermal will not wait around, but will lift off as a small, weak runt. Sound familiar?

Other thermal behavior can also be explained without resorting to exotic surface tension theories. Yes, thermals tend to rise from sheltered bowls, but not because the air pools there or because thermals bump into tree lines or houses and are jostled into the sky, but because these so-called collectors are sheltered from the mixing and cooling effects of wind. Ridges can perform the same function, on their lee and windward sides. A ridge or other high ground reliably generates lift, not because it wicks air skyward, but because it usually has faces that are more perpendicular to the sun than flat ground, it tends to be sparsely vegetated, and it is well drained and DRY (more about the role of water later).


The Roots of Myth

With such weak (I would say non-existent) scientific support, why is the surface tension/bubble theory of thermals so popular? The main reasons are:

1) Appealing Explanation for a Mysterious Phenomenon We humans seek neat, clean mental models, and if the process in question is largely invisible, we are quick to invent something to hold in our imaginations. ["That thunderstorm came out of nowhere! There must be gods up there, throwing lightning bolts and waiting for us to ask for favors."]

2) Anthropocentrism Humans have a natural inclination to see themselves at the center of the universe. Will Gadd writes, "How many times have you landed in a likely field only to watch someone else climb out above you?" The implication: "Since there was a thermal just after I landed, I must have caused it!" ["It rained after we danced, therefore."]

3) Sampling Bias A pilot who believes in tractor thermals will fly from tractor to tractor, thus meeting more thermals that seem to come from tractors than if he believed in parking lots or yellow barns or pinto ponies. [We perform our most intense rain dances after we've been afflicted by a long drought. And what defines the end of a drought? Rain!]

4) Selective Memory People tend to remember data that supports their conceptions and forget what doesn't. If you press someone who believes that flying low over a field can "release a thermal," you'll find a pilot who has landed plenty times after flying low over a field and triggering.nothing! ["Sure we danced last week and it hasn't rained yet.but we didn't dance hard enough."]

5) Coincidence with Reality If a false theory leads one to correct decisions most of the time, it can be almost as good as an accurate understanding. When other factors can produce similar results, it's easy to forget that correlation does not imply causation. This is a key element of a durable myth, so it is worth exploring further with some examples.

Case 1: Tractors stir up dust, so if a thermal lifts off nearby, the dust can help make it visible. If the dust lies on the ground in a long trail, we ignore that tractor and fly toward the next one. This gives us insight into a key role of the tractor. Since they move rather slowly, why wouldn't a parked tractor in a 2 m/s (5mph) wind work just as well as a moving one? Or how about a barn in a light wind? Those also disturb the field of moving air. But the best tractors are the active ones, because they raise dust. If I have to choose between two equally attractive dry fields, one with a tractor, one without, I'll favor the tractor-not because I believe it will kick a thermal loose, but because it might provide useful information. On the other hand, opting for a shaded field with a tractor instead of a sunnier one without can end a flight prematurely. Correctly understanding the benefits and limitations of tractors can sometimes tip the balance between a low save and an early landing.

Case 2: Ridges are usually good thermal producers, not because thermals stick to them and drip upward off their crests, but for the reasons previously noted. The problem with the ridge wicking and dripping model is that if it's over-applied, it can lead us to misinterpret conditions where ridges are worse thermal generators than the surrounding flatlands. One common example is an east-west ridge late in the day, in a west wind. It no longer faces the sun as well as the flats, the wind ventilates and cools it, and we give up precious ground clearance by flying over a ridgeline rather than over the flats.

Case 3: Pagen writes: "One site in Pennsylvania has a train that wends up the valley and releases thermals on schedule." Aside from the sampling bias and selective memory factors, real physical effects could also create the illusion that trains trigger thermals. Railroads are built in right-of-ways, cleared of vegetation, on mounds of gravel, topped with dark-colored ties and steel rails. That's a decent thermal prospect with or without a train. In addition, the engines' waste heat could be a significant contribution. One freight engine can produce up to 4,000 horsepower. Assuming that the engines are 1/3 efficient and that the equivalent of two such engines are running at full power, they will produce 16,000 to 24,000 HP worth of heat (depending on how much work goes into lifting the train up a grade vs. heating the surroundings through friction), or 171 million to 256 million calories per minute. This in turn equals 21 to 31 Standard Gliders per minute (and per mile if the train is doing 60 mph), or six to nine optimal acres worth of sunlight. Since a 30 m wide right of way amounts to 12 acres per mile, a mile-long train might (briefly!) increase the area's thermal output by 50-75 percent.

Can tractors also help us if they don't bump thermals loose from the ground? Not enough to bother with. Farm tractors come in the range of about 100 to 400 horsepower. Let's assume that an average one is 250 HP, and (generously) that it operates at 200 HP constant output. Because the engine and drive train are only about 25% efficient, such a tractor actually creates 800 horsepower worth of heat, so let's assume that all 8.6 million calories per minute go into heating the air. That's equivalent to about 0.7 hectar (0.3 acre) in full sun. A typical field in eastern Washington covers 1/4 square mile (65 hectars ) so adding a tractor might increase the field's thermal output by 1/5 of one percent. This contribution could be more than balanced by the cooling effect of damp soil that the tractor turns over.

Returning to the anthropocentrism and selective memory angles, if we believe in thermal triggers, why do we imagine that they generally work in our favor? What would cause a tractor to bump a thermal loose just when we happen to need it, rather than few minutes too early or late? And, if a trigger did release a thermal, wouldn't it be one that hadn't ripened to the point of bursting its surly bonds on its own? In other words, triggered thermals should be weaker than the ones that aren't so favored. As we've seen, it's all about energy, and human-scale vehicles or objects cannot contribute more than a minuscule fraction of the required heat. A freight train, possibly, but not a tractor, glider, or rabbit.

Psychology professor Gregory W. Lester explores the roots of myths in a fascinating article, "Why Bad Beliefs Don't Die" (Skeptical Inquirer, Nov./Dec. 2000, www.csicop.org/si/2000-11/beliefs.html). Lester illustrates the crucial survival value of beliefs (conceptions of the world that do not rely on immediate sensory data), and he gives compelling reasons for resistance to changing our beliefs, even in the face of contradictory evidence.


Hydro-powered Lift: New Myth in the Making?

Pagen writes: "Ground that is moist after a rain is generally a poor producer of thermals because of the cooling effects of evaporation." Gadd writes: "Moist ground cover absorbs the sun's energy and uses it to evaporate water, a cooling process that kills thermals." Disputing this, Jim Palmieri (letter, April 2001 Hang Gliding) claims that water vapor is lighter than air, and is therefore good for creating lift. For example, a benefit of plowed versus flat fields is that the "furrows allow moisture to rise.and then vaporize." Then, "the heated water vapor will rise, not so much because it is warmer but because water has a low molecular weight and is less dense than the rest of the atmosphere." In fact, water vapor has less than 2/3 the density of air. To equal the buoyancy of water vapor, we would need to heat an equal volume of air from 26.7C (80F) to 210C (410F)! Sounds good, huh?

Ample flying experience indicates that Gadd and Pagen are right about this one, but why? The key is energy. Evaporating a quantity of water requires 300 times more energy than raising its temperature by one degree Fahrenheit. Remember that making 113 kg (250 pounds) of air buoyancy consumes 8.2 million calories. Using the same energy to evaporate water produces only 9.6 kg (20.4 pounds) of lift, which makes water vapor less than 1/12 as effective! Also, the higher heat capacity of water vapor means that more energy is needed to raise its temperature (and volume), so it is about 13% less effective than air for producing lift after it evaporates. Yes, humid air is somewhat more buoyant than dry air at the same temperature, but it only reaches the same temperature at a tremendous energy cost-energy that could have gone into far more efficient dry-air lift production. There's a good reason that sweating works so well.

I predict that the water-vapor-benefit notion will fail as a myth, despite its ostensible grounding in physics, because it doesn't meet the Coincidence with Reality test noted above. After a few blunders into territory that I had forgotten was assaulted by thunderstorms the previous day, I'm not inclined to make the same error on purpose. It's no coincidence that few world's records are set in regions that get more than 50 cm of annual precipitation.


Better Soaring through Physical Chemistry

While no one needs a formal education in thermodynamics to fly cross country, a basic sense of the interactions of air and energy can't hurt. I have already found that knowing about the sheer tonnage of thermals helps me understand how they are affected by time, wind, and terrain. Most of our myths do not drastically cut our performance, or we would soon abandon them. However, a sharper sense of what to search for and what to ignore can make the difference when we're at unzip-the-harness altitude, desperately scratching for one more climb. I hope this article is a step in that direction.

 

Dennis Pagen's response