Thermals cannot always be rising columns of air heated from the ground

Monday, May 8th, 2017 at 6:49 pm

I’m getting tired of having “learning experiences” when I really want more “fun experiences”. But in the meantime, here goes.

On 2017-04-29 I was at the hang-gliding competition on Camlo hill in Wales, where I didn’t take any thermals over the back — like the folks who knew what they were doing — and I landed back on the top with nil points and little satisfaction.

For this learning experience, I downloaded the tracklog of one of the guys who did make it and snipped out the first 12kms of flight, like so:

Direction of flight north is to the right (start of flight bottom left near (0,0)), the coordinates are in metres.

Having convinced myself I can extract the SRTM3 terrain, this is the graph of the flight altitude from the hill for those 12km against the terrain altitude:

Or you can plot the actual height above ground by subtracting the two:

This looks like he was circling with a pretty consistent height of 350m as the air mass was carried up and down over the terrain, in a “bubble” of rising air.

Except there is no way this could be a bubble, because even if the bubble extended all the way to the ground 350m below, it would have certainly been been expended in less than 6 minutes at a rate of 1 metre per second to support an efficiently flying glider.

After 25 minutes of existence, we can rule out that it has anything to do with any packets of warmed air which may have risen from the ground 12kms to the south.

“Ah,” the usual response goes, “the glider was flying in a chain of thermic bubbles along the track of the flight, each one rising up just in time to pick up from where the last left off.”

This explanation is bogus. I don’t seem to pick up thermic bubbles that easily along my track, while the pilot that stayed with the thermal reported a continuously existing atmospheric formation which strengthened and subsided, but was always there.

I also don’t buy the idea that this structure is somehow kicking off thermic bubbles on the ground 350m below at least five minutes downwind of its track in time to reach his altitude.

No, this must be a self-contained, self-sustaining convection structure that may have been initiated by a thermic bubble, but which has clearly morphed into something altogether different.

But let’s get a clue from a guy (me) who didn’t get the thermal. This is what an hour-long flight on the ridge not going anywhere looks like (coordinates in metres):

There are some attempts to follow a thermal on the left (going north and west), which always end in bottling out and flying in a southeasterly direction back to the ridge against the strong wind.

The altitude and entropy plot looks like so:

Recall that entropy — a number that remains constant under adiabatic change — is calculated as:

```(tempdegC+273.16)**1.4 * ExpFilter(pressure, temp_rE)**-0.4)
```

[We are filtering the pressure by the thermal time lag observed in the thermometer to make them comparable]

And, consistent with the bubble of rising air theory of thermals, the glider seems to climb when the entropy is high, and descends when the entropy drops off.

Not always, but usually.

Let’s examine the minutes around the 14:34:30 when the entropy dropped off and the glider dropped 100m in 2 minutes.

Well, something happened concurrently. But in case you don’t trust this entropy business, let’s look at the raw temperature log:

The temperature rise of 0.1degreeC between 14:34:00 and 14:34:15 could be explained by the 15m descent from 620m to 605m in that period, which would account for 0.15degC at the approximate lapse rate (observed in the data) of 1degC per 100m.

But the temperature *decline* of 0.1degreeC between 14:34:30 and 14:34:45 during a similar ~15m descent is in the opposite direction. It has to be due to a change in the air/energy temperature commensurate with leaving the thermal.

And so, if we plot the transition in XY, we can capture the exact moment where I stopped circling in the thermal, crossed through its diameter and left its lift zone, like a numpty.

I did this because I didn’t think I was high enough.

I can rotate the plot of section where I was in the thermal like so:

And then tip it back and view it in profile, including the leading in and leading out:

This shows clearly the effect when I was tracking it for 2.5 minutes from the right to the left, before dropping out of it.

The thing is maybe 100 or 200m wide, and I don’t believe it is connected to the ground or to a bubble of rising air.

Areas of sink are often associated with a thermal, which if you think about it, has to be, because rising air has to push something down to make room for itself.

Here’s my theory so far:

Suppose the air at 750m is 0.6degrees cooler than at 700m. This means that if a bubble of air is thrust upwards by 50m it will have been cooled by 0.5degreesC, and thus be 0.1degrees warmer than the surrounding air. This produces a force upwards due to buoyancy.

This flow of rising air displaces/sucks a bubble of air downwards (to fill in the gap below it). Air taken from 750m to 700m warms by 0.5degreesC, and is this 0.1degrees cooler than the surrounding air. This produces a force downwards due to its weight.

This flow of sinking air displaces/sucks a bubble of air upwards to fill the void it has left behind.

Energy is released because the sinking air is denser than the rising air, so that matter is descending by gravity.

It is extremely important that the sinking air is not mixed with the rising air, for if some previously risen air is accidentally sucked back down from 750m to 700m then it will not be heavier than the surrounding air and will not release energy with which to force the next bubble of air back upwards and continue the cycle.

Glider pilots in these thermals report constantly shifting areas of sink and lift in these very weak and long maintained thermals, which would match this theory. It is not a horizontal donut shaped vortex; the donut is on its side with air seeming to flow around the ring, except it must be different trunks of air going up and going down.

Here begin the dodgy calculations.

Suppose the lifting air formation is 200m in diameter and 200m high, and lets scale all temperatures and pressures to the middle to avoid having to do any calculus.

The mass of air going up is 100**2*3.14*200*du kg, where du is its density. An equal mass of air must be going down with density dd. The air density at pressure 94600 and temperature 6.9degreesC is 1.17398, while at 6.8degreesC it is 1.17442, producing a difference of 0.00043 kg/m^3.

At an airspeed in the system of 1m/s, the kinetic energy will total about m*1^2/2 = 6280000Joules. The net difference in mass between the rising and falling air masses is 5506kg, which is flowing at a rate of 1m/s downwards continuously, and releasing 54019Joules per second (multiplying by g), so this thermic formation can keep persisting with this size and temperature differential so long as it doesn’t lose more than 1% of its energy per second.

The surface area of the two volumes of moving air is 251200m^2, so this energy consumption scales down to 0.2Joules per m^2 per second.

Now the absolute viscosity of air is supposed to be 0.00001983 m^2/s — and I really do not know what I am talking about here — looks surprisingly small as it’s 10000 times smaller than the energy we have available — and half that if the shear layer is 2metres wide instead of 1metres wide.

Meanwhile a glider of about 120kg descends at 1m/s will consume 2% of that energy, so if we get 20 of them in the same thermal we might start to kill it.

Basically, everything is dwarfed by the 12560000 Joules of kinetic energy in the formation. If the average sunlight energy is 120 Watts per day, then we have about 0.01 Joules per second per m^2 on the ground at the height of the day, so to raise this energy in 20 minutes would require a circular area of diameter sqrt(6280000*2/0.01/(60*20)/3.14)*2=1154m — kind of in the right ball-park.

And then, once going and free in the middle of the air, the energy of the vertically moving air with temperature differentials of as little as 0.1degreeC is enough to keep it going and even extend it upwards (and downwards) till it hits the cloud base and starts sucking warm air from above it in the inversion, which kills it.

And the more balanced and weaker the thermal formation is, the longer it’s going to last, so long as it’s continuing to move in a differentially horizontally moving shear layer in order that it can continue to suck and blow fresh air all the time.

Accordingly, if I am in weakly rising air, and I think I can cling onto it, then I should convince myself to go over the back even though there is obviously no room for a prolonged rising bubble to exist within the available layer of air, because the kinetic energy is the key to its existence.