The
potential temperature is the temperature a package of air obtains when it is
brought adiabatically from a temperature T and a pressure P to a certain
reference pressure Po.
One can
do the above as an experiment and measure Tp accurately during the proces,
however using the following relative simple thermodynamic relation:
Tp = T . (P0 / P) ^ (R / Cp),
one can quite comfortably calculate Tp.
In this
thermodynamic relation the different factors mean:
Tp = potential temperature (in
Kelvin=Celsius+273)
T =
local temperature (in Kelvin)
P0 = reference pressure (1000 hPa)
P =
local pressure (in hPa)
R/Cp =
(gas constant / specific heat capacity) = 287.05/1005 = 0.28562
When a
package of air is brought adiabatically, i.e. without any heat exchange, to a
higher level, than both the pressure P and the temperuture T inside this
package of air will go down. This is what happens in nature automatically and
is in fact this experiment on a large scale. Not considering horizontal flows
and heating up and cooling down effects of the earth surface on a 24 hr scale,
a completely mixed adiabatic layer of air between ground level and high up in
the sky will be formed. Every pilot will be familiar with this of course. Many
books on meteo talk about this.
Now
suppose that we fly with our glider at an altitude of 1200m and that we measure
a local temperature of 5 °C. Besides we
measure a local pressure of 910 hPa.
The
potential temperature at 1200m is than calculated as:
Tp = (5 + 273) . (1000 / 910) ^ 0.28562 = 285.6K = 12.6 °C.
In an
other glider flying 500m below us but in the same type of air, the pilot
measures a local temperature of 10 °C and with that a local pressure of 968
hPa.
The
potential temperature for this glider at 700m is than:
Tp = (10 + 273) . (1000 / 968) ^ 0.28562 = 285.6K = 12.6 °C.
Hé, the
same potential temperature for both gliders, while one of them flies 500m lower
than the other one. That’s remarkable. But in fact under adiabatic conditions
of the air and at an identical temperature at ground level the potential temperature
Tp is the same everywhere no matter height or horizontal position.
Some
flightcomputers can calculate and present to the pilot the potential
temperature Tp using the simple equation mentioned above. However one may ask
for the use of this while at all locations in adiabatic air the potentential
temperture Tp is the same.
Now
suppose that in this adiabatic, just stable air, vertical columns of somewhat
warmer air are formed because at certain locations on ground level the air is
slightly heated up. We all know the effect of this: because of the somewhat
lower specific density, the warmer air will adiabatically rise, cools down but
stays warmer than the environmental air while rising. But some mixing and
spread out will occur of course, especially near the boundaries of the columns
of rising air.
Further
suppose that we fly at a random height in air with a potential temperature Tp =
12.6 °C of the example above. Than, as soon as we fly into the column of air
for which at ground level the temperature was a little higher than its
environment, the flightcomputer will show a temperature Tp somewhat higher than
12.6 °C. This is because in our formula, the local temperature T is somewhat
higher than the adiabatic value of unheated air at the specific height, while
the local pressure P corresponds of course to the specific height. Now we can
fine tune our trajectory in such a way that the flightcomputer indicates ever
higher values of Tp, thereby optimizing our chance of finding rising air. If,
while searching around, Tp starts to decrease we obviously fly into the wrong
direction.
While circling and climbing in the rising air we have
found, Tp will basically remain constant. If
Tp still gradually increases, than obviously warmer air flows in from
below and the thermal will get better. If Tp decreases while circling it is
time to look for a new thermal further on track.
Several
pilots with the right equipment make use of this important additional
information. I surely do that myself also and found this to be of great help,
especially in blue conditions. It is obvious of course to combine the Tp readings
with those of a stable well compensated fast variometer to find the best
location for circling and gaining height.
Of course
it makes sense to watch Tp also carefully while just gliding on track. In this
way one may try to find a best path to the next thermal.
Karel Termaat
Arnhem,
28/june/2009