Author Topic: Why is ISA important?  (Read 618 times)

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Offline Adrian Chitan

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Why is ISA important?
« on: May 14, 2017, 05:52:47 PM »
Hi guys,

a little free time for a little post. So let's get into it because it's somehow advanced. So let's say two friends have both bought airplanes, one has a C172 and the other a Piper 180. One lives in Sibiu and the other in Bucharest. They both are eager to fly theirs and brag about the performances when they meet at airshows :))). So, the subject of climb profile (plotting altitude over time) comes into discussion as a good method of comparing the two planes.

So they both agree to climb at the best climb speed to 10'000 feet. Comparing the profiles will set the dispute. But they live in different cities, with different weather and to top it all off, one is recording his climb during the winter, while the other in the summer. So, putting their profiles together actually means nothing. It's like comparing apples and melons because the two planes didn't fly in the same fluid. That's why ISA was invented to standardize performances of airplanes.

ISA
International Standard Atmosphere is an artificial atmosphere defined by a sea level pressure of 1013.25 mb (101'325 Pa) and temperature of 15o C (59o F, 288.15 K). Using the barometric formula, one can compute the pressure and temperature for any altitude in ISA. So before comparing the two climb profiles each pilot has to convert the real climb profile into the ISA climb profile.

To be able to do this, the pilot doesn't just have to write the altitudes and times on a piece of paper but also the temperatures (OAT for our small planes, TAT for larger ones). But this can be skipped if the precision is not so important, so the pilot can only note the airfield OAT and compute temperatures as ISA deviations.

Reduce a climb to ISA
The idea is to transform the real altitudes recorded by our pilots into ISA altitudes. For this we will use the barometric formula and the ideal gas equation which requires us to know the real densities that our altitudes were read at. But, our pilots can read the altitude, temperature and time, not density. We can get the density using the altitudes and temperatures we read with:
p0/R/ti (1+L hi/t0)g M/R/L
, where p0 is the QNH of the airfield, R is the ideal gas constant, L is the standard atmospheric temperature lapse rate, t0 is the temperature at sea level (not airfield temperature, unless the airfield is near sea level), g is the gravitational constant, M is the molar mass of air and hi and ti are the altitudes and temperatures recorded during the climb

Having the real densities of the air, we can translate these into ISA altitudes by reversing the formula and changing t0, ti and p0 to the ISA values.

And there is one more thing to do. The vertical velocity indicator is an absolute indication of the climb rate, be it ISA atmosphere or not. Meaning that it shows the correct climb rate in any atmospheric conditions (except really extreme temperatures). So, this means that even in ISA conditions, the two planes would have the same climb rates between the altitude readings. That translates into different times than the times read by the pilots during the climb. So we can use the rule of three to get the times between the ISA altitudes and make an ISA time chart which will be different than the real climb time values.

Because the ISA climb doesn't start from an altitude of 0 (especially if the airfield is not at 0 MSL), the pilot can extrapolate the first climb to starting from 0 MSL by keeping the same climb rate as the first climb segment. This can sometimes give a start time less than 0 but that is not a problem.

So, now the two pilots have the ISA altitudes and the ISA times which we can use to plot the ISA climb profile. They can thus compare the performance of the two climbs.

Example (Majestic Software Dash-8 Q400)

So I have made an example in which I have taken off in an empty Dash-8 from LRCK in two different weather scenarios. One climb was made on the 5th of January 2017 (winter - blue) at 16:10z, while the other climb was made on the 5th of July 2016 (summer - red) at the same hour. The airfield conditions were:
winter: QNH 1009, OAT 3o C
summer: QNH 1016, OAT 25o C

Some initial observations on the conditions, as you can see the winter atmosphere starts at a lower pressure (bad for flying), but the temperature is also much lower (good for flying), while the summer atmosphere starts off at a higher pressure (good for flying) but much higher temperature (bad for flying).

Also, the takeoff and climb procedures were: MTOP until VCLIMB, then MCL still on VCLIMB up until 10'000 feet and then still MCL but IAS 180 for the rest of the climb. The readings were made every minute for 10 minutes.

The raw (real) data is:
winter:
357, 4140, 7190, 9640, 11420, 13860, 16000, 17990, 19740, 21310, 22690 feet
3, 0, -4, -8, -13, -19, -23, -28, -31, -35, -38 oC

summer:
357, 4580, 7580, 10100, 12000, 14340, 16520, 18440, 20000, 21580, 22880 feet
25, 16, 10, 6, 2, -2, -6, -10, -14, -17, -20 oC

If we put the two profiles side by side, we get:


This will make us believe that during the summer climb, the aircraft performed better. And this is in accordance with the fact that the summer atmosphere is at a higher pressure. But, the temperature difference should make us restrict from drawing any conclusion until we have the ISA reduced profiles. After doing the computations (I think it's better not to fill this post with intermediate numbers), we get:


Now, we can see that the plane performed very close between winter and summer because
the lower temperature in the winter leveled off the effect of the higher pressure of summer. At  18'000 feet the winter climb clearly overtakes the summer climb because the temperature effect has a greater magnitude than the pressure effect. So, on the whole, during the winter, the plane performed better as opposed to what the un-reduced to ISA climb profiles showed us.

Hope this makes for a nice read as always,
Adrian

 

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