In my last blog I looked at how the characteristics of the atmosphere are computed from some simple assumptions. Namely that the air is at a high enough pressure to hold up the air above it and that there are simple relationships between the temperature and altitude.
Today we are going to look at what happens on a non-standard day. We start with the equation from last week’s blog and alter it only slightly:
The subscript 0 indicates values at zero height, i.e. at sea level. OK, this isn’t the simplest arrangement of the equation, but it makes life easy from now on. What this says is that for a given altimeter setting, the left hand side of this equation is a constant and so the right side, which shows the ratio of temperatures between sea level and the aircraft altitude must also be constant.
Imagine are flying on a perfect ISA day. You have set 1013mBar on the pressure altimeter and the altimeter shows 17,000 ft. You are flying over Mont Blanc which, at 15,774 ft, is more than 1,000 ft below you.
By Joe MiGo – Own work, CC BY-SA 3.0
A week later, the air is colder and you are in cloud on the same route. The altimeter shows 17,000 ft as before, but are you going to miss the mountain?
Now, the outside air pressure is the same as it was the previous time we were here – we know this because the altimeter, which is really an air pressure meter, is showing the same reading. The temperature at this height is given by the lapse rate, but remember it’s colder than before.
Fortunately we know that the static air temperature outside the aircraft today is given by the temperature at sea level today minus the lapse rate.
More sums later and we have:
We know L, T0 and the height on an ISA day is what the altimeter is showing us. We can read today’s air temperature from the aircraft’s air data system and do some sums. To put it in graphical form, with an indicated 17,000 ft, here are the actual altitudes for different temperature variations from ISA.
Or to put it another way, with a variation of -18.3C you’ll hit the top of Mont Blanc even though your altimeter is showing over 1,200 ft clearance. Let’s face it, a variation from ISA of 18.3C corresponds to a temperature of -3.3C at sea level, and I have known days like that here in England so this is not so rare.
The moral of the story? Don’t fly over mountains if you can help it. This is advice from somebody whose test flying was mainly carried out over the fields of the West of England, navigating by village pubs and railways.