I am trying to understand WHY...

A: if you go up 500 feet the adiabatic lapse rate will reduce the temperature by 1 Deg C, which is because the air is less dense as you go up... less dense equals less heat over the same volume, so it's cooler.

BUT,

B: if the ISA says standard is 15 Deg C at MSL and your non-standard temp is 16 Dec C, you compensate by 120 feet (higher) because warmer air is less dense. Which is basically the same reason as in 'A'.

So why the HELL does one degree equal four times as much altitude difference in A as it does in B? They're both measuring vertical shift to temperature ratio, aren't they? What is it that I don't get?

Nobody is saying that if you go up 500 ft the air will cool by 1C. What is being said is that if you increase the temperature of the air by 1°C it will have a similar effect on density as increasing its height by 120 ft. On a day that is 20°C hotter than standard, an aircraft will perform as though it was 1200 ft higher. The aircraft isn't 1200 ft higher, it behaves as though it was. That's got nothing to do with the adiabatic lapse rate.

You have to be clear as to whether you are considering the stationary ambient air (referred to as the environment) or the expanding parcel of rising air that is passing through it. The air with no vertical movement in ISA is not cooling by expansion. As you climb through this air you are simply getting further away from the hotter surface. The actual temperature lapse rate is extremely variable in the environment air and is measured regularly with radiosondes. In ISA the environmental lapse is assumed to be 2°/1000 ft, but that's only for the sake of theory.

The parcel of air that's rising through the environment is another story. It is cooling for a different reason. It's cooling due to its expansion as it encounters reducing external pressure. When the heat that once occupied a given volume expands to occupy a larger volume, the heat that's present is spread over that larger volume so it's temperature drops.

The temperature is dropping even though no heat is subtracted. The heat that's present simply occupies a larger volume so it has less effect. That's called adiabatic cooling. This occurs only when a gas changes its volume (rising in the atmosphere).

Compression causes a gas to warm, expansion causes a gas to cool. The two processes (environmental cooling and adiabatic cooling) are unrelated.

Great answer, thank you! I think I get it now.

Some extra thoughts to tack onto Bob's comments.

if you go up 500 feet the adiabatic lapse rate will reduce the temperature by 1 Deg C, which is because the air is less dense as you go up... less dense equals less heat over the same volume, so it's cooler.

Not quite.

The basis for the lapse rate is, as Bob indicated, necessarily tied up with vertical motion of a parcel of air. The atmospheric pressure reduces with height (as the pressure is related to the amount of stuff above the location and, the higher we go, the less the amount of stuff there is above us to make the pressure). As our little parcel of air goes up, it encounters reduced pressure, so it can expand to fill the hole, as it were. However, to expand it has to do some work. To do some work, it needs some grunt power.

Now the grunt can come from external sources (eg what happens to water heating on the stove due to the gas burner or electric hotplate) ... but, in the atmosphere with a parcel of air moving, there's really nothing there which can heat/cool the parcel of air.

So, if we can't get any grunt from our surroundings, we are left with having to pull some energy from the parcel of air itself. When we pull this energy out to run the expansion, the internal result is a drop in the temperature of the parcel of air. Same thing happens when you purse your lips and blow. The air inside your mouth increases in pressure a little bit (and heats up a little bit - but that cools back down by conduction to the buccal environment). As the air moves through the embouchure (I admit to being a woodwind player in years gone by) the pressure decreases and, there being no source of energy to run the expansion, the expansion pulls the energy needed from the air itself and the temperature drops, quite noticeably.

The term "adiabatic" comes from thermodynamics (ie physics) and simply means a process which occurs without any energy or mass transfer to or from the surrounding environment.

if the ISA says standard is 15 Deg C at MSL and your non-standard temp is 16 Dec C, you compensate by 120 feet (higher) because warmer air is less dense.

First consideration is that the number is not a constant and, if you look at the history, 120 ft/deg is, itself, an approximation to 118-ish ft/deg, which is, itself, an approximation to what the real variation is.

As the explanation was given in a previous thread, I'll link to that rather than repeat the story.

bobtait.com.au/forum/performance/6777-altimetry-rates#13257

They're both measuring

... different things. You need to be comparing apples with apples to do your sort of sums, I fear.

Yet another brilliant answer. Thanks very much John.

The maths I can do... not a problem. It's understanding why that maths works that really drives me nuts.

It's understanding why that maths works that really drives me nuts.

If you delve into the early history of aviation (ie before the techo folk got involved to any extent) you will find that all the enthusiasts came up with all sorts of ideas as to why this and that caused all the other things. Tended to be long on imagination and, very often, short on technical competence and mathematical rigour.

Many of the early ideas became entwined within the fabric of aviation and so, for the early training regimes, we have to put up with a whole host of ideas which are not quite right but remain enduring.

If you want to get stuck into the mathematics you will need to get into the serious engineering texts. Fortunately, these days, there are many authoritative texts which can be located (often gratis) on the net. Be aware that you will need a big pot of coffee if you go down that pathway, though.

Yeah... last time we talked you gave me Kermode. That has taken me about 6 bottles of Nescafe Instant!

last time we talked you gave me Kermode

Kermode is a really good book for pilot folks. However, it is pitched at an introductory engineering level. If you want to get a bit into things, you need to start on the undergraduate engineering standard texts, of which there are quite a few.