Yep, that's right...

Sorry buddy, didn't spot this as you were posting it as I was posting another...

The formula for temperature is similar to the one for pressure, but whilst
Pressure x Volume-to-the-power-gamma = constant
Temperature x Volume-to-the-power-gamma-minus-one = constant

So if we assume gamma for air is 1.4, a compression of 10:1 starting at 1 bar and 25 degrees C (298K) gives us a pressure of:

1 bar x 10^1.4 = 25.11 bar, which as we're working relative to a volume of 1 needs no further calc to give the pressure (for any other resulting volume along the way, you'd need to divide by that volume raised to the power of 1.4)

The temperature, would be

298K x 10^0.4 which is 748K, or 475 deg C

Similarly, the temp for any intermediate volume along the way would be given by dividing that result by the volume raised to the power 0.4...

Of course, this is all slightly approximate anyway as there is some heat lost to the cylinder walls etc during the compression - not a lot, but enough to distort the cylinder pressure trace noticeably in our data...

Geek out.

Thanks dja, your original explanation spells it out most convincingly for me.


Other things mentioned:

standing up on your bike at higher altitudes is definitely easier than at sea level: decreased air resistance

Is this something others have noticed too, or could it just be an impression (possibly caused by lack of oxygen to the brain? ;-)
Put that way it does make sense, but I've freewheeled down from as much as 5300m and can't say I noticed I was hurtling down effortlessly with no drag due to the thin air. But I was probably not thinking about that - like most I was trying to keep on the road. And a day or 2 later, crossing a 4000m plain into a strong headwind didn't feel any less of a drag than normal.

One small correction about intercoolers. AFAIU it's not so much about cooler air increasing compression and detonation resistance (though they may be side benefits). Cooler air is denser and so carries more oxygen. With more oxygen you can up the fuel rate (with a screwdriver or chip) to get a broad spread of extra power (but also more heat to the point where I've thought of fitting an EGT gauge).
Fitting a bigger IC is commonly done on TD 4x4s.

Another thing I wondering is whether petrol-engine efi manages a perfect mixture at 4000m just as it does at normal elevations. No reason why it shouldn't I suppose, and the XCountry mpg in the Pamirs seems to prove it.

More geek fodder, thanks Chris...

Yes, there will be less air resistance at altitude, though this is most noticeable for airliners (and their cruising altitude is approximately the optimum compromise between reduced air resistance and reduced engine performance - but their engines are optimised for that altitude, and could be re-engineered to produce more power at sea level if the materials had been developed that could take the pressures and temperatures).

The compromise for motorcycles is not so great cos the engine has not been optimised to spin faster at altitude to make up for the less dense air (you just spin it at that speed at sea level and enjoy more performance!)

Meanwhile, intercoolers cool the charge so:
- Increase charge density - more oxygen means more fuel can be burnt means more power
- Reduce charge temperature - in a diesel, more fuel always equals higher exhaust temperatures and high speed performance is commonly limited by turbine inlet temperature limits

There still comes a point of course at which you crash into the hardware limits (or straight through the hardware limits if you're "chipped"), but it all helps. The bits the general public are less interested in are reduced NOx emissions (which is formed by the same high pressures and temperatures that cause knock)

As to whether a fuel injection system will result in a perfect mixture at 4000m, that depends on the system and how well it's been calibrated during development. In theory, most are capable of perfectly adjusting for the change in barometric pressure, but only those running a lambda sensor and closed loop fuelling will get it spot on, and only while they're operating closed loop (i.e. in the part of the operating map that gets used on the emissions test).

Oh - and while I remember, the improved fuel economy at altitude...

One of the most significant losses in IC engines is the power used by the engine to pump the air into and out of the engine. In the case of a gasoline engine, the throttle restricts the airflow into the engine to reduce the power output to that required to just cruise along at constant speed (as opposed to accelerate full bore). That means the engine is continuously pumping air from a low pressure (the pressure after the throttle) to a high pressure (atmospheric pressure/exhaust back pressure). That takes a lot of work when you add it up for the whole time the engine is running.

At altitude, the absolute pressure at the inlet port for a given power is the same as at sea level, but the exhaust is being pumped out into a lower atmospheric pressure. So the pumping losses are greatly reduced...

So, so long as you have a fuel system that doesn't over fuel at altitude (i.e. a carb set up for sea level) you will see better fuel economy when up a mountain.

Introducing the exhaust into it opens up a whole new kettle of worms........!