# The Earth's three highest mountains - by three definitions

#### steve_bank

##### Contributor
Diapers? Those astronaught diapers should be sturdy enough.

Hilary and Norgay did the Everest first ascent in the 50s with crude equipment and clothes by today's standards. I don't think they used O2.

#### lpetrich

##### Contributor
I'd earlier calculated the geopotential height as
$$\displaystyle{ \frac{g}{g_0} h }$$

But that is a first-order approximation, and I must be more careful. The gravitational potential is (-G*M/r) for gravitational constant G, mass M, and distance from the center r. Adding h to r and expanding in a series in h gives us
$$\displaystyle{ \frac{g}{g_0} h - \frac{GM}{r^3} h^2 + \text{higher-order terms, overall O(h**3), nonspherical O(h**2)} }$$

For Ötzi, this additional correction is -1.65 m, and for Everest, -12.29 m, giving 3208 m and 8823.09 m.

#### steve_bank

##### Contributor

By setting 29.92 inHg/1013.4 mb, the altimeter will immediately read pressure altitude. If no altimeter is handy, a simple math formula will provide the same answer. Pressure altitude = { (Sea Level Pressure – 29.92) x 1,000} + true altitude (or field elevation if on the ground) Pressure Altitude Versus Density Altitude

In aviation, pressure altitude is the height above a standard datum plane (SDP), which is a theoretical level where the weight of the atmosphere is 29.921 inches of mercury (1,013.2 mbar; 14.696 psi) as measured by a barometer. It indicates altitude obtained when an altimeter is set to an agreed baseline pressure under certain circumstances in which the aircraft’s altimeter would be unable to give a useful altitude readout. Examples would be landing at a high altitude or near sea level under conditions of exceptionally high air pressure. Old altimeters were typically limited to displaying the altitude when set between {\displaystyle 950~\mathrm {mb} } and {\displaystyle 1030~\mathrm {mb} } . Standard pressure, the baseline used universally, is {\displaystyle 1013.25} hectopascals ({\displaystyle \mathrm {hPa} } ), which is equivalent to {\displaystyle 1013.25~\mathrm {mb} } or {\displaystyle 29.92} inches of mercury ({\displaystyle \mathrm {inHg} } ). This setting is equivalent to the atmospheric pressure at mean sea level (MSL) in the ISA. Pressure altitude is primarily used in aircraft-performance calculations and in high-altitude flight (i.e., above the transition altitude).

The density altitude is the altitude relative to standard atmospheric conditions at which the air density would be equal to the indicated air density at the place of observation. In other words, the density altitude is the air density given as a height above mean sea level. The density altitude can also be considered to be the pressure altitude adjusted for a non-standard temperature.

Both an increase in the temperature and a decrease in the atmospheric pressure, and, to a much lesser degree, an increase in the humidity, will cause an increase in the density altitude. In hot and humid conditions, the density altitude at a particular location may be significantly higher than the true altitude.

In aviation, the density altitude is used to assess an aircraft's aerodynamic performance under certain weather conditions. The lift generated by the aircraft's airfoils, and the relation between its indicated airspeed (IAS) and its true airspeed (TAS), are also subject to air-density changes. Furthermore, the power delivered by the aircraft's engine is affected by the density and composition of the atmosphere.