Altitude

What it's for

Barometric pressure at altitude, and the Cross correction for using sea-level tables at altitude. Combine it with the depth functions by passing the altitude's surface pressure.

Formulas

The ICAO barometric formula:

$$P(h)=1.01325{(1-\frac{0.0065h}{288.15})}^{5.25588}$$

The Cross correction (theoretical ocean depth):

$$d_{TOD}=d\cdot \frac{P_0}{P(h)}$$

• $P(h)$: barometric pressure at altitude $h$, bar.
• $h$: altitude above sea level, m.
• $P_0=1.01325$ bar: sea-level standard pressure.
• $d$: actual depth at altitude, m. $d_{TOD}$: the sea-level depth with the same pressure ratio, m.
• $288.15$ K is the sea-level temperature, $0.0065$ K/m the lapse rate and $5.25588$ the exponent $g_{0}M/(RL)$.

Using it with depth math

surfaceAtaAtAltitude returns the surface pressure relative to sea level (1.0 at 0 m). Pass it as surfacePressure to any depth function:

import { surfaceAtaAtAltitude } from 'dive-math/altitude'
import { mod, gas } from 'dive-math/gas'

mod(gas(0.32), 1.4, { surfacePressure: surfaceAtaAtAltitude(1500) })

Assumptions and limits

• ICAO standard atmosphere, troposphere only. Altitude must be in the range −500 m up to (not including) 11 000 m, otherwise a RangeError is thrown.
• A standard atmosphere is assumed. Real weather shifts the surface pressure by a few percent.
• This is pressure math only. It says nothing about decompression at altitude.

Sources

• ICAO Doc 7488/3: $T_0=288.15$ K, lapse rate 0.0065 K/m, exponent 5.25588.
• Sea-level pressure: ISO 2533 / ICAO (101 325 Pa).

Examples

import { surfacePressureAtAltitude, surfaceAtaAtAltitude, theoreticalOceanDepth } from 'dive-math/altitude'
import { ataAtDepth } from 'dive-math/pressure'
surfacePressureAtAltitude(1000) // => 0.899
ataAtDepth(10, { surfacePressure: surfaceAtaAtAltitude(1000) }) // => 1.887
theoreticalOceanDepth(30, 1000) // => 33.82

API

See the altitude API reference.