<p> Explode to see Thiele </p>

9885c9eb-ce07-4d14-8768-aa3b96b058da 109 9 12 decimal

&[DATE] &[TIME] - &[FILENAME]

vx vy char size color plotG n vx length : plot vx 1 el vy 1 el char size color augment : i 2 n range plot plot vx i el vy i el char size color augment stack : for plot 41 line :

The standard air pressure at sea level is 14.7 pounds per square inch, or about 100 kilopascals. Air pressure is so minimal at the top of the thermosphere that an air molecule can travel large distances before hitting another air molecule.

km.. ρ...hPa......°C 11 mat

ISA 00101315 0.5 0955 11.8 10900 8.5 1.5 0845 5.3 207942 2.5 0746 1.3 - 30700 4.5 - 3.5 0658 7.8 - 4061711 - 50541 17.5 - 6047124 - 70411 30.5 - 8035737 - 90307 43.5 - 10026550 - 110227 56.5 - 120194 56.5 - 130165 56.5 - 140141 56.5 - 150121 56.5 - 2005546 - 3001138 - 40035 - 500 0.9 1600 0.25 20 - 1000 0.0004 64 - 2000 0.0000013 52.2 - 3000 0.0000002 95.3 - 4000 0.000000044 97.3 - 5000 0.000000011 97.7 - 304 mat :

P ISA 1 col ISA 3 col . 10 black plotG : T ISA 1 col ISA 4 col . 10 blue plotG : °C ISA 1 col ISA 4 col augment : 31 line

P T °C 56.5 - 3 1 sys T °C 56.5 - 97.7 - 4 1 sys

β 1.30644000006 104 -^* 38518.8995295 38510.6720344 64.7372080910 68.7237058260 25.4827261347 4.84161810338 105 -^* 1483390476.38 2.74067434956 2.79372428294 575.381616331 111 mat :

'β' Collected from Mathcad 11 x J β 1 el β 7 el x β 2 el + β 8 el x β 3 el - β 9 el x β 4 el - β 10 el x β 5 el - β 11 el x β 6 el - / + / + / + / + / + :

ISA2085 20 0.072 25 0.032 30 0.015 32 0.011 35 0.006705 40 0.003144 45 0.001536 47 0.001165 50 0.000798 52 0.00062 55 0.000432 60 0.000233 61 0.000205 71 0.00005242 85 0.00000568 152 mat :

L H N xd U 0 : dx H L - N / : i 1 N 1 + range U i el L dx - (dx i * + : for U 41 line :

L 20 : H 85 : N 260 : 13 mat U L H N xd : X ISA2085 1 col : Y ISA2085 2 col : 41 line

ISA2085 i 1 U rows range vy i el U i el J eval : for U vy augment 21 line :

Pts blak by default i 1 X rows range p i el . : for X Y p augment 31 line :

V i 1 X rows range vy i el X i el J eval : for X vy augment 21 line :

Air specific 'ρ' @ geopotential x = km [ISA2085]. Coefficients from Mathcad 11 [Strato/Mesosphere].

Pts ISA2085 20 1 20 0 2 2 mat 3 1 sys

`

Atmosphere segments ... 1 - 11 range (rational ≡ 1120 range (expDecay ≡ 2085 range (rational ≡ 31 mat Thiele QUICK [PDAS11].sm Genfit Minimize [PDAS1120].sm Thiele QUICK [ISA2085].sm 31 mat ≡

ISA 0.5 - 1.0489 01 0.5 0.9529 1 0.9075 1.5 0.8638 2 0.8217 2.5 0.7812 3 0.7422 3.5 0.7048 4 0.6689 4.5 0.6343 5 0.6012 5.5 0.5694 6 0.5389 6.5 0.5096 7 0.4816 7.5 0.4548 8 0.4292 8.5 0.4047 9 0.3813 9.5 0.3589 10 0.3376 10.5 0.3172 11 0.2978 11.5 0.2755 12 0.2546 12.5 0.2354 13 0.2176 13.5 0.2012 14 0.186 14.5 0.172 15 0.159 15.5 0.147 16 0.1359 16.5 0.1256 17 0.1162 17.5 0.1074 18 0.0993 18.5 0.0918 19 0.0849 19.5 0.0785 20 0.0726 25 0.032 30 0.015 32 0.011 35 0.006705 40 0.003144 45 0.001536 47 0.001165 50 0.000798 52 0.00062 55 0.000432 60 0.000233 61 0.000205 71 0.00005242 85 0.00000568 562 mat :

PDAS 0.5 - 1.0489 01 0.5 0.9529 1 0.9075 1.5 0.8638 2 0.8217 2.5 0.7812 3 0.7422 3.5 0.7048 4 0.6689 4.5 0.6343 5 0.6012 5.5 0.5694 6 0.5389 6.5 0.5096 7 0.4816 7.5 0.4548 8 0.4292 8.5 0.4047 9 0.3813 9.5 0.3589 10 0.3376 10.5 0.3172 11 0.2978 11.5 0.2755 12 0.2546 12.5 0.2354 13 0.2176 13.5 0.2012 14 0.1860 14.5 0.1720 15 0.1590 15.5 0.1470 16 0.1359 16.5 0.1256 17 0.1162 17.5 0.1074 18 0.0993 18.5 0.0918 19 0.0849 19.5 0.0785 20 0.0726 422 mat :

L H N xd U 0 : dx H L - N / : i 1 N 1 + range U i el L dx - (dx i * + : for U 41 line :

X ISA 1 col : Y ISA 2 col : 21 line

Pts i 1 X rows range p i el . : for X Y p augment 21 line :

You may encounter this formula, so many decimals wrt uncertainty are unjustified.

Reconciliation wrt PDAS data

45 Aops compared to ρ11(x) [9 Aops] x ρ11 1 22.557 x * 0.001 * - (4.256^:

Much better fit to PDAS x β ρ20 β 1 el β 2 el x β 3 el / - exp * + :

β 0.0001376 1.67547 6.36715 31 mat :

A much better fit @ low computing cost !
Reserved for the  x < 11 x ρ11 1.604858 174.727169 x 43.473225 + 1286.481982 x 5.24242 + 0.000159 x 5.14073 - / + / + / - :

The two PDAS segments, rated exact fit to data, which data are pure convention for comparative reference/tracability. .. ρ = specific gravity

x ρ11 x β ρ20 11 0.5 11 0 2 2 mat Pts 20 0.5 20 0 2 2 mat 5 1 sys

ρ [kg/m³]=1.225 @ 0km,15°C

Absolute residuals... The three segments are "Exact" wrt 4 decimals ISA

Δ11 xy ISA 124 range 12 range el : i 1 xy rows range u i el xy i 1 el : δ i el xy i 2 el u i el ρ11 - : 21 line for u δ augment 31 line :

Δ20 xy ISA 2542 range 12 range el : i 1 xy rows range u i el xy i 1 el : δ i el xy i 2 el u i el β ρ20 - : 21 line for u δ augment 31 line :

Δ85 xy ISA 4356 range 12 range el : i 1 xy rows range u i el xy i 1 el : δ i el xy i 2 el u i el J - : 21 line for u δ augment 31 line :

Δ Δ11 Δ20 Δ85 stack :

Δ 11 mat 0.5 - 000 0.5 010 1.5 020 2.5 030 3.5 040 4.5 050 5.5 060 6.5 070 7.5 080 8.5 090 9.5 0100 10.5 0110 11.5 0120 12.5 0130 13.5 0140 14.5 0150 15.5 0160 16.5 0170 17.5 0180 18.5 0190 19.5 0200250300320350400450470500520550600610710850562 mat 11 mat

http://www.pdas.com/atmosTable2SI.html

ρ11 x 0.5 - 11 0.45 - range : i 1 x rows range f11 i el x i el ρ11 eval : for x f11 augment 31 line :

ρ20 x 1120 11.1 range : i 1 x rows range f20 i el x i el β ρ20 eval : for x f20 augment 31 line :

ρ85 x 2085 20.5 range : i 1 x rows range f85 i el x i el J eval : for x f85 augment 31 line :

P ISA 1 col ISA 2 col . 10 black plotG :

Global ρ Air @ km altitude ... *1.225 x ρ x ρ11 0.5 - x ≤ (x 11 ≤ (& x β ρ20 11 x ≤ (x 20 ≤ (& x J 20 x ≤ (x 85 ≤ (& cases :

kg_m³ 1 :

Mont 'K' 8.8 ρ 1.225 * kg_m³ 0.478

Airbus A380 11.3 ρ 1.225 * kg_m³ 0.348

ρ11 ρ20 ρ85 P 4 1 sys

specific ρ [ISA] @ km altitude

Troposphere The troposphere starts at the Earth's surface and extends 8 to 14.5 kilometers high (5 to 9 miles). This part of the atmosphere is the most dense. Almost all weather is in this region. Stratosphere The stratosphere starts just above the troposphere and extends to 50 kilometers (31 miles) high. The ozone layer, which absorbs and scatters the solar ultraviolet radiation, is in this layer. Mesosphere The mesosphere starts just above the stratosphere and extends to 85 kilometers (53 miles) high. Meteors burn up in this layer Thermosphere The thermosphere starts just above the mesosphere and extends to 600 kilometers (372 miles) high. Aurora and satellites occur in this layer. Ionosphere The ionosphere is an abundant layer of electrons and ionized atoms and molecules that stretches from about 48 kilometers (30 miles) above the surface to the edge of space at about 965 km (600 mi), overlapping into the mesosphere and thermosphere. This dynamic region grows and shrinks based on solar conditions and divides further into the sub-regions: D, E and F; based on what wavelength of solar radiation is absorbed. The ionosphere is a critical link in the chain of Sun-Earth interactions. This region is what makes radio communications possible. Exosphere This is the upper limit of our atmosphere. It extends from the top of the thermosphere up to 10,000 km (6,200 mi)

<p> Explode to see Thiele </p>

x g 3635000 / x 20 - 153940886712500000 / - x 25 - 396366140000000 / - x 30 - 14786731000 / x 35 - 6660677125000000 / - x 45 - 90510683871000000000 / - x 52 - 39973877500000000 / x 60 - 192760 - x 71 - 689200000000 / - / + / + / + / + / + / + / + / + :

Collected from ThieleQUICK [ISA2085]

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

support 20 0.0726 25 0.032 30 0.015 35 0.006705 45 0.001536 52 0.00062 60 0.000233 71 0.00005242 85 0.00000568 92 mat :

ρ85 sub ISA 4256 range 12 range el : i 1 sub rows range ρ i el sub i 1 el g eval : for sub ρ augment 31 line :

sub ISA 4256 range 12 range el :

header km ρISA ρ85 13 mat :

ρ85 header ρ85 stack :

sub . 10 black plot x g support + 20 blue plot 3 1 sys

ρ85 km ρISA ρ85 20 0.0726 0.0726 25 0.032 0.032 30 0.015 0.015 32 0.011 0.01086677 35 0.006705 0.006705 40 0.003144 0.00311256 45 0.001536 0.001536 47 0.001165 0.00117574 50 0.000798 0.00079759 52 0.00062 0.00062 55 0.000432 0.00042801 60 0.000233 0.000233 61 0.000205 0.00020634 71 0.00005242 0.00005242 85 0.00000568 0.00000568 163 mat

alt . . . . . . altitude in kilometers.

sigma . . . density divided by sea-level density.

delta . . . . pressure divided by sea-level pressure.

theta . . . . temperature divided by sea-level temperature.

temp . . . . temperature in kelvins.

press . . . . pressure in newtons per square meter.

dens . . . . density in kilograms per cubic meter.

a . . . . . . . the speed of sound in meters per second.

visc . . . . viscosity in 10**(-6) kilograms per meter-second.

k.visc . . . kinematic viscosity in square meters per second.

N/m²=Pa

http://www.pdas.com/atmosTable1SI

]]>