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変換式 > Link > 気圧から高度 > International Standard Atmosphere:ISA

Last updated at Posted at 2016-06-02

International Standard Atmosphere:ISA

http://www.geocities.jp/zattouka/GarageHouse/micon/Arduino/Pressure/Pressure1.htm
にて実装されている気圧から高度への変換式。

検索して見つかったのは以下。

国際標準大気(International Standard Atmosphere:ISA)

別途、googleで[pressure altitude 44330.8]で検索したときに出てくる「A Quick Derivation relating altitude to air pressure - Resea...」というPDFファイルにて該当の係数を使った計算が記載されている。

式7の変形

@it__ssei さんに教えていただいた資料の式7の変形

P / P0 = (1 - 0.0065 h / T0)^{5.2561} -- (1)

以下の式を使う

t^a = exp(a * logt)

(1)式は

P / P0 = exp ( 5.2561 * log(1 - 0.0065 h / T0) )

両辺の対数を取り

log(P / P0) = 5.2561 * log(1 - 0.0065 h / T0)

after some of algebra

1 / 5.2561 * log(P / P0)  = log(1 - 0.0065 h / T0)
0.190255 * log(P / P0) = log(1 - 0.0065 h / T0)
log(P / P0) ^ {0.190255} = log(1 - 0.0065 h / T0)
(P / P0) ^ {0.190255} = (1 - 0.0065 h / T0)
0.0065 * h / T0 = 1 - (P / P0) ^ {0.190255}
h = T0 / 0.0065 * (1 - (P / P0) ^ {0.190255})

T0 = 288.15の時、T0/0.0065 = 44330.8

係数 0.190263 と 0.190255 の違いがあるようだ。

式変形は最初から両辺の対数を取ったほうが早かったかも。。。

関連資料

Lapse rate (0.0065 K/m)

など

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