User:Paul Lockheed/Sandbox

V_{i}=C_{s0}\,{\sqrt {{\frac {2}{\gamma -1}}\left[\left(1+{\frac {q_{c}}{P_{0}}}\right)^{\frac {\gamma -1}{\gamma }}-1\right]}}

where

$V_{i}$ is indicated airspeed in knots

$C_{s0}$ is ISA sea-level speed of sound (661.48 knots)

$P_{0}$ is ISA sea-level pressure (101 325 pascals)

$q_{c}$ is dynamic pressure

$\gamma$ is ratio of specific heats (1.4)

M={\sqrt {5\left[\left({\frac {q_{c}}{P_{s}}}+1\right)^{\frac {2}{7}}-1\right]}}

where

$M$ is mach number

$P_{s}$ is static pressure

$q_{c}$ is dynamic pressure

At levels below that where $V_{mo}=M_{mo}$ :

V_{mo}=C_{s0}\,{\sqrt {{\frac {2}{\gamma -1}}\left[\left(1+{\frac {P_{s}}{P_{0}}}\left[\left({\frac {V_{em}^{2}}{5\cdot C_{s0}\cdot \sigma }}+1\right)^{\frac {\gamma }{\gamma -1}}-1\right]\right)^{\frac {\gamma -1}{\gamma }}-1\right]}}

At levels above that where $V_{mo}=M_{mo}$ :

V_{mo}=C_{s0}\,{\sqrt {{\frac {2}{\gamma -1}}\left[\left({\frac {P_{s}}{P_{0}}}\left[\left(1+{\frac {(\gamma -1)M_{mo}^{2}}{2}}\right)^{\frac {\gamma }{\gamma -1}}-1\right]+1\right)^{\frac {\gamma -1}{\gamma }}-1\right]}}

where

$V_{mo}$ is max operating IAS

$C_{s0}$ is ISA sea-level speed of sound (661.48 knots)

$P_{s}$ is static pressure

$P_{0}$ is ISA sea-level pressure

$V_{em}$ is max allowable EAS in knots

$M_{mo}$ is max operating mach number

$\gamma$ is ratio of specific heats (1.4)

{\frac {R_{t}}{R_{0}}}=1+\alpha \left[t-\delta \left({\frac {t}{100}}-1\right)\left({\frac {t}{100}}\right)-\beta \left({\frac {t}{100}}-1\right)\left({\frac {t}{100}}\right)^{3}\right]

where

$t$ is element temperature in °celsius

$R_{t}$ is element resistance at t°celsius

$R_{0}$ is resistance at 0°celsius (usually 500 ohms)

$\alpha$ is 0.003832

$\delta$ is 1.81

$\beta$ is 0 for positive t; 0.1 for negative t

SAT = TAT / (1 + 0.2 M²) – where M is mach number, and SAT and TAT are in kelvins

speed of sound (a) = 38.968 √SAT where the SAT is in kelvins (t°celsius + 273.15).

True airspeed is equal to mach number (M) multiplied by the speed of sound (a).