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).