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


 * $$M = \sqrt {5 \left [ \left ( \frac{q_c}{P_s} +1 \right )^ \frac{2}{7} -1 \right ]}$$

where

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


 * $$\frac {R_t}{R_0} = 1+ \alpha \left [ t- \delta \left ( \frac{t}{100} -1 \right ) \left ( \frac{t}{100} \right )- \beta \left ( \frac{t}{100}-1 \right ) \left( \frac{t}{100} \right )^3 \right ]$$

where


 * SAT = TAT / (1 + 0.2 M&sup2;)    – where M is mach number, and SAT and TAT are in kelvins


 * speed of sound (a) = 38.968 &radic;SAT   where the SAT is in kelvins (t&deg;celsius + 273.15).

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