Aerodynamics. Airspeed.
Givens:
1. Baro altimeter setting $= 30.42″$ Hg
Difference in altitude = Sea Pressure altitude – Baro altimeter setting $= -30.42 +29.92 = -0.5”$ Hg
$1 Hg = 1000 ft$ it means $-0.5 Hg =-500 ft$
Pressure altitude = Indicated altitude – Difference in altitude $= 15500 -500 =15000$ ft
2. Pressure ratio at sea level
$Delta$ = Pactual/Pstandardsealevel $= 30.42/29.92 = 1.0167$
pressure ratio at altitude
$Delta 1 = 0.5643$ from table 2.1 corresponding to an altitude of 15000 ft
3. temperature ratio at altitude
(temperature is given in deg R (deg R = 460 +F)
$theta$ = Actual temperature/Standard sea level Temperature $= (59+5+460)/(59+460) =524/519 =1.00963$
4. Density ratio
$sigma =$ pressure ratio/temperature ratio $= 0.5643/1.00963 =0.5589$
5. Density altitude
from table 2.1 we have
at 0 ft we have sigma =1
at 20000 ft we have sigma = 0.5328
at 15000 ft we have sigma = 0.6292
for every ft higher than 15000 ft we have $(0.6292-0.5328)/5000 =1.928*10^{-5}$ variation of $sigma$
total variation of $sigma$ is $0.6292-0.5589 =7.03*10^{-2}$
which means a variation in altitude of $7.03*10^{-2}/1.928*10^{-5} =3646.3$ ft above $15000$ ft
the density altitude is $15000 +3646.3 =18646.3$ ft
6. calibrated air speed= indicated air speed +(-) position error
CAS = IAS – position error
For IAS = 250 KIAS we have from chart the error -2.4 Knots
CAS =250 -2.4 = 247.6 Knots
7. equivalent air speed is
EAS = CAS – Compressibility correction
compressibility correction is 4.25 knots from figure 2.6
EAS = 247.6 – 4.25 = 243.35 Knots
8. True air speed
TAS $= EAS/sqrt{sigma} = 243.35/sqrt{0.5589} = 325.5$ knots
9. Dynamic pressure
$q= sigma*V^2/295$
where V is the TAS in knots $=325.5$
$sigma =0.5589$
$q =(325.52)^2 *(0.5589)/295 = 200.74 (lb/ft^2)$