Number of engines: 2
Wing surface: s=88.3 m^2
Diameter of engine inlet: d=1.1180 m
Oswald efficiency: e=0.67
Span: b= 23.7m
Mass: m= 30000 kg
(ISA) Air density at cruise altitude: rho = 0.5 kg/m^3
Cruise speed: V(TAS)= 450 kts
Zero-lift drag coefficient: 0.015
For the International Standard Atmosphere (ISA) please use:
Gravity acceleration: g=9.80665 m/s^2
Gas constant for air: R=287.00 J/(kg.K)
Sea-level pressure: 101325 Pa
Sea-level temperature: 288.15 K
Sea-level density: 1.225 kg/m^3
A) Calculate the cruise altitude of this Gulfstream IV in feet.
To calculate the cruise altitude in feet, we need to convert the given cruise speed from knots to meters per second.
Given:
Cruise speed (V(TAS)) = 450 kts
To convert kts to m/s, we use the conversion factor 1 kts = 0.5144 m/s.
So, the cruise speed in meters per second (V(TAS)) = 450 kts * 0.5144 m/s = 231.48 m/s.
Now, we can calculate the cruise altitude in feet by using the formula:
cruise altitude (ft) = (pressure altitude (ft) * 3.28084) + 10,000,
where pressure altitude is given by:
pressure altitude (m) = (sea-level temperature (K) / lapse rate (K/m)) * [1 - ((Pressure (Pa)) / (sea-level pressure (Pa))) ^ (1/exponent)].
Since the lapse rate, exponent, and sea-level pressure are not given, we will assume standard values based on the International Standard Atmosphere (ISA) conditions. The standard values are:
Lapse rate (K/m) = -0.0065
Exponent = 5.2561
Sea-level pressure (Pa) = 101325 Pa
Using these values, we can calculate the pressure altitude (m) as:
pressure altitude (m) = (288.15 K / -0.0065 K/m) * [1 - ((Pressure (Pa)) / (101325 Pa)) ^ (1/5.2561)].
To convert pressure altitude from meters to feet, we use the conversion factor 1 m = 3.28084 ft.
Finally, we can substitute this into the cruise altitude formula to calculate the cruise altitude in feet.