Number of engines: 2

Question

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.

Answer 1

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.