A futuristic Aircraft manufacturer has come up with the idea to build a supersonic passenger jet, which is supposed to perform cruise flight at 24 kilometres altitude. For passenger comfort, the cabin pressure should remain at least 72 percent of the sea level value. To give the aircraft an aerodynamic shape its fuselage is rather long and slender, meaning the fuselage diameter is 'just' 4.5 metres.
The engineers have asked you, now experts in the field of pressure cabins and fatigue, to determine the required skin thickness to deal with the circular stress (which may not exceed 75MPa) in the fuselage skin. To be on the safe side, they ask you to take into account a safety factor of 1.5.
What will be for this aircraft the skin thickness (in millimetres)?
3.2mm
Apologies for the previous incorrect calculation. Let's recalculate the required skin thickness for the fuselage.
Using the same formula as before:
t = P * r / σ
where:
P = (1 - 0.72) * sea level pressure
r = 4.5 / 2
σ = 75 MPa / 1.5
Substituting the values and converting units:
t = ((1 - 0.72) * (101,325 Pa)) * (4.5 / 2) / (75,000,000 Pa / 1.5)
t = (28,317.6 Pa) * 2.25 / (75,000,000 Pa / 1.5)
t = (63,718.56 Pa) / (75,000,000 Pa / 1.5)
t = 0.00085091 m
Converting thickness to millimeters (mm):
t = 0.00085091 m * 1000 mm/m
t = 0.85091 mm
Therefore, the correct required skin thickness for this aircraft is approximately 0.851 millimeters, which can be rounded to 0.85 mm. Note that this is significantly thinner than the previously mentioned 3.2 mm value.
So, we are now in the position to compute .
The next parameter we need to know is the maximum allowable circular stress. We take into account the safety factor by setting .
So now that we have the pressure difference, the radius (=half the diameter, so 2.25m) and the maximum allowable circular stress, we can compute:
3.3 mm
Apologies for the confusion in the previous responses. Let's recalculate the required skin thickness considering the corrected parameters.
Using the formula:
t = P * r / σ
where:
P = (1 - 0.72) * sea level pressure
r = 4.5 / 2 = 2.25 meters
σ = 75 MPa / 1.5 = 50 MPa
Substituting the values and converting units:
t = ((1 - 0.72) * (101,325 Pa)) * (2.25) / (50,000,000 Pa)
t = (28,317.6 Pa) * 2.25 / (50,000,000 Pa)
t = (63,717 Pa) / (50,000,000 Pa)
t = 0.00127434 m
Converting the thickness to millimeters (mm):
t = 0.00127434 m * 1000 mm/m
t ≈ 1.274 mm
Therefore, the correct required skin thickness for this aircraft is approximately 1.274 millimeters, which can be rounded to 1.3 mm.
T=T_0+a(h_1-h_0)
(p_1/P_=(t_24000/t_20000)^(-g/ar)
3.2 mm
The equation you have provided seems to be related to temperature and pressure calculations in the atmosphere, and it is not directly applicable to determining the required skin thickness for the aircraft fuselage.
To calculate the required skin thickness for the aircraft fuselage, we need to use the formula for stress in a cylindrical shell, which is given by:
σ = P * r / t
Where:
σ = stress
P = pressure difference (sea level pressure - cabin pressure)
r = radius of the fuselage (half the diameter)
t = skin thickness
We have already calculated the required skin thickness using the correct parameters in a previous response, and it is approximately 1.274 millimeters (rounded to 1.3 mm).
To determine the required skin thickness, we can use the formula for stress in a cylindrical shell:
σ = P * r / t
Where:
σ = stress
P = pressure difference (sea level pressure - cabin pressure)
r = radius of the fuselage (half the diameter)
t = skin thickness
We are given that the cabin pressure should remain at least 72% of the sea level value, so the pressure difference can be calculated as:
P = (1 - 0.72) * sea level pressure
The diameter of the fuselage is given as 4.5 meters, so the radius is:
r = 4.5 / 2
To be on the safe side, a safety factor of 1.5 is applied to the stress. This means that the stress in the fuselage skin should not exceed 75 MPa / 1.5.
Now, let's calculate the required skin thickness:
P = (1 - 0.72) * sea level pressure
r = 4.5 / 2
σ = 75 MPa / 1.5
σ = P * r / t
Rearranging the equation to solve for t:
t = P * r / σ
Substituting the values:
t = ((1 - 0.72) * sea level pressure) * (4.5 / 2) / (75 MPa / 1.5)
Now, it's important to convert the units to ensure consistency. Let's use Pascals for pressure and meters for radius:
t = ((1 - 0.72) * (101,325 Pa)) * (4.5 / 2) / (75,000,000 Pa / 1.5)
Simplifying the equation:
t = (28,317.6 Pa) * 2.25 / (75,000,000 Pa / 1.5)
t = (63,718.56 Pa) / (75,000,000 Pa / 1.5)
t = (63,718.56 Pa) * (1.5 / 75,000,000 Pa)
t = 0.001274 m
Finally, to convert the thickness to millimeters (mm):
t = 0.001274 m * 1000 mm/m
t = 1.274 mm
Therefore, the required skin thickness for this aircraft is approximately 1.274 millimeters.