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.

Question

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 is the minimum required skin thickness for this aircraft (in milimeters)?

Answer 1

First, we need to determine the maximum cabin pressure and the corresponding differential pressure that the fuselage skin will need to withstand.

From the given information, we know that the cabin pressure should remain at least 72% of the sea level value. At a cruise altitude of 24 km, the atmospheric pressure is approximately 22.4% of sea level pressure. Therefore, the cabin pressure should be at least 72% of 22.4% of sea level pressure, which is:

0.72 x 0.224 x 101325 Pa = 16424 Pa

To this cabin pressure, we need to add the external pressure at cruise altitude, which is:

101325 x 0.224 x exp(-0.00012 x 24000) = 11820 Pa

Therefore, the maximum differential pressure that the fuselage skin will need to withstand is:

16424 - 11820 = 4604 Pa

Next, we can use the formula for hoop stress in a thin-walled pressure vessel to calculate the required skin thickness:

hoop stress = P x D / (2 x t)

where P is the pressure, D is the diameter of the vessel, and t is the skin thickness.

Rearranging the formula, we get:

t = P x D / (2 x hoop stress)

Taking into account the safety factor of 1.5, we can use a maximum hoop stress of:

75 / 1.5 = 50 MPa

Substituting the values, we get:

t = (16424 + 11820) x 4.5 / (2 x 50 x 10^6) x 1.5

t = 0.0132 m = 13.2 mm

Therefore, the minimum required skin thickness for this aircraft is 13.2 mm.