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.

Answer 1

To determine the required skin thickness for the fuselage, we need to consider the circular stress on the fuselage skin. The formula for circular stress is:

σ = P * r / t

Where:
σ is the circular stress
P is the pressure difference
r is the radius of the fuselage
t is the skin thickness

To calculate the pressure difference, we need to consider the cabin pressure at altitude. The cabin pressure should be at least 72 percent of the sea level value. Assuming the sea level pressure is standard atmospheric pressure (101.325 kPa), the cabin pressure at 24 kilometers altitude would be:

P = 0.72 * 101.325 kPa = 72.99 kPa

Next, we need to calculate the radius of the fuselage. Since the diameter is given as 4.5 meters, the radius would be half of that:

r = 4.5 / 2 = 2.25 meters

Now, we can rearrange the formula to solve for the skin thickness:

t = P * r / (σ * safety factor)

Using the given data, with a circular stress limit of 75 MPa and a safety factor of 1.5, we can plug in the values to calculate the skin thickness:

t = (72.99 kPa * 2.25 m) / (75 MPa * 1.5)
t = 194.8 mm / 112.5
t ≈ 1.73 mm

Therefore, the required skin thickness for the fuselage is approximately 1.73 mm to withstand the circular stress limit of 75 MPa with a safety factor of 1.5.