In chapter 18 on page 483 the title of example 18.5 should be changed to "cabin pressure" or "cabin pressurization". It is only very tangentially related to altimetry.
Also, it says
The fuselage does not rupture because the force is distributed over a very large area.
As the saying goes, it's bad luck to prove things that aren't true. A damaged or under-strength fuselage can explode, sometimes with very unpleasant results. (DeHavilland Comet, AAH 243, JAL 123)
Perhaps more importantly, neither the pressure nor the total force is the thing that you ought to be looking at. You ought to care about the tension i.e. the force per linear distance. This is the thing that exhibits some reasonable scaling behavior. For example, making a cylinder longer (at constant pressure) increases the total force, but not the tension. In contrast, increasing the diameter does increase the tension.
For something essentially cylindrical such as the main fuselage (or the tube in a bike tire), the tension in the dθ direction is just pressure times radius. Homework: Prove this. Hint: Principle of Virtual Work. See #149 for a directory of PVW issues. Remark: This is one of the reasons why fat mountain-bike tires run at lower pressure than thin racing-bike tires. If you put 120 psi in the mountain-bike tire, it would pop right off the rim.
For something like the aft bulkhead on JAL 123, you might care about tension in the dZ direction. This is the pressure times the projected area (projected onto the XY plane) divided by circumference. This is less than the tension in the dθ direction, but only slightly.
Remark: Scaling laws are important! Always check the scaling! If a calculation gives a number that doesn't scale properly, it's the wrong calculation. Scaling arguments have been part of modern science since Day One (1638). They remain part of cutting-edge physics even today. They are easy to use and very powerful, yet they don't get nearly enough coverage in introductory physics courses.
In chapter 18 on page 483 the title of example 18.5 should be changed to "cabin pressure" or "cabin pressurization". It is only very tangentially related to altimetry.
Also, it says
As the saying goes, it's bad luck to prove things that aren't true. A damaged or under-strength fuselage can explode, sometimes with very unpleasant results. (DeHavilland Comet, AAH 243, JAL 123)
Perhaps more importantly, neither the pressure nor the total force is the thing that you ought to be looking at. You ought to care about the tension i.e. the force per linear distance. This is the thing that exhibits some reasonable scaling behavior. For example, making a cylinder longer (at constant pressure) increases the total force, but not the tension. In contrast, increasing the diameter does increase the tension.
For something essentially cylindrical such as the main fuselage (or the tube in a bike tire), the tension in the dθ direction is just pressure times radius. Homework: Prove this. Hint: Principle of Virtual Work. See #149 for a directory of PVW issues. Remark: This is one of the reasons why fat mountain-bike tires run at lower pressure than thin racing-bike tires. If you put 120 psi in the mountain-bike tire, it would pop right off the rim.
For something like the aft bulkhead on JAL 123, you might care about tension in the dZ direction. This is the pressure times the projected area (projected onto the XY plane) divided by circumference. This is less than the tension in the dθ direction, but only slightly.
Remark: Scaling laws are important! Always check the scaling! If a calculation gives a number that doesn't scale properly, it's the wrong calculation. Scaling arguments have been part of modern science since Day One (1638). They remain part of cutting-edge physics even today. They are easy to use and very powerful, yet they don't get nearly enough coverage in introductory physics courses.