Everyone has the picture in their mind of a rocket being a shiny high technology marvel. The Buck Rogers rocket ship. However if rockets were designed by MBAs instead of NASA PHD rocket scientists, low grade plumbing would be the standard. Consider the question of steel verses aluminum. Ask anyone in the rocket industry and they will tell you that booster rockets should be made of aluminum at the minimum with expensive composites being preferred. But is that really cheaper?
Rockets are defined by the equation:
Delta V = ISP * Ln(MR) * G
Delta V is the change in velocity in ft/sec
ISP is the specific impulse of the engine
Ln(MR) is the natural log of the mass ratio (expressed as total weight /final weight in pounds)
G is the gravity constant 32
Delta V, or change in velocity is all you really want from a rocket, it's what rockets do!
Steel is stronger than aluminum. Common steel usually will take about 35,000 psi in tensile strength, while aluminum is about 20,000 psi, a ratio of about 1.75. However aluminum is much lighter than steel with density of about 2.7 compared to steel's 7.8 or a ratio of about 2.8. The cost of aluminum to steel at the local scrap yard is $0.70 for aluminum and $0.12 for steel or 5.83. So aluminum is weaker but lighter but more expensive. So, is it better?
Now if we take a rocket design with 100 pounds of fuel and a mass ratio of 3.3 in steel with, and say an ISP of 250, which gives us a delta V = 250 * 1.19 * 32 = 9520 (note, there is a scientific calculator in Windows, so leave your slipstick in storage) Substituting aluminum for steel in the basic rocket equation gives a mass ratio of 4.5 and a delta V of 12032. Aluminum looks better, but is it cheaper?
Now we can determine the delta V per buck which is what Minimum Cost Design is all about.
12032/(27.8#@$0.70/#) =
12032/$19.46 = 618 ft/sec/buck
9520/(42.8#/$0.12/#) =
9520/$5.14 = 1852 ft/sec/buck
Steel is cheaper, a lot cheaper, and gives better delta V per buck, and is therefore, better. Also steel is very easy to weld, while believe me aluminum is NOT. So, if you walk up the bottom of a rocket, expect to see steel if the designer knows what he is doing.