I was in a case class in my MBA program many years ago. I don’t remember the case, or the class, particularly, but I do remember answering a professor’s question about a financial decision “that’s a marginal difference.” The professor replied “All decisions are made on the margin.”
I probably attributed more to his comment than it was worth, but it stuck with me. In a sense, all decisions ARE made on the margin, if by the margin you mean the space where the information changes.
Say you’re lost in a forest of identical trees. You wander about but you can’t differentiate between the trees and can’t orient yourself. It’s only when you get a piece of outside information, e.g. the direction of the sun or the edge of the trees, that you can start making productive decisions. On the margin.
We tried making brick of the same thickness but with frogs and failed the strength test. I was going to hang it up with the results from the previous tests, then realized that brick thickness itself is not a critical criterion for us.
We are trying to establish the energy that can be saved by making bricks with the same strength and absorption as standard brick mixes. We are not actually using these as paving bricks (except in my yard), so maintaining a thickness established by custom is not pertinent.
Since the 1600 gram had passed the strength test by so much, we decided to make one more run at making a lighter brick. The bricks made at 1850∞F with a 20 minute soak met the standards for Cold Water Absorption, and strength:
Dry weight Absorption Strength Average Strength
1499 6.3% 2419 2410
1505.5 6.2% 2401
Although this set of two does not meet the statistical standard, it is apparent that the 20 minute soak also makes an adequate brick. At an average breaking strength of 2410, the 20 minute soak bricks exceeded the strength standard by
2410/1900 = 1.268:1
Flexure strength is proportional to the square of the depth, so it may be possible to make bricks exceeding the 1900 pounds strength standard with a thickness of
1/(1.268)^.5 = .888
times the thickness of the first set of bricks.
The first bricks used 1600 grams of dry raw materials, so the new set will weigh
.888*1600 = 1420 grams dry.
We also mentioned previously that the bricks appeared to not be fused completely in the middle. This may meant that we can reduce the weight even more and get full fusion (and thus strength) in the middle. So for the second test run, 1400 grams of dry material is used. The standard mix for this run is:
∑ 700 grams 12 mesh glass
∑ 700 grams Redart Fireclay
∑ 231 grams water
A set of five bricks is made and tests as follows:
Dry weight Absorption Ave. Absorption Strength Ave Strength
1302.5 5.6% 5.74 1769 1914
1302 5.8% 1942
1318.5 5.9% 1921
1321 5.6% 1913
1307 5.8% 2026
So this set of bricks meets the ASTM standard for both Absorption and Strength.
On the other hand, the grog bricks we fired to 2100F did not truly meet the strength standard. For a true comparison of energy, we had to make one more firing to 2125F. Those bricks tested as follows:
Max Temperature Dry weight Absorption Strength Average strength
2125∞F 1468 5.3% 1918 1979
1478 5.3% 2040
The 2125∞F bricks meet both standards (albeit not statistically valid), so they will be used as the reference for energy used to make a brick.