Diminishing returns situation

Temperature limits of flight engine alloys have been steadily inereasing about 20 °F (11 °C) per year sinee 1945. Transpiration and internally eooled metal blades have resulted in higher temperatures and more effieient operation. But the direet eorrelation between effieieney and fabrieation eost has resulted in a situation of diminishing returns for the superalloys. As more and more eooling air is needed for the superalloy eomponents, the effieieney of the engine drops to a point where turbine inlet temperatures around 2300 °F (1260 °C) are the optimum and, at that point, they are uneeonomie for automotive use. 

The examples discussed in the previous sections Illustrate models for deriving Isotherms for binary systems. A variety of variants (e.g. mobile adsorbates), alternatives (e.g. models based on computer simulations) and extensions (e.g. multimolecular adsorption. Inclusion of surface heterogeneity, can be, and have been, proposed. The extensions usually require more parameters so that agreement with experiment is more readily obtained, but as long as various models are not compared against the evidence, discrimination is impossible. As there are numerous theoretical (e.g. distinction between molecules in the first and second layer) and experimental (presence of minor admixtures, tenaciously adsorbing on part of the surface) variables one tends to enter a domain of diminishing returns. On the other hand, there are detailed models for certain specific, well-defined situations. Here we shall review some approaches for the sake of illustration. 

Table 8.4 compares heat tfansfer rates for 6" (152 mm) square billets in a Curve 2 versus Curve 4 situation, both with spacing ratios of 3 1 and 2000 F (1090 C) furnace gas. Gains from wider spacing have diminishing returns (especially for four-side heating). All curves droop at low spacing-to-thickness ratios because all radiation is less with narrower spacing. 

This diminishing effect on cost plus return resulting from a uniform incremental increase in capacity as the total capacity level is increased is usually referred to in the chemical industry as the law of diminishing returns. In classical economics the same law refers to the situation in which an increase in one of the factors of production (land, labour or capital) results in a reduction in output rather than an increase. 

In the earlier part of this chapter, it was shown that increasingly complicated mathematics is required if the stress situation in a single adhesive lap joint is to be determined. Even so, the law of diminishing returns applies, together with the irony that end effects, particularly where a spew fillet is involved, are the most difficult to model accurately while this is the most critical region since failure almost always occurs here. 

Let us look at the pattern of the reductions in risk probability for conjoint failure given the increases in the number of coins that we flipped. Note that there is a diminishing return on increasing the number of coins, such that as more coins are added, we see smaller reductions in the probability of conjoint failure. This is the general pattern that you will find for this type of situation. What this means is that there are very real limits on the value of inereasing the size of the supply base. 

Occasionally, a response from a system will act as a true factor to the same system, a phenomenon that is generally referred to as feedback. (This is not the same as the situation of masquerading factors.) Feedback is often classified as positive if it enhances the response being returned as a factor, or negative if it diminishes the response. 

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