Saturday, October 18, 2008

Justification of the Shape Factor

Idioma: EspaƱol


To verify the concept of the Shape Factor the TABLE 3 it was used, made by a computer program according to the following procedure:

  1. Improvements were adopted in a controlled way.
  2. With the improvements the Shape Factor (f) of each stage was determined, using the equation (c).
  3. The index b was calculated applying the equation (d).
  4. With the equation (b) the values of the MLO of each stage were calculated.



IMPROVEMENTS ADOPTED

For the stage 1 (S = 1) it is fixed an initial improvement of 40%. The values of the successive improvements it was adopted according to a 0.5 coefficient: 40%; 20%; 10%; 5%; et cetera). The improvement of each stage is, in this way, the half of the improvement of the previous stage.

This way of generating improvements simulates the existence of constant Current Performing Conditions (CPC). For successive approaches it is determined, in the stage 25, a final value of the MLO, appropriate to the quantity of considered decimals.



Of the analysis of the TABLE 3 it is result:

  1. In the stage 25 the values of the MLO coincide (adopted and calculated).
  2. The successive values of the calculated MLO diminish as the curve leaves flattened, until reaching the final value.
  3. They repeat numbers due to the scarce quantity of printed decimals.
  4. The index b calculated fixes the first decimal in the stage 3, the second decimal in the stage 6, the third decimal in the stage 10, the fourth decimal in the stage 11, the fifth decimal in the stage 14, the sixth decimal in the stage 19 and the decimals seventh and eighth in the stage 21.
  5. The difference among the index b calculated for the stages 3 and 25 is of 6%, what indicates a remarkable stability of the considered equations.
  6. The values of the calculated MLO tend quickly toward the correct final value, what is important considering that the projects should be solved in few stages (in the stage 2 they differ in 12%, in the stage 3 they differ in 2% and in the stage 4 they differ only in 0.4%: for an estimated method, this differences are excellent.


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