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TWEET # Formula expansion ratio a guest Mar 28th, 2020 98 Never
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1. L = cte //Longitud
2. n = cte //numero de celdas
3. ratio = cte //expansion ratio
4. sum c0...cn-1 = L
5.
6. Como indexamos desde 0, va hasta n-1
7. c0 = l
8. c1 = cratio * c0
9. c2 = cratio * c1
10. .
11. .
12. .
13. cn-1 = cratio * cn-2 = ratio*c0
14.
15. cn-1 = cratio^2 * cn-3 = ratio*c0
16. (reemplazando para atras)
17. cn-1 = cratio^(n-1) * cn-n = ratio*c0
18. cn-1 = cratio^(n-1) * c0 = ratio * c0
19. cratio^(n-1) = ratio
20. cratio = ratio^(1/(n-1))
21.
22. Ademas sum c0...cn-1 = L
23. sum(cratio^i * c0) = L
24. c0 sum(cratio^i) = L
25. https://en.wikipedia.org/wiki/Geometric_series#Sum
26. c0 (1 - cratio^n)/(1 - cratio) = L
27. c0 = L * (1 - cratio) / (1 - cratio^n)
28.
29.
30. Para nuestro caso
31.
32. L = 0.08
33. n = 800
34. ratio = 10
35. cratio = 10^(1/799) ~ 1.00288599
36. c0 ~ 0.08 * (1- 1.00288599) / (1 - 1.00288599^800) = 0.0000255712
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