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@ -81,22 +81,26 @@ Here is the logarithm plot, with some smoothing applied:
And furthermore, a table:
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| Year | Rate of progress before | Discontinuity in terms of time of travel = New record - current record | How much extra time would have been needed? = (point - previous predicted point)/ previous rate of progress = (discontinuity - expected progress) / previous rate of progress |
|------|---------------------------------------------------------|-------------------------------------------------------------------------|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| 1586 | (1082-1018) days /(1577-1519) years = 1.1034 days/year | 1018-781 = 237 days | (237 days - (1589-1577)*1.1 days) / 1.1 days / year= 203 years |
| 1870 | (781 – 605) days / (1841 – 1586) years = 0.69 days/year | 605-80 days = 525 days | (525 days - (1870-1849 years)*0.69 days / year ) / 0.69 days/year = 740 years |
| 1931 | (80-21) days / (1929-1870) years = 1 day / year | 21-8 days = 13 days | (13 days - (1931 - 1929) years * 1 day/year) / 1 day/year = 11 years |
| 1961 | (94 - 45) hours / (1957- 1949) years = 6.1 hours / year | 32 hours and 49 minutes - 108 minutes = 31 hours | ( 31 hours - 6.1 hours/year *(1961-1957) years ) / 6.1 hours / year ~ 1 year |
| 1586 | 1.1034 days/year | 237 days | 203 years |
| 1870 | 0.69 days/year | 525 days | 740 years |
| 1931 | 1 day / year | 13 days | 11 years |
| 1961 | 6.1 hours / year | 31 hours | 1 year |
And here is that same table if we measure progress according to the logarithm (i.e., if halving the time needed is always equally impressive).
| Year | Rate of progress before (where log = log of base 2) | Discontinuity in terms of time of travel = New record - current record | How much extra time would have been needed? = (point - previous predicted point)/ previous rate of progress = (discontinuity - expected progress) / previous rate of progress |
|------|-------------------------------------------------------------------------------------|-------------------------------------------------------------------------|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| 1586 | (log2(1082)-log2(1018)) log2(days) /(1577-1519) years = 0.001444656 log2(days)/year | log2(1018)-log2(781) = 0.3823431 log2(days) | (0.3823431 log2(days) - (1589-1577)*0.001516602 log2(days)) / 0.08796 log2(days)/year= 240 years |
| 1870 | (log2(781) – log2(605)) days / (1841 – 1586) years = 0.001444656 log2(days)/year | log2(605)-log2(80) days = 2.9 log(days) | (2.9 log(days) - (1870-1849 years)*0.001444656 log2(days)/year ) / 0.001444656 log2(days)/year = 1986 years |
| 1931 | (log2(80)-log2(21)) days / (1929-1870) years = 0.03270527 log2(days)/year | log2(21)-log2(8) days = 1.39 log2(days) | (1.392317 log(days) - (1931 - 1929) years * 0.03270527 log(days)/year / 0.03270527 log2(days)/year = 40.5 years |
| 1961 | (log2(94) - log2(45)log2(hours) / (1957- 1949) years = 0.132842 log2(hours) / year | log2(32 hours and 49 minutes) - log2(108 minutes) = 4.18836 log2(hours) | ( 4.18836 log2(hours) - 0.132842 log2(hours) / year *(1961-1957) years ) / 27.52888 log2(hours) / year ~ 27.5 years |
| Year | Rate of progress before (where log = log of base 2) | Discontinuity in terms of time of travel = New record - previous record | How much extra time would have been needed? = (point - previous predicted point)/ previous rate of progress = (New record - previous record - predicted advance) / previous rate of progress |
|------|-----------------------------------------------------|--------------------------------------------------------------------------|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| 1586 | 0.00151660237 log2(days)/year | 0.3823431 log2(days) | 240 years |
| 1870 | 0.001444656 log2(days)/year | 2.9 log(days) | 1986 years |
| 1931 | 0.03270527 log2(days)/year | 1.39 log2(days) | 40.5 years |
| 1961 | 0.132842 log2(hours)/year | 4.18836 log2(hours) | 27.5 years |
### Sources:
[Wikipedia: List of circumnavigations](https://en.wikipedia.org/wiki/List_of_circumnavigations)