Wikipedia has a formula s = 83 * 10^(c/15) for the top wind speed for a category c hurricane, though the formula has no citation, so I suspect it is original work and bogus.
However, assuming it to be true, after some munging, we have c = A*log(B*s) where A = 6.5144172285487774147669337837490762346, B = 0.014047161459997972724688583095129757552, s = sustained wind speed in mph, and c is a real number "category" which should be rounded down if an integer is desired. The logarithmic scale is reminiscent of the magnitude scale for earthquakes.
Hurricane Patricia, with 200 mph sustained winds, would be category 6.7292785493186093707146781404584766967.
| Category | Minimum speed | Maximum (mph) |
|---|---|---|
| -4 | 38.5 | 44.9 |
| -3 | 44.9 | 52.4 |
| -2 | 52.4 | 61.1 |
| -1 | 61.1 | 71.2 |
| 0 | 71.2 | 83.0 |
| 1 | 83.0 | 96.8 |
| 2 | 96.8 | 112.8 |
| 3 | 112.8 | 131.5 |
| 4 | 131.5 | 153.4 |
| 5 | 153.4 | 178.8 |
| 6 | 178.8 | 208.5 |
| 7 | 208.5 | 243.1 |
| 8 | 243.1 | 283.4 |
| 9 | 283.4 | 330.4 |
| 10 | 330.4 | 385.3 |
A hurricane with sustained winds at the speed of light would be category 104. The amount of damage such a storm would cause is unimaginable.
There's no way a storm could reach category 9000.
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