Matching one's economy is one thing. Matching one's total military power is another. Matching one's projected military power in a selected geographical area is yet another. And on top of that one should really add total influence or political power, which is a different variable altogether.
*IF* both sides keep on going at some predictable pace, interpolated from the history of other countries in similar positions and from the history of China/US own growth in the last 20 or so years...
China might match US economy sometime in 2030-2035 period.
Matching total military power is much more harder, as that involves catching up decades of US investments in quantitative and qualitative lead. It really might take a whole generation of lifetime of military systems, say some 30-ish years or so. So i would expect China to match that sometime in the 2060-2070 period.
Matching local projected military power is different. Farther one is from home, the harder it gets. People most often neglect the logistical drawbacks power projection requires half way around the world. China may not project its power near US shores for another 100 years or so. Likewise, projecting US power, even with existing bases near China, is very demanding. When it comes to projecting power around some mid point between first and second island chains, I would expect China to match US sometime after 2030 perhaps by 2040. It's hard to tell, this one. (yes, that does mean that matching projected power just to the first island chain might not take very long anymore. It might happen in as little as a decade from now)
Overall political influence is much, much harder to achieve than any of this.
We have the example of USA versus UK. USA matched UK's nominal GDP back in 1880. By the start of ww1 it doubled its lead over UK's GDP. Some might argue USA still wasn't premier political power in the world, that it didn't achieve that title until start of ww2. That was 60 years after passing UK's GDP and at that point US had three times as large GDP as UK.
Even so, China's climb might be harder and slower than that as there are alleviating circumstances that US enjoyed back then. Cultural influence was more easely achieved as A) they used the same language and similar culture as the power they replaced in the World. B) Mass media and globalization didn't really exist in time period when UK ruled the World. USA was basically the first power that embraced those as a tool to spread its cultural influence. So it has a decent century long lead over China in that regard.
Further helping facts that US enjoyed and China might not is the fact US increased the usage of its territory and its population very quickly. Its population grew 260% from 1880 to 1940. UK's population grew some 90% in the same period. Now, as we know, simply increasing population can be counterproductive. It's exactly what drew down India and even China, before one child policy. One first needs to achieve a certain level of wealth and productivity per capita and be able to maintain it with added population. UK and US managed that a century ago. But simply adding poor population which will require more of the State than it will give back to the State is not productive. UK to an extent, but especially USA, also had natural resources and free territory inside their borders to utilize that extra potential from the extra population.
China on the other hand seems content to stick to its current population levels and first will want to bring the large portion of its population to some standard that's closer to current western world levels. All that is very tricky stuff to predict, but its decades of work.
Altogether, all these issues make me personally believe China won't really match overall influence in the world before 2100, in the best case (where its economy keeps growing as it is) and perhaps it will take as long as 2150, (if its economy keeps decelerating, as it would appear all economies do at some stage)
I would think it's safe to say no one here at this forum will be alive to see the day China overtakes US. It's a natural process and as with all such processes, it takes time.
And none of this takes into account possible earthshattering developments. Revolutions, plagues, world wars, asteroid strikes or whatever, which may or may not sway US and/or China's power in any direction and at any pace.
All this is just personal opinion of one single person, please don't take it too seriously and start a crusade against my writings.
