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That is why I am looking to get smaller teeth chainring but since Tijs says it does not matter what is changed I will get the freewheel in 22t. The current chainring is 47t. The current freewheel is 18t
Remember that removing 1 tooth from the chainring doesn't have the same effect as adding 1 tooth to the cog/freewheel; it's about the ratio between the two.
So for example 48/16 is equal to 42/14 (divide both sets of numbers and you get the equal number of 3). How many teeth you need to add to your cog/freewheel to achieve the gear ratio best suited for you is for a large part trial and error and dependent on how hilly your area is and how strong you are.
Going from 47/18 to 47/22t is a huge difference though. I ride 48/19 on my city bike (which is slightly easier than your 47/18) and I find it quite spinny. But your miles may vary!
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Will higher teeth on freewheel (eg 22t) reduce rolling resistance as much as the lower tooth chainring?
I don't think this is a relevant argument (for you and this bike), especially since budgeting is a (big) theme of this project (and not speed/efficiency). So I'd go for the cheaper solution.
I think you're correct in that less teeth cause less resistance, but firstly you won't be able to notice this and and secondly less teeth wear down the cogs/chainring faster.
If you're talking about the gear ratio then yes indeed, it doesn't matter if you use a smaller chainring or a bigger cog/freewheel; the ratio between the two changes in a way that the pedaling will become easier using both methods.
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People create rat rods on purpose:

Ideally you want your bike to become ratty by using and abusing it over the years, but realistically this isn't viable for most people who don't use their bike 24/7 and still like the look. So I get why they're helping their bike a little, although this might makes you look like a poser to the 'hardcore' rat connoisseurs (do they exist?). It's not super authentic, I agree. But in the end; who cares? It's kind of like hating on people with 'fixies' because they're not 'true' fixed gear bike lovers. Different strokes. As long as people enjoy their bikes.
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You don't like it ?
I like it :)I didn't mean anything negative by calling it a clone, @Paulo_C. In fact; I quite like it! Haters gonna hate and all that. Enjoy your bike!
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Nah, I'll give you 10 quid for it.
That Vivalo is proper nice though. Any plans to build it up?