Bicycle Mechanics - changing spocket size

I have a 3sp KHS Green (http://www.khsbicycles.com/09_green_m_sil_10.htm). From what I understand the rear sproket has 18 teeth, and if I wish to have a higher (or is it lower?) gearing (going faster with the same rpm) , I need to change out the sprocket for one with fewer teeth. The front crankset has 32 teeth, if I'm reading the specs right.

What I like to achieve is that what currently is my second gear, would become my first gear, and all subsequent gears are higher. Using Sheldon Browns calculator (http://www.sheldonbrown.com/gears/internal.html), it looks like I need to switch from 18 teeth to 13 teeth.

Does that sound right, or am I understanding that wrong. Are 13 teeth going to be way to hard? Any thoughts?

Thanks in advance.

That is correct. The smaller the number of teeth in the back the higher the gear it is. A typical range on a road bike on the back cassette is from 11 to 27 or so. A 32x 13 isn't going to be too difficult at all.

Thanks. So, but now I am reading that the wear on sprockets 14 and smaller can become an issue? Is that right?

According to your link the bike has a Shimano Nexus 3-speed, and they can't take any smaller than a 16T sprocket. To achieve what you want you'd have to go for another crankset, it's unlikely that yours would have a replaceable chainring.

But you should consider your attempt. That bike stock should let you get to about 20 MPH before running out of gear, which seems like plenty for a bike in that configuration. Besides, pushing a too high gear is an easy way of messing up your knees.

..now I am reading that the wear on sprockets 14 and smaller can become an issue? Is that right?

That mainly applies to bikes with external gear hubs, where sprockets have become ever increasingly thinner to allow for more gears w/o increasing the space needed for the sprocket stack. Yours is an IGH, so you'll have a considerably thicker sprocket, w/o any shifting ramps or any other issues. Durability is unlikely to be an issue.

thanks dabac, this is helpful.

A 32 tooth single chainring is very small. If yours is replaceable and a larger one will fit inside your chaincase, that would be the way to go (or you could ditch the chaincase). I've got two bikes, one with a Nexus 7 and the other Nexus 8. The Nexus 7 came with a 38 tooth chainring and 21 tooth rear cog [since replaced with a different crankset--(46 tooth) and 23 tooth rear cog]. The Nexus 8 runs a 44 tooth chainring and 21 tooth rear cog, but I've got a 42/23 combo to swap in if I start riding hillier terrain. You might notice a difference by going to a 16 tooth rear cog and leaving the 32 tooth chainring, but it wouldn't be a dramatic change.
CC

Others have helped you do what you want, but I have to ask why you want to. Many people think their gears are too low when they are not. There is a risk of damage to the knees if you use a high gear, possibly permanent. Measure your pedaling cadence. You don't have to be dead accurate. Time how many times your right foot comes around in 15 seconds. Multiply by four. That's your cadence, measured in RPM. It should be at least 70 rpm. You're not doing yourself a favor by pedaling harder in a higher gear.

3 spline cogs common to 3 speed hubs which follow on from Sturmey Archer's standard start from 13 teeth
can be purchased in 3/32" thickness,
I got a 13t on my Brompton as stock , and 1/8" standard Sturmey cogs start at 14t.

Others have helped you do what you want, but I have to ask why you want to. Many people think their gears are too low when they are not. There is a risk of damage to the knees if you use a high gear, possibly permanent. Measure your pedaling cadence. You don't have to be dead accurate. Time how many times your right foot comes around in 15 seconds. Multiply by four. That's your cadence, measured in RPM. It should be at least 70 rpm. You're not doing yourself a favor by pedaling harder in a higher gear.
Thanks noglider. I have done what you said, and found that I am most comfortable (riding leisurely) at around 80-85 rpm. Frequently I would hit 100, one time I topped out at 144.
I guess the reason why I am asking is more because the 1st gear seems to be for riding through rough terrain (wet grass or something) or up some hills, neither of which I do. So essentially I have 2 gears that I use, which is fine, but it would be nicer if I had three, even if I use the third only on those nice days when I have 35 mph rear wind.

OK, you have my approval. :thumb: ;)