Gates belt drive: installing larger front sprocket I ordered a Cube Hyde Race bike with Gates belt drive. I live in an area where it rains a lot, and I use my bike year round, so I was sold on the promise of virtually maintenance-free drivetrain.

The bike has a 46 teeth front sprocket (Gates S150 CDN 46T), 22 teeth rear (Gates CDN 22T) and Shimano Alfine 8 hub. If I understand correctly, the maximum gear ratio is 46 / 22 * 1.61 ≈ 3.37, compared to 48 / 11 ≈ 4.36 on my current bike. Probably enough for daily commute, but not for faster rides (I ride with my friends outside of town every now and then).

I tried to find belt drive bikes with higher maximum ratio, but 46/22 (or similar ratio) seems to be the most common. However, it is possible to order front sprockets with higher teeth count: 50, 55, ..., 70, which I will probably end up doing.

Will I need to order a longer belt as well in this case? If so, how do I calculate the correct belt length? 
There also seem to be 3 different types of belts/sprockets: CDX, CDN and CDC. CDC is obviously different mechanically (does not have the center track), but are CDX and CDN compatible? Can I use CDX front sprocket instead of CDN?
Any other things to consider?
On Gates' site there's a free spreadsheet called Gates Drive Calculator  that you can use to determine your belt length needed. It's  a weird tool in that instead of plugging in your desired gears and chainstay length, and minimum/maximum adjustment range and outputting what belt length you need, which would have been the smart or at least more intuitive way to do it, it makes you plug in your gears, then plug in a given belt length, and it outputs the resultant center-to-center dimension, minimum installation center-to-center, and minimum center-to-center for tensioning, which you then check whether it's in your adjustment range, and you have to repeat until you find a belt that fits.

Gates lists the pitch for their belts as 11mm and wants you to have an adjustment range of X-10 on the slack end and X+2 on the tight end, where X is the calculated center-to-center. So you could alter a magic gear calculator spreadsheet by replacing the 12.7s with 11s and that would be another way of figuring it out barring the Gates tool.

CDN and CDX belts have the same form factor and only differ in construction and materials. According to Gates they're cross-compatible.