I recently noticed an issue with my Carbon Drive bike where pedaling was difficult at a certain point of rotation for the crank. Within about 30 degrees of movement of the crank, the tension on the belt becomes much higher, almost doubling. For the rest of the rotation of the crank, the tension is normal. This happens regularly with each rotation, which implies to me that (1) there is some defect or irregularity with the front sprocket, or (2) the crank is rotating irregularly. I suspect it is more likely (1), since the tension only changes for a very small range of motion of the crank, but I have no idea how to tell for sure. My question now is, is there a good way to diagnose problems with a front sprocket on a belt drive bike? More generally, are there good troubleshooting steps for dealing with tension inconsistencies like this?
As previously mentioned, this is a common problem on both chain and belt single speed systems. Gates, in their troubleshooting guide, mention "centring the pulley on the spider" which is somewhat difficult as the chainring bolts generally fit into the holes in the crank spider quite snugly. You could set the position of the cranks to the point at which the belt is tightest, loosen the chainring bolts and retighten them and check to see if the small amount of movement in the chainring has improved the situation. When I encountered this problem myself with my Gates belt, I moved from a square taper bottom bracket (Shimano 600 cranks) to a Shimano hollowtech-type (in my case Miche) external bearing (with Shimano Ultegra cranks) and this improved the consistency of the tension enormously. I was fortunate enough to have the parts to hand to try this.
To my awareness, the Gates-ness won't introduce any factors here not present in other single ring, single cog bikes without chain tensioners, other than making it way more expensive to do any replacing of drivetrain parts that may wind up being needed.
One of the questions in this scenario is whether you have reason to suspect the increased tension spot was acquired in use, over time, or by violence, versus occurring immediately after wheel re-installation. Concentricity is never perfect; if the tight spot started after the belt tension was re-established either from the wheel being off or sliders being adjusted if applicable or anything else, it's likely that donking the wheel forward a bit will make things how they were, i.e. there will be a tightest spot that you just don't notice, which is how all bikes without sprung tensioners are.
If the "front pulley" (Gates speak for chainring) was damaged from impact, something like this can result. You'd likely be able to see it by backpedaling the bike while carefully observing it turn against a fixed reference point. They're stiff and need their dimensional precision, so you should probably replace it if you find significant problems. If the tight spot is always in the same spot in the crank rotation, it's not the rear cog unless the quotient of the front and back teeth count is a whole number. It can be then.
The last avenue is messing around with improving front concentricity by trying different spindle positions, especially if the cranks were removed and re-installed recently, or squirming the "front pulley" on the spider tabs, which is kind of the most likely cause and fix of the whole problem if other mechanical changes or a traumatic event didn't precede the issue. Barnett's is a good reference to read about procedure for the former and Sheldon the latter.