Looking for a German black powder sporting cartridge

I recently picked up a single shot bolt action Dreyse sporting rifle (octagon barrel, double set triggers, light engraving) and I’m trying to determine what cartridge it is chambered for. The bore is .44, and I made a chamber casting. It’s a slightly bottlenecked case, with a second step at the mouth which I assume is for a paper patch. The gun is not proofed, which dates it to pre-1890, but it has no other useful markings.

These dimensions are all approximate; it was hard to judge when I was starting to squeeze the chamber cast with the calipers.

Any help identifying this cartridge would be much appreciated - thanks!

The measurements you give are very close to the 10.85x47R Martini cartridge,but I could be wrong…Pete.

The dimensional data match quite well those of the 11.2 x 44 R Target cartridge.

This was developed by Lorenz and cartridges in this caliber were made by DWM, oth and Dreyse.

Thanks Pivi!