That muffler looks very like the Trojan one, and the cooling fins are somewhat similar too. Does this mean the Trojan had a 50 cc predecessor?
My bicycle Trojan fitment was completely home-brew, Jack. The engine was far too powerful for the job, and wore out both the wooden roller and the front tyre in short order. The decreasing size of the roller, though, had advantages: the machine became capable of lower road-speeds, which was both more comfortable and safer. It started off at about 2.5" or so (it's a long time since 1961, so I don't remember exactly) and the little engine liked to run at about 6,000 rpm. If roller slip were zero (obviously it wasn't, or the roller wouldn't have worn away) that should have given it a road speed of about 42 mph. It went fast enough to cause considerable eye-watering from the wind of passage, anyway.
