One of the characteristics of this type of engine "The Vertical Twin" is that there is a sweet spot in the rev range where initial vibes smooth out, before entering another more vicious phase. This smoother speed depends on the difference in mass of the moving parts.
BSA employed a balance factor, expressed as a % of the reciprocating mass, that is pistons, rings, rods etc. This was then converted into an actual chunk of metal (a service tool to clamp on the crank) to mimic this weight and placed on the big end journals of the crankshaft and the whole ensemble placed on knife edge rollers and allowed to come to rest. Material was then remove from the flywheel so that there was no heavy spot, often seen as drillings in the flywheel. There is a BSA Service Sheet detailing the procedure.
Any change in the weight of these reciprocating components over time will affect the balance factor and hence the engine speed at which the motor is smoothest. Back in the day 50-60 MPH was where you wanted the smoothest ride, and that's what an engine in good order will give with the standard balance factor. Alternative published figures are available for different purposes, particularly racing. Pretty crude, these days dynamic balancing is the way it is done. Even back in the day it was far from perfect, identical machines differing in perceived smoothness. Then add general wear, piston rattle etc and there is your rough ride.
My Plunger bike was a real shaker at normal road speeds, 'til I discovered it was a low geared sidecar bike in an earlier life. Standard gearing for a solo machine is 42 teeth on the rear sprocket, 19 teeth on the gearbox. Worth a look, revving its socks off at normal road speeds is not what you want!
To state the obvious, frame to engine mountings and engine steady links need to be good and tight, the steadies running forwards from the rockerbox/cylinder head to a lug between the frame down tubes are often absent, as is a bracing bar across the underside of the fuel tank. Don't expect a smoothness found on modern machines, oldies just can't do that.
Swarfy