My '53 Plunger was an ex sidecar bike....found out the hard way trying to keep up with a mate on a Matchless G3 on the A38 between Lichfield and Burton in 1976. The whole thing was shaking its sox off, blurred vision, hands numb, Chronometric dancing at somewhere between 85-90MPH. As to the accuracy, we just seemed to be passing most things, so it was pretty quick. It's still a fast and dangerous road even today.
But it turned out what I thought was the standard solo rear sprocket was in fact the 49 tooth sidecar gearing dinner plate. An A10 solo bike runs at 42 teeth. Swapping that changed everything, and it became a reasonable smooth runner unless pushed hard. With more experience and thus closer attention to the dynamics of crank balancing it turns out the sweet spot for least vibration depends on the balance factor used when the engine was built and the rotational speed of the crank. So you'll be hard pressed to get a motor that is smooth all the time.
These days the gearbox sprocket can be changed for a 20 or even 21 teeth which gives less revs for a given road speed and for smooth cruising, worth thinking about next time a Plunger motor is on the bench. Rigid and plunger bikes have no choice changing primary drive gearing but S/A owners have it easy, with more choice of crank sprocket and easy access to the gearbox sprocket. Again the speedo accuracy is academic, flawed by being driven from the gearbox with no consideration of what comes before or after in the way of different ratios from standard.
For those folks with newly acquired plunger bikes, get counting those teeth. All may not be as it seemed.
Swarfy.