Hi Robert,
Not many brown motorcycles in the 1920s - but it was the stock colour for New Hudson. Your grandfather's bike is probably a 1924 model, 350cc "Tourist". I've attached the only photo I could find of the left side of a similar model - from 1923 - which has a slightly different rear carrier. The 1924 is a better match. The distinguishing features are the gently sloping top frame rail, heel brake pedal, angled spark pug at the top rear of the cylinder, and foot boards swept up at the front. There was a similar 500cc model, but I don't think this is it.
In the period New Hudson offered a sidecar for their 350: not something we'd think of doing these days. But nice and flat in Holland!
Cheers
Leon