No one seems to know much about the Brooklands Ralf. There are lots of illustrations, sketches, photos and soon but near zero practical technical information.
Years ago I chased up everything I could about the Villiers engines used in the 1924-25 175cc Ultra Lightweight TT’s and found lots of drawings showing various internals but you never know how accurate they are and they don’t have dimensions anyway. Plus of course they used a hotted up Sport in 1924 and the prototype Super Sport in 1925. It earned its full name, the Super Sport TT the hard way.
The Brooklands appeared in 1925 and seemed intentionally designed for flat out track work without any need for going up and down the mountain as in the Isle of Man.
It’s all now rather a mystery no one seems to know anything.
Finally your piston is obviously an oversize 175 job. Standard bore was 57.15 mm so it would seem the engine has had a rebore at some stage. No surprise there at all. I think I’d be far more surprised if it was still on standard bore.
Sorry this isn’t very helpful.
