Wooden side rabbet plane

Hi all,

Hope you’re all doing well. I bought a old wooden side rabbet plane (not because I widen grooves very often, but I was seduced by youtube videos that said it is a great thing to have in a pinch; and being a bit of a cheapskate I wondered if this 5 euro wooden plane would work well when the metal ones I see on ebay are a multiple of that). Unfortunately, it’s just the one of the pair (so if I get in that pinch, I hope the grain will be with me).

I noticed though that the side before and after the iron isn’t in the same plane (isn’t flat/level). It’s the side that touches the wood and from which the iron protrudes to cut to side of the groove. Actually, the sole seems to have a slight curve along its length too. See last photos. For reference, the sole is about 5 mm wide and it seems about 1 mm out (on one side – the other side is out too, but guess that doesn’t matter)

Does anyone know if the plane warped (which I assumed) or that this is supposed to be this way? If it warped, would you recommend fixing it by planing/sanding it flat (not sure if I would be left with much of sole – widthwise- if I take the whole curve out)? Any other tips on using/setting up such a plane?

I test ran the plane and didn’t really manage a nice cut all the way along the groove. It seemed to cut thicker in the middle of the groove, although very likely that’s inexperience as well and I have to play with it a little more.

Many thanks!

Sebastiaan

PS, sorry photos are a bit dark