How long would that ruler have to be to measure the curvature of an ocean?

Most of the oceans don't freeze over, but the ones which do freeze (a few miles or so of them anyway - enough to measure such curvature) you could do with the same standard ruler the crazy (and obsessively committed, no doubt) person in my first hypothetical used.

Are you implying that it's impossible to measure the curvature of the Earth unless the surface is perfectly smooth?

Again, i am confused by your interpretation of the things i've said. What specifically did i say to make you think i implied that? Please provide specific quotes, as it will help me to understand the disconnect and possibly communicate with you more effectively in the future!

I was saying that measuring the surface of water to determine its curvature (or distinct lack thereof as the case may be) is much easier when the water is frozen solid - and mostly smooth. Accounting for and navigating topology is obviously not impossible - but it is much more difficult.

Such as?

A surveyor's/trundle wheel for one! Lol.