Sombrero for sun - and for wind

I did the Trailtrekker recently and part of the essential kit was a wide brimmed sun hat. So i went browsing on t'interweb. Most of these are called sombreros - similar to those decorative monstrosities that the Mexicans wear. The idea obviously is to keep the sun off your face and off your neck, perfect.

I bought one without a rope or string or whatever it's called that goes under your chin to keep it on your head. S the slightest breeze and it was attempting to head off my head and into oblivion. Now this may be ok if you're heading to the park or somewhere with no wind but I don't recall going anywhere in the hills and there be no wind so in hindsight it was a rubbish purchase, never again always buy a sombrero with a chin rope or similar.