From growing carrots to sorting out the lawn...
Many thanks for your recent message regarding the possibility of producing some Christmas carrots and the problems associated with hand scarifying a large area of grass. It’s getting very late to sow carrots for a winter crop, and I’m not sure of where you live, but there’s still just about time (especially in the South) to squeeze in some seeds which should give you some baby carrots during December. Choose from any of the early varieties (including Amsterdam and Nantes) for this planting and cover the seedlings with a cloche once the Autumn proper takes hold.
As far as for trying to scarify a half acre plot by hand – I’d shy at that task and I don’t have weak wrists! It looks like you need mechanical help with this task and I’d be on the phone to a local plant hire centre to see if they have a petrol-driven scarifier you can borrow. I’m aware of garden tractors which have scarifying and sweeping attachments as well, which I would imagine could also be hired – or you could look at employing a local landscape contractor or gardening company to do the job for you.
Hopefully this information is of help and the best of luck with your carrots, should you choose to grow them!