It sounds like you have a perfect opportunity for a raised bed. If you put in a raised bed with compost/manure/good soil and plant Danvers Half-long or Chantenay, you should have some great carrots! I am sure there are other varieties of carrots that would do well also, but these are the two that do best for us.

I use compost and green sand.
An excellent variety that matures early with a good flavor is 'Mokum'. I do two plantings, May 1 and June 1
I plant 'Bolero'for late season; takes long to size up but is always good.
'White Satin' can get large and is fun to cook with.
I also enjoy 'Yellowstone'.

I use raised beds without soil. 12" deep for carrots. 12" is overkill for most plants, but not carrots.

I had heavy clay in one bed and found out from the folks on
the Soil, Compost & Mulch forum to never use sand to loosen clay soil. Even though it seems logical to add sand, it actually will turn your soil to something like cement. Add some nice loose compost and keep working on it. Last year that bed had such heavy clay that I turned it into a lasagna bed and got a HUGE yeild of squashes.

We had great luck with doing what marlingardener suggested. My carrot bed was poor rocky soil so I sifted it and made a raised bed with lots of compost. We planted the carrots using Dick Raymonds wide rows method of planting and got a really good yield of Danvers half long.

Check out the other forum for great tips on improving your soil. Good Luck.

I use peat moss ,till it into your soil.I also use it as a mulch.

You can always grow your carrots in raised mounds if raised beds aren't your thing. Simply mound up the soil in the carrot row, add some peat to loosen it up a bit or use vermiculite, and plant.

Raised row gardening is beneficial for many different crops when soil tilth is a problem. It also has the side benefits of warming the soil faster and improving the soil drainage.

Dave

Thanks everyone! One question, how is green sand different from regular sand in the weight/composition? I have seen it at the garden shop, but don't know if one type is better than the other. . .

Greensand is quite fine, not powdery, but like 'hourglass' sized grains. I have used Greensand for years and am very
pleased with the results, if you are patient. It takes a year or 2 to really notice a big difference but it did a
great job of loosening-up my ( formerly ) clay soil.

One thing to keep in mind about GS is that it has some Potash ( potassium )content to it, so you may want a soil test to see if you are lacking that nutrient.

I agree with ( never-give-up ) about regular brown (builders ) sand. They used to recommend adding it to clay soil but then they discovered it binds with clay over time, again,
in my experience of using Greensand in my current location for almost 15 years it does a great job.

GL hth