I make my own seed tapes for beets. I use some leftover drywall mudding tape, or strips of paper towels (my hubby cuts the whole role for me). I make them about 5 feet long.
To make them I lay out the strips on the kitchen table or counter top. Then dab a spot of elmer's school glue every 3 inches, then drop a seed on each glue dot.
When it's time to plant I roll it out in the garden and cover slightly with soil.
Even spacing every time :)

If your soil is rocky or very heavy, the beets may have a hard time growing in it (as would carrots). You could amend the soil with grass clippings or shredded leaves to help lighten it.

Interesting, so no wasted seeds and no hunching over to thin out the seedlings and sow the seeds.

Any issues with the glueing of the seeds on germination?

I like the idea of something besides sand to lightnen up the soil like grass/leaves, that was you can just till it all together the following year.

The glue is water soluable, so no impact to germination that I have noticed.
Another alternative for school glue is to mix flour and water. That gets a little messy (in my opinion) and I have the little bottle of school glue handy.

The paper also degrades rather quickly once in the garden. By the time I am harvesting the beets, there is nothing left of it.

Root vegetables grow better in "lighter" soil. For more useful info, see link below.

Here is a link that might be useful: Growing Carrots and Other Root Vegetables in the Garden

I've always started mine in small clay pots early in like Feb/March and then transfer them to my growboxes once they sprout. I used just plain potting soil. There's nothing like homegrown produce! The taste is just AMAZING!

Jessica
http://www.agardenpatch.com

Here is a link that might be useful: Garden Patch

dirtbert: Do you rhink this tape idea might work with parsnips???

For straight rows in my garden, which is 21 x 35, i use a yardstick in my beds. A long board like a 1 x 4 which is easier to handle than larger, thicker pieces of wood will allow for a perfect long row. Simply make a depression on the soft soil and then push your finger to make a hole the desired depth. you can do this on top of a flattened row or on flat level ground.

I have sandy soil here in South Minneapolis. The better I amend it the better everything produces. I also mulch where possible and pay attention to regular watering. Spring planting is generally in wide, well fertilized trenches that I can flood as needed when dry later on in the summer. For many things that also helps with the mulching and you know that water is going to where it is needed. It also helps to side dress with fertilizer a time or three during the growing season, especially when one needs strong tops as with carrots and alliums. I can't say enough good about Milorganite.

BTW I grew up on Iowa Black Dirt (zone 4) which is very clay based. We had no problems growing beets, carrots, potatoes, tomatoes, coles or melons on that in zone 4. You don't necessary need sand for root crops, but you gotta handle your soil, whatever it is, properly and amend its fertility or none of them will produce much.

Beets, I've read, can be seeded 6 weeks before frost, so I've put them in a lot earlier (April 1) this year, finding that they seemed slow last year. They can handle cool weather and you can reseed for a second crop if you harvest in early July.