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I'm new to vegetable gardening and am just beginning to plant a few seeds into raised beds. On every seed packet, and in almost every other guide or reference I've found, on- and off-line, instructions are given on the correct spacing in two perpendicular dimensions, yet none offers any explanation whatsoever of the reasoning or implementation details of this mysterious practice.

So for example I'm told that for carrots I should aim for final spacing of 4 inches on the x-axis and 12 inches on the y-axis. In keeping with tradition I hope to produce a carrot which is approximately circular about the horizontal plane, so I'm at a loss to see why its space requirements should be any greater in one dimension than the other.

The larger given distance isn't typically wide enough to offer walk-in access, so what on earth could the reasoning be? And how am I supposed to be orienting these axes with respect to their natural environment anyway? Should one or other axis be aligned to the midday sun? The magnetic pole? Ley lines? I wouldn't want to think I'd planted my whole garden at right angles to its proper orientation...

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    The questions you're asking are similar to the questions that Mel Bartholomew asked before he invented Square Foot Gardening. It's a method that uses square foot grids and the smaller spacing. So if your packet says plant 4" apart in 12" rows ignore the rows and just put 3 rows of 3 (9 total) in one square foot. Very popular method. See squarefootgardening.org for more info. Check it out, it might be appealing to you. – OrganicLawnDIY Apr 23 '14 at 2:55
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The planting instructions on seed packets are just a rough guideline to help people plan for the amount of room a mature plant will take up. (Many gardeners, especially new ones, tend to plant their seeds far too closely in the garden and the resulting plants generally don't live up to their potential as a result.) The packet instructions are also generally intended for those who like to plant their vegetables in rows - hence, the 4" apart in the row, with 12" between rows. The 4" measurements gives the carrot's top enough room to spread to a mature width, which is necessary if the carrot root is to receive the nutrients it needs to grow properly. The 12" is the closest that the seed company recommends you place your rows, to allow for hoeing weeds from between the rows without too much chance of damaging the roots of your crop. Other plants will have different suggested spacings.

However - if you want to plant your carrots 4" apart each way in solid blocks, that will work also. This is called "block planting," and is a way to grow more food in less space. You will still need to have spacing between your blocks to allow you to care for the carrot bed, but the amount of cultivation space required is much less than if you were to plant the same number of carrots all in multiple straight file rows.

Here is an article on block planting - and they even are using carrots as their example!

Garden beds or rows are generally oriented perpendicular to the sun's path in the sky so that the full solar arc passes over the planting area during the day. In other words, this would require a north-south orientation, although this is not a hard and fast rule. If you have more than one crop in the bed and your crops have different heights or light requirements, you may choose to orient your beds differently.

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The spacing given on packets is for a traditional row garden, where the 12" space would indeed be the space you would walk in. Generally, the orientation does not matter too terribly much, except when it comes to tall plants which might shade the others as the sun moves through the sky. I am in the Northern Hemisphere and when I still planted in rows, I liked my rows to run east/west, and I planted my tallest plants on the north end of the garden.

If you want to plant your garden in beds rather than rows, you can do a quick internet search on "square foot garden spacing" or "intensive bed spacing" and you will get spacing advice that is more regular on each side.

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