How can I create an efficient tree farm?

I've created a wooden tower with wood platform bridges to find floating islands. As a result, I need a lot of wood and my supply is running low.

I had actually planned for this and created a tree farm, but it isn't very productive. I set it up as follows, which repeats across a leveled "field" wide enough for forty saplings total. I know the torches aren't necessary — I used them as a ruler when laying everything out and left some in for looks.

Unfortunately, this seems to produce about one tree per game week or less, which is painfully slow compared to my needs. My suspicion is that the tall grass which grows constantly is blocking the growth of trees, which I know need some room around them. I try to "weed" the farm pretty regularly, but grass starts regrowing by the time I get from one end to the other.

What can I do differently to make my tree farm more efficient?

From the Terraria wiki page on Trees:

Growing conditions

Planting an acorn in grass will create a Sapling that will eventually grow into a tree of a random size and shape. Saplings can only grow under the following conditions:

1. A planted acorn can only be planted on a dirt block covered with grass, corrupt grass, crimson grass, hallow grass, a mud block covered with jungle grass, or on snow.
2. The acorn requires one space of open ground to either side.
3. There must be at least two open tiles between saplings or only one will grow into a tree. This matches the previous rule, i.e. each acorn needs both adjacent tiles free, which means the closest two trees can be is with two tiles between them.
4. The acorn requires at least 32 feet (i.e. 16 tiles) of vertical clearance to grow into a tree.
5. An acorn will not grow indoors - all background walls or overhanging ledges must be removed, and if you have a ceiling it must be at least 32 feet above the block where the acorn was planted as measured by a Depth Meter (e.g, if you are planting an acorn at 300 feet above, there may only be blocks at 332 feet or higher directly above it in order for it to grow into a tree).
6. Acorns will not grow in the presence of torches, wood platforms or sunflowers within its 2-block radius.
7. Saplings must be off-screen in order to become trees. They will not grow when currently in view, unlike most other plants which can spawn while you watch.

Saplings can be destroyed with a Pickaxe.

So, you can't grow a tree at the edge of a step or cliff, or next to a step or cliff, or at the edge of a patch of grass, even though you can plant acorns there. While trees can, very rarely, grow a distance of three tiles apart (two empty columns between them), they grow much faster at a distance of four tiles apart (with three empty spaces between them). For these reasons, it is recommended to plant acorns every four tiles on a long flat row of surface grass. Tiles more than 14 units above the planted grass do not have any effect on tree growth, so an optimal tree farm can have multiple 15-tile high levels."

You seem to have your acorns spaced correctly, there are no walls, and I assume you have enough head room. Although it's not explicitly mentioned in the wiki, your torches may be keeping the trees from growing. Try removing them. At least some of the acorns should grow to full trees in a matter of minutes.

Terraria wiki guide on Gardening

By placing a dirt wall inside the layer of grass blocks (not behind the tree, the block below the tree), one can prevent tall grass from spawning, maximizing efficiency. The dirt wall should peek out from behind the grass blocks and be visible behind the tree, but not actually being in the block behind the tree. The dirt wall should be behind every block of grass, not just the one under the tree.

So place one dirt wall behind the grass that the trees are on, so it just barely sticks out, and there will be no tall grass and you'll never have to weed again.

Most answers are literally missing the forest through the trees (by focusing on one and only one solution), and ignoring the original problem.

The OP asked two questions:

As a result, I need a lot of wood and my supply is running low.

and steered people towards one solution:

What can I do differently to make my tree farm more efficient?

Since no one has answered the original question -- I'll present the two solutions to get a lot of wood:

The fast way

Ironically, I found the fastest way to get a lot of wood was not to have a tree farm at all! I found it far more efficient (time wise) to just create a new world, pick a direction say East, and just chop every tree until you hit the ocean. Use the mirror (or Save & Exit then reload the world) and travel the opposite direction as a lumberjack. YMMV but on a small world travelling in just one direction netted:

• 1015 Wood
• 627 Rich Mahogany
• 158 Palm wood
• 102 acorns

Travelling in both directions netted a grand total of:

• 1459 wood
• 748 Boreal Wood
• 627 Rich Mahogany
• 255 Palm wood
• 26 Ebonwood
• 223 Acorns

And the stats:

• Total wood: 3115 / Total time: 19 mins = ~ 163 wood/min
• Total platforms: 6230 platforms = ~ 327 platforms/min

Rinse and Repeat. This should be enough wood to make those extra long sky bridges arenas. The bonus is that you can save all those acorns to (cough) seed your tree farm. :-)

The slow way

Traditionally, the tree farm is most popular -- partially due to aesthetics -- but it is dog slow.

1. First, you have to prepare a flat surface.

   I recommend 1,000 tiles of dirt (optionally also sand if you want/need Palm wood. If you want jungle trees your tree farm needs mud deep Underground)

   • Plant trees with 4 spaces between saplings. This gives 2 block radius on either side of each tree.
   • Use a hammer so you don't have dirt wallpaper behind as this will block the trees from growing.
   • Place torches below ground so as not to impede the growth of the trees

2. Hurry-up-and-wait.

   Maintenance of the tree farm will require you to continually clear all the grass. If you use a hammer and aim in the sky you can clear all the grass and leave the trees & dirt safely alone.

   To speed up growing the tree farm, hole up like a hobbit near the surface, preferably with a lava trap above, and leave the world running over night. In the morning you should have most of the trees growing and you'll have also made a few extra coins.

Once you have a large enough tree farm setup it will produce more wood quantity-wise in the long run but setup & maintenance time is just a huge PITA compared to just clear cutting on a brand new temporary world.