Archives for posts with tag: geometry

Both the east and west planters are now completely occupied but we’re not done for the day.  This year we are thinking (and moving) outside the boxes and planting vegetables directly in the ground.

Yesterday, we removed the sod (see May 26, 2013) from the now-sunny area west of the west planter and covered it with mulch.  Today, we laid out the locations for the six mounds on which the squashes will grow.  A week ago, we had figured three-foot-diameter mounds spaced at three feet on center (see May 19, 2013) but looking at my sketch today, I noticed that I didn’t leave any walking space at the far end.

As I reconsidered the layout, I realized that because we are staggering the mounds, they can be spaced closer together.  We adjusted the west walkway from 2’-0” to 1’-9” and the spacing from 3’-0” to 2’-9” and were able to gain 1’-9” at the west end (I find the symmetry to be pleasantly reassuring).  This will be very helpful because the grade drops off steeply just beyond the garden area.

We extended a measuring tape along the ground longitudinally to form a baseline and then used a carpenter’s rule to measure the offsets in the short direction.  At the center of each mound, we pounded in a wooden stake.  After setting each stake, we checked our spacing both longitudinally and diagonally (we calculated that each mound should be about 3’-10 1/2” from its kitty-corner neighbor) and everything checked out.

When we got to the end, however, the final dimension looked a little short.  In fact, after measuring it I found that it was off by 3 inches.  In setting out the stakes, I had forgotten to reduce the first dimension (measuring twice doesn’t help if you are using the wrong number!).  We could have moved all of the stakes but decided that what we had was good enough.  Plus, having more clearance next to the planter is probably better than having symmetrical edges.

Next, we set our tape measure and rule to 18” and, placing one end against each stake, slowly rotated around it, removing the mulch to create a three-foot-diameter clearing.  We redistributed the mulch to the surrounding areas and were left with what looked like a small set of crop circles (we’ll keep an eye out for alien invaders).

Then, we dug.  Or, more accurately, we picked at the soil with shovels.  As I have noted many times before, the soil in this part of the yard is fill brought in during the pool renovation many years ago.  It is not of very high quality (from a gardening point of view) and is composed primarily of clay and rock.  Digging it is a slow, tedious project (the kind of task usually given to prison inmates).

After an hour of hacking away, each of us had dug one hole about 16 inches in diameter and six inches deep.  A large rock protruded into the hole I was digging and even with both of us working on it, we could not get it to budge; the squash plant who will live here will just have to work its roots around it.  Because it was getting late in the afternoon, we opted to plant these two locations and come back to the others later.

To fill the hole and create mounds (to elevate the plants above grade), we combined equal parts (roughly) of compost and peat moss, using the wheelbarrow as a mixing bowl.  I dumped the soil into the holes and Rachel formed it into mounds.  At the top of each mound, we dug a small hole into which we placed a summer squash seedling.

Finally, we covered the mounds with straw mulch.  In addition to helping the soil to retain moisture and discouraging the growth of weeds, the mulch should prevent the soil from washing away in a heavy rainfall (of which we can expect many over the course of the summer).

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We finally arranged for our tree guy, Jerry, to come by with one of his helpers to remove the two maples that shade our garden in the late afternoon (see February 6, 2013).  We had meant to get this done before the trees sprouted their leaves (it would have made less of a mess) but didn’t get around to it.  Now that the garden is in full swing, though, we need the extra solar exposure.

When Jerry removes a tree near the house, he follows a very careful and elaborate procedure.  First, he cuts off the outer branches, then he tops the tree, and brings the trunk down section by section.  Sometimes, as a final step, he removes the stump by grinding.  The stump-grinding equipment is truck-mounted so accessibility is an issue; consequently, we have several stumps on our property.

Jerry chips all but the largest branches and takes the rest away.  When we have needed firewood, he has cut the trunk into appropriate lengths and left it for me to split and stack (see, for example, February 5, 2012).  Tree removal is a very labor-intensive activity but when Jerry and his crew are done, the only signs of their having been there are tire tracks and a scattering of sawdust.

The same approach would not be practical for today’s project.  The trees in question are just outside the border between our pool area and the surrounding woods, a transitional zone between order and chaos.  They are over 100 feet from the road and their bases are on a steep slope.  The trees could be cut down in the same way but removing the branches and wood would require an unjustifiable amount of effort.

So instead, we will leave the downed trees in place.  And if we are going to do that, there is no reason to cut them into pieces.  Bringing them down in one fell swoop (each, for a total of two fell swoops) is more appropriate.  (I had hypothesized that felling trees was the literal origin of the saying, “one fell swoop,” but my research revealed otherwise.  Fell can mean cruel or fierce while swoop in this context refers to the sudden dive of a bird of prey.  Given the sound a tree makes when it is felled, I like my story better.)

Felling a tree with a single cut at the base is much more difficult than it might at first seem, especially if the direction in which the tree will fall is of concern.  In fact, it can’t be done reliably with only one cut.  If the saw is not properly aligned with the direction the tree wants to fall (due to the location of its center of gravity), the weight of the tree will close the kerf as the tree starts to lean and that will bind the blade.  Unfortunately, I have to admit that I know this from firsthand experience.

Most often, three cuts are needed.  The first two cuts are made on the fall side of the tree to remove a wedge of the trunk.  This forms a hinge about which the falling tree will rotate.  The third cut is made on the side opposite the wedge and if all of the cuts have been done properly, the tree will start to fall due to gravity before the final cut makes it all the way through the trunk.

Geometry cannot be ignored, however, and even if the cuts are made correctly, the tree still might want to fall in another direction.  Based on Jerry’s assessment, this is the case with our trees, both of which are leaning slightly uphill, towards the pool.  Obviously, this is not the direction we want the trees to fall.  To counteract the trees’ gravitational tendencies, Jerry attached a rope near the top of each one to pull them in the direction he wanted them to fall.

Getting the ropes into the trees took a certain amount of finesse.  For the first tree, Jerry knotted the rope to a length of lightweight line—string, almost—at the end of which was a small beanbag slightly bigger than a Hacky Sack.  He carefully launched the beanbag up and into the tree with an underhand motion, aiming for a branch high on the trunk.  It took two tries but the second toss sailed through the crotch and dropped back to the ground.

Using the lightweight line, Jerry hoisted the main rope up to the top of the tree and back down.  Then, he formed a loop (tree work requires as much knotting skill as sailing, it appears) and cinched the rope around the tree trunk.  His helper took the free end downhill (the direction we want the tree to fall) until the rope formed about a 45-degree angle with the horizontal.  There, he anchored the rope to another tree trunk.

Using an in-line winch called a come-along, the helper took out the slack in the rope and then applied some tension.  At this point, Jerry starting cutting the notch on the fall side of the tree.  After confirming that the rope was taut enough to prevent the tree from shifting in the uphill direction, he completed the notch.

Then, the dramatic part began.  The helper continued to winch up the rope while Jerry commenced the final cut.  As the helper cranked up the tension, we could hear the tree trunk creaking and see it starting to list downhill.  When the tree was leaning by about 15 degrees from the vertical, there was a loud crack as the trunk gave way.  Both Jerry and his helper moved back and with a loud thwump, the tree fell to the ground, precisely where Jerry had intended it.  Quite a spectacle!

The second tree had several branches extending almost horizontally from the trunk.  Jerry judged that these outriggers would interfere with a clean fall so he decided to cut them off.  He strapped on a lineman’s belt and climbing spikes and scrambled nimbly up the tree, pulling two ropes with him.

When he got near the top of the tree, he tied himself off with one—his safety line—and looped the other over a branch to use a belay line for the cut branches.  I have described this process before (see October 31, 2011) and it is particularly elegant when Jerry rappels between locations, his chainsaw and pruning blade dangling from his belt.

After trimming and dropping the protruding branches, Jerry returned to earth.  He freed himself from his safety line, knotted a loop in it and cinched it up to use as the tension rope.  His helper again marched the end of the rope downhill and, following the same procedure as before, he and Jerry brought down the second tree, felling it almost exactly parallel to and on top of the first tree.

Described this way, it seems like it would take a long time to perform all of these steps.  But after only an hour and a half, Jerry and his helper were packing their gear up and heading to their next project.