Appendix A

1. Site Capacity and Buffer Zone Requirement Calculations

Assumptions:
1). windrow cross section is approximately a semi-circle
2). site is rectangular
3). all windrows are the same size

For individual windrow, let:
w = width
h = height
l = length
Ac = cross-sectional area
Ab = area of base
V = volume

Then for an individual windrow:
w = 2h
Ac = 1 / 2 p h2
Ab = w1=2h l
V = Acl=ph2 1
2

For the site, let:
ws = width
ls = length
As = ws ls
VT = total volume of windrows
Va = volume of windrows per acre, for portion of site used for windrows (including aisles but not buffers,      staging, etc.)
a = aisle width (average if variable)
N = number of windrows

For a large site, assuming that windrow runs entire length of site, with an aisle on each side (one aisle per windrow, although aisle width may vary):

l = ls

N = Ws
-----
2h+a

Notes:

Assumption 1). Assuming a triangular shape will underestimate windrow volume, while a rectangular shape will overestimate. For some turning machines, using a trapezoidal shape may give a slightly better estimate. However, the value calculated will be nearly the same, and probably not worth the extra effort.

Assumptions 2) and 3). These assumptions are made for ease of calculation, and do not directly affect the result.

Table A1 shows the resulting site capacities, in cubic yards, for various windrow and aisle sizes, considering the area used for windrowing only (including aisles between windrows, but not buffer zones, staging areas, roads, etc.). For example, for 6 foot high windrows with average 14 foot wide aisles, 3509 cubic yards per acre can be composted.

Table A2 can be used to determine the acres of site capacity (for windrowing only) required for a given leaf collection (in cubic yards). For a given windrow size and aisle width, find the acres needed per thousand cubic yards of leaves collected. Then multiply by the thousands of cubic yards collected. For the example above (6 foot high windrows, 14 foot aisles), 0.285 acres is required per 1000 cubic yards of leaves. For a leaf collection of 18,000 cubic yards, therefore, 18 x 0.285 = 5.13 acres is needed.

Table A3 can be used to determine the approximate additional acreage required to provide a buffer zone of a specified width on all sides of a site. For a given buffer size and windrowing area find the additional acres needed from the table. For the example above, if a 150 foot buffer zone is needed in addition to the approximately 5 acres used for windrowing, this would require an additional 8.5 acres. The total acreage required would then be 5.13 + 8.5 , as well as 1 or 2 acres for staging, roads, etc., or about 15 acres.

Table A4 shows the dramatic effect of increasing buffer zone requirements on site capacity. For a given size site, with a specified buffer zone on all sides, the table gives the percentage of the total acreage that is available for composting. For example, for a 5 acre square site, a requirement for a 150 foot buffer on all sides would limit the available composting area to only 13% of the total site (Table A4a), or about 0.65 acres - enough space to compost only about 2000 cubic yards of leaves. A 50 foot buffer would make 62% of the site available, or 3.1 acres, giving a capacity of over 10,000 cubic yards. Sites which have a long rectangular (rather than square) shape have less available windrowing area.

Table A1. Maximum Initial Site Capacity
(cubic yards per acre of windrowing area)
 windrow height average aisle width (feet) (feet) 2 4 6 8 10 12 14 16 4 4055 3379 2896 2534 2253 2027 1843 1689 4.5 4665 3948 3421 3019 2701 2444 2231 2053 5 5280 4525 3960 3520 3168 2880 2640 2437 5.5 5897 5111 4509 4035 3650 3333 3066 2839 6 6517 5702 5068 4562 4147 3801 3509 3258 6.5 7138 6298 5635 5099 4655 4283 3966 3692 7 7761 6899 6209 5644 5174 4776 4435 4139 7.5 8385 7503 6788 6198 5702 5280 4916 4598 8 9011 8109 7372 6758 6238 5792 5406 5068

Table A2. Minimum Required Site Size
(acres of windrowing area needed per 1000 cubic yards)

 windrow height (feet) average aisle width (feet) 2 4 6 8 10 12 14 16 4 0.247 0.296 0.345 0.395 0.444 0.493 0.543 0.592 4.5 0.214 0.253 0.292 0.331 0.370 0.409 0.448 0.487 5 0.189 0.221 0.253 0.284 0.316 0.347 0.379 0.410 5.5 0.170 0.196 0.222 0.248 0.274 0.300 0.326 0.352 6 0.153 0.175 0.197 0.219 0.241 0.263 0.285 0.307 6.5 0.140 0.159 0.177 0.196 0.215 0.233 0.252 0.271 7 0.129 0.145 0.161 0.177 0.193 0.209 0.225 0.242 7.5 0.119 0.133 0.147 0.161 0.175 0.189 0.203 0.217 8 0.111 0.123 0.136 0.148 0.160 0.173 0.185 0.197

Table A3. Buffer Zone Area Requirements
(additional acres needed for specified buffer size)
 buffer zone (feet) Windrowing Area Required (acres) 1 2 3 5 10 20 30 50 50 1.2 1.6 1.9 2.4 3.3 4.5 5.5 7.0 100 2.8 3.6 4.2 5.2 7.0 9.5 11.4 14.5 150 4.9 6.1 7.0 8.5 11.2 14.9 17.8 22.4 200 7.5 9.1 10.3 12.2 15.8 20.8 24.7 30.8 250 10.5 12.5 14.0 16.5 20.9 27.2 32.0 39.6 500 32.5 36.5 39.6 44.4 53.3 65.8 75.4 90.7 1000 111.0 118.9 125.0 134.7 152.4 177.5 196.8 227.3

Assumes site is square; if length = 2 x width, add 5%; if 3 x, add 10%.

Table A4. Buffer Zone Area Requirements
(percent of site available for composting depending on buffer size)

a. Site Shape = Square (length = width)
 buffer zone(feet) Site Size (acres) 1 2 3 5 10 20 30 50 50 27 44 52 62 72 80 83 87 100 0 10 20 33 49 62 68 75 150 0 0 3 13 30 46 54 63 200 0 0 0 2 16 33 42 53 250 0 0 0 0 6 22 32 44 500 0 0 0 0 0 0 2 10 1000 0 0 0 0 0 0 0 0

b. Site Shape = Rectangular (length = 2 x width)
 buffer zone (feet) Site Size (acres) 1 2 3 5 10 20 30 50 50 21 40 49 59 70 78 82 86 100 0 2 13 27 45 59 66 73 150 0 0 0 5 24 42 51 61 200 0 0 0 0 8 27 38 50 250 0 0 0 0 0 15 26 40 500 0 0 0 0 0 0 0 2 1000 0 0 0 0 0 0 0 0

c. Site Shape = Rectangular (length = 3 x width)
 buffer zone (feet) Site Size (acres) 1 2 3 5 10 20 30 50 50 12 33 44 55 67 76 81 85 100 0 0 3 19 39 55 63 71 150 0 0 0 0 16 36 46 57 200 0 0 0 0 0 19 31 45 250 0 0 0 0 0 5 18 33 500 0 0 0 0 0 0 0 0 1000 0 0 0 0 0 0 0 0

2. Water Requirement Calculations for Leaf Composting

Let r = wet weight of leaves as received (tons).

Let b = initial moisture content (%, wet basis) before wetting.

Let w = weight of water added during wetting (tons).

Let a = desired final moisture content (%, wet basis) after wetting.

Then because the dry weight has not changed during wetting:

(100-b)r = (100-a)(r+w)

Rearranging:

r+w = (100-b)r
(100-a)

w = (100-b)r
(100-a)- r

The tons of water (w) which must be added per ton of leaves received (r), to go from moisture content "b" to moisture content "a", is:

w = 1   (   (100-b)r  - r    ) = (100-b)  - 1
r     r         100-a                  (100-a)

Conversion factors:

1 ton of water is about 240 gallons.

1 ton of leaves varies widely, but let us use as a rough average 5 yd3.

Then:

Table A5 shows the calculated water requirement (gallons of water per cubic yard of leaves) for leaves coming to a site at moisture contents of 20-50%, with a desired final moisture content of 50-60%.