I figure the SSA based on a sphe

I figure the SSA based on a spherical - or round rock. Actual SSA of each rock will vary based on the overall shape, and smoothness of the rock. The below figures are based on smooth round rocks. Some rocks will have higher SSA's, while others will have lower SSA's. These figures should be used as "averages".

Here is how to figure SSA for gravel/rocks. I am figuring rocks to have mostly a spherical shape. Here is the formula for figuring surface area of a sphere.

http://www.teacherschoice.com.au/Maths_Library/Area%20and%20SA/area_2.htm

Here is the formula to convert square inches into square feet.

http://www.metric-conversions.org/area/square-inches-to-square-feet.htm

It is 4 x Pie x radius squared. ( Pie is 3.14 -remember that from Junior High algebra?) (Radius is 1/2 the diameter) All SSA is figured in One Square Foot at 2" thick of what ever the media is.

1/2" rock has a .25" radius.

4 x 3.14 x (.25 x .25) = .75 square inches of surface area on 1 piece of 1/2" gravel.

1 foot equals 12 inches. 12" divided by 1/2" rocks = 24 individual 1/2" rocks. 24 x 24 rocks = 576 1/2" rocks in one square foot. We need 2" of depth for SSA comparison. So 2" divided by 1/2" rocks = 4 rocks high. Now multiply the 576 rocks per square foot by 4 rocks high to get how many rocks are in 1 square foot at 2" thick. 576 x 4 = 2,304 individual 1/2" rocks in one square foot at 2" thick. Now multiply those 2,304 rocks by the surface area of .75" to get how many square inches of surface area. 2,304 x .75 = 1,728 square inches of surface area. There are 144 square inches in 1 square foot, so divide the 1,728 square inches by 144 to get square feet. 1,728 / 144 = 12.

So 1/2" gravel has an average of SSA of 12. You can add or subtract up to about 40% depending on how rough or smooth the gravel is.

Now let’s do it again for 1" gravel

1" rock has a .5 radius.

4x3.14x(.5x.5) = 3.14" square inch surface area

12" / 1" rock = 12 rocks per linear foot.

12 rocks x 12 rocks = 144 rocks per square foot

2" / 1" = 2 rocks high

144x2=288 rocks per square foot at 2" thick

288 rocks x 3.14 square inches of surface area each = 904.32 total square inches

904.32 square inches / 144 = 6.28 square feet of surface area

So 1" smooth rock has 6.28 SSA

Now let’s do it again for 2" gravel

2" rock has a 1" radius.

4x3.14x(1x1)= 12.56 square inch surface area

12" / 2" = 6 rocks per linear foot

6 rocks x 6 rocks = 36 rocks per square foot

2" / 2" = 1 rock high

36 x 1 = 36 rocks per square foot at 2" thick

36 rocks x 12.56 square inches of surface area each = 452.16 total square inches

452.16 / 144 = 3.14 square feet of surface area

So 2" smooth rock has 3.14 SSA

4" rock has a 2" radius

4x3.14x(2x2)= 50.24 square inches of surface area

12" / 4" rock = 3 rocks per linear foot

3 rocks x 3 rocks = 9 rocks per square foot

2" / 4" rock = .50 rocks high

9 x .5 = 4.50 rocks per square foot at 2" thick

4.5 rocks x 50.24 square inches each = 226.08 total square inches

226.08 / 144 = 1.57 square feet of surface area

So 4" smooth rock has 1.57 SSA

8" rock has a 4" radius

4x3.14x(4x4) = 200.96 square inches of surface area

12" / 8"rock = 1.5 rocks per linear foot

1.5 rocks x 1.5 rocks = 2.25 rocks per square foot

2" / 8" rock = .25 rocks high

2.25 x .25 = .56 rocks per square foot at 2" thick

.56 rocks x 200.96 square inches each = 112.54 total square inches

112.54 / 144 = .78 square feet of surface area

So 8" smooth rock has a .78 SSA

16" rock has an 8" radius

4x3.14x(8x8) = 803.84 square inches of surface area

12" / 16" = .75 rocks per linear foot

.75 rocks x .75 rocks = .56 rocks per square foot

2" / 16" rock = .13 rocks high

.56 x .13 = .07 rocks per square foot at 2" thick

.07 rocks x 803.84 square inches each = 56.27 total square inches

56.27 / 144 = .39 square feet of surface area

SO 16" smooth rock has a .39 SSA

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