Formula to calculated the perfect carbon filter size [FONT="]If you like a bit math have fun, if not so better run!
This thread will explain how to take the dimensions of your grow cabinet or room and and find the proper CFM rate. After the CFM rate for your exhaust is found we use that number to distinguish the length and radius dimensions for your ideal can-filter carbon scrubber.
I in no way take credit for devising this formula.
Formula to convert grow room dimensions and CFM ratings to find the ideal length and radius of a can-filter carbon scrubber.
I will be using a 38"'Wx28"Dx42"H cab equipped with a 250 watt light and an additional 50 watts of equipment as an example. I will be rounding where appropriate, I may round up even if the numerical value is below 5. I will also make note of when I have done so.
Let us begin!
1.) Convert all inches into feet
Quote:
inches ÷ 12 = feet
38÷12=3.16'ft W (rounded up to 3.2)
28÷12=2.3'ft D (rounded up to 2.4)
42÷12=3.5'ft H
2.) Find the volume, feet cubed, of your cab.
Quote:
multiply Width × Depth × Height
W × D × H = feet cubed
3.2'ftW × 2.4'ftD × 3.5'ftH = 26.88'ft3
3.) Find for Exchange CFM rate. We want to exchange the volume of the cab 4 to 5 times a minute. I will use the value of 5.
Quote:
feet cubed × 5 = Exchange CFM
26.88'ft^3 × 5 = 134.4CFM
4.) Find for Additional Electrical Cooling CFM rate. Add all the watts of all equipment inside the cab.*see bottom of page for details
Quote:
total watts of all equipment ÷ 4 = Additional Electrical Cooling CFM
250 watt light + 50 watt additional equipment = 300 Total Watts
300 Total Watts ÷ 4 = 75 AEC CFM
5.) Add the two CFM rates to get Total CFM
Quote:
Exchange CFM + AEC CFM = Total CFM
134.4 Exchange CFM + 75 AEC CFM = 209.4 CFM
6.) Find the CFH (Cubic Feet per Hour) from the Total CFM rate.
Quote:
Total CFM × 60 = CFH
209.4 Total CFM × 60 = 12564 CFH
7.) Find for the amount of carbon needed for the filter.
Quote:
CFH × grams per foot of activated carbon (0.36) = total amount of carbon required.
12564 CFH × 0.36g per ft = 4523.04g
8.) Divide the amount (in grams) of total carbon by the length to yield the radius quotient. This is done with 2.6cm thickness as a constant.
This one is a bit tricky. You could yield a perfect square of the number and this will net you a very square looking can filter (diameter and length will be equal). The best way is to play it by ear and round. In all of the examples above the amount of carbon was rounded to the nearest thousand. It's probably safer and more accurate to round to the nearest five hundred, but whichever you want to do will still give you roughly the same size can filter.
Another method is to subtract (in cm) the desired length of your carbon scrubber. For example; if you know you want your carbon scrubber to only be 1 ft long then convert 12 inches into cm and then divide from the total amount of activated carbon. The formula to convert inches to centimeters is inches × 2.54. You can also search online, there are dozens of converters and Goggle even has a built in one.
Example:
12in × 2.54 = 30.48
4523.04 ÷ 30.48 = 148.393 and change.
So, the length of the can filter will be 30.48cm and the quotient is then carried over to find for the radius. Remember to set aside the number you divide the amount of carbon by, this is your length.
(A ÷ B = C you want to set aside B, this is your length)
One more thing, when simplifying the value and finding the ideal square, take the smaller number out and use that for your length (cm). The larger number should be used for the outer surface. Otherwise you wind up with a [i/]very[/i] round and short carbon scrubber. You'll understand in a minute.
Quote:
Activated carbon surface area squared to desired length.
In this example we will be rounding 4523.04 to 4500. This way we can guesstimate what decent sized length will fit into the equation.
50 × 90 = 4500
so we will use 50cm to divide 4523.04 by.
*note - remember to set aside the number you are dividing the amount of carbon by. (A ÷ B = C ; set aside B, this is your length)
4523.04 ÷ 50cm = 90.4608cm
9.) Find for the desired radius.
Okay, hope you're still with me. Now that we have divided by the length we need to find the radius. We will use the product we got from dividing the total surface area of carbon by the desired length for this formula. If you are at all confused, I will put a condensed example (numbers and abbreviations only) of the formula towards the end of this article.
Quote:
radius quotient ÷ pi = base surface
base surface √ (square root) = radius
*note- pi is 3.1415 we will be using 3.14
90.4608 ÷ 3.14 = 28.8091....
√ of 28.8091 = 5.3674....
There, 5.3674...cm is your radius. Multiply by 2 to yield the diameter
Radius is the distance from the center of a circle to the edge.
Diameter is the distance from one edge of a circle to the other edge, passing through the center.
So... now we take the following numbers and apply them to what we need for the carbon scrubber.
Quote:
Step 7 will give us the total number (in grams) needed to cover the surface area required by the carbon scrubber. This is the amount of activated carbon you will need to fill the carbon scrubber. A thickness of 2.6cm is automatic. If your carbon scrubber is going to be thinner (not recommended) then you will need slightly less carbon.
The number set aside in step 8 is the length of the carbon scrubber in centimeters.
The number yielded in step 9 is the radius of the cylinder in centimeters. Multiply the radius by 2 to achieve the diameter in centimeters.
Okay, quick rundown... you ready? Let's go!
Quote:
cab is 3.2'ft x 2.4'ft x 3.5'ft = 26.88'ft3
26.88 x 5 = 134.4CFM
300Watts ÷ 4 = 75CFM
134.4CFM + 75CFM = 209.4CFM
209.4CFM x 60 = 12564CFH
12564CFH x 0.36 = 4523.04
4523 rounded to 4500
4500 evaluated for simple division
value decided upon are 50 and 90
50, being the smallest, is excluded and reserved to stand as the length
90 ÷ 3.14 (pi) = 28.66...
square root of 28.66 = 5.35
amount of carbon needed = 4500 grams (about 10 lbs.)
length of can filter carbon scrubber = 50cm (19.5"in)
radius of can filter carbon scrubber = 5.35cm (diameter = 10.7cm) (2"in rounded(diameter = 4"in))
*note- the final parameters in this rundown are slightly different due to rounding 4523.04 to 4500
Additional formulas:
28 grams in an ounce.
16 ounces in a pound.
Centimeters to inches: cm x 0.39
Inches to centimeters: in x 2.54
Diameter: Radius x 2
Inches to feet: in ÷ 12
Surface area of a cylinder: (pi × R2)H * R=radius H=length
Note that these numbers are ideals and are meant to create a carbon scrubber that will remove 100% odor and last up to a year or so in use. These measurements are based on professional carbon scrubbers. I compared what kind of can filter I would need for my grow space (32"x16"x36") and then did this equation, it was dead on.
You can build a smaller carbon scrubber if need be. However, the carbon will need to be replaced more often than a larger unit. Remember, activated carbon has an incredibly vast surface area. The activated carbon in your can filter can be shaken and then reconnected. This will expose new areas of activated carbon that have not been fully used to their potential. This procedure cannot be done indefinitely, but refilling every other time saves some cash.
*this step is necessary only if you have, or predict you will have heat issues. This Additional CFM (ACFM) rate can be excluded if you are not using your main exhaust to compensate for heat issues. In other words, unless you are using your exhaust vent to address heat issues, you do not need to factor this step into your carbon scrubber dimensions.[/FONT]
