Things you will need:
Pencil
Paper
Calculator
I worked each equation step by step to help you guys understand. It's actually rather easy. This will be more accurate than the box calculators online. Feel free to correct any mistakes I made.
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There are a few different equations to determine port length. They can be found on numerous sites. I use the following.
This one comes from a loudspeaker cookbook I read once upon a time. It also can be found online at numerous sites.
Lv= {(14630000 x R²) / (Fb²) x [(Vb/Np) x 1728]} - 1.463 x R
Lv= Port Length (inches)
Fb= Tune Frequency (Hertz)
R= See ******* (this will use different equations depending on round or square vents)
Vb= total internal airspace (cubic ft)
Np= Number of ports
******This is for square vents and will take place of R.
R= √[( H x W) / π]
√= square root
H= height of port (inches)
W= width of port (inches)
π = 3.141592 (pi)
******This is for round vents and will take place of R
R= (Dia / 2)
Dia= Vent Diameter
This is just an example for a 6" port.
R= (Dia / 2)
R= (6 / 2)
R= 3
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Here we go. The box I want is 6 cubic ft. tuned to 40hz, so lets fill in what we already know. I'll be using a square vent.
Lv= {(14630000 x R²) / (Fb²) x [(Vb/Np) x 1728]} - 1.463 x R
Lv=?
Fb=40
R=?
Vb=6
Lets solve for R. This is a square so we use the asterisk for a square vent. The vent of my box is going to be 15.5" x 8", (these
numbers are up to you, multiplying these numbers together determines your port area in inches, which is a number we don't need
but will help in deciding how big to make the port).
R= √[(H x W) / π]
√= square root
H= 15.5 (inches)
W= 8 (inches)
π = 3.141592 (pi)
R= √[(15.5 x 8) / 3.141592]
R= √[124 / 3.141592]
R= √39.470434098380693610118691415053
R= 6.282549967837955334674739903437
Now let's fill in the rest of the equation and solve.
Lv= {(14630000 x R²) / (Fb²) x [(Vb/Np) x 1728]} - 1.463 x R
Lv=?
Fb=40
R=6.282549967837955334674739903437
Vb=6
Lv = {(14630000 x 6.28254996783795533467473990343700²)/ (40²) x [(6 / 1) x 1728]} - 1.463 x 6.28254996783795533467473990343700
Lv= {14630000 x 39.470434098380693610118691415053) / 1600 x [6 x 1728]} - 9.1913706029469286546291444787283
Lv= {577452450.85930954751603645540223 / 1600 x 10368} - 9.1913706029469286546291444787283
Lv= {577452450.85930954751603645540223 / 16588800} - 9.1913706029469286546291444787283
Lv= 34.809778335944103703464774751774 - 9.1913706029469286546291444787283
Lv= 25.618407732997175048835630273042
There we have it, my port will be 25.6" long.
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Now to figure the box to acquire this port. First let's find how much air displacement this port has. We're assuming the box
has the port in the middle so we add wood thickness to the port width twice because of the walls found inside the box, the
top and bottom of the port are part of the outer walls resulting in no displacement for those. This will change depending
on how your port is. You should be able to figure out where you should and shouldn't need to add wood thickness in the
following equation. We also assume we're using 3/4" mdf for the wood.
Dp = {[Lv x (Ph + wt + wt)] x [(Pw + Wt + Wt)] / 1728} x Np
Dp= Port displacement (cubic ft)
Pw= Port width (inches)
Lv= Port length (inches)
Ph= Port height (inches)
Wt= wood thickness (inches)
Np= number of ports
Dp = {[Lv x (Ph + wt + wt)] x [(Pw + Wt + Wt)] / 1728} x Np
Dp= ? (cubic ft)
Pw= 8 (inches)
Lv= 25.6 (inches)
Ph= 15.5 (inches)
Wt= .75 (inches)
Np= 1
Dp = {[25.6 x (15.5 + 0 + 0)] x [(8 + .75 + .75)] / 1728} x 1
Dp = {[25.6 x 15.5] x [9.5] / 1728} x 1
Dp = {395.25 x 9.5 / 1728} x 1
Dp = {3754.875 / 1728} x 1
Dp = 2.1729600694444444444444444444444 x 1
Dp = 2.1729600694444444444444444444444
The equation for figuring out the displacement of round vents is as follows.
Dp = {[(R² x π) x Lv] / 1728} x Np
Dp= Port displacement (cubic ft)
R= Radius of Vent (inches)
π= 3.14592 (pi)
Lv= Port length (inches)
Np= Number of ports
This is just an example for 2 6" ports 17" long.
Dp = {[(R² x π) x Lv] / 1728} x Np
Dp= Port displacement (cubic ft)
R= 3 (inches)
π= 3.14592 (pi)
Lv= 17 (inches)
Np= 2
Dp = {[(3² x 3.14592) x 17] / 1728} x 2
Dp = {[(9 x 3.14592) x 17] / 1728} x 2
Dp = {[28.31328 x 17] / 1728} x 2
Dp = {481.32576 / 1728} x 2
Dp = .278545 x 2
Dp = 0.55709
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Now lets make the box. My maximum dimensions are 35 x 30 x 17 (L x W x H) I only need to solve
for one side so pick one and go with it. I'll pick the width and use the following equation.
W = {(Dp + Vb + Sw + Ex) x 1728 / [L - (wt x 2)] x [(H - (wt x 2)]} + (wt x 2)
L= Length (inches)
W= Width (inches)
H= Height (inches)
Ex= Extra displacements: braces, dope, guns, whatever etc. (cubic ft.)
Dp= Port displacement (cubic ft)
Vb= Total internal airspace (cubic ft)
Sw= Subwoofer displacement (cubic ft)
Wt= wood thickness (inches)
We already know most of it so let's fill it in and solve it. You can find subwoofer displacement
by looking at the T/S parameters usually listed as Vd.
W = {(Dp + Vb + Sw + Ex) x 1728 / [L - (wt x 2)] x [(H - (wt x 2)]} + wt x 2
L= 35
W= ?
H= 17
Dp= 2.1729600694444444444444444444444
Vb= 6
Sw= .2
Wt= .75
Ex= 0
W = {(2.1729600694444444444444444444444 + 6 + .2 + 0) x 1728 / [35 - (.75 x2 )] x [(17 - (.75 x 2)]} + .75 x2
W = {8.372960069444444444444444444444 x 1728 / [35 - 1.5] x [17 - 1.5]} + .75 x 2
W = {14468.474999999999999999999999999 / [33.5 x 15.5]} + 1.5
w = {14468.474999999999999999999999999 / 519.25} + 1.5
w = {27.864179104477611940298507462667} + 1.5
w = 29.364179104477611940298507462667
That's it, we're done. The box is 17" x 35" x 29.3" with a square port in the center of the box 15.5" x 8" x 25.6"
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The formulas to remember:
Vent Length
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Lv= {(14630000 x R²) / (Fb²) x [(Vb/Np) x 1728]} - 1.463 x R
Lv= Port Length (inches)
Fb= Tune Frequency (Hertz)
R= See ******* (this will use different equations depending on round or square vents)
Vb= total internal airspace (cubic ft)
Np= Number of ports
R value for Square vent
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R= √[( H x W) / π]
√= square root
H= height of port (inches)
W= width of port (inches)
π = 3.141592 (pi)
R value for Round vent
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R= (Dia / 2)
Dia= Vent inside Diameter
Square vent displacement
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Dp = {[Lv x (Ph + wt + wt)] x [(Pw + Wt + Wt)] / 1728} x Np
Dp= Port displacement (cubic ft)
Pw= Port width (inches)
Lv= Port length (inches)
Ph= Port height (inches)
Wt= wood thickness (inches)
Np= number of ports
Round vent displacement
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Dp = {[(R² x π) x Lv] / 1728} x Np
Dp= Port displacement (cubic ft)
R= Radius of Vent (inches)
π= 3.14592 (pi)
Lv= Port length (inches)
Np= Number of ports
Box Layout
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W = {(Dp + Vb + Sw + Ex) x 1728 / [L - (wt x 2)] x [(H - (wt x 2)]} + (wt x 2)
L= Length (inches)
W= Width (inches)
H= Height (inches)
Ex= Extra displacements: braces, dope, guns, whatever etc. (cubic ft.)
Dp= Port displacement (cubic ft)
Vb= Total internal airspace (cubic ft)
Sw= Subwoofer displacement (cubic ft)
Wt= wood thickness (inches)
