1. ## How To: Design a ported box using pencil & paper

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)
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
__________________________________________________ ________________________________________
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
__________________________________________________ ________________________________________
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
__________________________________________________ ________________________________________
R= (Dia / 2)

Dia= Vent inside Diameter

Square vent displacement
__________________________________________________ ________________________________________
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
__________________________________________________ ________________________________________
Dp = {[(R² x π) x Lv] / 1728} x Np

Dp= Port displacement (cubic ft)
π= 3.14592 (pi)
Lv= Port length (inches)
Np= Number of ports

Box Layout
__________________________________________________ ________________________________________
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)

2. ## Re: How To: Design a ported box using pencil & paper

I did very well in calculus thank you very much...

but I seriously just **** myself. Unless you can write a source code for that and pack it into a nice little program for people to use, then I just can't see it being sought after by very many people. I'm not doubting it's accuracy, I'm just saying it's not exactly "ca.com user friendly". People around here like instant gratification

3. ## Re: How To: Design a ported box using pencil & paper

Originally Posted by DNick454
I did very well in calculus thank you very much...

but I seriously just **** myself. Unless you can write a source code for that and pack it into a nice little program for people to use, then I just can't see it being sought after by very many people. I'm not doubting it's accuracy, I'm just saying it's not exactly "ca.com user friendly". People around here like instant gratification
I'll look into writing a program when I get home. Depends whether or not I can remember how And if I still have all my programs etc.

4. ## Re: How To: Design a ported box using pencil & paper

I could work this into an excel formula I might give it a try

5. ## Re: How To: Design a ported box using pencil & paper

That'd be insanely easy to make a little vb prog to do.

Might actually do it later tonight...

im

7. ## Re: How To: Design a ported box using pencil & paper

Originally Posted by Anniku989
That'd be insanely easy to make a little vb prog to do.

Might actually do it later tonight...
That's what I was gonna do though

8. ## Re: How To: Design a ported box using pencil & paper

OR... you could just use this...

Which is the same thing, but with much less number crunching. We use winISD to do the port length. You could also use the above method with any number of excel spreadsheets...

It's common sense, simple algebra, and has been type up nearly the same way hundreds of times...

9. ## Re: How To: Design a ported box using pencil & paper

too much math involved here. theres a reason i switched from an engineering major to a construction management major.

but... to the op, good job being able to figure that **** out

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