# Need port calculation info quick!

Discussion in 'Archived Threads 2001-2004' started by Neil Joseph, May 16, 2001.

1. ### Neil Joseph Lead Actor

Joined:
Jan 16, 1998
Messages:
8,332
1
Trophy Points:
0
Real Name:
Neil Joseph
I remember seeing a post some time back with a formula for calculating port length.....
Lv = (8466)(R^2)(Np)/(Vb)(Fb^2) - 1.463(R) + 1
Lv = vent length
Np = number of ports
Vb = box volume (Ft ^3)
Fb = tuning frequency
I need to know if this is a valid formula for calculating vent length and also where did this formula come from? I have some speaker designers that were amazed that my port length would be 27.5" (dual ports at 4" diameter - 2" radius, tuned to 24Hz with a 4ft^3 box). They said they would plug the numbers into their computer when they got the chance but I know if the numbers don't agree, they will be asking me where I got this formula from. They have designed other subwoofers around this driver I am using and they sound great although none were quite as large as my 4ft^3 box design.
Also, the specs that come with this dual 4 ohm voice coil driver are as follows...
Fs = 26Hz
QES = 0.39
QMS = 7.87
QTS = 0.38
Sd = 483cm^2
MMs = 180g
Xmax = +-14mm
Vas = 56L (1.97ft^3)
The spec sheets also have some designs for subs for this driver, one being a 4ft^3 box with a single 4" port only 8" long tuned to 25Hz with a -3dB at 21.4Hz.
You see my dilemma.
Help.
orangeman
Power = 450W rms
------------------
Neil's H.T. Site
(plus large selection of H.T.Links and movie images)

2. ### Patrick Sun Studio Mogul

Joined:
Jun 30, 1999
Messages:
38,763
488
Trophy Points:
9,110
I think that "+1" is to be added if you are using one of those nice flared ports, otherwise, don't added that extra inch.
It's a valid formula, you should probably look for the Loudspeaker Cookbook by Vance Dickason, it's on its 6th edition now, probably find it at a Barnes & Noble. I'm sure the formula is in that book.
------------------
PatCave ; HT Pix ; Gear ; Sunosub I + III ; DVDs ; LDs

3. ### Isaac C Stunt Coordinator

Joined:
Aug 1, 2000
Messages:
140
0
Trophy Points:
0
Hi,
That Lv equation takes into consideration the "end correction" for the port length. The effective port length is juuust a bit longer than the physical length (because there is actually a small mass of air on both vent mouths). Here's another equation that you might find useful. For a cylindrical port the amount of end correction is
delta Lv = 16*Av/(3*pi)
With this, the required physical length of Lv can be derived and it is given below. Some of the constants in your Lv equation have already been substituted for. You will find the exact derived Lv equation below (for cylindrical ports ).
R.H. Small recommends the "absolute" minimum port radius (in meters) should be
Av = sqrt((0.8*Fb*Sd*Xmax)/pi)
and the vent Mach number can be calculated from
Vent Mach number = (vent velocity) / c
The "physical" length (in meters) of the port equals
Lv = ((c*c*Av*Av)/(4*pi*Vab*Fb*Fb)) - ((16*Av)/(3*pi))
===derivation==========
Mmv = pi*Av*Av*Lveff*po
but
Lveff = Lv+(16*Av/(3*pi))
therefore
Mmv = po*pi*Av*Av*(Lv+(16*Av/(3*pi)))
Lv = (Mmv/(po*pi*Av*Av))-(16*Av/(3*pi))
Given
Fb = 1/(2*pi*sqrt(Mmv*Cmb))
and
Cmb = Vb/(po*c*c*Sp*Sp)
then we have
Mmv = 1/(4*pi*pi*Fb*Fb*Cmb)
Mmv = po*c*c*pi*pi*Av*Av*Av*Av/(4*pi*pi*Fb*Fb*Vb)
Mmv = po*c*c*Av*Av*Av*Av/(4*Fb*Fb*Vb)
Now
Lv = ((po*c*c*Av*Av*Av*Av/(4*Fb*Fb*Vb)
)/(po*pi*Av*Av)) - (16*Av/(3*pi))
Finally, after simplifying we get:
Lv = ((c*c*Av*Av)/(4*pi*Vab*Fb*Fb)) - ((16*Av)/(3*pi))
where:
pi = 3.1415...
Fb (Hz)= given tuning frequency
Sd (sq.m.) = effective cone area of driver unit
Xmax (m) = linear cone travel of driver unit
c (m/s) = 344.8, speed of sound
Vab (cu.m.) = effective box volume
If you just want to calculate the tuning frequency given both the port radius and physical length, Fb is equal to
Fb = 1/(2*pi*sqrt(Vab*pi*Av*Av*(Lv+(16*Av)/(3*pi))/(c*c*Sp*Sp)))
where Sp is the port area (in sq.m.).
Hope that helps and good luck.
Isaac
------------------
Nelson Pass: Descriptions of push-pull often illustrate this type of operation with a picture of two men sawing a tree by hand, one on each side of the saw. Certainly this is an efficient way to cut down trees, but can you imagine two men playing a violin?

4. ### Neil Joseph Lead Actor

Joined:
Jan 16, 1998
Messages:
8,332
1
Trophy Points:
0
Real Name:
Neil Joseph
quote: Av = sqrt((0.8*Fb*Sd*Xmax)/pi)[/quote]
My Xmax is +-14mm then should I use an Xmax of 0.028m? or 0.014m? My Sd is 483cm^2 or 0.0483m^2.
I notice that all measurements are in meters
quote: Lv = ((c*c*Av*Av)/(4*pi*Vab*Fb*Fb)) - ((16*Av)/(3*pi))[/quote]
Here I would convert my 4ft^3 = 0.1132674m^3
Sorry for asking but here are my known values...
Fb = 24Hz
Vab = 4ft^3 = 0.1132674m^3
Np = 2 ports
R = 2in = 5.08cm
Xmax = +-14mm (0.028m? 0.014m?)
Sd = 483cm^2 = 0.483m^2
c = 344.8m/s
What then would be the end result if you plug in the numbers? Is the end result the in meters?
------------------
Neil's H.T. Site
(plus large selection of H.T.Links and movie images)

5. ### Isaac C Stunt Coordinator

Joined:
Aug 1, 2000
Messages:
140
0
Trophy Points:
0
Given:
Fb = 24Hz
Sd = 0.0482sq.m
Xmax = +/- 14mm
Av = sqrt((0.8*24*0.0482*0.014)/pi)
Av = 0.0642189 m
or
Av = 2.53in.

------------------
Nelson Pass: Descriptions of push-pull often illustrate this type of operation with a picture of two men sawing a tree by hand, one on each side of the saw. Certainly this is an efficient way to cut down trees, but can you imagine two men playing a violin?

6. ### Patrick Sun Studio Mogul

Joined:
Jun 30, 1999
Messages:
38,763
488
Trophy Points:
9,110
You folks are making this really more complicated than it needs to be. Just use WinISD or LspCAD and let it ride.
------------------
PatCave ; HT Pix ; Gear ; Sunosub I + III ; DVDs ; LDs

7. ### Isaac C Stunt Coordinator

Joined:
Aug 1, 2000
Messages:
140
0
Trophy Points:
0
Xmax in the equation for minimum Av is the peak one-way excursion. And yes, all the above-mentioned equations are in SI units
From the Loudspeaker Design Cookbook
Dt = sqrt((D1*D1) + (D2*D2))
where:
Dt = "total" diameter of the combined diameters
D1, D2 = individual port diamter
For equi-diameter vents, D1 = D2, and so
Dt*Dt = 2*D1*D1
Dt*Dt/2 = D1*D1
D1 = D2 = sqrt(Dt*Dt/2) = Dt/sqrt(2)
Now
D = 2*A
so
Av1 = Av2 = Av/sqrt(2)
where Av1=Av2 are the radius of the two ports. With this equation, one can calculate the required minimum value for the two ports, Av1 and Av2, after calculating
Av = sqrt((0.8*Fb*Sd*Xmax)/pi)
Then Lv for each port can be calculated from the slightly modified equation
Lv = ((Np*c*c*Avx*Avx)/(4*pi*Vab*Fb*Fb)) - ((16*Avx)/(3*pi)) (corrections please? )
where:
Np = number of ports
Avx = Av1 or Av2...
Since you're planning to make each port with radius = 2 inches, then
Lv = 0.6622m
or
=====
Lv = 26.1 inches (each -- quite lengthy)
=====
Hope that helps
------------------
SPICE simulations
------------------
Nelson Pass: Descriptions of push-pull often illustrate this type of operation with a picture of two men sawing a tree by hand, one on each side of the saw. Certainly this is an efficient way to cut down trees, but can you imagine two men playing a violin?

Joined:
Aug 1, 2000
Messages:
140