Need port calculation info quick!

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

  1. Neil Joseph

    Neil Joseph Lead Actor

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    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
    R = port radius
    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
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  2. Patrick Sun

    Patrick Sun Studio Mogul

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    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

    Isaac C Stunt Coordinator

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    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 [​IMG] ).
    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))
    ===end derivation====== (corrections please? [​IMG] )
    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

    Neil Joseph Lead Actor

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    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?
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  5. Isaac C

    Isaac C Stunt Coordinator

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    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.
    [​IMG]
    ------------------
    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

    Patrick Sun Studio Mogul

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    You folks are making this really more complicated than it needs to be. [​IMG] Just use WinISD or LspCAD and let it ride.
    ------------------
    PatCave ; HT Pix ; Gear ; Sunosub I + III ; DVDs ; LDs
     
  7. Isaac C

    Isaac C Stunt Coordinator

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    Xmax in the equation for minimum Av is the peak one-way excursion. And yes, all the above-mentioned equations are in SI units [​IMG]
    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? [​IMG] )
    where:
    Np = number of ports
    Avx = Av1 or Av2...
    In your case, each port (2 ports?) radius should be about 1.78 inches -- minimum [​IMG]
    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 [​IMG]
    ------------------
    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?
     
  8. Isaac C

    Isaac C Stunt Coordinator

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    [​IMG] LOL [​IMG]
    Pat, my "overkill" reply was meant to help him while I kill time simultaneously hehe [​IMG]
    Isaac
    ------------------
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    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?
     

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