A vented loudspeaker is analogous to a 24dB/octave cutoff highpass filter, characterized by an enclosure having an open tunnel or port which allows the passage of air in and out of the box. 
At low frequencies, the vent contributes substantially to the sound output of the system. 
It does so however, by increasing the acoustc load at the rear of the cone, reducing cone motion, and the output of the driver. 
As such, a vent only adds as much as it subtracts. 
Compared to closedbox systems, vented enclosure posses several unique characteristics: 
A: Lower cone excursion near the box resonance frequency. 
B: Lower cutoff using the same driver. 
C: In theory, a +3dB higher efficiency for the same volume closedbox system. 
On the downside, vented enclosurs are much more sensitive to misaligned parameters.This factor makes the vented box loudspeaker somewhat more difficult for the inexperienced homebuilder. 
Just like at closed boxes nearly everyone Q_{ts}waarde can be used, although generally only values between 0.2 and 0.5 will lead to a good reproduction. 
f_{3} 
3dB halfpower frequency. 
f_{s} 
resonance frequency of driver 
f_{c} 
resonance frequency of the closed box system 
Q 
ratio of reactance to resistance (series circuit) or resistance to reactance (parallel circuit) 
Q_{ts} 
total Q of driver (woofer) at f_{s}, considering all driver resistance. 
Q_{tc} 
total Q of speaker system at f_{c}, including all system resistance. 
V_{as} 
volume of air having the same acoustic compliance as the driver suspension. 
V_{ab} 
volume of air having the same acoustic compliance as the enclosure. 
X_{max} 
peak linear displacement of driver cone. 
S_{d} 
effective surface area of driver cone. 
Vd 
peak displacement volume of driver cone. 
Vb 
net internal volume of enclosure. 
Parameters: 
V_{as} = 57,2 Liter
f_{s} = 42,5 Hz
Q_{ts} = 0,32 
Calculation V_{b}: 
V_{b} = 15 * Vas * Q_{ts}^{2,87} = 32,6 Liter 
Calculation f_{3}: 
f_{3} = 0,26 * f_{s} / Q_{ts}^{1,4} = 54,5 Hz 
Calculation f_{b}: 
f_{b} = 0,42 * f_{s} / Q_{ts}^{0,9} = 49,8 Hz 
Port : S_{v} = 72cm² 
Lve = ((10*343^{2}*S_{v})/(4*3,14^{2}*fs^{2}*V_{b}))0,825*wortel(S_{v}) 
Lve = ((84707280)/(2322280,88))7 = 29,5 cm 
Parameters: 
V_{as} = 57,2 Liter
f_{s} = 42,5 Hz
Q_{ts} = 0,32 
Calculation V_{b}: 
V_{b} = 17,6 * V_{as} * Q_{ts}^{3,15} = 27,8 Liter 
Calculation f_{3}: 
f_{3} = 0,3 * f_{s} / Q_{ts}^{1,33} = 58 Hz 
Calculation f_{b}: 
f_{b} = 0,42 * f_{s} / Q_{ts}^{0,95} = 52,7 Hz 
Port : S_{v} = 72cm² 
Lve = ((10*343^{2}*S_{v})/(4*3,14^{2}*f_{s}^{2}*V_{b}))0,825*wortel(S_{v}) 
Lve = ((84707280)/(1980350))7 = 35,8 cm 
Firstly, calculate the Efficiency Bandwidth Product: EBP = f_{s}/Q_{e}.
If EBP is around 100, this indicates that a vented box would be a better choice.
If you have Q_{e} and Q_{m}, you can take external resistance into account when calculating Q_{ts}.
Q_{ts} = 1/((1/Q_{m}) + R_{s}/((R+R_{s})Q_{e})) where R is the resistance of the wiring, typically 0.5 ohm.
Alternatively, use Q_{ts} as specified in the TS parameters. 

Source: The Loudspeaker Design Cookbook, Vance Dickason




