Input Parameters

1. Thiele/Small Parameters (for the subwoofer driver):

   • Fs: Driver's resonant frequency (Hz).

   • Vas: Equivalent compliance volume (liters).

   • Qts: Total Q-factor (dimensionless).

   • Sd: Effective piston area (cm²).

   • Xmax: Maximum linear excursion (mm) for port air velocity calculation.

2. Design Targets:

   • Fb: Desired tuning frequency (19Hz).

   • Maximum SPL/Power: To calculate port area and avoid chuffing (noise from turbulent air).

3. Physical Constraints:

   • Maximum allowable enclosure size (liters).

   • Port diameter (D) or desired port area (S_p).

Key Formulae

1. Enclosure Volume (Vb)
   For a vented box, use alignment-specific formulas. A common alignment is:

   % Enclosure Volume (Vb)
   V_b = \frac{V_{as}}{\left(\frac{F_b}{F_s}\right)^2 - 1} \quad \text{(if \(F_b > F_s\))}

   If Fb​<Fs​, iterative methods or software are typically required.

2. Port Tuning Frequency (Fb)
   Helmholtz resonance formula:

   % Port Tuning Frequency (Fb)
   F_b = \frac{c}{2\pi} \sqrt{\frac{A}{V_b \cdot L_{\text{effective}}}}

   • c: Speed of sound (343 m/s or 34300cm/s).

   • A: Port cross-sectional area (Sp=πr2Sp​=πr2, cm²).

   • L_effective​: Effective port length (physical length + end corrections).

3. Port Length (Lv)
   Physical port length including end corrections:

   % Port Length (Lv)
   L_v = \frac{c^2 \cdot S_p}{4\pi^2 \cdot F_b^2 \cdot V_b} - k \cdot D

   • k: End correction factor (0.8230.823 for flanged ports, 0.6140.614 for free ports).

   • D: Port diameter (cm).

4. Port Area (S_p)
   To avoid air velocity >17 m/s (prevents chuffing):

   % Port Area (Sp)
   S_p = \frac{0.24 \cdot \sqrt{P_{\text{rms}}}}{F_b \cdot v_{\text{max}}}

   • P_rms​: RMS power (W).

   • v_max​: Max allowable air velocity (e.g., 17 m/s).

Design Steps

1. Calculate Vb​: Use alignment formulas or iterate based on driver parameters.

2. Determine Sp​: Size the port to limit air velocity.

3. Solve for Lv​: Use the port length formula.

4. Validate: Check if Vb​ and Lv​ fit physical constraints. Adjust D or Vb​ if needed.

Example Calculation

Assume:

% Example Calculation
F_s = 25 \, \text{Hz}, \quad V_{as} = 50 \, \text{L}, \quad Q_{ts} = 0.35, \quad F_b = 19 \, \text{Hz}, \quad S_p = 50 \, \text{cm}^2 \, (\text{D} \approx 8 \, \text{cm}).

1. Enclosure Volume:
   Since Fb​<Fs​, use software or iterative methods. Assume Vb​=70L.

2. Port Length:

   L_v = \frac{(34300^2 \cdot 50)}{4\pi^2 \cdot 19^2 \cdot 70} - 0.823 \cdot 8 \approx 34.2 \, \text{cm}.

Annular Ring Areas

10"-12" annulus: 11π in²

8"-10" annulus:9π in²

6"-8" annulus:7π in²

4"-6" annulus:5π in²

12" circle:36π in²

10" circle:25π in²

8" circle:16π in²

6" circle:9π in²

4" circle:4π in²