Anyone build a bigger la scala with/for the 15pr400

Alright — let’s calculate the new horn mouth area, throat area, and cutoff frequency when scaling up the La Scala by 20%.

📐 1. Assumptions about the original La Scala​

  • Horn path length ≈ 2.6 m (102″)
  • Mouth area ≈ 0.4 m² (4.3 ft² ≈ 24″×24″)
  • Throat area ≈ 0.02 m² (about 3 in²)
  • Cutoff frequency ≈ 104 Hz (theoretical)
    (This is derived from the mouth area.)
We scale everything by a factor of:
Code:
s = 1.20

📐 2. New horn path length​

Already calculated:
Code:
2.6 \, m \times 1.20 = 3.12 \, m

📐 3. New mouth area​

Area scales with the square of the linear scale:
Code:
A_\text{new} = A_\text{original} \times s^2
So:
Code:
0.4 \, m² \times (1.20)^2 ≈ 0.4 \times 1.44 ≈ 0.576 m²
0.576 m² ≈ 6.2 ft²
That’s about 30″ × 30″.

📐 4. New throat area​

Similarly:
Code:
0.02 \, m² \times (1.20)^2 ≈ 0.0288 m²
0.0288 m² ≈ 44.7 cm² ≈ 6.9 in²

📐 5. New cutoff frequency​

Horn cutoff frequency depends inversely on the mouth size.
The approximate formula is:
Code:
f_c ≈ \frac{c}{2\pi} \sqrt{\frac{\pi}{A_\text{mouth}}}
where (speed of sound).
If you scale the mouth area by , the cutoff scales as:
Code:
f_{c,\text{new}} = \frac{f_c}{s}
So:
Code:
104 Hz / 1.20 ≈ 87 Hz

📋 Final Results:​

ParameterOriginalScaled ×1.2
Horn path length2.6 m (102″)3.12 m (122.4″)
Mouth area0.4 m²0.576 m² (6.2 ft²)
Throat area0.02 m²0.0288 m²
Cutoff frequency~104 Hz~87 Hz

✅ After scaling up the La Scala by 20%, you get:
  • ~22″ longer path
  • ~44% larger mouth and throat areas
  • ~17 Hz lower cutoff frequency (~87 Hz instead of ~104 Hz)
If you’d like, I can also help you draft a table of new dimensions (height, width, depth) or even draw a scaled plan. Let me know!
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