Chapter 6: Master Engineering Formula Reference

Precision in automotive audio is achieved through the application of physics and mathematics. This library aggregates the fundamental and advanced formulas used throughout the Ohmic Audio Labs Knowledge Base. Every calculation here is verified for accuracy within the specific constraints of the automotive environment.

6.1 Electrical Power & Ohm's Law

The foundation of all power delivery systems.

      
      V = I * R (Voltage = Current * Resistance)

      P = V * I (Power = Voltage * Current)

      P = V² / R (Power = Voltage Squared / Resistance)

Wire Voltage Drop

      Vdrop = (2 * L * Rwire * I) / 1000
    

Where L is length in feet, R_wire is resistance in milliohms per foot, and I is current in Amps.

6.2 Acoustic Physics & Wavelength

The Wavelength Equation

      λ = c / f
    

Where c is the speed of sound (~1125 ft/s or 343 m/s) and f is the frequency in Hz. Use this to identify quarter-wave cancellation distances.

Helmholtz Resonance (Fb)

      fb = (c / 2π) * √[ S / (V * (L + 0.825√S)) ]
    

Where S is port surface area, V is enclosure volume, and L is physical port length.

6.3 Digital Signal Processing (DSP) Math

Time Alignment Calculation

      Delay (ms) = (ΔDistance / c) * 1000
    

Example: To align a driver 1 foot further than the reference, add 0.88ms of delay.

Decibel Conversions

Voltage Gain: dB = 20 * log10(Vout / Vin)
Power Gain: dB = 10 * log10(Pout / Pin)
Distance vs. SPL: -6dB for every doubling of distance (Inverse Square Law).

6.4 Thiele/Small Derivations

Reference Efficiency (η₀)

      η₀ = (9.64 * 10⁻¹⁰ * Vas * fs³) / Qes
    

Reflects the actual efficiency of the driver independently of the enclosure.

Bl (Motor Strength)

      Bl = √[ (2π * fs * Re * Mms) / Qes ]
    

6.5 Geometric Modeling

Net Enclosure Volume (Vb)

      Vnet = Vgross - (Vdriver + Vport + Vbracing)
    

Wedge Enclosure Volume

      Volume = [ (D1 + D2) / 2 ] * W * H
    

Where D1 and D2 are the top and bottom depths of the wedge.

6.6 Physical Constants Reference

Constant	Standard Value
Speed of Sound (Sea Level, 20°C)	1125.3 ft/s \| 343 m/s
Density of Air (ρ)	1.204 kg/m³
Reference Pressure (P₀)	20 µPa
Standard Gravity (g)	9.806 m/s²

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