Motor Force (BL) Isn't Constant: What Happens at High Excursion
The BL product (force factor) is one of the most important driver specifications. It determines how much force the motor can apply to the cone for a given current. Higher BL means more control, more output, and less distortion - at rest.
But the spec sheet gives you BL at one position: the rest position. What happens when the cone moves?
BL varies with position
The BL product is the product of magnetic flux density (B) and voice coil length inside the gap (L). When the voice coil is centered in the magnetic gap, L is at its maximum - the entire winding is immersed in the field.
As the cone moves outward or inward, the voice coil moves with it. Part of the winding exits the magnetic gap, where the flux density is much lower. The effective L decreases, and BL drops.
This is not a small effect. At Xmax (the rated maximum linear excursion), BL has typically dropped by 30–50% from its rest value. At excursions beyond Xmax, the drop accelerates.
The shape of the falloff
The BL-vs-position curve for most drivers follows a smooth, bell-shaped profile. At the rest position, BL is at its peak. As the cone moves in either direction, BL rolls off progressively — gently at first, then more steeply as the coil moves further out of the gap.
At Xmax, BL has typically dropped to around 60–70% of its rest value (depending on the motor geometry). Beyond Xmax, the falloff accelerates — at twice Xmax, the motor may be producing less than a third of its rated force.
Why this matters
Power compression at high excursion. As the cone approaches Xmax, the motor is weaker. Less force per ampere means less acceleration, which means less output. The driver's response compresses - you put in more power but get diminishing returns in SPL.
Increasing distortion. The BL curve is symmetric around the rest position only for perfectly symmetric motor designs. In practice, most drivers have slight BL asymmetry (BL is different for inward vs outward excursion). This asymmetry produces even-order harmonic distortion that increases with excursion level.
Excursion limiting. BL falloff is actually a natural limiting mechanism. As the driver approaches Xmax, the decreasing BL reduces the force driving the cone, which limits how far it can travel for a given input voltage. Without BL falloff (if BL were constant), the cone would travel further and might exceed the mechanical limits of the suspension.
SPL accuracy. Simplified models that assume constant BL overpredict output at high excursion levels. The real output is lower than the linear prediction because the motor is weaker at excursion extremes.
Spec sheet Xmax: what it really means
Xmax is usually defined as the excursion at which BL has dropped to about 70% of its rest value (or equivalently, where the output deviates by more than 10% from the linear prediction). Some manufacturers define it more loosely.
This means that at Xmax, you have already lost roughly 30% of your motor force. The driver is still "working" but it is operating non-linearly. Distortion is rising, and the output-vs-input relationship is no longer straight.
Designing a system where the driver routinely hits Xmax means accepting this level of non-linearity. For SQ builds, keeping peak excursion to 70–80% of Xmax maintains the motor in its more linear region.
How different motor designs affect the BL curve
Underhung voice coils have a coil that is shorter than the magnetic gap. The coil stays fully immersed over a wider excursion range, producing a flatter BL curve (more linear region). The tradeoff is lower peak BL because not all the gap height is used.
Overhung voice coils have a coil that is taller than the gap. At rest, the top and bottom of the winding are outside the gap. As the coil moves, new turns enter the gap from one end while others exit from the other end. This produces higher peak BL but a steeper falloff.
Most car audio subwoofers use overhung designs for maximum BL, accepting the steeper falloff as a tradeoff for higher output at moderate excursion levels.
How RokketBox models BL compression
RokketBox incorporates BL falloff directly into the circuit-domain simulation. At each frequency point, the excursion is calculated, the corresponding BL is looked up from the falloff curve, and the reduced motor force feeds back into the solution.
The result is an SPL curve that accurately reflects the real output at the specified power level — not the optimistic linear prediction. The impedance curve also reflects the BL change because the driver's electrical damping varies with excursion.
In the simulator, you can increase the power level and watch the SPL curve compress in the regions where excursion is highest. This is the real-world behaviour that you would measure on a test bench — and that most online calculators miss entirely.