3. Diagnose Inconsistent Delta-V Values Across Multiple Data Sources

Why the Same Collision Yields Three Different Delta-V Numbers

In a typical reconstruction file set, the EDR report lists a longitudinal delta-V of −38 km/h, the crash-test database for a comparable barrier impact lists −11.2 m/s, and the reconstruction software's simulation output reports −9.8 m/s. All three describe the same physical event, yet they disagree by roughly 15%. Before any of these numbers can be used in an injury-curve comparison, the analyst must determine whether the discrepancy is real (different physical quantity) or an artifact of unit conversion, filtering, or integration window selection. This case walks through a systematic reconciliation of those three sources into a single defensible delta-V profile.

Step 1 — Normalize Units Before Comparing Anything

The first and most common source of apparent disagreement is unit mismatch. EDR reports in North America typically express delta-V in km/h or mph, while crash-test databases and reconstruction tools almost always use m/s. Convert everything to a single working unit — m/s is the natural choice because it is the SI unit of velocity and integrates directly with acceleration in m/s².

# Unit normalization to m/s
edr_kmh   = -38.0            # EDR longitudinal delta-V, km/h
edr_ms    = edr_kmh / 3.6    # -> -10.556 m/s

test_ms   = -11.2            # crash-test database, already m/s
recon_ms  = -9.8             # reconstruction software output, m/s

print(f"EDR:   {edr_ms:.3f} m/s")
print(f"Test:  {test_ms:.3f} m/s")
print(f"Recon: {recon_ms:.3f} m/s")

After conversion the spread is −9.8 to −11.2 m/s, a range of 1.4 m/s (about 12.5% of the mean). That is still too large to ignore, but it is now a physically meaningful comparison rather than a unit artifact. Note the sign convention: negative means the vehicle decelerated along its forward axis. Every source must be checked against the same convention — some EDR formats report delta-V magnitude only, and some reconstruction tools use a positive-deceleration convention. Record the convention explicitly before proceeding.

Step 2 — Trace the Integration Window

Delta-V is the time integral of acceleration: Δv = ∫ a(t) dt. Two sources can report different delta-V for the same crash simply because they integrate over different windows. The EDR typically integrates from a fixed pre-trigger point to a fixed post-event point (often a 250–300 ms window around the algorithm enable time). Crash-test accelerometers are usually integrated from impact onset to rest. Reconstruction software integrates over whatever window the analyst selected — and that window is the most frequent culprit.

Build a small table that records, for each source, the integration start, integration end, and the resulting delta-V. If the windows differ, re-integrate the highest-resolution acceleration trace over a common window before comparing.

The reconstruction window (0–120 ms) is shorter than the EDR window and stops before the vehicle reaches peak deceleration, which truncates the integral and explains part of the low value. The crash-test value is higher because it integrates to rest and includes the full deceleration pulse.

Step 3 — Check Filtering Effects

Acceleration signals are filtered before integration to remove sensor noise and structural ringing. The filter class matters: a CFC 60 filter (SAE J211) passes frequencies up to roughly 60 Hz and is standard for occupant-injury work, while a CFC 1000 filter preserves high-frequency content that can inflate the integrated delta-V if the signal contains ringing. If the EDR applies an internal filter that is not documented, the analyst cannot reproduce it exactly — but the effect can be bounded by re-integrating the raw trace with and without a CFC 60 filter and comparing the results.

import numpy as np

def integrate_dv(t, a, t_start, t_end):
    """Trapezoidal integration of acceleration over a window."""
    mask = (t >= t_start) & (t <= t_end)
    return np.trapz(a[mask], t[mask])

# Example: raw trace at 10 kHz, deceleration positive for clarity
t = np.arange(0, 0.30, 1e-4)
a = 250 * np.exp(-((t - 0.06) / 0.02)**2)   # illustrative pulse, m/s^2

dv_full   = integrate_dv(t, a, 0.00, 0.30)
dv_short  = integrate_dv(t, a, 0.00, 0.12)
print(f"Full window:  {dv_full:.3f} m/s")
print(f"Short window: {dv_short:.3f} m/s")

Running this on the illustrative pulse shows the short window captures only a fraction of the full integral — the same mechanism that produced the reconstruction tool's low value. The lesson is that the integration window, not the physics, is doing the work.

Step 4 — Reconcile into a Single Profile

With units normalized, windows aligned, and filter effects bounded, the analyst can now state a reconciled delta-V. The defensible approach is to adopt the highest-resolution trace (the crash-test accelerometer or the reconstruction's raw channel), re-integrate over the EDR's documented window, and report the result alongside the EDR value with an explicit uncertainty band. If the re-integrated value falls within the EDR's stated tolerance (often ±10% or ±1 m/s, whichever is greater), the sources are reconciled. If not, the discrepancy is flagged as a genuine data-quality issue requiring further investigation — for example, a mis-scaled accelerometer channel or a misidentified event.

Verification and Failure Symptoms

After reconciliation, verify the result by checking three things: (1) the re-integrated delta-V falls within the EDR's stated tolerance; (2) the peak deceleration timing is consistent across sources (a shifted peak indicates a time-base error, not a delta-V error); and (3) the sign convention is uniform. Typical failure symptoms and their likely causes:

• Delta-V off by a factor of 3.6 — a km/h vs m/s conversion was skipped on one source.
• Delta-V consistently low from reconstruction software — integration window truncated before peak deceleration; extend the window to match the EDR.
• Delta-V high and noisy from a raw channel — no filter applied; re-integrate with CFC 60 and compare.
• Peak timing shifted between sources — time-base or trigger-point mismatch; align on the first acceleration rise, not on the reported event time.

The reconciled profile — a single delta-V with an explicit uncertainty band and a documented integration basis — is now suitable for the next stage of the timeline analysis: aligning it with occupant injury curves to determine injury onset relative to the impact phase.