The spatter that was not there

The Question

What the physics requires

The prosecution's case rests on the assertion that a single .30 caliber rifle round, fired from the rooftop position, struck the victim in the neck. If that account is correct, the resulting hydrodynamic event has well-characterized signatures: an outward-traveling cone of fine blood mist from the entry wound (back spatter), a possible forward-directed cone of larger droplets ejected with the bullet wake (forward spatter, subject to modeling assumptions discussed below), and visible vascular bleeding onset within tens of milliseconds for any major neck vessel.

The back-spatter prediction and the bleeding-onset prediction follow directly from the peer-reviewed physics with no adjustable modeling knobs. The forward-spatter prediction is more sensitive: under standard single-particle drag, model droplets do not reach a backdrop 61 cm downstream at all, and a 2-phase-jet wake-drag reduction must be applied for the model to predict backdrop deposition. This page reports both, and this section is explicit about which finding depends on which assumption.

These signatures have been quantitatively characterized in the peer-reviewed forensic-fluids literature, primarily by Comiskey, Yarin, Kim and Attinger between 2016 and 2019.

This page applies those models to the parameters of the prosecution's stated scenario, generates the predicted patterns, and compares them with what the recorded evidence actually shows. The full Python pipeline is downloadable below for independent verification. Every modeling knob is exposed at the top of the source code.

The Model

Three independent hydrodynamic predictions

The analysis combines three physics models, each derived from peer-reviewed work. Each predicts a specific, observable signature. Each is independent of the others.

Model 1 — Back spatter through the entry wound

Comiskey, Yarin, Kim & Attinger 2016 (Phys. Rev. Fluids 1, 043201) treats a slender conical bullet penetrating a vascular tissue surface. The bullet's potential-flow field accelerates blood at the free surface outward (against the bullet direction), and Rayleigh–Taylor instability of that accelerated surface determines drop size and count.

Model 2 — Forward spatter through the exit wound

Comiskey, Yarin & Attinger 2017 (Phys. Rev. Fluids 2, 073906) treats forward (downrange) spatter from the bullet wake exiting tissue. The same Rayleigh–Taylor framework applies, with a different potential-flow geometry. Drag deceleration over the 61 cm flight to the backdrop is then computed via Reynolds-dependent drag coefficient (Eq. 25):

Model 3 — Visible bleeding onset

Independent of the ballistic models, the time from wounding to visible blood on the skin surface is governed by pressurized flow through the wound channel. Torricelli's equation for jet velocity from a vessel at pressure P:

Prediction 1 — Entry Shirt

What the shirt should look like

The model predicts approximately 4.4 million back-spatter droplets of 27–84 µm diameter, ejected in a wide ~57° cone toward the shooter, depositing on any surface within centimeters of the entry wound. With the shirt 5 mm in front of the skin and the wound site exposed, essentially every droplet reaches the fabric within 1–2 ms.

Drop diameters spread on impact according to the Weber/Ohnesorge stain-spreading law (paper Eq. 29), producing visible stains of 120–240 µm. The dominant pattern is a dense radial halo of fine, individually resolvable stains extending 2–3 cm from the bullet hole, fading into scattered satellite drops at the periphery.

Exhibit BS-01

Predicted entry-shirt pattern

3,000 individually rendered stains, scaled and oriented per the impact velocity and angle from each subfamily. Central black region is the predicted bullet perforation (7.6 mm). Scorching halo represents thermal/contact transfer. The dense 2–3 cm halo of fine elongated stains is the back-spatter signature. Scale bar 2 cm.

Exhibit BS-02

Droplet size distribution and pattern statistics

Four-panel diagnostic: predicted droplet size distribution from the Rayleigh–Taylor instability, predicted stain radial distribution at the close shirt and far backdrop ranges, and the 2D pattern projection.

Prediction 2 — Forward Spatter (modeling-dependent)

What the backdrop might have shown

The forward-spatter model integrates thousands of individual droplets from the bullet wake through Reynolds-dependent quadratic drag over a 61 cm gap to a downstream backdrop. The predicted pattern is sensitive to how drag on trailing droplets in a dense spray is modeled.

Exhibit BS-03 — WAKE_FACTOR=0.2 scenario

Predicted backdrop pattern under wake-drag reduction

Multi-panel diagnostic of forward-spatter trajectory integration with WAKE_FACTOR=0.2 applied. Top left: free-surface velocity v_z(r) and droplet diameter l^*(r). Top right: number-weighted size distribution. Bottom: radial stain distribution and 2D pattern with color encoding impact speed. Peak stain density at 15.7 cm, consistent with cone projection. Under standard drag (WAKE_FACTOR=1.0), this figure would show an empty backdrop.

Prediction 3 — Bleeding Timing

The 429–461 millisecond anomaly

Frame-by-frame analysis of video2_1.mp4 (30 fps), the closest available eyewitness recording with an unobstructed view of the seated subject, establishes the bleeding-onset interval directly from the source video. Three reference frames anchor the measurement:

Exhibit BS-04 — video2_1.mp4 timing reference

Frame 68 → Frame 81 / 82: 429–461 millisecond onset interval

Frame 68 (t = 2.239 s): subject seated, shirt clean, no posture distress; this frame defines the t=0 reference. Frame 70 (+66 ms): posture beginning to shift; no blood visible. Frame 81 (+429 ms): first mark appearing on the right side of the neck. Frame 82 (+461 ms): blood unambiguously visible. Throughout the 461 ms window, the wound site is on exposed skin with no fabric obstruction.

For comparison, Torricelli–Bernoulli flow through an open wound channel of bullet diameter, from a vessel at typical physiological pressure, predicts the following:

For an exposed neck wound (no fabric to wick through), the expected delay to a photographically resolvable bloodstain is 1–5 ms for carotid involvement, 5–15 ms for jugular involvement. The observed 429–461 ms interval is 30× to 110× longer than physics predicts.

Three explanations are consistent with the observed timing:

Methodology

How the pipeline works

The complete analysis is implemented in approximately 350 lines of Python (NumPy + SciPy + Matplotlib). The core computation has three phases: subfamily generation (discretizing the continuous distribution of drop sizes into rings of constant r/a), trajectory integration (vectorized RK2 with Reynolds-dependent drag and adaptive sub-stepping per drop), and stain rendering (Weber/Ohnesorge spreading with radial-direction elongation).

Subfamily generation

For each ring i defined by inner radius b_i and outer radius b_i+1 (geometrically spaced from 1.05a to 5a), the closed-form mass integral (Eq. 23 of the 2017 paper for forward spatter; Eq. 24 of the 2016 paper for back spatter) gives M_i. The droplet diameter l_i^* is evaluated at the bin midpoint. The number of drops per bin is then n_i = M_i / (ρ π l_i^*3 / 6).

def back_subfamilies(n_rings=80):
    h = h_penetration
    r_min = theta_tip * h * 1.05
    r_max = 0.05
    r_edges = np.geomspace(r_min, r_max, n_rings + 1)
    r_mid = np.sqrt(r_edges[:-1] * r_edges[1:])

    # Eq. 21: A = -theta^2 V^2 / r
    A_mag = theta_tip**2 * V**2 / r_mid

    # Eq. 22: l* = 2 pi w / sqrt(rho |A| / 3 sigma)
    l_i = 2*np.pi * w_slender / np.sqrt(rho * A_mag / (3 * sigma))

    # Eq. 23: v_z = -theta^2 V (h/r)
    v_z = theta_tip**2 * V * h / r_mid

    # Eq. 24: M_i = 2 pi rho (h theta)^2 (b_i+1 - b_i) c
    db = np.diff(r_edges) / h
    M_i = 2 * np.pi * rho * (h * theta_tip)**2 * db * c_slender
    M_i *= (target_volume * rho) / M_i.sum()

    n_i = M_i / (rho * (4/3) * np.pi * (l_i/2)**3)
    return r_mid, l_i, v_z, n_i, M_i

Vectorized trajectory integration

Each drop's trajectory in 3D with quadratic drag and gravity is integrated using midpoint (RK2) stepping. All drops are integrated simultaneously as NumPy arrays. Per-drop step size is adapted to each drop's stopping time, so a 20 µm drop and a 400 µm drop both integrate to acceptable accuracy without forcing the small-drop step on every drop. Reynolds-dependent drag coefficient (Eq. 25) and a phenomenological dense-spray wake-drag-reduction factor are applied.

Summary

Two robust null observations, one modeling-dependent observation

The peer-reviewed hydrodynamic models, applied to the prosecution's stated impact parameters, predict a dense back-spatter halo around the entry wound and visible bleeding within tens of milliseconds for any major neck vessel. Neither is present in the recorded evidence. Both predictions are robust to the modeling knobs discussed in Section 07 (back-spatter geometry depends only on the potential-flow field and Rayleigh–Taylor instability, both of which act within millimeters of the wound; bleeding-onset timing depends on Torricelli jet velocity and a stated resolvable-volume threshold). The 429–461 ms observed bleeding-onset delay is 30× to 110× longer than the physics predicts for any major vessel involvement.

The third prediction discussed on this page — a forward-spatter cone on the downstream backdrop — is more modeling-dependent. Under standard single-particle drag, no droplets reach the 61 cm backdrop and no backdrop pattern is predicted; under a 2-phase-jet wake-drag reduction, approximately 22 million drops are predicted to deposit in a ~16 cm-radius pattern. The recorded backdrop shows no such pattern. This absence is consistent with either the wake-drag-reduction model being inapplicable at this geometry, or with the wound-mechanism alternatives discussed in Section 06. The forward-spatter absence does not, on its own, distinguish between those possibilities. The substantive forensic weight of this page rests on the two robust null observations.

The simplest explanation that accounts for both robust null observations is that the wound mechanism was not what the prosecution claims. A localized internal energetic event — documented elsewhere in this site through dense optical flow, gas-release imaging, acoustic source localization, and shooter-position analysis — produces no high-velocity bullet wake through tissue and no major vascular jet, and would not be expected to produce the predicted back-spatter halo or rapid bleeding onset.

This page does not assert what did happen. It establishes what the physics requires if the prosecution's account is correct, and documents the failure of the robust requirements against the recorded evidence. The forward-spatter analysis is documented for completeness with its modeling assumptions made explicit; the back-spatter and bleeding-onset findings are what the page rests on.