"""
Vascular bleeding visibility onset for an EXPOSED neck wound (no fabric).

Physics:
  - Pressurized jet from vessel: v = sqrt(2 P / rho)  (Torricelli)
  - Volumetric flow: Q = v * A_hole
  - Time to a PHOTOGRAPHICALLY RESOLVABLE blood volume on the skin surface:
    t_visible ~ V_visible / Q
  - V_visible: ~0.1-1 mL for a confidently identifiable blood bolus at
    typical video resolution and field of view

Sources:
  - Carotid systolic: 110-140 mmHg (Guyton & Hall Medical Physiology)
  - Carotid diastolic: 70-90 mmHg
  - Jugular venous: 5-12 mmHg
  - Blood density: 1060 kg/m^3
  - Wound channel diameter for ideal jet: ~bullet caliber 7.6 mm
"""
import numpy as np

rho = 1060.0
mmHg = 133.322

cases = [
    ("Carotid (systolic, peak)",   130, 8.0),
    ("Carotid (mean arterial)",    93,  8.0),
    ("Carotid (diastolic, trough)", 80, 8.0),
    ("Jugular (mean venous)",       8,  8.0),
]

print(f"{'Case':35s}  {'P (kPa)':>8s}  {'v_jet (m/s)':>12s}  {'Q (mL/s)':>9s}  {'t_0.1mL (ms)':>13s}  {'t_1mL (ms)':>11s}")
print("-" * 110)
for label, P_mmHg, hole_mm in cases:
    P = P_mmHg * mmHg
    v_jet = np.sqrt(2 * P / rho)
    A_hole = np.pi * (hole_mm * 1e-3 / 2)**2
    Q = v_jet * A_hole * 1e6   # mL/s
    t_01mL = 0.1 / Q * 1000
    t_1mL = 1.0 / Q * 1000
    print(f"{label:35s}  {P/1000:>8.1f}  {v_jet:>12.2f}  {Q:>9.1f}  {t_01mL:>13.2f}  {t_1mL:>11.2f}")

print()
print("OBSERVED: 440 ms delay between shirt movement (impact) and first visible blood")
print()
print("EXPECTED for direct skin observation, no fabric:")
print("  Carotid (any pressure):  visible blood within 1-5 ms")
print("  Jugular (venous):        visible blood within 5-15 ms")
print()
print("RATIO observed/expected: 30x to 440x longer than physics predicts.")
print()
print("Cardiac cycle at HR=60 bpm: 1000 ms (440 ms = 44% of one cycle)")
print("Cardiac cycle at HR=72 bpm: 833 ms (440 ms = 53% of one cycle)")
print()
print("Possible explanations (the page should lay these out neutrally):")
print("  1. No major vascular structure struck in the wound channel")
print("     -> would also explain absence of ballistic back-spatter")
print("  2. Vascular pressure already absent before t=0 (pre-existing arrest)")
print("  3. The 't=0' reference point (first shirt movement) is not the")
print("     true moment of impact")