The Falling Droplet
A single blood drop leaves its source on a ballistic path.
- ~50 µL: Typical drop volume (from a wound or weapon)
- ~25 ft/s: Terminal velocity (reached after ~1.5 m fall)
- Sphere: Drop shape in flight (surface tension dominates)
- 0–90°: Impact angle range (measured from surface plane)
Why drops stay round in flight
Surface tension pulls a falling drop into a near-perfect sphere.
Impact angle defined
The angle between the flight path and the surface it strikes.
Gravity sets the approach speed
Fall distance and gravity together set impact velocity.
Impact and Stain Formation
On contact the sphere flattens, spreads, and leaves a directional mark.
- ~1 ms: Impact timescale (sphere to stain)
- Radial: Spine formation (points away from travel)
- Common: Satellite spatter (small droplets break off)
- High: Surface texture effect (rough surfaces add scalloping)
Flattening on contact
Kinetic energy spreads the sphere into a thin stain.
Directional spines
Scalloped edges and spines point toward travel direction.
Angle shapes the outline
Shallow angles stretch the stain; steep angles keep it round.
Recording the Stain Shape
Analysts measure the stain's width and length with calipers.
- Minor: Width axis (perpendicular to travel)
- Major: Length axis (along direction of travel)
- Digital calipers: Measurement tool (or calibrated photo scale)
- 1.0: Ratio at 90° (width equals length)
Two axes, one ratio
Width divided by length encodes the impact angle.
Elongation at shallow angles
Low-angle impacts produce long, narrow ellipses.
Circularity at steep angles
Near-90° impacts leave almost circular stains.
Calculating the Impact Angle
The arcsin formula converts stain shape into a source angle.
- sin θ = W/L: Core formula (width over length)
- θ = arcsin(W/L): Solved for angle (inverse sine)
- ±0.5 mm: Input precision (typical measurement error)
- ~2–5°: Angle error propagation (from measurement noise)
Where the formula comes from
A sphere hitting at angle θ projects an ellipse of ratio sin θ.
Solving for θ
Taking arcsin of the width-to-length ratio isolates the angle.
Sources of error
Blurred edges and irregular stains reduce accuracy.
Locating the Blood Source
Directionality lines from many stains cross at one origin point.
- 3+: Minimum stains needed (for a reliable convergence)
- Stringing / trigonometry: Method name (physical or digital)
- Area of origin: Output (3D point in space)
- HemoSpat software: Modern tool (automates the geometry)
Directionality lines
Each stain's long axis points back toward its source.
Convergence in 2D
Multiple lines intersect at one point on the surface plane.
Height from the angle
Impact angle and distance give the source's height above the floor.
Courtroom use
Area-of-origin evidence helps reconstruct a crime scene.