AGR-CSI53-05 · Lesson 5 · 13 clock hours · lab
Area of Origin: Stringing and Trigonometric Methods
Objective. Students will use convergent stringing and basic trigonometry to determine the two-dimensional area of convergence and estimated height of origin for a simulated blood-spatter scene
⚠ Pending professional review
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What Is Area of Origin?
When blood strikes a surface, it leaves stains whose shape, size, and direction reveal where the blood came from. Investigators distinguish two related concepts. The area of convergence is the two-dimensional zone on a floor or horizontal plane where the paths of individual stains appear to meet when you project them backward along their long axes. The area of origin adds the third dimension — the estimated height above that convergence zone from which the blood was shed. Together, these two findings help reconstruct the position of a victim, a wound, or a transfer event during a crime.
Determining area of origin is a core skill tested by the IAI Certified Crime Scene Investigator (CCSI) examination and is central to courtroom-ready documentation under any state evidence technician framework.
How Blood Stains Tell Direction
An elliptical bloodstain has a long axis and a short axis. The ratio of the short axis width to the long axis length gives you the sine of the impact angle. A stain that is nearly circular struck the surface at close to 90 degrees (nearly straight down). A stain that is very elongated struck at a low, glancing angle. The tail or satellite spatter, when present, points in the direction of travel. Always photograph each stain with a scale before touching or disturbing the surface.
Stringing: The Two-Dimensional Step
Stringing is a physical technique for finding the area of convergence.
1. Select stains. Choose at least six well-formed elliptical stains spread across the scene. Avoid stains that are smeared, overlapping, or whose long axis is unclear.
2. Measure and record. Using two fixed reference points (a corner, a doorframe), record the position of each stain's center in your field sketch. Note which end is the tail end.
3. Affix string. Anchor a length of colored string at the tail end of each stain and run it along the long axis of the stain, extending backward (opposite to the direction of travel) across the floor toward where the strings converge. Tape flag each string at the stain so you can identify it later.
4. Read the convergence. Where the strings cluster together is the area of convergence. It will rarely be a perfect single point; map the bounded zone where most strings cross and record its dimensions and position relative to your reference points.
5. Photograph from above. Use a stepladder or overhead vantage to photograph the full string layout. Include a scale and north arrow in the image.
If your strings do not converge, re-examine your stain selection. A stain whose long axis is misread will throw a string far off.
Trigonometry: Adding the Third Dimension
Once you have the area of convergence on the floor, you can estimate how high above that point the blood originated. This requires two pieces of information for each stain:
- Impact angle (α): calculated from the stain dimensions using `sin(α) = width ÷ length`.
- Horizontal distance (d): measured from the stain's position on the floor (or wall, converted to a horizontal equivalent) to the center of the convergence zone.
The height of origin is then:
> H = d × tan(α)
Where H is the estimated height, d is the horizontal distance, and α is the impact angle. Calculate H for each of your six or more stains and average the results. Outliers may indicate a stain that was not part of the primary event — note them but do not discard them without written justification.
Wall Stains and Projection
When stains appear on a vertical wall, the geometry changes slightly. You must determine the horizontal distance from the stain's location on the wall to the convergence point on the floor, and the vertical height of the stain on the wall. The trigonometric relationship still applies, but the "d" value is now the straight-line horizontal distance from the base of the wall below the stain to the convergence point. Measure carefully and document all intermediate measurements.
Documentation Standards
All measurements must be recorded in your field sketch at the time of collection — not reconstructed later. Use metric or US customary units consistently throughout a single case. Your written interpretation paragraph must:
- State the mapped convergence zone dimensions and location.
- State each impact angle used and the resulting height calculation.
- State your averaged height of origin.
- Acknowledge the margin of variation among individual stain calculations.
A finding that cannot be traced back to recorded field measurements will not survive cross-examination.
Safety in the Lab
Simulated spatter scenes use non-biological materials, but standard PPE habits must be practiced every time you process a mock scene, because the habits carry over to real scenes. Wear nitrile gloves and eye protection throughout. If any real biological material were present, a fluid-resistant gown and face shield would be required per OSHA Bloodborne Pathogens standard. Keep the floor clear of loose string that could cause a trip hazard, especially when moving with a camera or climbing a stepladder. A second person should steady any ladder used for overhead photography.
Key terms8
Area of convergenceThe two-dimensional zone on a surface where the projected long axes of multiple bloodstains meet when traced backward, indicating the general location directly below or at the blood source.
Area of originThe three-dimensional location from which blood was shed, combining the two-dimensional area of convergence with an estimated height above that zone.
Impact angle (α)The angle at which a blood droplet struck a surface, calculated as the arcsine of the ratio of the stain's width to its length; smaller angles produce more elongated stains.
StringingA physical technique in which strings are aligned with the long axes of selected bloodstains and extended backward to locate the area of convergence.
Long axisThe greatest length of an elliptical bloodstain, running in the direction of the droplet's travel; used for both directional interpretation and impact angle calculation.
Short axisThe maximum width of an elliptical bloodstain, measured perpendicular to the long axis; used together with the long axis to calculate impact angle.
Horizontal distance (d)The measured distance along the surface plane from a bloodstain's position to the center of the area of convergence; used in the trigonometric height-of-origin calculation.
Height of origin (H)The estimated vertical distance above the area of convergence from which blood was shed, calculated for each stain as H = d × tan(α) and then averaged across multiple stains.
Worked examples4
1. A bloodstain measures 18 mm long and 9 mm wide. What is the impact angle?
- Write the formula: sin(α) = width ÷ length
- Substitute values: sin(α) = 9 ÷ 18 = 0.500
- Find the angle: α = arcsin(0.500) = 30°
Answer: The impact angle is 30 degrees.
2. Using the stain from Example 1 (impact angle 30°), the horizontal distance from the stain to the center of the convergence zone is 52 cm. What is the estimated height of origin?
- Write the formula: H = d × tan(α)
- Identify values: d = 52 cm, α = 30°
- Find tan(30°) = 0.5774
- Calculate: H = 52 × 0.5774 = 30.0 cm
Answer: The estimated height of origin for this stain is approximately 30.0 cm above the convergence point.
3. A student calculates heights of origin from six stains as follows: 31 cm, 29 cm, 30 cm, 45 cm, 28 cm, 32 cm. The known drop height is 30 cm. Which value is most likely an outlier, and what is the average of the remaining five values? Does the remaining average fall within the required 20% tolerance?
- Identify the outlier: 45 cm is far from the cluster of 28–32 cm values; note it in writing but set it aside for averaging.
- Sum the remaining five values: 31 + 29 + 30 + 28 + 32 = 150 cm
- Average: 150 ÷ 5 = 30.0 cm
- Calculate 20% tolerance band: 30 cm × 0.20 = 6 cm; acceptable range is 24–36 cm
- Compare: 30.0 cm falls within 24–36 cm, so the result passes the check criterion.
Answer: 45 cm is the outlier. The average of the remaining five stains is 30.0 cm, which is exactly at the known height and well within the 20% tolerance band of 24–36 cm.
4. A stain on a wall is located 40 cm above the floor. The base of the wall directly below the stain is 65 cm from the center of the convergence zone on the floor. The impact angle determined from stain dimensions is 32°. What is the estimated height of origin above the floor?
- The horizontal distance d from the stain's base-of-wall position to the convergence center is 65 cm.
- Write the formula for height above the convergence plane: H_above_floor = d × tan(α)
- Calculate: H_above_floor = 65 × tan(32°) = 65 × 0.6249 = 40.6 cm
- Add the height of the stain on the wall (40 cm) to get total height of origin above the floor: Total H = 40 + 40.6 = 80.6 cm
- Note: the trigonometric component gives the height above the convergence point, and the stain height on the wall gives the vertical position of the stain itself; both are needed for wall stains.
Answer: The estimated height of origin is approximately 80.6 cm above the floor.
The math in this lesson1
Learners use arcsin(width/length) and H = d × tan(α) to estimate height of origin.
G-SRT.8
In class: Set up a pre-made simulated spatter scene on a floor and adjacent wall; students identify a minimum of six individual stains suitable for stringing, photograph them, and record stain locations with measurements from two fixed reference points · String the scene: students use colored string lines and tape flags to project the long axis of each selected stain back toward convergence; photograph the convergence zone from above and record the mapped area in a field sketch · Calculate height of origin using impact angle data from Lesson 4 methodology and the horizontal distance from stain to convergence point; present a written one-paragraph interpretation of the area-of-origin finding
Materials: Pre-set simulated spatter scene (card-stock stains affixed to floor and wall), colored string (minimum 50 ft), tape, tape measure, protractor, calculator, field sketch paper, camera
Check: Instructor compares student-mapped convergence zone to the known origin point; zone must encompass the true origin point; height calculation must be within 20% of the known drop height; written interpretation must reference specific measurements to pass
Practice check8
Answer each question, then check it. Nothing is recorded; this is your own practice.
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