Lab 5

Faculty Notes

Blood Spatter Analysis

Introduction

Bloodstain pattern analysis is a very broad topic. This laboratory deals with only a few of the basic topics involving impact bloodstain patterns on smooth surfaces. After an introduction to the terminology of blood spatter, students investigate two issues – how to determine possible wounding agents, and how to locate the victim's general location at the time of wounding.

While working on this lab, the students will use the following mathematics tools:

1. the circle and ellipse
2. the sine, tangent, and the arcsine
3. estimation of angle measurements
4. frequency distribution
5. scatter plots for a set of data and determining regression curves
6. the metric and English systems of measurement and
7. different coordinate planes.

The students may discover that other mathematical tools are useful in investigating this problem.

In order to simplify the mathematics to the pre-calculus level, several assumptions were made. First, all impact surfaces are assumed to be smooth. Second, all oscillations of the blood drop during flight were ignored; therefore, the drop remains spherical when it hits the surface. Third, the diameter of the blood drop (its width) remains the same after it impacts a surface. Finally, the impact angle calculated using the inverse sine function is accurate to within 5 to 7 . In criminal cases, this is usually accurate enough to verify or refute a suspect's account of the events.

Due to sensitive nature of this topic, we have chosen not to include pictures of real bloodstain patterns in our lab. If you wish to do so, you can find pictures in the sources listed in the bibliography. These photographs give real life illustrations of the topics discussed in the lab. In particular, some photographs illustrate very clearly the effect of the wounding agent's velocity on the size of the resulting blood spatter.

Due to the risk of contamination by viruses or bacteria, it is imperative that students be prohibited from using human or animal blood samples in the experimental portion of this lab. We recommend that any violation of this policy result in severe consequences such as failure of the course or expulsion from the Math Works Club. On the advice of a forensic expert, we recommend using milk (food coloring optional) to simulate blood in the experimental portion of this lab. For purposes of impact angle analysis, most liquids act similarly.

Following are some specific comments relative to the lab exercises in the Model Development section.

Due to inaccuracies in measuring, students may have different results in Table 1. In Table 2, students are given the ranges for spatter size in millimeters but must research the corresponding velocity ranges and wounding agents. There is an interval gap in velocity range between medium and high impact velocity. A similar interval gap occurs in Table 3, where the students are converting from millimeters to inches.

Part A       Directionality of a Bloodstain

In this material, the connection is made between the shape of a blood drop and the mathematical ellipse. The material is written with the assumption that students are already familiar with ellipses and with angle measurement. If this is not the case, you may need to guide students through some of the exercises.

Part B       Two-Dimensional Point of Convergence

To find the source of the blood, students need to collect two measurements. The first measurement is the point of convergence, which identifies the source in a two-dimensional plane such as the floor. Allowing for errors in measurement, students should get one point of convergence in the first sketch of bloodstains and two points of convergence in the second sketch of bloodstains.

Part C       Angle of Impact

The second measurement needed to identify the source of blood is the angle of impact. This measurement, combined with the point of convergence, will locate the source in three-dimensional space. The purpose of the milk experiment is to help students predict the shape of a bloodstain from the angle at which the blood drop strikes a two-dimensional surface. The addition of food coloring is optional and will not affect the resulting fluid motion. Students may need to perform the experiment more than one time to obtain useful results. The students change the incline of the paper to simulate different angles of impact. You may need to clarify that the paper actually represents the floor in this experiment.

The width/length ratios collected in Table 4 should generally increase with the angle of impact up to a maximum value of 1. With the visual support of the scatter plot, the students should discover that the sine function fits the pattern reasonably well.

Due to the nature of experimental data, students may find that when they perform the regression analysis there are other functions that fit the data better than the sine function. However, the sine function may be more useful for the purpose of determining the angle of impact. The exercises involving the angle of impact and the width and length measurements can be calculated using the right-triangle definition of the sine function.

The exercises involving the geometric diagram of the angle of impact are designed to help the students realize that angle C is equal to the angle of impact. The resulting equation for the impact angle then matches the equation derived earlier from data involving the width to length ratios of the bloodstain ellipses.

Part D       Determining the Point of Origin

Using the angle of impact, students can now determine the height of the blood source above the point of convergence. A right triangle can be constructed with the height above the target surface as one leg and the horizontal distance from the point of convergence to the blood source as the second leg. Students can solve for height by substituting the distance from the blood source and the angle of impact into the tangent definition. When applying this process to the bloodstains in Exercise 36, many students may determine one point of convergence but more than one height. This should lead to differing creative interpretations.

We enjoyed discovering the discipline of Bloodstain Pattern Analysis. We hope you will do the same!