Part of Lesson Plan: Blood Spatter - Understanding the Clues
Activity Overview / Details
Think back to your lab. Remember that when the juice dropped straight down it formed a sun-like pattern on the paper? If a drop of liquid such as juice or blood hits a relatively smooth object at 90 degrees, it will form a circular stain. If the surface is hard, like ceramic or glass, the edges will be clearly defined. If the surface is merely firm, like cardboard or paper, the stain will have rays around its edge. The closer the stain of a single drop is to a circle, the closer to 90 degrees was its angle of impact.
Now, think of the stain that you made for category 2, blood splashes. It was elongated. One edge of the stain was relatively smooth. The other edge was narrower and had a distortion, like one or more rays extending from it. In your mind draw an imaginary line down the length of the blood stain starting at the smooth edge and stopping at the rayed edge. This is the "direction of travel" of the blood splash that left the stain. It points, in two dimensions only, towards the source of the blood. If you do this with several drops of blood in the same stain pattern we call the area where the lines cross the area of convergence. This is a two-dimensional representation. To actually find where the source of the blood was, we need three-dimensional directions. Believe it or not, the third direction is written in the blood, if you know how to read it.
We begin by looking at the shape of a drop of liquid in flight. When we looked at the juice dangling from the eyedropper it was teardrop shaped. However, when it detached and started falling, it formed a sphere, like a ball. That means that the diameter of the drop was functionally consistent and equal in all directions within the drop. Think of the diameter as a line between two surface points we will call "A" and "B" and that line, by definition, passes through the center of the drop. Now visualize this particular line as being perpendicular to its direction of travel. Point "B" is the first portion of the drop to come in contact with the surface it hits. Freeze that image in your mind. See the line "AB" extending up from point "B" as one edge of a right triangle that is in the process of being made.
The portion of the drop that we called Point "A" continues on its original trajectory until it strikes the surface. We will call that point of contact, "Point C." We now can construct our triangle. We have line "AB" as one side, line "AC" is another side, and the length of our stain, which is line "BC," is the hypotenuse of the triangle.
As you know, the interior angles of a triangle add up to 180 degrees. As we visualized our triangle, angle A, formed at the intersection of lines AB and AC is 90 degrees. That leaves 90 degrees to divide up between the other two angles. As line "BC" is our hypotenuse, then it follows that line "AB" is the opposite side and line "AC" is the adjacent side. By dividing the length of the opposite side by the length of the hypotenuse, we discover the ratio which is known as the sine.
Find the arc sine to this ratio and it tells you the angle of impact. For simplicity's sake I have attached a table to this lesson. Look up the ratio on the table and read the angle in degrees. Alternately you can go to http://www.rapidtables.com/calc/math/Arcsin_Calculator.htm or using Excel input =degrees(asin(0.n)). Substitute your ratio for the "n" and you will get the angle in degrees.
To explain arc sine further you will find the logic spelled out in a trigonometry textbook.
Now, let’s look more closely at the stain.
Materials / Resource
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