Identifying the Height of Victim and Subject

Part I.  Now it's time to determine the height of some bones found at the crime scene  using the osteometric board. Osteometric Board

The osteometric board is used to make linear measurements on bones, especially long bones that are larger than a sliding caliper can measure.  The units are centimeters, which must be converted to millimeters for comparison with published tables of metric data.  The level of accuracy is 1 mm but you can estimate to 0.1 mm.

  1. Open the osteometric board by sliding the right end of it to the right.
  2. Gently place the bone to be measured in the board.  If the bone is very fragile, lay it on a piece of bubble wrap (but be sure the bubble wrap does not interfere with the instrument.)
  3. Very slowly and carefully slide the right end to the left to close the board to the end of the bone.
  4. Read the measurement.  The numbers are centimeters and the tick lines between the numbers are millimeters.  You have to estimate the tenths of a millimeter.  For example, your answer might be 45.65 cm.
  5. Slide the board to the right again to open it up.
  6. Remove the bone from the osteometric board.
  7. Close the osteometric board.
  8. Record the measurement in cm. 
  9. Use the information below to determine the height of the person to whom the bones at the crime scene belong.

Now for the harder part...analyze the measurements:

MATHEMATICS IN FORENSIC SCIENCE

Knowing the exact physical dimensions of a victim of a crime is extremely useful in identifying the victim. When a skeleton is found, a forensic scientist uses the lengths of certain bones to calculate the height of the living person.

 All measurements are in centimeters.

 These calculations below can be used on the femur, tibia, fibula, humerus, radius to determine height of males or females .

Male

2.238 (bone length) + 69.089 +/- 3.27cm = F (femur)

2.392 (bone length) + 81.688  +/- 3.27cm = T (tibia)

2.970  (bone length) + 73.570 +/- 3.27cm =  H (humerus)

3.650 (bone length) + 80.405  +/- 3.27cm = R (radius)

Female

2.317 (bone length) + 63.29  +/- 3.27cm =  F

 2.533 (bone length) + 72.572 +/- 3.27cm =T

3.144 (bone length) + 64.977  +/- 3.27cm =H

3.876 (bone length) + 73.502  +/- 3.27cm = R

After the age of thirty, the height of a person begins to decrease at the rate of approximately 0.06 cm per year. This shrinkage must be considered when the age of the victim is known.

applications 

Practice Problems

1. The femur of a 25-year-old male measured 49.7 cm. What was the height of the person?

          2. The tibia of a 32-year-old female measured 33.5 cm. What was the height of the person?

Answers.

1. 180.31 cm.  Converted to inches that is centimeters x 0.3937 = 70.98 inches and then convert to feet  inches divided by 12 = 5 feet 9 inches tall

2. 157.4 cm  Converted to inches that is  61.9 inches and then convert to feet  5 feet 1 inches tall.

Source: George KnLA. "Mathematics in Forensic Science." .mathematics Teacher February 1981): 31-32.

Part II.  Determining the Height of the Suspect(s) and victim from Footprints

This is another method that can be used to determine height if bones are not available.

 Follow the procedure to determine whether or not the bones found at the crime scene and analyzed above could be the bones of the victim or not.

After doing both procedures determine which is most accurate and therefore which you choose to use in analyzing the data and writing your conclusion.

Technique courtesy of http://www.cyberbee.com/whodunnit/foot.html

THE FEET CAN MEASURE THE HEIGHT

The bones of the feet can tell a lot about a person. What do feet reveal about a person's height? Forensic anthropologists team up with law enforcers to help solve crimes.

Bones of the feet can reveal an interesting fact about an individual. Let's combine math with forensics to see how.
List the individuals name, height, and foot length.
  1. Have each of your  CSI team  remove their shoes and measure their height by standing against the wall covered with a piece of white butcher paper, placing a ruler on the top of the head and using a pencil to mark the paper.  Now use the tape measure to determine the height by measuring from the ground to the chalk mark. Record.
  2. Measure the length of each of your CSI team members  left foot from the wall to the tip of the big toe.  Record.
  3. Examine the numbers. Do you see a pattern?
  4. Divide the length of each person's left foot by his/her height. Multiply the quotient by 100. What do you get?
The results of your calculations should be about 15, illustrating that the length of a person's foot is approximately 15 percent of his or her height.

When a forensic scientist has the length of a foot, the forensic scientist will be able to approximate the height of the individual.

1.  Use the footprints obtained at the crime scene to determine the height of your suspect.

Use this proportion (or the one you obtained from your calculations)  for your calculations: Example 15/100 = Length of Foot/x (person's height)

2.  Record the data