Key concepts
Height
Distance
Walking
Estimation

Introduction
Do you ever find that you need to walk faster to keep up with some people whereas you have to decrease your pace to walk with others? This is likely because of the difference in leg length between you and the person you are walking with. In this science activity you'll get to investigate just how much faster or slower different people walk, and see if you can use the relationship between a person's walking pace and their height to estimate your own height.

Background
A pedometer is an instrument that is often used by joggers and walkers to tell them how far a distance they have gone. On some pedometers, when a person sets the instrument to record an outing they must enter their height into the pedometer to get an accurate reading.

Why is height an important variable for measuring how far a person has walked? One part of the answer has to do with ratios. Our bodies have many interesting ratios. For example, when your arms are outstretched, the distance from the tip of one hand to the other is usually about equal to your height. There are other ratios as well, each describing how one part of the body relates to another in size. Because the length of a person's legs is related to a their height by a ratio, the latter will affect how long of a step they take. The longer each step, the more distance a person travels when taking the same number of steps while walking, jogging or running. This ratio, combined with the motions involved in walking and running, is used by pedometers to calculate traversed distances.

Materials
• 20 feet of straight sidewalk or hallway
• Sidewalk chalk or two small objects to mark off 20 feet of distance
• Tape measure
• At least three volunteers to walk a short distance (Ideally, they should be different heights.)
• Pen or pencil
• Scrap piece of paper
• Calculator

Preparation
• Find a place that has 20 feet of straight sidewalk or find a straight hallway that is at least 20 feet long.
• Using a tape measure, measure out a distance of 20 feet and mark the beginning and end points with a piece of sidewalk chalk (if you are using a sidewalk) or mark them each with small objects that will not be moved (if you are using an indoor hallway).

Procedure
• Measure a volunteer's height. How tall are they? Write their height down on a scrap piece of paper.
• Ask the volunteer to walk from the beginning to the end of the 20-foot course you marked at a normal pace and stride. As they do, count the number of steps they take. How many steps did you count? Write down the answer.
• Repeat this process for at least two more volunteers. How tall is each volunteer? Did they take a similar number of steps or was there variation? Be sure to write the results down.
• For each volunteer, figure out their step length (in feet) by dividing 20 feet by the number of steps each took. What was the step length for each volunteer?
• For each volunteer, figure out their ratio of step length to height by dividing their step length by their height (both in feet). What numbers do you get for this ratio? Are they similar for the different volunteers or is there variation? Average the step length to height ratio for all of your volunteers. Be sure to write your answers down.
• Lastly, use your results to estimate your own height. Walk from one end to the other of your 20-foot course while counting the number of steps you take. Divide 20 feet by the number of steps you took. What was your step length? Then divide your step length by the volunteers' average ratio of step length to height. Based on your data, what is your estimated height?
Extra: Try this activity with a greater number of people. For example, you could go to a park with a jogging path or a similar location with an adult where you can ask for volunteers as they pass by. Try to collect data from at least 10 volunteers. Is there much variation in the ratio of step length to height when comparing many people? Does collecting more data make your height estimation more accurate?
Extra: You could do this activity again, but this time have volunteers walk slowly, moderately fast or very fast. How does a person's speed affect their step length?
Extra: The human body has many other interesting ratios, such as those mentioned in the Background of this activity. You could look into other ratios in the human body and come up with an activity like this one to investigate them. See the More to Explore section for relevant resources. What other ratios are consistently found in the human body from person to person?

Observations and results
When you divided your volunteers' step lengths by their heights, did you get a ratio value close to 0.4? Were you able to roughly estimate your height based on this, accurate to within a couple inches?

The measurements of a pedometer are based on the hypothesis that all people have common ratios and proportions, even if they are different heights. In this activity you should have found this hypothesis to be pretty accurate. On average, adults have a step length of about 2.2 to 2.5 feet. In general, if you divide a person's step length by their height, the ratio value you get is about 0.4 (with a range from about 0.41 to 0.45). This is why you can take a person's step length and divide it by about 0.43 to roughly estimate their height—the estimated height will likely be within two inches of (and probably much closer to) their actual height.

More to explore
Pedometers for Kids Track Physical Activity, from Peaceful Playgrounds
Simple Ratios of the Human Body, from Kim Moldofsky at Bedtime Math
How to Determine Stride for a Pedometer by Height and Weight, from Amy Sutton at the Houston Chronicle
Keeping Up, from Science Buddies

This activity brought to you in partnership with Science Buddies