Human Walking Speed

Course Outcome 5, Unit Outcome 2-1

Materials:

• writing utensil
• ruler or measuring tape
• at least 2m x 1 m of open floor space
• digital device with spreadsheet program
• digital device with internet access
• stopwatch or digital device with stopwatch feature

Observation

Not everyone has the same natural walking pace. It often appears that taller people have greater walking speed.

Question Generation

What is the variation in walking speed between individuals? Does height really affect natural walking speed in a predictable way?

Existing Knowledge Search

1) Spend a few minutes looking for an answer to the previous questions.

• Did you find any useful information from a reliable source? If so, provide the source(s) and summarize the information below.

Hypotheses Generation

2) Generate a quantitative hypothesis. Testing your hypothesis should provide information that helps to answer your question.

• If each person in the class measures their walking speed, then the variation in the speeds will be + ___________m/s around the average value.

3) Provide a qualitative hypothesis on how walking speed depends on height.

• If each person in the class measures their walking speed and height, then speed will be found to clearly __________________ as height increases.

4) Explain your reasoning in choosing how the speed will depend on height.

Experimental Hypothesis Testing

You will each measure your height and walking speed and use the combined class data to test your hypotheses.

Data Collection: Height

5) Find a way to measure your height. You may need to get creative to measure your height with limited equipment. For example, to measure your height with a only ruler and no assistant you could lay on the floor with your feet against the wall and drop a small object from the top of your head. Then use the ruler to measure from the wall to the object by successively marking the end and sliding the ruler along. Explain the measurement method you will use, including any difficulties you expect to encounter and how you will address them:

6) Estimate the uncertainty in a single measurement made with your method and explain your reasoning. (Hint: the uncertainty in a single measurement is not necessarily same as the precision in your instrument. For example, a ruler with marks every 1 mm can provide roughly 0.5 mm precision, but the uncertainty will much greater if your hands are shaking while you make the measurement).

7) Measure your height 10 separate trials and record in the chart below.

• Fill in the blank units with the unit you used and convert as necessary to get height in units.
• If you encountered a problem during a trial then record a note explaining the problem, repeat the trial, cross out the original value, and record the new value next to it.

8) Enter your data into a spreadsheet. Use the spreadsheet to calculate the average and standard deviation of the height values in meters and use a neighboring cell to label each. The video below demonstrates how to do this.

9) Record your average and standard deviation below:

10) Divide the standard deviation by the square root of the number (N) of samples you used in the average (). This is known as the Standard Error of the Mean.

11) In many cases (but not all) the SEM tells us the amount by which the our average value of our measurements might be different from the actual value. We often use the SEM an estimate of the uncertainty in result based on averaging many measurements. In that case we claim 68% certainty that the actual value is not different from the average of our measurements by more than the SEM. Ideally we would base our SEM on more than 10 values, but we will use only 10 in this learning situation to reduce the time needed to make the measurements.

• Using the SEM as your uncertainty in your height, write your average height along with uncertainty as : average value + uncertainty. Be sure to use the correct number of significant figures (ask for help or see Unit 3 as needed):

12) How does the uncertainty compare to the estimate of the uncertainty you made before measuring? If one is more than 5x the other, explain why you think your estimate was too high or too low.

Data Collection: Walking speed

13) Now you will need to measure your walking speed. Use Google Maps to identify a nearby building or landmark that is between 5 and 10 minutes away, walking time. Write down the walking distance to the landmark provided by Google Maps (be sure to choose walking as the mode of transportation so that the distance will be calculated using walking directions). Convert the Distance to meters and record here: __________________

14) Now use a stopwatch to record the time it takes you to walk to the landmark and record here________:

15) Estimate the uncertainty in your time measurement to only one significant figure. (For example, was the uncertainty 0.1 s, 1 s, 10 s, 100 s, …?).

16) Explain your reasoning behind your estimate, including what you think was the main contributor to the time uncertainty. (For example, how long did it take you to hit the stop button when you arrived?)

17) Assuming the distance provided by Google Maps was accurate, estimate the uncertainty in the distance measurement to only one significant figure. (For example, was the uncertainty 0.1 m, 1 m, 10 m, 100 m). Explain your reasoning behind your estimate. (For example, did you cut a corner on a turn? Did you wander back and forth along the sidewalk to avoid other people?)

18) Calculate your walking speed by dividing the distance by the time:

19) Calculate the uncertainty in your speed. Anytime you only multiply or divide a set of numbers, the relative uncertainty in the result can be calculated by adding the relative uncertainties. First, calculate the relative uncertainty in the distance by dividing the distance uncertainty by the distance value. Then do the same for the time uncertainty and time value.

20) Add the two relative uncertainties you calculated to get the total relative uncertainty for the speed.

21) Finally, multiply that relative uncertainty for the speed by the actual speed value to get back to absolute uncertainty in the speed.

22) Enter your average height, height uncertainty, speed, and speed uncertainty into the class spreadsheet. You can use your student ID number instead of your name, if you prefer.

Data Analysis

23) Now we will analyze the class data in order to test our different hypotheses. Copy and paste data from the class spreadsheet into your own spreadsheet. Below is a video demonstrating how to use a spreadsheet to perform some of the analysis data analysis for this lab.

24) Create an x-y graph of height vs. speed.  Our model is going to assume that height determines walking speed, not that walking speed determines height.  We are treating height as the independent variable (what we are changing in the experiment) so it should be on the horizontal (x-axis). Speed should be on the vertical axis (y-axis), because speed that will be our dependent variable (what is changing in response to the independent variable).

25) Be sure to give your graph a title and label the axes with the variable names and the units of measure.

26) Based on the graph, does it appear that  your qualitative hypothesis supported by the data? Explain.

27) In order to really answer the question about whether or not the experimental results support the hypothesis we need to think about uncertainty. (Unit outcome 3-4). We have done all the work of estimating uncertainty values for both the height and speed values, so let’s put them to use! Use the uncertainty columns of the class spreadsheet to add horizontal (height) and vertical (speed) error bars to the class data points. (Ask for help or search the web for instructions on your program of choice as needed).

Qualitative Conclusions

28) Considering the error bars, does the data clearly support your qualitative hypothesis. (Are the speeds clearly increasing or decreasing as height increases? Keep in mind that if the vertical error bars overlap then you can’t actually be sure if some points are really higher or lower than others.) Explain.

Quantitative Conclusions

(Outcome 2-2)

29) Use your excel spreadsheet to calculate the average speed and standard deviation in the speeds from the class data. Record here.

30) Do the results support your quantitative hypothesis about the variation in human walking speeds? Explain.

Modeling

31) Use your spreadsheet program to fit a line to class data and display the fit equation and R² value. The R² measures how well the fit equation can explain the variation in the data (related to the difference between the individual values and the average of all the values). Values closer to 1 correspond to more of the variation being explained by fit. For example, an R² of 0.5 implies that 50% of the variation in the data was explained by the fit equation, but 50% was caused by something that the fit equation could not predict.

32) Write the fit equation and R² value here:

33) Does this fit equation generally fall within the uncertainty of your data points as indicated by the error bars? Explain.

34) This fit equation might provide us with a way to predict walking speed from height. Based on R² and overall the agreement between the fit equation and the data, would you trust this equation to accurately predict the walking speed based on a persons height most of the time? Explain.

35) If we repeated this experiment for a much larger population and we also happened to find that the fit equation had an R² that was close to one and the fit line passed within most of the error bars then we could trust that equation to predict walking speed. Would that be a qualitative or quantitative model? Explain.

36) Would that model be empirical or mechanistic (physical)? Explain.

37) The inverted pendulum model is a commonly used, relatively simple model of walking^[1]. Would the inverted pendulum model be an empirical or physical model? Explain.