# Snotty Plots: How Do You Graph A Sneeze?

## Simulation, graphing data, mathematical models

You and a friend are sitting down to lunch, and all of a sudden…“AAACHOOOO!” One of you sneezes! Your first thought after “bless you” might be to wonder: “Did the cell phone, notebook, or peanut butter and jelly sandwich that I left on the table get covered in sneeze?”

If you’re curious about how far sneezes travel, you aren’t alone. Because sneezing can spread infectious diseases like the flu and the common cold, many scientists and doctors are interested in better understanding how far a sneeze can travel. For example, Lydia Bourouiba and John Bush of MIT’s Applied Mathematics Laboratory wrote mathematical equations to predict and describe the path of a sneeze. Their predictive equations, called mathematical models, incorporated a branch of physics called fluid dynamics (how fluids move) and accounted for gases as well as larger particles of spittle in three dimensions. The team then tested these predictions by actually filming and observing sneezes using a high-speed camera and computer imaging software. Grab a tissue and watch as they describe their findings in the Science Friday video “Nothing to Sneeze At”:

Video Transcript – Nothing To Sneeze At

The research of Bourouiba and Bush focused primarily on the gases and small particles (< .1 millimeters) in a sneeze, showing that the small particles can become “suspended” or buoyant within a sneeze cloud, enabling them to travel great distances. However, as they hint in the video, larger sneeze particles behave a bit differently. In the following experiment, you will use a dropper and some paint to simulate a sneeze in order to better understand how these large droplets behave.

Using the data from your sneeze simulation, you will create a histogram of the number of sneeze droplets that fall at various distances from the sneezer. A histogram is a type of graph that represents how often an event occurs over fixed intervals, such as distance or time. Using your histogram, you will be able to answer the question, “At what distance from a sneeze is your notebook or cell phone at greatest risk of getting hit by large snot and spit droplets?”

## Objectives: Students Will Be Able To

• Collect and summarize data of the landing distribution of large droplets in a sneeze.
• Display data of sneeze droplet number and distance traveled in a histogram.
• Interpret graphic representations of sneeze droplet data to identify the riskiest distance for coming into contact with large sneeze droplets after a person has sneezed.
• Predict how behavioral changes, such as covering your mouth when you sneeze, might alter the distances that droplets travel.

## Materials

• Small 1 milliliter (1ml) plastic bulb dropper
• 6 sheets of printer paper
• Sneeze stand: a stool, empty waste bin, or cardboard box, at least a foot tall
• Tape
• Washable, tempera paint in three colors, distributed in small paper cups
• Small paper cup of water
• Damp paper towel
• Pencil and metric ruler
• *Optional: place to dry painted papers
• *Optional: painting drop cloth

## Experiment

1. Simulate a sneeze with a dropper and paint:

On a washable or protected flat surface, lay six pieces of paper in a line, long end to long end. At one end, set a box or overturned waste bin (“sneeze stand”). Label each piece of paper with a range that represents its distance from the sneeze stand, starting closest to the trash bin. For example, the first page will be labeled 0-21.5 centimeters (cm), the next 21.5-43 cm, etc. See an example below.

With your dropper, gently squeeze the bulb to suck up a very small amount (0.25 ml, or about 4 drops) of paint. Make sure that the paint stays in the very tip of the dropper. Hold the dropper horizontally on top of your sneeze stand, and barely peek over the edge of the stand. Make sure the dropper is facing the papers so that when you squeeze the dropper, most of the paint lands on the paper. Count to three, and then squeeze the dropper very quickly—you are simulating a sneeze. You can shout “ACHOOOO”! at the same time for added effect. See an example of the setup above.

2. Count large sneeze droplets. Where do most of them fall?

With a pencil, draw a circle around every sneeze droplet that is over 5 mm. Count the circled droplets on each page, and record those numbers on the sneeze droplet data table and analysis sheet. Now look at the smaller (<5 mm) droplets. What do you notice about where they fell? Record your observations in the notes section of your data table and analysis sheet.

3. Graphically answer: Where do most (large) sneeze droplets fall?
You will now make a histogram of the number of large droplets that fell on each piece of paper. Start by choosing a scale for the y-axis of your graph that encompasses the highest and lowest sneeze droplet number you recorded, and label the scale units. The x-axis is represented by the pieces of paper in this experiment, which make great “fixed intervals” for representing distance in your histogram. In each of the intervals on the histogram, draw a rectangle whose height matches the number of large droplets you recorded on the data sheet, using your y-axis labels as a guide. For example, if there were 3 large sneeze droplets on the first sheet of paper (0-21.5cm interval), you would draw a bar within the 0-21.5cm interval that goes up 3 units on the y-axis. You can work with the “sneeze histogram” on the data table and analysis sheet, or you can make your own. Here’s an example:

4. Conclude and evaluate: What patterns does your histogram show?
(these questions are also available on the data table and analysis sheet)

• Compare where you found large sneeze droplets to your observations of tiny sneeze droplets.
• Does it look like the tiny droplets (<5 mm) traveled as far as the larger ones?
• Based on your histogram, what is the distance away from a sneezer where you would least want to leave your notebook or sandwich?
• If you wanted to advise someone about the best place to leave their cell phone around a sneezing person, what would you tell them?
• How did the distribution of large sneeze droplets compare to your casual observations of tiny sneeze droplets? Describe what differences you would expect between the histogram you made and a histogram of tiny sneeze droplets and distance traveled. Would the total number of droplets be the same, higher, or lower? Which column would be the tallest?
• Did any sneeze droplets travel farther than the six pages or off the sides? How would you modify this experimental setup next time to improve your data collection?
• How do you think this simulated sneeze compares to real human sneezes? You may use both your own observations and the observations of Bourouiba and Bush from the video in your response.

## Extensions

• Once the pages have dried, line them back up as you did before, but this time divide each piece of paper in half. Re-label each half with a new range representing its distance from the sneezer, starting closest to the sneezer (for example, the first page will now have two ranges, 0-10.75 cm, and 10.75-21.5 cm). Count the large droplets again, this time recording your data in a new data table. Make a new histogram, or modify your original one with new interval measurements on the x-axis. Does using shorter distance intervals in your histogram change your opinion about where most droplets fall?
• Advanced: Use a ruler to measure the size of every droplet over 2 mm and its distance from the dropper to create a “sneeze scatter plot,” with droplet size on the x-axis and droplet distance on the y-axis. Is there a pattern or correlation between droplet size and distance traveled? Do larger droplets travel farther?
• How does holding a tissue up to the dropper before a “sneeze” change the distribution of droplets? Use a different paint color and repeat the experiment, except hold a tissue in front of the dropper before simulating your sneeze. Compare histograms to see how using a tissue changes the distribution of large droplets.

## What else can you describe with numbers?

Find out with these Science Friday articles:
Music preferences – This Startup Knows What Tunes You Want to Hear
Taxi trips, fares, and routes – Hello, Stranger, Wanna Share a Cab?

## Standards

Next Generation Science Standards

DCI: PS1.A: Structure and Properties of Matter

• Gases and liquids are made of molecules or inert atoms that are moving about relative to each other. (MS-PS1-4)
• In a liquid, the molecules are constantly in contact with others; in a gas, they are widely spaced except when they happen to collide. In a solid, atoms are closely spaced and may vibrate in position but do not change relative locations. (MS-PS1-4)
• The changes of state that occur with variations in temperature or pressure can be described and predicted using these models of matter. (MS-PS1-4)

SEP: Analyzing and Interpreting Data

Analyzing data in 6–8 builds on K–5 and progresses to extending quantitative analysis to investigations, distinguishing between correlation and causation, and basic statistical techniques of data and error analysis. Construct and interpret graphical displays of data to identify linear and nonlinear relationships

CCC: Scale, Proportion, and Quantity

Proportional relationships (e.g. speed as the ratio of distance traveled to time taken) among different types of quantities provide information about the magnitude of properties and processes.

Common Core Standards

• CCSS.MATH.CONTENT.6.SP.B.4
Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
• CCSS.MATH.CONTENT.6.SP.B.5
Summarize numerical data sets in relation to their context, such as by:
• CCSS.MATH.CONTENT.6.SP.B.5.A
Reporting the number of observations.
• CCSS.MATH.CONTENT.6.SP.B.5.B
Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
• CCSS.MATH.CONTENT.8.SP.A.1 (extension)
Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

Topics: Probability and statistics, epidemiology, measurement, data analysis, histograms.

Assessment: Interpret a histogram of sneeze droplet number and the distance each droplet traveled to determine the area of greatest risk of getting soaked by a sneeze.

Accessibility: After paint has dried, visually impaired students can feel droplets in order to count their number and relative size as a means of data collection.

Extensions: Compare the number of droplets and distance they traveled when no tissue was used to the number and distance they traveled when a tissue was held up to the bulb dropper “nose.”