Kitesurfing function of Kite Size, Rider Weight, and Wind and Gust Speed in MPH; Kite Design

Dear Mathlete Parents:

It was such a privilege this week for me to share my passion for kitesurfing math with your children. Most weeks, I will post a recap summary and documents on my website www.mathletenation.com on the Saturday following the lesson. Just in case you do not visit the site today, I wanted you to have a detailed summary of our first class in order that you might help them to explore the math and science as a team. REMEMBER, YOUR CHILDREN CAN DO AS MUCH OR AS LITTLE AS THEY LIKE. I ALWAYS ADD MORE DETAIL FOR CHILDREN AND FAMILIES THAT WANT TO GO A STEP FURTHER. THE BOTTOM OF THIS EMAIL HAS THE CHALLENGES IF THEY/YOU SHOULD WISH TO EXPLORE.

First, I introduced the kitesurfing equipment used including: 

• 4/3 wetsuit which means 4mm thickness in the torso and 3mm thickness in the arms and legs for flexibility (this suit is safe in water temperatures down to 52 degrees Fahrenheit; I will need a 5/4 wetsuit after November given the dropping water temperatures (November 51, December 42, January 40, February 36 degrees Fahrenheit).
• booties to protect the feet from cuts with a thickness of 5mm (good for winter surfing) 
• 154 x 44 kiteboard with foot straps (the measurements are in centimeters); I had the children estimate the dimensions by showing them a meter (100 cm) stick (I also used my hand span of fully spread out pinky to thumb which is 21 cm and easily estimated the actual)
• harness that goes around my torso to which the kite bar is attached
• kite bar with four lines and safety leash, chicken loop, and donkey stick
• 12m kite and pump (inflated the leading edge and three struts to 8PSI which is pounds per square inch or pound-force per square inch; this is the unit of pressure and stress on one square inch of surface area [bike tires are pumped to 90 PSI and my stand up paddle board is pumped to 15 PSI]

I introduced the children to a measure of one meter having them emulate that distance with their outstretched arms. Since some of the younger children are one meter tall, their corresponding arm span is about the same one meter. Just to make things easier, I explained the a meter is slightly more than one yard or three feet. 

With a few groups, I was able to lay out the kite lines and have them estimate the length in meters or feet. Using one of my steps as one meter or slightly more than three feet, as I walked it off, the children counted by three’s until we reached a length of 25 meters or slightly more than 75 feet.

I challenged the children to determine how the kite is measured at 12 meters. They conjectured (guessed) that this was the perimeter of the kite (using my meter sticks we determined that the perimeter is about 16 meters). When I explained that kite size is a function of the wind speed and the weight of the kitesurfer, they correctly determined that 12 meters refers to the square surface area of the kite. I created a one square meter apparatus allowing them to see that two dimensional measurement. I challenged them to identify the shape of each section of the kite. They identified the far sections as pentagons but had trouble identifying the middle sections until  mentioned that the two struts are parallel. Then they were able to see a trapezoid with one set of parallel opposite sides.

Before I decide where to go kitesurfing, I look at a map of popular kitesurfng spots analyze the projected wind (my favorite site is ikitesurf.com and maps. If I choose Waquoit Bay for Friday, September 9th, I see that the wind is between 11 and 15 miles per hour (MPH) from 1-6pm out of the south west. Then, I look at a chart that includes three variables: kite size, rider weight, and wind speed. At an average wind speed of 13 mph, and 160 pounds, the chart says I need a 14 meter kite. My 12 meter kite appears to be too small to power me across the water; however, since I have a large surface area board, I can use a smaller kite. I CHALLENGED THE CHILDREN TO LOOK AT THE WEATHER REPORT THIS WEEK AND DETERMINE WHAT SIZE KITE THEIR PARENTS WOULD NEED BASED ON WEIGHT AND WIND SPEED. THIS WILL ALLOW THEM READ TWO DIMENSIONAL MULTIVARIABLE CHARTS AND GRAPHS. (I DO NOT EXPECT K/1ST GRADERS TO BE READING THESE CHARTS YET, BUT ….

The other variable I look at is the difference between the wind speed and gust speed. If that difference is greater than 8 mph, the kitesurfing conditions may be dangerous. Last Tuesday, I chose to kite surf when the differences in wind speed and gust were greater than 15 mph. I had to be extra careful to compensate for the unpredictable gusts. I CHALLENGED THE CHILDREN TO CALCULATE THE DIFFERENCES AT MY FAVORITE FOUR KITESURFING LOCATIONS: WAQUOIT BAY, CHAPIN BEACH, CHAPPAQUIDDICK ON MARTHAS VINEYARD, AND WAUWINET IN NANTUCKET. FOR EXAMPLE, IF THE WIND SPEED IS 15 MPH AND THE GUST SPEED FOR THAT HOUR IS 35 MPH, THE DIFFERENCE IS 20 MPH. FOR THE K/1ST GRADERS I ONLY GAVE THEM ONE LOCATION AND THE DIFFERENCES WERE ALL SINGLE DIGITS. THE K/1 KIDS MAY STILL WANT TO LOOK AT THE CHART ON THE FIRST PAGE OF THE OLDER KID’S PDF.

FOR THE OLDER CHILDREN, I CHALLENGED THEM TO LOOK AT FIVE HOURS OF WIND DATA AND DETERMINE THE AVERAGE WIND SPEED. FOR EXAMPLE, IF THE WIND SPEEDS WERE 28, 21, 21, 7 AND 9, ADD THOSE FIVE SPEEDS TOGETHER TO GET 86 AND THEN DIVIDE BY 5 TO GET AN AVERAGE SPEED OF 17 1/5 MPH.

FINALLY, FOR FUN, I GAVE THE CHILDREN TWO PAGES OF COLOR PICTURES OF DIFFERENT KITE IMAGES AND TWO BLANK PAGES OF A LINE DRAWING OF A KITE THAT THEY COULD DESIGN THEIR OWN GRAPHICS.

https://www.youtube.com/watch?v=F_hgd3e0G3U

I wanted to remind you that you are encouraged to work with your children on these challenges I call “fun work” which is elective as opposed to “homework” which is required. The worksheets they received in class are attached below.