**With this Instructable I will be showing you how to build a diamond kite with a little math behind it.**

I was tasked by my teacher to construct a kite using materials I have laying around my house. For example, I could use a plastic bag and some chopsticks. then do the following:

- Find the surface area.
- Find the Centroid.
- Fly your kite and record how long the kite stays in the air.
- Find a partner and plot the surface area vs. time in the air.
- Answer the following question: Do you think that a kite with more or less surface area will fly longer? Justify your answer with mathematics.

## Step 1: Finding the Materials

I started off by looking for materials. I knew the kite has to be lighter than the lifting force, so I found some lightweight items.

- String (Fishing Line)
- Frame (Wooden Dowels)
- Face (Force Flex Garbage Bags * with Glade)
- Tail (Lacing)
- Hot Glue
- Rubber Cement

## Step 2: Planning

Whenever you decide to build anything, it is always a good idea to make a plan with a sketch.

I am making a traditional kite , so it needs to be quadrilateral with two distinct pairs of equal adjacent sides. A quadrilateral means to have 4 Straight sides. (Fg. 1)

## Step 3: Making a Sketch

In my sketch I need to know the length of all four sides, the length of the diagonals, and the centroid.

Lets start by deciding on how large of a kite I want. I know by having more surface area, I cam get better lift and drag, so I made a medium size kite with the materials on hand.

- The centroid is the intercept of the diagonals.

I had 4 36" wooden dowels so, so to play it safe I made the sides 16" x 16" x 20" x 20" knowing the largest diagonal will be no larger than 16" + 20".

## Step 4: Doing the Math

I need to use some math to get the length of the diagonals and the surface area of the kite.

**Getting the diagonals.**

With the given length of sides, I can calculate the length of the diagonals. If you take a closer look you can see our kite is made of two triangles. We can use the Pythagorean Theorem with the known sides to discover the diagonals length.

Pythagorean Theorem = a^2 + b^2 = c^2

(20")^2 + (20")^2 = Vertical diagonal = 25.6"

(16")^2 + (16")^2 = Horizontal diagonal = 22.6"

**Getting the surface area.**

To calculate the surface area I can use the length of the diagonals using the following formula.

L = Longer diagonal

W = Shorter diagonal

A - (L x W) / 2

25.6" x 22.6" = 289.28 Sq. Inches

## Step 5: Putting It All Together

- Now that we have all the measurements, lets cut the pieces and put it all together. Remember the less weight the better, so be sparing with the hot glue. Lay out your frame and hot glue all the corners to make it one solid piece.
- Once the glue has cooled, take your garbage bag and split it into one solid sheet. Lay down your kite frame on top of the bag, and then trim a 1" boarder around the frame. Once you have completed that rubber cement the face around the boarders of the frame.
- Next cut 1 ' of string for the bridal. Tie one end near the bottom vertex and the other to the centroid. take your line and angel it 90 degrees from the centroid, move it up a little bit from there and tie it to your flying string. this will create a slight angle of attack, helping create lift and drag.
- You can adjust this angle by moving the strings depending on how windy it is out that day.

- Attach a tail to the bottom vertex to create drag to prevent rotation of the kite.
- Finally wait for some wind and GO FLY A KITE!

## Step 6: Conclusion

I was assigned to graph my results with another classmates results in relation to surface area vs. time of flight. I created my graph with the following data.

**My data**

Surface area = 289 Sq. inches

Mean of my flight times - 8.5 minutes

I calculated my mean by the following formula - (a + b + c + d) / the amount of numbers in the set.

(6 + 8 + 8 + 12) / 4 = 8.5 minutes

- Flight 1: 6 minutes
- Flight 2: 8 minutes
- Flight 3: 8 minutes
- Flight 4: 12 minutes

**My classmates data**

Surface area = 48 Sq. inches

Mean of my flight times - .22 minutes

**My Conclusion**

From this data we are to determine if more or less surface area contributes to longer or shorter flights.

**Answer. **From the data I have it shows that there is a positive slope, which means the more surface area equivilates to more flight time.

I do want to note there are many other factors that contributes to the vertical lift of a kite, so this is a broad edjucated assumption. Other factors that can effect lift can be i.e. velocity, weight, angle of attack...

## Step 7: Thank You

Thank you for taking your time in discovering my Instructable. I encourage you and your family to try this out. Math can be fun, and it is every where in our lives. You can alsways discover more if you just look a little deeper.