Geometry Project - Kite Shapes

by Jayden
(Oklahoma City, OK, USA)

Q:

Both a square and rhomboid (diagonal) kite are perpendicular to the wind. They both have effective areas. What shapes would those be? And whats the difference from the effective areas?

And where on a box kite would I tie string to get the greatest effective area?

A:

After a little research I was able to figure out what you are actually asking :-) I believe you are enquiring about differences between the traditional square Box kite and the slighly flattened version called the Rhomboid kite?

The geometry question only makes sense if the Rhomboid kite is just the Box kite with the bracing cross-pieces changed in length. To put it in a non-mathematical way, imagine the square Box kite is 'squashed' so the cells look diamond-shaped instead of square. Of course, both kites have exactly the same amount of sail area.

The question states that both kite designs are placed perpendicular to the wind. Let us imagine that they are sitting on their tail ends on the ground too, and being held there, ready to launch. Just down-wind of the kites is a large smooth wall. It is night time and the kite-flier, way upwind, is shining a very bright light towards the kites. CASTING SHADOWS ON THE WALL.

These shadows can represent the effective areas of the kites. Both shadows will show 2 rectangles for each kite. An upper and a lower one, corresponding to the upper and lower cells of the kites.

But look - the Rhomboid kite is casting wider shadows than the Box kite! Since the heights of all the shadows are the same, what does that mean? It means the Rhomboid has a larger effective area than the Box, despite having the same amount of sail material covering it. If it is stopping more light from hitting the wall, it must also be a bigger obstacle for the air flowing around it!

If you did a little trigonometry, you could calculate the exact difference in effective area between the 2 kites. Ask another question if you would like that explained in detail. Of course, kites cannot fly perpendicular to the wind, so in real life the effective areas are smaller.

I hope all this helps to make the concept of 'effective area' a little clearer.

Regarding the last part of your question, about getting the largest effective area for a box kite... You would tie the string to the exact middle of one of the long main spars. But of course, the kite wouldn't fly! You could perhaps toss it out the back of a drag racer as an air-brake ;-)

One more comment... It's funny that the Rhomboid Kite has that name, since technically the cell shape is a Rhombus. That is, a shape with all 4 sides of equal length. A Rhomboid is the more general case where adjacent sides are of unequal length. That is, 2 sides have one length and the other 2 sides have another length.

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