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It's been quite a while since I've been here, but I was reminded this morning about my childhood when a friend of mine and I got a hold of a spool of string that was purported to have been 5 miles in length. Thinking about it I think it was probably more like some 5000 feet in length.

Since that was almost 40 years ago, I can't really say that I remember exactly what was going on.

What we did was to attach our paper kite to it-- the kind that existed in the late 1960's-- and let it fly.

I remember it taking some 3 or 4 hours to let it all the way out, and another 5 or 6 to reel it back in. We started out at sunrise, and didn't get done until sunset.

My point for this whole "exercise" is to determine if I can obtain the altitude, and horizontal distance it was from our location.

The primary components that I've been able to identify/remember at this point are:

Kite mass

String mass/unit length

Wind velocities- speed, trajectory/vectors

Initial height would've been 3 feet on my end

Atmospherric density differential due to altitude changes

Length of string/thread.

Area of kite body/face exposed to winds

As stated, this was a simple paper kite kids flew back in the 1960's. For those among you who are younger, go ask your fathers/mothers.

They were made of thin, dyed/colored paper, and light sticks (the kind Charlie Brown flies in the comic strip). Something akin to a pop-sickle stick, but longer, and shaped almost like a dowel. We then connected the top end to a string, and a few inches up from the lower end, to another string. These were then connected at the center of mass to the flight string. This allowed for balanced flight dynamics.

I detail it like this because the kites in existence today are far more advanced, and fancy than we had back then.

I've gone to Wikipedia, and found the discussion they've provided on catenaries. FRom what I remember, a catenary is the natural shape a suspended string takes when attached at both ends.

And the arc length would be (if I remember it correctly): S= Int(Int(sqrt(dx^2/dy^2 + 1)), 0, N, x), 0, M, y) where M, and N are the maximum distances the string could go.

They have a function for y as follows:

y= a* cosh (x/a) = a/2 * (exp(x/a) + exp(-x/a))

Where a = T_o/P

Where T_o is the horizontal component of the tension-- a constant, and P is the weight/unit length.

Sadly, it was a foggy day, and never really cleared up, so I have no idea how far away it got, or how high it went, and I'm curious if it's possible to mathematical solve this to get a general idea.

The kite did however survive, and we used it again the next time we went to play with it. We never did try that one again though. It took too long to do the entire roll.

Strange the things we remember.

Anyone have any ideas as to how I could solve this?

Thanks for your feedback, and responses.

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# Kites, and really long strings

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