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Thread: Maths Question

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    LUSE Galant's Avatar
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    Question Maths Question

    Okay Mathematicians, here's a challenge that concerns bunting. I have two friends who have been throwing Pythagoras around for about half and hour already. If it were me I'd just measure the thing but they seem hooked on the maths of it.

    Here's the question:

    What the formula to work out how much horizontal loss occurs (let's say in centimetres) for every centimetre of dip at the centre point (when the bunting is hanging)?

    Any one up for it?

    No trees were harmed in the creation of this message. However, many electrons were displaced and terribly inconvenienced.

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    Pork & Beans Powerup Phage's Avatar
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    Re: Maths Question

    Too many variables surely ? Weight and rigidity of the bunting, distance and tension come to mind immediately.
    Society's to blame,
    Or possibly Atari.

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    Grumpy and VERY old :( g8ina's Avatar
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    Re: Maths Question

    I believe it to be an inverse parabola.
    Cheers, David



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    Galant (04-02-2013)

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    LUSE Galant's Avatar
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    Re: Maths Question

    Is that where Jesus makes a simple statement and someone else goes and makes a complicated story out of it?

    But seriously... can you break that down into x=a-y Where x=the hanging width, a=the actual length, and y = the height of the dip?

    Ignore tension and rigidity, just a theoretical straight line. How much width does it lose as it sags assuming an even curve?

    Or is it really impossible to figure?
    Last edited by Galant; 04-02-2013 at 10:13 PM.
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    Re: Maths Question

    Pythagoras only works for straight lines, so you'll only be getting a rough approximation. I'd get the bunting out and get some empirical data.

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    Re: Maths Question

    Even assuming a straight line, you'd still need to know the length of the bunting to calculate the loss.

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    Re: Maths Question

    If we call then length L then the loss would be:

    L - 2 x sqrt((L/2)^2-1)

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    Re: Maths Question

    Just to clarify, I wasn't suggesting Pythagoras was the right way to about this. Just that my mates had been trying to make use of it. Without success.

    Also, what I'm after is the formula to calculate the loss in length that occurs relative to the gain in dip, so you can use any starting length you please. The idea is to find the formula and then use it to calculate the length of straight bunting required to cover any specific distance when hanging (with a specific dip, of course).
    No trees were harmed in the creation of this message. However, many electrons were displaced and terribly inconvenienced.

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    jim
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    Re: Maths Question

    I believe that the formula for a parabola is y=ax^2 + bx + c

    I can't remember how you substitute in for a, b and c values, but the point is that if you pump in the values relating to x, then you'll get a result for y. Of course the x values relate to distance across, and the y value relates to the height.

    Using the formula, I recall being able to work out what the minimum/maximum point of y was, which in your case would be equal to the deflection and therefore give you your answer.

    As for precisely how to use it, you'd need to google... I certainly can't remember off the top of my head. Sorry this is so vague, I am this vague about it in my own head.

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    Re: Maths Question

    Use chord and offset if the curve is circular.

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    The late but legendary peterb - Onward and Upward peterb's Avatar
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    Re: Maths Question

    Iirc, the formula for a light inextensible string involves the hyperbolic functions, sinh, cosh and tanh.

    The curve formed by a light inextensible string is a catenary. Of course in real life there is no such thing as a light inextensible string, but the formulae are a good approximation.

    x^2 - y^2 = 1 is the formula for the curve.

    The hyperbolic functions do for a hyperbolic curves what the trigonometric functions do for trigonometric curves.

    http://en.wikipedia.org/wiki/Hyperbolic_function
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    Re: Maths Question

    Quote Originally Posted by Galant View Post
    Just to clarify, I wasn't suggesting Pythagoras was the right way to about this. Just that my mates had been trying to make use of it. Without success.

    Also, what I'm after is the formula to calculate the loss in length that occurs relative to the gain in dip, so you can use any starting length you please. The idea is to find the formula and then use it to calculate the length of straight bunting required to cover any specific distance when hanging (with a specific dip, of course).
    With 1 dip or a variable number of dips?

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    DDY
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    Re: Maths Question

    Quote Originally Posted by Galant View Post
    Just to clarify, I wasn't suggesting Pythagoras was the right way to about this. Just that my mates had been trying to make use of it. Without success.
    Well, you can actually derive an integral for your problem using Pythagoras

    It's a bit beyond me, now - it's been a while since I did calculus, but it involves taking infinitesimally small hypotenuses over the length of a curve or something like that...

    I'm saying this just in case you make a bet with your mates that it's impossible to do it using Pythagoras!

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    Re: Maths Question

    Even if you knew the equation of the curve, which we don't, the integral would calculate the area underneath the line, not the length.

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    DDY
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    Re: Maths Question

    Quote Originally Posted by Willzzz View Post
    Even if you knew the equation of the curve, which we don't, the integral would calculate the area underneath the line, not the length.
    As I said, an integral derived from Pythagoras, not the integral of the function.

    http://en.wikipedia.org/wiki/Arc_length

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