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  1. #11
    GrizzlyAdams's Avatar
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    engineering math

    Quote Originally Posted by hitchman View Post
    Here is my math: Sin of 30 is 0.5, meaning that for a 30 degree angle the vertical component is half of the tension on the rope. Each end carries half of the weight. So for a 200 lb weight, or any weight for that matter, the rope tension on each end is the same as the weight (multiplied by 0.5 and divided by 2).
    W = weight

    W*0.5/2 = W/4

    not W.
    ??

    The thing to worry about is dynamic tension, not static, me thinks. Getting mass times acceleration involved, and all that.

    Grizz

  2. #12
    New Member hitchman's Avatar
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    The 0.5 factor is multiplied not divided. The tension on the rope is the resultant from the vertical component (weight) and the horizontal component (pulling the trees together). So at 30 deg the tension on the rope is twice the vertical load (half the weight on each end).
    I wouldn't think the dynamic component is that great unless you are in earthquake country. Otherwise let me point out that the rope is rated at the breaking point (for new undamaged rope). Rope accessories are generally rated at the recommended work load, which is around 1/3 of the breaking load.
    Last edited by hitchman; 05-31-2007 at 15:42.

  3. #13
    Senior Member FanaticFringer's Avatar
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    I hate math.
    "Every day above ground is a good day"

  4. #14
    Senior Member blackbishop351's Avatar
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    Math is hard.

    I have that on a t-shirt...nobody gets the joke, though
    "Physics is the only true science. All else is stamp collecting." - J. J. Thompson

  5. #15
    GrizzlyAdams's Avatar
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    fun with figures

    There are two kinds of math : easy math, and hard math.
    Easy math is the kind you understand, hard math is the kind you don't.

    Also a joke that most don't get, or at least don't think is funny.

    I've got a degree in the stuff, my wife's joke is that I double majored in math, and more math. However my courses ran to the crystal tower variety, and not the useful stuff like elementary engineering.

    Not to belabor the point, but if you take half the weight (W/2) and if
    The 0.5 factor is multiplied not divided
    then that's (W/2)*0.5. But these are just words...I now understand the physics of the situation by your description
    The tension on the rope is the resultant from the vertical component (weight) and the horizontal component (pulling the trees together).
    So I gather that the way to think about this is that the known force is W/2, understood to be the vertical projection of the (unknown) total force T on the rope. The ratio of the vertical projection to the total component (hypotenus) is the sine of the angle theta between the hypotenus and adjacent side, so sine(theta) = (W/2)/T. With sine( pi/6 ) = 0.5 we solve for T in 0.5 = (W/2)/T, which is T = (W/2)/0.5 = W.

    When you say that the 0.5 factor is multiplied and not divided, I guess you mean 0.5*T = (W/2).

    so all is clear now.

    Grizz the occasionally obtuse

  6. #16
    New Member hitchman's Avatar
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    Smile

    Couldn't have put it better myself!

  7. #17
    Senior Member angrysparrow's Avatar
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    Quote Originally Posted by GrizzlyAdams View Post
    There are two kinds of math : easy math, and hard math.
    Easy math is the kind you understand, hard math is the kind you don't.
    I personally always thought 'hard math' was the kind that Newton, Bernoulli, Leibniz, Euclid, and Einstein struggled with.

    Quote Originally Posted by GrizzlyAdams View Post
    so all is clear now.
    Yes, the outlined principle is clear enough. It doesn't make me any less inclined to want my hammock ridiculously over-engineered, though. My backside, and my ego, don't like taking falls.
    I think that when the lies are all told and forgot the truth will be there yet. It dont move about from place to place and it dont change from time to time. You cant corrupt it any more than you can salt salt. - Cormac McCarthy

  8. #18
    Hooch's Avatar
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    For those of you who do math so well, I have but one thing to say. I hate you. Just kidding, thanks for the science to back up the hanging, I appreciate it.
    "If you play a Nicleback song backwards, you'll hear messages from the devil. Even worse, if you play it forward, you'll hear Nickleback." - Dave Grohl

  9. #19
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    Quote Originally Posted by GrizzlyAdams View Post
    There are two kinds of math : easy math, and hard math.
    Easy math is the kind you understand, hard math is the kind you don't.

    Also a joke that most don't get, or at least don't think is funny.

    I've got a degree in the stuff, my wife's joke is that I double majored in math, and more math. However my courses ran to the crystal tower variety, and not the useful stuff like elementary engineering.

    Not to belabor the point, but if you take half the weight (W/2) and if

    then that's (W/2)*0.5. But these are just words...I now understand the physics of the situation by your description


    So I gather that the way to think about this is that the known force is W/2, understood to be the vertical projection of the (unknown) total force T on the rope. The ratio of the vertical projection to the total component (hypotenus) is the sine of the angle theta between the hypotenus and adjacent side, so sine(theta) = (W/2)/T. With sine( pi/6 ) = 0.5 we solve for T in 0.5 = (W/2)/T, which is T = (W/2)/0.5 = W.

    When you say that the 0.5 factor is multiplied and not divided, I guess you mean 0.5*T = (W/2).

    so all is clear now.

    Grizz the occasionally obtuse
    Hey now show some respect.

    Hitchman, you have a good looking product. I broke and got dropped using 550 lbs rated paracord. It broke in the middle and not at the knot. It was at a decent angle, 30-45 deg. For me it is nothing rating below 1000lbs.
    Is that too much to ask? Girls with frikkin' lasers on their heads?
    The hanger formly known as "hammock engineer".

  10. #20
    Senior Member Redtail's Avatar
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    "multiplied by 0.5" = "divided by 2"
    Maybe the confusion was stating the same thing two different ways.

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