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Thread: Physics / maths of riser & limb combinations

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    It's an X Corax67's Avatar
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    Physics / maths of riser & limb combinations

    I have been asked by one of our more inquisitive juniors why, for a given set of limbs the poundage is different depending on the length of the riser.

    I know it is to do with the string/limb/riser geometry but cannot find any proper mathematical explanation which will satisfy the lass in question.

    If someone could point me in the right direction I would be very grateful.



    Karl
    I meant to do that - honest ! !

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    It's an X I've taken part in an AIUK Ironman Shoot.The Fonz Award.AIUK subscriber. Timid Toad's Avatar
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    If your riser was 2", and you drew your medium limbs back to 28, they would be very bent. If it were a 40" riser it permit them to need to bend less. So your 2" riser would produce a much higher poundage, as you have effectively bent them more. And the 40" riser much lower for the opposite reason. Limbs are made with optimal draw lengths in mind.
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    In the Gold AndyW's Avatar
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    Same with compound limbs - they are rated as a certain poundage at a known deflection.
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    It's an X Corax67's Avatar
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    Thanks guys - what I need is the science behind it.

    i need formulae, pictures of bows and triangles and geometry and stuff not just "because...." - whilst I understand the concept that greater deflection of the limbs with a shorter riser stores more energy there has to be a mathematical expression showing it which I can utilise as an explanation.



    Karl
    I meant to do that - honest ! !

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    Take a piece of string and hold it against a wall. Mark how far up the wall it reaches from the floor. From half way up the string, pull that point away from the wall by 18" to represent a draw length of 28"( less the 10" brace height). Let the lass hold the ends; one on the floor against the wall and the other on the wall where ever it reaches. mark where it reaches. You can talk about isosceles triangles and longest side, and how much shorter the longest side is compared to the straight length.
    Repeat with a clearly shorter piece of string and again note the straight length on the wall and the height reached when drawn 18" from the wall at the midpoint. As the string used is shorter it will show that the ends close even more towards each other. requiring the limbs to be bent further and hence an increase in draw weight.
    If you want more "sums" you can look at the isosceles triangles as a pair of right angled triangles back to back. Do a Pythagoras with hypotenuse being half the string; base being draw length and third side being half the distance apart of the end loops. Do some calculations on easy numbers to prove how shorter strings with the same deflection at the midpoint (approx) end up with significantly shorter third sides

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    It's an X I've taken part in an AIUK Ironman Shoot.The Fonz Award.AIUK subscriber. Timid Toad's Avatar
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    Quote Originally Posted by Corax67 View Post
    Thanks guys - what I need is the science behind it.

    i need formulae, pictures of bows and triangles and geometry and stuff not just "because...." - whilst I understand the concept that greater deflection of the limbs with a shorter riser stores more energy there has to be a mathematical expression showing it which I can utilise as an explanation.



    Karl

    That you'll need to do yourself.
    "Time is an illusion. Lunchtime doubly so." Douglas Adams

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