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Math Help - basic triangle leg formula help?

  1. #1
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    basic triangle leg formula help?

    Hi -

    Is this formula correct for calculating standover heights on a bicycle?

    Please let me know where I have made a mistake if there is any?

    basic triangle leg formula help?-screen-shot-2014-04-14-2.53.33-pm.png



    PS - this is the bike I am calculating from as their standover is grossly wrong at 19 inches?

    http://www.bikesdirect.com/products/...-bar-bikes.htmhttp://www.bikesdirect.com/products/...-bar-bikes.htm
    Last edited by joebikes; April 14th 2014 at 12:59 PM. Reason: included link tor relevant bike
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: basic triangle leg formula help?

    Looks OK to me. The only quibble is that what you called the diameter of the wheel should actually be the outer diameter of the tire, and that may change as it deforms under the weight of a rider.
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  3. #3
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    Re: basic triangle leg formula help?

    For the upper blue triangle, you say that the length of the hypotenuse is 430 and the angle is 75 degrees. The cosine of an angle is "opposite side over hypotenuse" or \frac{x}{450}= cos(75). So x, the length of the vertical, is 450 cos(75). For the lower blue triangle, the length of the base leg is 270 and the angle s 75 degrees. The tangent of an angle "opposite side over near side" so \frac{x}{270}= tan(75). So x, the length of the vertical, is 270 tan(75).

    The total height is, of course, the sum of those two.
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    Re: basic triangle leg formula help?

    Thanks - standover height is important for cyclists that are not riding the bike. Thus, no significant weight is borne by the tire. I am using wheel/tire diameter to mean the outermost diameter of the wheel/tire combination.

    What percentage of in-accuracy would be introduced if the wheel/tire diameter was off by say 5mm or 10mm?
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  5. #5
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    Re: basic triangle leg formula help?

    Thanks - did my math come out right on this?

    Quote Originally Posted by HallsofIvy View Post
    For the upper blue triangle, you say that the length of the hypotenuse is 430 and the angle is 75 degrees. The cosine of an angle is "opposite side over hypotenuse" or \frac{x}{450}= cos(75). So x, the length of the vertical, is 450 cos(75). For the lower blue triangle, the length of the base leg is 270 and the angle s 75 degrees. The tangent of an angle "opposite side over near side" so \frac{x}{270}= tan(75). So x, the length of the vertical, is 270 tan(75).

    The total height is, of course, the sum of those two.
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  6. #6
    MHF Contributor ebaines's Avatar
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    Re: basic triangle leg formula help?

    HallsOfIvy- I think you misinterpreted the lower triangle. It's not a triangle at all - the OP is trying to say that the height of the bottim of the seat tube is at height off the ground equal to the radius of the wheel minus the "bb drop," or 339-69 = 270 mm. No angles are involved.

    Joebikes - you calculated a stand-over height of 270mm + 415mm = 685mm. A 5mm error in the radius of the tire gives an error of 5/685 = 0.73%. I'd say that's prett insignificant.
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  7. #7
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    Re: basic triangle leg formula help?

    Thanks - here is revised graphic / formula for clarity.

    Can anyone point out any errors? Thanks
    Joe

    basic triangle leg formula help?-screen-shot-2014-04-22-12.15.26-pm.png
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  8. #8
    MHF Contributor ebaines's Avatar
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    Re: basic triangle leg formula help?

    As I pointed out before - triangle Y is not necessary. The height from the ground to the bottom bracket has nothing to do with a triangle, so you should remove it.

    Also, triangle X as drawn is misleading - it would be clearer to have that triangle with hypotenuse aligned on the seat tube.

    Finally, regarding the definition of stand-over height - what you have calculated is the height of the top of the seat tube off the ground, but I think what you may actually want is the height of the top edge of the cross bar directly above the bottom bracket - right? To get that dimension you would need the angle of the crossbar to the seat tube and also the dimension from the bottom bracket to the point where the top edge of the crossbar meets the seat tube. See the attached fig - does that make sense?

    basic triangle leg formula help?-bike..jpg
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  9. #9
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    Re: basic triangle leg formula help?

    Here is a revision for an even more accurate calculation which takes into account the slope of the top tube
    and gives us the standover exactly over the center of the BB shell

    We know the seat angle is 75 deg -
    the complementary angle is 15 degrees (90-75)
    angle of 88.9 deg of top tube relative to seat tube as shown in the diagram

    Triangle Calculator

    the vertical leg which is now the hypotenuse is 442.89 measured -
    subtract the drop from to top of seat tube to top of top tube surface which is 30mm (diagram)

    = 412.89mm distance from center of bb vertically to top of top tube surface
    + (1/2 wheel diameter - bb drop which is 270mm)
    = standover centered over bb of 682.89 mm

    This is 2.46mm lower than the previous formula since this is the exact vertical distance on the BB center.

    On another note- can anyone tell me how to come up with an excel formula I can plug into a spreadsheet? That would be amazing!

    Thanks
    Joe
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  10. #10
    MHF Contributor ebaines's Avatar
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    Re: basic triangle leg formula help?

    You're asking how the 442.89 dimension is calculated? Using the Law of Sines: if A, B, and C are the lengths of the leg of the triangle and s, b, ans c are the opposite angles, then A/sin(a) = B/sin(b) = C/sin(c). In this case you have a=15 and b = 88.9, therefore c = 180-a - b = 76.1 degrees. Length C is 430, so length B is:

    B = sin(b) x C/sin(c) = 442.89 mm.

    One minor correction - you don't subtract 30 mm from this but rather the vertical projection of that 30 mm, since it's at an angle of 15 degrees to the vertical. So you subtract 30 x sin(b)/sin(c) = 30.90mm. This gives an end result of 442.89 - 30.90= 411.99 mm. You could have gotten this directly by using the length of the seat tube to the crossbar of 430-30 = 400 mm and using the Law of Sines as above.

    400 x sin(88.9)/sin(76.1) = 411.99
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  11. #11
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    Re: basic triangle leg formula help?

    I think I figured out the Excel formula

    Is this correct?

    =D4*(SIN(RADIANS(I4))/(SIN(RADIANS(K4))))
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  12. #12
    MHF Contributor ebaines's Avatar
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    Re: basic triangle leg formula help?

    Yes, though you've got some extra parentheses that aren't needed:

    =D4*SIN(RADIANS(I4))/SIN(RADIANS(K4))
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  13. #13
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    Re: basic triangle leg formula help?

    One more diagram I need help on - a trapezoid this time.

    I have the diagonal, a leg, angles. Need to know the length of the top base and how to calculate?

    basic triangle leg formula help?-screen-shot-2014-04-29-10.06.47-am.png
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  14. #14
    MHF Contributor ebaines's Avatar
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    Re: basic triangle leg formula help?

    You can use the same Law of Sines if you know the angle opposite the '?' leg (angle 'a' in the attached). To get that you first need to determine the angle opposite the 140mm leg ('b' in the figure). Again - Law of Sines is your friend.

    basic triangle leg formula help?-triangle3.jpg
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  15. #15
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    Re: basic triangle leg formula help?

    thanks - the declination of the diagonal is 86.9 degrees so I can figure the top right angle (apex) is 180 - 86.9 = 93.1 degrees

    but something must be wrong as I come up with the wrong dimensions for the diagonal which should be 547.6mm ??

    Sides:
    diagonal = 526.424 mm
    lower base = 499.952 mm
    right leg = 140 mm

    Angles:
    apex = 93.1
    right corner = 71.5
    left corner = 15.4
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