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Math Help - highway curves problems solving

  1. #1
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    Thumbs up highway curves problems solving

    Two tangents that intersect at an angle of 27 degrees 24 minutes are connected by a 4 degrees curve whose degree is based on a chord of 100 feet and whose point of curve is at station 3 + 35. What is the distance along the long chord from the point of curve to the foot of the perpendicular at station 4 + 00?
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  2. #2
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    The PC is at station 3+35. By foot of perpendicular, I suppose you want to know how far it is from station 3+35 to station 4+00, 65 feet, a straight distance and not along the curve?. I am not sure I am understanding correctly.

    The radius of the curve can be gotten from \frac{5730}{D}=\frac{5730}{4}=1432.5. I am assuming you mean the degree of the curve is 4 degrees and the Delta angle is 27.4 degrees?.

    The angle deflection can be gotten from \frac{28.648}{1432.5}=.02. That is degrees per foot.

    Multiply by 65 to find the angle of deflection at 65 feet and we get

    1.3 degrees. That is the angle we would turn with our transit to fix that station 4+00.

    2(1432.5)sin(1.3)=64.999

    That is the length of the short chord. Which is 65 feet for all intents and purposes.

    Remember, the delta angle is 27.4. If you were to set up the transit, back sight, turn over and turn a deflection of half the delta, that should put you on your PT(point of tangency).

    I hope I understood your problem correctly. I have laid out many roads and bridges, so if I know what you mean I should be able to help.
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