Setting Out Arc

  1. Hello all

    I was hoping someone could help me with a geometry problem.

    Firstly this is not a homework question – this is work related I am just not very good with Maths.

    I have been asked to set out an arc for a wall. I have been given all the values I need but I do not know how the values were work out.

    The problem is this:-

    I have an arc with a radius and start co-ordinates and end co-ordinates, there are straight lines that are tangent to the arc on either side.

    If I was standing on the start of the arc and walked 10m in the x axis what would the Y value be to the arc.

    Hope that makes sense.

    I have attached a sketch to help get my point across. I really want to know how it is worked out.

    Thanks
     

    Attached Files:

    Last edited: Apr 23, 2014
  2. jcsd
  3. phinds

    phinds 8,748
    Gold Member

    Problem is indeterminate given that information. The most significant piece of information not provided is what KIND of arc is it? I guess we can assume circular with radius R, but asking people to help solve a problem based on assumptions can be a waste of time. Also, you HAVE to specify at least one of Y1, Y2. Also, is the blue line supposed to be vertical?

    You should post your image up and down, not sideways.
     
  4. I see the confusion.

    The idea was to find a generic way of getting the results but by stating R=2000 I realize the issue the problem it has caused.

    So to be specific:-

    The green line is straight and tangent to the arc at co-ordinates 860,102.800.
    The arc has a radius of 2000 & is circular.
    The blue line is straight and tangent to the arc at co-ordinates 900, 103.202.
    The points are all in a flat plane and is represented in a standard Cartesian coordinates system.
     
  5. phinds

    phinds 8,748
    Gold Member

    So X1 is both 200 and 860 and X2 is both 230 and 900. You have lost me completely.
     
  6. X1= 860, y1= 102.800
    x2 = 900, y2 = 103.202
     
  7. phinds

    phinds 8,748
    Gold Member

    Yes, I heard that the first time. So what are the X axis indicators on the chart itself?
     
  8. I have redone the sketch, hopefully this will clear things up
     

    Attached Files:

  9. phinds

    phinds 8,748
    Gold Member

    OK, NOW I belive that you have a full problem statement that probably has a solution. I'm hoping, for your sake that there is an easier way than what I have to find the solution, but here's one way:

    You have two points (X1,Y1 and X4,Y4) which will give you the slope of the line between them

    You can easily get the midpoint between the two

    Now you have a point and the inverse of the slope, which gives you the equation of a line.

    You have one point on the line and you know that there is another point on the line that is the center of the circle (but you don't know how far away it is) and you know the radius of the circle

    From that you can construct a rather messy equation for the circle that will have unknowns in it

    You have two points on the circle and an equation for the circle.

    The SHOULD, I think, be enough to solve for the unknows, thus giving you the equation of the circle.

    From there you just plug in the X values and solve for the Y values.

    Good luck with that.

    The green and blue lines, by the way, are totally irrelevant and can be erased. They have no bearing on the solution.

    Also, based on the numbers you gave for X1,Y1 and X2, Y2 (which I assume is not X4,Y4), your drawing is massively out of scale so I'm dubious about this actually being a real-world problem.
     
    Last edited: Apr 23, 2014
  10. LCKurtz

    LCKurtz 8,369
    Homework Helper
    Gold Member

    Your first post would mean (900, 103.202) is (x4,y4) and your second post means it is (x2,y2). You have both phinds and me confused about that. Which is it?

    Also, are the two straight lines given ahead of time and the curve has to match their slopes or do you make them tangent to the circle after you are done?
     
  11. phinds

    phinds 8,748
    Gold Member

    That's irrelevant. You have 2 points and a radius so the circle is defined. If the lines are to be tangent to the circle, it doesn't matter whether you draw them first or later. In one sense they matter in that they tell you that the defined circle is a specific one of the two that are possible given 2 points and a radius.
     
  12. LCKurtz

    LCKurtz 8,369
    Homework Helper
    Gold Member

    Yes, I am aware of that. But I don't know if the OP is, and I don't know if he has given all the pertinent information. For all we know, he may have data inconsistent with the arc actually being a circle, even though he has specified a circle (after being asked). Given that he is setting out an arc for a wall, I would doubt that the direction of the wall is arbitrarily determined by the arc. And, for that matter, maybe the wall doesn't really have to be literally tangent to the arc.
     
    Last edited: Apr 24, 2014
  13. LCKurtz

    LCKurtz 8,369
    Homework Helper
    Gold Member

    @tomtomtom1: Is this a real world construction site problem where you have the two walls specified and need to lay out a chalk line for the arc between them?
     
  14. phinds

    phinds 8,748
    Gold Member

    Reasonable point.
     
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