Eg:
Calculate the ordinates on a long chord at 10m. interval for a circular curve of radius 450m. & long chord of 100m.
Given data:
Radius of curve = R = 450m.
Length of long chord = L = 100m.
Ordinate interval over long chord = x = 10m.
To find:
Length of ordinates at 10m. intervals to draw a curve.
Calculation:
1. Length of Mid-ordinate = Oo
= [ R - √ {R² - ( L/2)²} ]
= [ 450m. - √ {450² - ( 100/2)² }]
= [ 450m. - √ 200000 ]
= [450m. - 447.214m.]
Oo = 2.786m.
Ordinate at various intervals is calculated by the formula
Ox = [√ R² - x² - ( R - Oo) ]
Where x is the distance of ordinates over the long chord.
2. 1st ordinate at 10m. interval
O10 = [√ ( R² - x²) - ( R - Oo) ]
= [√ (450² - 10²) - ( 450 - 2.786)]
= [√ 202,400 - (447.214)]
= [449.888 - 447.214]
O10 = 2.674m.
Similarly,
3. 2nd ordinate at 20m. interval
O20 = [√ (450² - 20²) - ( 450 - 2.786)]
= [ √ 202,100 - 447.214]
= [449.555 - 447.214]
O20 = 2.341m.
4. 3rd ordinate at 30m. interval
O30 = [√ (450² - 30²) - ( 450 - 2.786)]
= [ √ 201,600 - 447.214]
= [448.998 - 447.214]
O30 = 1.784m.
5. 4th ordinate at 40m. interval
O40 = [√ (450² - 40²) - ( 450 - 2.786)]
= [ √ 200,900 - 447.214]
= [448.21 - 447.214]
O40 = 1.005m.
Note:
As the length of the long chord is 100m., the length of half of the long chord i.e. L/2 = 50m. So the length of the 5th ordinate at 50m. distance should be equal to zero.
Check:
6. 5th ordinate at 50m. interval
O50 = [√ (450² - 50²) - ( 450 - 2.786)]
= [ √ 200,000 - 447.214]
= [447.214 - 447.214]
O50 = 0m. ✔
Now, let us draw the curve by calculated measurement of ordinates as shown below.
Go through the article 👇
👀. Deriving long chord method for ordinates to draw a curve.
Note:
By symmetry, the length of the ordinates on another half of the curve will be the same at a given interval over the long chord.
To understand A to Z of surveying, click here.
Thank you for going through these calculation steps❤. Have a good day 😄.
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