Civil Engineering - Surveying - Discussion

Given:

Accuracy of offset measurement = 1 in 40
Permissible error on paper = 0.05 cm.
Scale = 1 cm = 20 m.

Step 1: Convert paper error to ground error.
So, the maximum permissible error on the ground = 1 m.

Step 2: Errors involved.

There are two independent errors:
1.Error due to measurement
Linear measurement error≈ L/40.

2.Error due to angular error:
Angular error ≈ L/40 rad for offset measurement.

Step 3: Resultant error.
√(L/40)^2+(L/40)^2 = L√2/40.
This should not exceed 1 m:

Step 4: Solve for L.
L√2/40<=1 m.

Final Answer: Maximum length of offset ≈ 28.8 m.

The displacement due to angular error =Lsin.
and it should be equal to displacement due to Linear error = L/r.
Corresponding displacement on paper=√2(L/r)(1/S)= √2(Lsin-/S).
Corresponding if a limit of accuracy in plotting is 0.05cm then,
√2(L/r)(1/S)=.05,
L= (.05x40x20)/√2.
= 28.28.
Where S=1 in accuracy.
r=1 in scale.

The center-to-center dimension for a 45-degree bend is equal to the desired size of the offset times the cosecant 1.414.

A cosecant is used to determine the distance between the centers of the two bends used to make an offset. A 45-degree angle has a cosecant of 1.414.

Actually, the maximum length of offset 1/40 cm it means 0.025mm.

But the above question's maximum length of offset 0 .05cm. It means 0.5 mm or 1/20 cm
So, the maximum length of offset=s/20*r/√2.
S = 20
r = 40.
So, 20/20*40/√2.
= 28.32m.

Formula : Limiting error = (L/sin@) * (1/r) * (1/S).

∠ = 45' for max limiting offset.
1/r = 1:40 = accuracy of measurement.
1/S= 1:20 = scale.
Limiting error = 0.05 cm.

L = 20*(2)^0.5.
L= 28.28 m.

I think 200 is the correct answer.

1/40 accuracy on the map means 50 cm on the ground according to scale.
This means the offset is rounded to the nearest 50 cm and this applies only on 200 m.

Nowhere is mentioned that linear measurement is equal to angular measurement then, what is the reason to get answer 28.28?

This formula is applicable maximum errorrs/√2.

28.28 correct answer.

1/100 = 0.01m.
40/100 = 0.4,
0.01m/20m = 0.4m/x,
X^2 = 800,
X = 28.28.

The maximum length or limiting length=L * S/sin0.
S=scale,
0=45°