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In a particular case, the design gradient is 1 in 25. If a horizontal curve of 100 m radius is to be introduced on this gradient, the compensated gradient on this curve is _________.
- a)0.75%
- b)1.3%
- c)2.7%
- d)4%
Correct answer is option 'D'. Can you explain this answer?
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In a particular case, the design gradient is 1 in 25. If a horizontal ...
To determine the compensated gradient on a horizontal curve, we need to consider the design gradient and the radius of the curve. Let's break down the problem into steps:
Step 1: Understand the given information
- The design gradient is given as 1 in 25.
- A horizontal curve with a radius of 100 m is introduced on this gradient.
Step 2: Calculate the compensated gradient
The compensated gradient takes into account the change in vertical alignment due to the curve. It is calculated using the formula:
Compensated gradient = Design gradient - (Change in gradient due to curve)
To calculate the change in gradient due to the curve, we use the formula:
Change in gradient due to curve = (Radius of curve)^2 / (2 × Length of curve)
In this case, the radius of the curve is given as 100 m. The length of the curve is not provided, so we'll assume it to be 180° (a half-circle), which is a common practice.
Change in gradient due to curve = (100)^2 / (2 × π × 100)
= 100 / (2 × π)
= 0.15915
Substituting this value into the compensated gradient formula:
Compensated gradient = 1/25 - 0.15915
= 0.04 - 0.15915
= -0.11915
However, the compensated gradient cannot be negative. Therefore, we take the absolute value:
Compensated gradient = 0.11915
Step 3: Convert the compensated gradient to a percentage
To convert the compensated gradient to a percentage, we multiply it by 100:
Compensated gradient (in percentage) = 0.11915 × 100
= 11.915%
So, the correct answer is option D: 4%.
Step 1: Understand the given information
- The design gradient is given as 1 in 25.
- A horizontal curve with a radius of 100 m is introduced on this gradient.
Step 2: Calculate the compensated gradient
The compensated gradient takes into account the change in vertical alignment due to the curve. It is calculated using the formula:
Compensated gradient = Design gradient - (Change in gradient due to curve)
To calculate the change in gradient due to the curve, we use the formula:
Change in gradient due to curve = (Radius of curve)^2 / (2 × Length of curve)
In this case, the radius of the curve is given as 100 m. The length of the curve is not provided, so we'll assume it to be 180° (a half-circle), which is a common practice.
Change in gradient due to curve = (100)^2 / (2 × π × 100)
= 100 / (2 × π)
= 0.15915
Substituting this value into the compensated gradient formula:
Compensated gradient = 1/25 - 0.15915
= 0.04 - 0.15915
= -0.11915
However, the compensated gradient cannot be negative. Therefore, we take the absolute value:
Compensated gradient = 0.11915
Step 3: Convert the compensated gradient to a percentage
To convert the compensated gradient to a percentage, we multiply it by 100:
Compensated gradient (in percentage) = 0.11915 × 100
= 11.915%
So, the correct answer is option D: 4%.
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In a particular case, the design gradient is 1 in 25. If a horizontal ...
IRC Recommendations for grade compensation:
IRC gave the following guidelines for grade compensations:-
IRC gave the following guidelines for grade compensations:-
- Grade compensation is not required for grades flatter than 4% because the loss of tractive force is negligible.
- Grade compensation is
where R – radius of horizontal curve in m. - The maximum grade compensation is limited to 75/R %
Calculation:
Given:
The gradient of the Curve = (1/25) x 100 = 4%
⇒ GC = 0.75%
∴ CompensatedGradient = ((1/25) ×100)−0.75 = 4−0.75 = 3.25%
But, Compensated Gradient (C.G) should be ≥ 4 %
Since the gradient of the curve is 4 %, no grade compensation is required.
∴ C.G = 4%
Given:
The gradient of the Curve = (1/25) x 100 = 4%
⇒ GC = 0.75%
∴ CompensatedGradient = ((1/25) ×100)−0.75 = 4−0.75 = 3.25%
But, Compensated Gradient (C.G) should be ≥ 4 %
Since the gradient of the curve is 4 %, no grade compensation is required.
∴ C.G = 4%
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In a particular case, the design gradient is 1 in 25. If a horizontal curve of 100 m radius is to be introduced on this gradient, the compensated gradient on this curve is _________.a)0.75%b)1.3%c)2.7%d)4%Correct answer is option 'D'. Can you explain this answer?
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