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In levelling, the correction for curvature (in meters) is approximately:

0.0785 D²

where DDD is the distance in kilometers. This correction accounts for the curvature of the Earth over the measured distance.

The length of a traverse line (L) can be obtained by:

L = √[(Latitude)² + (Departure)²]

Here, "Latitude" refers to the north-south component of the line, and "Departure" refers to the east-west component. This formula uses the Pythagorean theorem to calculate the distance between two points in a traverse.

The amount of super-elevation on railways is equal to:

Gv²/127R

Explanation:

• G: Gauge of the railway track (in mm)

• V: Speed of the train (in km/h)

• R: Radius of the curve (in meters)

This formula is derived from equilibrium conditions where the centrifugal force is balanced by the component of the weight of the train due to superelevation.

The deflection angle may be directly obtained by setting the instrument to read 0° on back station.

By setting the instrument to 0° on the back station, the reading on the fore station will directly give the deflection angle. This is because the deflection angle is the angle between the prolongation of the previous line and the new line.

To find the true bearing of the line, you need to adjust the magnetic bearing by the magnetic declination. Since the magnetic declination is east, you subtract the declination from the magnetic bearing to get the true bearing.

Given:

• Magnetic bearing: S 35° 30' E
• Magnetic declination: 4° 10' east

Here’s the calculation:

1. Convert the magnetic bearing to a standard format if necessary. For S 35° 30' E, this is 180° + 35° 30' = 215° 30' in a standard format.
2. Convert the declination to standard format: 4° 10' = 4.1667°.
3. Subtract the declination from the magnetic bearing: 215° 30' - 4° 10' = 211° 20'.

Convert 211° 20' back to the bearing format:

• Since it falls in the S E quadrant, the true bearing is S 31° 30' E.

So the true bearing of the line is S 31° 30' E.

To find the magnetic declination given the magnetic bearing of the sun at noon, you need to compare it to the true bearing, which is typically 180° (due south) at noon.

Given:

• Magnetic bearing of the sun at noon: 185° 20'

The true bearing of the sun at noon should be 180° (due south). The difference between the magnetic bearing and the true bearing indicates the declination.

1. Calculate the difference between the magnetic bearing and the true bearing: 185° 20' - 180° = 5° 20'

Since the magnetic bearing is greater than the true bearing, the declination is east.

So the magnetic declination is 5° 20' east.

To find the true bearing of a line when given the magnetic bearing and magnetic declination, you need to adjust the magnetic bearing based on the declination.

Here's the process:

1. Magnetic Bearing (MB): 55° 30'
2. Magnetic Declination (MD): 4° 30' west

Since the declination is west, it means the true bearing will be less than the magnetic bearing. You need to subtract the declination from the magnetic bearing:

True Bearing=Magnetic Bearing−Magnetic Declination\text{True Bearing} = \text{Magnetic Bearing} - \text{Magnetic Declination}True Bearing=Magnetic Bearing−Magnetic Declination

Convert both to decimal degrees:

• Magnetic Bearing: 55° + 30'/60 = 55.5°
• Magnetic Declination: 4° + 30'/60 = 4.5°

Calculate:

True Bearing=55.5°−4.5°=51°\text{True Bearing} = 55.5° - 4.5° = 51°True Bearing=55.5°−4.5°=51°

So, the true bearing of the line is 51°.

The shift (or deflection) of a curve is a measure of how much a curve deviates from its theoretical position due to its radius and length. For a simple circular curve, the shift can be calculated using the formula:

Shift=L224R\text{Shift} = \dfrac{L^2}{24R}Shift=24RL2​

Where:

• LLL is the length of the curve.
• RRR is the radius of the curve.

So the correct answer is:

L224R\dfrac{L^2}{24R}24RL2​

90°

At the magnetic poles, the amount of dip (or inclination) is 90°. This is because the Earth's magnetic field lines are vertical at the magnetic poles, meaning the dip angle, which measures the angle between the Earth's magnetic field and the horizontal plane, is 90°.

The hydraulic efficiency of an impulse turbine is the ratio of the work done on the wheel to the energy of the jet.

This efficiency measures how effectively the kinetic energy of the jet is converted into mechanical work on the turbine wheel.