Magnetic Declination

Magnetic declinations

Sample Problems

Magnetic Declinations

Magnetic declination, or magnetic variation, is the angle on the horizontal plane between magnetic north and true north. This angle varies depending on position on the Earth's surface and changes over time.

The magnetic bearing of line XY is S 45°15’ E, compute its true bearing if the magnetic declination at that instant is 1°15’ east.

TN

solution

MN

Sketch:

1°15’

Given:

Magnetic Bearing = S 45°15’ E

Magnetic Declination = 1°15’ E

45°15’

Find:

True Bearing (θ)

MS

Note: Sketch is not drawn to scale.

TS

TN

solution

MN

Sketch:

1°15’

True Bearing:

θ = 45°15’ - 1°15’

1°15’

45°15’

= 44°00'

θ = S 44°00’ E

MS

Note: Sketch is not drawn to scale.

TS

In 1991 a line AB had a magnetic bearing of Ñ 22°15’ W. The declination of the needle at that place in 1991 was 02°25’ west. In 2006 the declination was 04°25’ east. What was the magnetic bearing of the line in 2006? Its true bearing?

TN

MN 1991

solution

Sketch:

MN 2006

2°25’

22°15’

4°25’

Given:

Magnetic Bearing 1991= N 22°15’ W

Magnetic Declination 1991 = 2°25’ W

Magnetic Declination 2006 = 4°25’ E

MS 2006

Find:

Magnetic Bearing 2006 (β)

MS 1991

True Bearing (θ)

Note: Sketch is not drawn to scale.

TS

TN

MN 1991

solution

Sketch:

MN 2006

2°25’

True Bearing:

22°15’

4°25’

θ = 22°15’ + 2°25’

= 24°40’

θ = N 24°40’ W

Magnetic Bearing 2006:

β = θ + 4°25'

= 24°40' + 4°25’

MS 2006

= 29°05'

MS 1991

β = N 29°05' W

Note: Sketch is not drawn to scale.

TS

PROCESS

PROCESs 01

Determine the given values

PROCESs 02

Sketch

PROCESs 03

Solve

Your turn!

The magnetic bearing of a property line was recorded as S 43°30’ E in 1862. At that time the magnetic declination at the survey location was 3o15’ W. What geodetic (true) bearing is needed for a subdivision property plan?In 2010 a line had a magnetic bearing of Ñ 80°23’ E. At that time the magnetic declination was 3o°45’ west. In a new survey performed in 2017, the declination in the same locality changed to 2o°50’ east. Determine the magnetic bearing and true bearing of the line based on the new survey. In 2015 a line had a magnetic bearing of Ñ 50°23’ E. At that time the magnetic declination was 3o°45’ west. Determine the true bearing and the present magnetic bearing of the line, if the annual variations of the same locality is 0°10’ east.

thanks!