COMPOSITE LAND IN DISPUTE PLAN

SURCON QUESTION: YOU HAVE BEEN ASKED TO PRODUCE A COMPOSITE LAND IN DISPUTE PLAN FROM THREE EXISTING ONE. PLAN MARKED EXHIBIT “A” WAS PREPARED IN 1923 WITH THE DIRECTION OF TRUE NORTH SHOWN AND SCALE INDICATED. NO BEARINGS AND DISTANCES WERE GIVEN. PLAN MARKED EXHIBIT “B” WAS PREPARED IN 1940 ON TRUE NORTH WITH BEARINGS, DISTANCES AND SCALE GIVEN. THE THIRD PLAN MARKED EXHIBIT “C” WAS PREPARED IN 1972 ON NATIONAL NORTH WITH BEARINGS, DISTANCES AND SCALE INDICATED. A SURVEY BEACON NUMBER TA 5429 IS FOUND COMMON TO ALL THE THREE PLAN. DESCRIBE HOW YOU WOULD PREPARE THE COMPOSITE PLAN ON UTM.

Plan “A”: Scale, True North

Plan “B”: Scale, True North, bearings and distances

Plan “C”: Scale, National North, bearings and distances

The composite plan shall be prepared through coordinate transformation as follows:

1.      Plan “A” shall be transformed to plan “B”

2.      Plan “B” shall be transformed to plan “C”

3.      Plan “C” shall be transformed to UTM

1. Transforming plan “A” to plan “B”

Plan “A” and plan “B” have common North direction. This implies that the axes of their reference ellipsoids, and that of their prime meridian is Greenwich. And since no bearing and distance is indicated, no coordinate transformation canbe carried out from one plan to the other. However, if the scales are different, we shall find the scale correction and apply it to the coordinates of plan “B”.

2. Transforming plan “B” to plan “C”

Plan “B” and plan “C” have two different north direction and therefore different coordinate systems, which can be transformed from one to another. Since plans have common survey beacon TA 5429, coordinates of the beacon shall be transformed from plan “B” to plan “C” using 7-parameter transformation. Thus,

Where

[X_B, Y_B] : Coordinates of plan “B”

[X_C, Y_C]: Coordinates of plan “C”

[d_X, d_Y]: Transformation vectors

[R_X, R_Y]: Rotations

M: Scale correction

3. Transforming plan “C” to UTM

Transformation of plan “C” to UTM shall be done by using the formular:

Where

[X, Y] : Coordinates of new UTM plan

[X_C, Y_C]: Coordinates of plan “C”

[X₀, Y₀]: Coordinates of local origin

R: Rotation matrix

The new plan will be drawn using the final transformed coordinates.

DISCLAIMER: This material is only an attempt to answer an examination question, though written from a background of solid knowledge and practical experience in Surveying and Geoinformatics. It has not gone through peer review. Therefore, all views and opinions expressed therein remain the responsibility of the author and do not necessarily represent that of any institution.  Feedback on corrections and constructive criticisms are welcome. ThanK you.