Calculating Area of Land using simple levelling tools

 Calculating Area of Land plot of un-equal sides just by using simple levelling tools Such as Auto level, Dumpy level etc.

yogendra borse

        Generally what we civil enginners are asked to build looks like as shown in below Plan (Sometimes typical type plans for certain organizations) , but actual land available may not suit it sometimes, so boundrirs and area calculation becomes important in such cases. It is also important because your Plot Area should match area mentioned in 7/12 so that future conflicts can be avoided.

Expected Building Plan (Just for Example)

Available Plot

Advantages:-

1) Survey can be carried out using simple tools

2) Calculations are relatively easy (No complex trignomerty)

Concepts Used:-

1) (Upper Stadia reading - Lower stadia reading) x 100 = L

Where L --> Distance between station and Point where level is taken.

2) Lcos Ө = Latitude (X- co-ordinate)  &  Lsin Ө = Departure (X- co-ordinate)

Where Ө => Whole Circle Bearing (WCB) 

3) Double meridian Distance Method  - To Calculate Area

Step 1:- Calculate Latitude (X- coordinate) & Departures (X- coordinate) of all points 

Point	Angle	Upper	Lower	distace	Latitude (Xi)	Departure (Yi)	Distance between 2 ponits
1	329	1.37	0.855	51.5	44.1441159861588	-26.5244608578678	104.047
2	122	2.61	2.055	55.5	-29.4105191649429	47.0666693366816	135.446
3	234	5.201	4.156	104.5	-61.4235588645635	-84.542275912182	43.102
4	257	5.256	4.156	110	-24.7446159778252	-107.180707126376	106.071
5	329	1.37	0.855	51.5	44.1441159861588	-26.5244608578678

Step 2:- Use Double Meridian distance Method to Calculate area

SR	Xi	Yi	xi*yi+1	xi+1*yi	xi*yi+1 - xi+1*yi
1	44.1441159861588	-26.5244608578678	2077.71651028066	780.098164400098	1297.61834588056
2	-29.4105191649429	47.0666693366816	2486.43222596311	-2891.00233456061	5377.43456052372
3	-61.4235588645635	-84.542275912182	6583.42047332248	2091.96615133828	4491.4543219842
4	-24.7446159778252	-107.180707126376	656.337597946794	-4731.39756686525	5387.73516481205
5	44.1441159861588	-26.5244608578678	0	0	0
Total					16554.2423932005

Area = ∑ (xi*yi+1 - xi+1*yi)/2

Hence Area of polygon = 8277.121 sq.m

In 7/12 area is 8000 sq.m, Hence it is necessary to consult Bhumiabhilekh department regarding boundries and then accordingly plan.