Omitted measurements in surveying: Type, Cases, Calculations and Law

Sometimes it becomes very difficult to measure all bearing and measurements due to field condition like a river or some other obstacles and for this some reading may be omitted.

Since there is calculation become hard, it is very important to know the theory of omitted measurements in the surveying.

Law of closed traverse for finding unknown measurement

In the closed Traverse, there is latitude and departure of each part. This is very important in surveying and traversing. From the rule of closed traverse we can easily find omitted measurements

The one basic law of surveying state that

• Algebraic sum of the all latitude is always zero. And Algebraic sum of all departure is zero.

If the Length of a Traverse Line is l and Angle is x then We can find Latitude as follow

• Latitude L= l cosx

And the Departure of a Line is

• Departure D = l sinx

And for finding length from latitude and departure is:

l = √(L²+D²)

Angle of the line or bearing is calculated by,

x = arctan(D÷L)

This calculation give us information about latitude and departure and length of traverse line for theodolite traversing.

Also some measurement which is omitted, they are also parts of closed traverse. Therefore we can apply this calculation for this.

For the latitude,

• ΣL= 0

And for departure

• ΣD= 0

From this equations we know two unknown.

Cases for omitted measurement

There is some common types of omitted measurement in closed traverse that is as follow.

1. Length of one line is omitted.
2. Length of two lines are not measured.
3. Length of one line and bearing of other line are not measured.
4. Bearing of one line is missing.
5. Bearing and length of same line are missing.
6. Bearing of two lines are missing.

For a closed traverse the omitted measurements may be calculated by above methods..

These cases is usually seen when there is some obstacles like river is between taking reading in field in theodolite surveying. 

However by using the above formula and some calculations, we can find all information related omitted readings.

There may be a question that How can we find this readings?

There is some methods for each case and by this methods we get the all omitted measurements. 

This methods are in details given below with the each case and the technique for each part to know omitted readings in the traversing.

Lets see the case of one line omitted.

Length of one line is omitted/ Bearing of one line or both is missing.

When we calculated traverse and there is bearing or length of one line is missing then it is known by using the method that is as follow.

• First a traverse is ABCDEF that is closed traverse.

• There is length of the line FA is missing or bearing of line FA is missing or both bearing and length is not measured.

• We can calculate the ΣL' and ΣD' for the five sides that we know.

• Therefore we can calculate ΣL' and ΣD' for AB, BC, CD, DE and EF.

If the length of unknown side is l and angle is x and the latitude is L and departure is D then we can find L and D as follow.

ΣL = 0 

ΣL = L+ ΣL' 

So, 

L+ ΣL' = 0

ΣL' = -L 

OR

L = -ΣL'

By same calculation we get departure of unknown

D = -ΣD'

From the above equations, we can know departure and latitude of unknown side.

If we want to find length or bearing of that side than we can calculate it as follow.

Bearing of unknown x is

x = arctan(ΣD'/ΣL')

and length of that side is

l = √(ΣL'²+ΣD'²)

So, we can find latitude, departure, bearing and total length of the one line that is omitted.

This is case when one line's information is omitted but as we see previously that there may be other case such as length of two sides omitted. For that we have to use different method to finding that length.

Let's see method for two sides of traverse.

Length of two lines are omitted.

This become difficult because we cannot directly use latitude or departure to calculate. There is different method that give us a way to know in this condition.

• First consider the traverse ABCDEF.

• This traverse is closed traverse, for this there is two sides are unknown that is EF and FA.

• Other sides of length is measured that is AB, BC, CD, DE.

• For this we can assume that ABCDE is closed traverse with the all information is known.

• For that traverse, length of EA is calculated by method of case of when one length omitted.

• Now we can assume the triangle for which is is easy to calculate the length of sides.

• Therefore, consider triangle AEF.

• In this triangle, one length is known and the all angles of triangle can be calculated.

Assume that this angle is x, y and z then we can calculate unknown length from the basic equations of triangle.


EF/sinx = FA/siny= EA/sinz


From this we have the all angles and one length EA, so we can for length EF,

EF = EA sinx/sinz

and the other unknown length

FA = EA siny/sinz

Therefore we can find both unknown length and after finding this we can calculate departure and latitude of it.