Chap.6 traverse surveys

CMgt2340 Surveying

Chapter 6 Traverse Surveys

Objectives

Match terms related to traversing with the correct definitions.

List major sources of error in traverse operations.

Perform traverse calculations in order to determine closure, accuracy, and area.

Perform a closed loop traverse.

Terms and Definitions

Angular Error Closed Traverse Departure Error of Closure Latitude Open Traverse

Sources of Error in Traverse Operations

Errors in measurement of angles and distances.

Poor selection of traverse points resulting in bad sighting conditions (into sun, through timber, etc.)

Failing to measure the angles an equal number of times direct and reversed (doubling and averaging)

9 Steps to Computing a Traverse’s Closure, Accuracy, and Area

1. Draw a sketch of the traverse with points and angles. 2. Compute the angular error and adjust the angles. 3. Compute the bearings or azimuths. 4. Compute Latitudes and Departures. 5. Compute the error of closure. 6. Compute the measure of accuracy. 7. Compute corrections for latitudes and departures. 8. Calculate Adjusted Latitudes and Departures. 9. Calculate the area of the traverse using the Double Meridian

Distance (DMD) method.

Problem (see figure 6.4 in text)

A five-sided closed field traverse has the following angles: A=101°24’00”, B=149°13’00”, C=80°58’30”, D=116° 19’00”, E=92°04’30”. The lengths of the sides are as follows: AE 350.10’, ED 579.03’, DC 368.28’, CB 382.20’, BA 401.58’.

Determine the traverse’s closure, accuracy, and area.

Closure (steps 1-5)

Step 1 Draw a sketch of the traverse with points and angles.

00”

00”

00”

30”

30”

Closure (steps 1-5)

Step 2 Compute the angular error and adjust the angles. (n-2)180= (5-2)180= 540°00’00”

BAE 101°24’00” +12” 101°24’12”

CBA 149°13’00” +12” 149°13’12”

DCB 80°58’30” +12” 80°58’42”

EDC 116°19’00” +12” 116°19’12”

AED 92°04’30” +12” 92°04’42”

Σ 539°59’00” +12” 540°00’00”

-1’00”/5=-12”

Closure (steps 1-5)

Step 3 Compute the azimuths (or bearings).

Course Azimuth Bearing

BAE 152°46’12” S27°13’48”E

AED 64°50’54” N64°50’54”E

EDC 1°10’06” N1°10’06”E

DCB 262°08’48” S82°08’48”W

CBA 231°22’00” S51°22’00”W

Closure (steps 1-5)

Step 4 Compute Latitudes and Departures. What are latitudes and departures? For any given line BA, latitude is the change in y and departure

is the change in x (see figure 6.6, p.167). Latitude (north is +, south is -). Departure (west is -, east is +). If a survey has been perfectly performed, the plus latitudes will

equal the minus latitudes and the same with the departures.

B

A

Dep. BA (-)

Lat. BA (-)

Closure (steps 1-5)

Step 4 Compute Latitudes and Departures.

Formula for finding Lats and Deps Latitude=Horizontal distance (H) cos θ Departure=Horizontal distance (H) sin θ

Closure (steps 1-5)

Step 4 continued

STA Distance Azimuth Latitude

(cos)

Departure

(sin)

BAE 350.10 152°46’12” -311.30 160.19

AED 579.03 64°50’54” 246.10 524.13

EDC 368.28 1°10’06” 368.20 7.51

DCB 382.20 262°08’48” -52.22 -378.62

CBA 401.58 231°22’00” -250.72 -313.70

On the TI-30xa calculator, enter 152.4612, 2nd key, DMS-DD, cos, X, 350.10

Closure (steps 1-5) Step 5 Compute the error of closure (E). Sum the latitudes and departures. Since they do not equal zero, the

traverse did not make it back to the original point. The mathematical distance between the original point and the new

point is the error of closure (E) (see Fig. 6.11, p 156). E=square root of (Σlat2+Σdep2)=sq rt (0.062+0.492)=0.49

Course Distance Azimuth Latitude

(cos)

Departure

(sin)

BAE 350.10 152°46’12” -311.30 160.19

AED 579.03 64°50’54” 246.10 524.13

EDC 368.28 1°10’06” 368.20 7.51

DCB 382.20 262°08’48” -52.22 -378.62

CBA 401.58 231°22’00” -250.72 -313.70

P= 2081.19 Σ= +0.06 -0.49

Accuracy (step 6)

Step 6 Compute the measure of accuracy. Precision Ratio= Error of Closure (E) to Total distance around

the traverse (P). Precision Ratio= E/P = 0.49/2081.19 Precision Ratios are always written with the numerator as 1,

thus if we divide both by the original numerator we have the new format (1/4247)

We then round the denominator to the nearest 100. = 1/4200

Accuracy (step 6)

What is the importance of the Precision Ratio? So that states and provinces are able to mandate the

level of competency on given works. A gravel road could pass with a 1/3000, whereas a

monorail would need a 1/7500 to 1/10000 level of precision.

In our example, if we specified that the survey must meet a 1/7500 Precision Ratio, we would have to resurvey because we are only at 1/4200.

Area (step 7)

Step 7 Compute corrections for latitudes and departures. Just like balancing angles, once we identify the sum of the

latitudes and departures, we need to distribute that error before proceeding.

One way to distribute the error is through the compass rule. This technique distributes errors in latitude and departure for

each course in the same proportion as the course distance is to the traverse perimeter.

Area (step 7)

The formula is as follows: C lat AB = Σ lat x AB/P Where C lat AB = correction in latitude AB Σ lat = error of closure in latitude AB = distance AB P = Perimeter of traverse (the formula for departure is the same, just substitute

dep for lat)

Area (step 7)

Using the calculator, we can set up a constant in memory such as .06/2081.19 and then multiply this by each course distance.

For example, for the latitudes, perform the above calculation and store it as M1. Then for each course, enter RCL1, X, the next course distance.

Area (step 7)

Since the sum of latitudes were positive error, the corrections become negative. The departures had negative error, so the corrections are positive.

Course Distance Latitude

(cos)

Departure

(sin)

C lat C dep

BAE 350.10 -311.30 160.19 -.01 +.08

AED 579.03 246.10 524.13 -.02 +.14

EDC 368.28 368.20 7.51 -.01 +.09

DCB 382.20 -52.22 -378.62 -.01 +.09

CBA 401.58 -250.72 -313.70 -.01 +.09

Σ= +0.06 -0.49 -.06 +0.49

Area (step 8)

Step 8 Calculate Adjusted Latitudes and Departures. Add the corrections to each original latitude and departure.

Latitude

(cos)

Departure

(sin)

C lat C dep Balanced

latitudes

Balanced

Departures

-311.30 160.19 -.01 +.08 -311.31 +160.27

246.10 524.13 -.02 +.14 +246.08 +524.27

368.20 7.51 -.01 +.09 +368.19 +7.60

-52.22 -378.62 -.01 +.09 -52.23 -378.53

-250.72 -313.70 -.01 +.09 -250.73 -313.61

+0.06 -0.49 -.06 +0.49 0.00 0.00

Area (step 9)

Step 9 Calculate the area of the traverse using the Double Meridian Distance (DMD) method.

To get started, transfer the dep for the 1st course into the DMD column.

Course Balanced

latitudes

Balanced

Departures

DMD DBL

Area

BAE -311.31 +160.27 160.27

AED +246.08 +524.27

EDC +368.19 +7.60

DCB -52.23 -378.53

CBA -250.73 -313.61

0.00 0.00

Area (step 9)

Next, multiply the DMD of the 1st by lat of 1st and record in DBL area for 1st.

Course Balanced

latitudes

Balanced

Departures

DMD DBL

Area

BAE -311.31 +160.27 160.27 = - 49,894

AED +246.08 +524.27

EDC +368.19 +7.60

DCB -52.23 -378.53

CBA -250.73 -313.61

0.00 0.00

X

Area (step 9)

Add DMD of 1st row to dep of 1st row to dep of 2nd row and record in DMD for 2nd row.

Course Balanced

latitudes

Balanced

Departures

DMD DBL

Area

BAE -311.31 +160.27 160.27 - 49,894

AED +246.08 +524.27 = 844.81

EDC +368.19 +7.60

DCB -52.23 -378.53

CBA -250.73 -313.61

0.00 0.00

+

Area (step 9)

Repeat the steps (multiply the DMD of the 2nd by lat of 2nd and record in DBL area for 2nd).

Course Balanced

latitudes

Balanced

Departures

DMD DBL

Area

BAE -311.31 +160.27 160.27 - 49,894

AED +246.08 +524.27 844.81 =+207,891

EDC +368.19 +7.60

DCB -52.23 -378.53

CBA -250.73 -313.61

0.00 0.00

X

Area (step 9)

Repeat the process until all calculations are made for all courses.

Course Balanced

latitudes

Balanced

Departures

DMD DBL

Area

BAE -311.31 +160.27 160.27 - 49,894

AED +246.08 +524.27 844.81 +207,891

EDC +368.19 +7.60 1376.68 +506,880

DCB -52.23 -378.53 1005.75 - 52,530

CBA -250.73 -313.61 313.61 - 78,631

0.00 0.00 533,716

Area (step 9)

Sum all of DBL areas and divide by 2 533,716 sq ft /2=266,858 sq ft Divide by 43,560 sq ft /acre to find answer in acres 266,858/43,560 = 6.126 acres

References Cited

Examples and step by step tutorials were copied directly from the following:

Mid-America Vocational Curriculum Consortium, Inc., Basic Surveying Technology, Stillwater, OK: Oklahoma State Department of Vocational Technical Education, 1987