8.3 Traverse Adjustment and Side Shots

8.3 Traverse Adjustment and Side Shots

Quick Answer: Compass (Bowditch) rule corrects each latitude by −Σlat × (L / P) and each departure by −Σdep × (L / P). On ABCD, that returns the loop to N 5,000.00, E 2,000.00. Transit rule uses |lat| / Σ|lat| and |dep| / Σ|dep| instead of length. A side shot is not a loop course: compute it from the adjusted station and leave it out of P. Neither Compass nor Transit is a BPELSG-mandated CES method; they are the standard hand methods the exam expects you to know.

Why adjust

Unadjusted A′ in Section 8.1 is 0.19 ft south and 0.17 ft east of held A. If you stake a catch basin from unadjusted C, then later hold A and B from a different crew’s adjusted file, the basin moves. Adjustment distributes the known loop residual so every station is on one consistent coordinate set. It does not prove the field measurements were perfect; it makes the geometry usable.

Do the angular balance first (Section 8.2). Compass rule then treats remaining Σlat and Σdep as distance-like error to be shared by length.

Compass (Bowditch) rule

For each course i:

Correction in latitude = −Σlat × (Lᵢ / P) Correction in departure = −Σdep × (Lᵢ / P)

ABCD: Σlat = −0.19 ft, Σdep = +0.17 ft, P = 1,770.20 ft.

−Σlat = +0.19 ft (add north, because the loop was 0.19 ft south). −Σdep = −0.17 ft (subtract east, because the loop was 0.17 ft east).

Length ratios:

Corrections (0.19 × L/P north, −0.17 × L/P east):

The longest course (DA) takes the largest Compass correction. That is the Bowditch idea: random linear error is assumed to accumulate with length.

Adjusted coordinates

Accumulate the unrounded adjusted latitudes and departures, then round stations to 0.01 ft:

Check: 5,000.00 + 285.1714 = 5,285.1714 → 5,285.17. Then 5,285.1714 − 156.5957 = 5,128.5757 → 5,128.58. Then 5,128.5757 − 411.0197 = 4,717.5560 → 4,717.56. Then 4,717.5560 + 282.4441 = 5,000.00. Eastings close the same way to 2,000.00.

If a CES item gives you only two courses and P, you can still compute one correction: corr_lat(AB) = −Σlat × 385.50 / 1,770.20. You do not need a spreadsheet.

Transit rule (know it; apply Compass on this loop)

Transit rule:

Correction in latitude of course i = −Σlat × (|latᵢ| / Σ|lat|) Correction in departure of course i = −Σdep × (|depᵢ| / Σ|dep|)

For the unadjusted ABCD table, Σ|lat| = 1,135.23 ft and Σ|dep| = 1,282.59 ft.

CD has the largest |latitude| (411.07 ft), so Transit piles latitude correction on CD even though DA is longer. Compass piled latitude correction on DA because DA is longest. The two rules agree only when |lat| (or |dep|) happens to track length—pure cardinal courses, not this mixed loop.

CES hand items almost always want Compass on a closed traverse of mixed bearings. Transit appears as a “which statement is true” discriminator. Least-squares network adjustment exists in office software; it is not what this chapter is teaching you to grind on a Prometric calculator. Do not claim Compass, Transit, or least squares is the method BPELSG requires. The test plan asks you to perform traverse calculations, including closure, error, and side shots.

Side shots

A side shot (radial shot, spur, side observation) locates a point from a traverse station but is not a side of the loop. Hydrants, catch basins, building corners, and utility inverts are usually side shots. They:

1. Do not enter the Σlat / Σdep table.
2. Do not enter the perimeter P used for Compass or Transit.
3. Are computed after the station is adjusted, using the adjusted northing and easting.

Worked side shot from adjusted B

From adjusted B (N 5,285.17, E 2,259.41), a hydrant H is N 12°00' E, 85.40 ft horizontal.

Azimuth = 12°00'. lat = 85.40 × cos 12° = 85.40 × 0.978148 = +83.53 ft dep = 85.40 × sin 12° = 85.40 × 0.207912 = +17.76 ft

Using unrounded addends: H northing = 5,285.1714 + 83.5338 = 5,368.71 ft H easting = 2,259.4130 + 17.7557 = 2,277.17 ft

If you instead computed H from unadjusted B (5,285.13, 2,259.45), you would be 0.04 ft south and 0.04 ft east of the adjusted hydrant—the AB Compass correction you skipped. On this tight loop that is a hundredth-level miss; on a 1:2,000 loop it is a tenth. The method error is the same: side shots inherit the adjusted station.

Exam trap: putting H in the Bowditch table as a fifth course so P becomes 1,855.60 ft. That steals closure correction from AB–BC–CD–DA and moves B, C, and D to make a random hydrant “fit.” The loop no longer represents the measured circuit. Leave 85.40 ft out of P.

Open traverse versus closed

Closed traverse: returns to the starting station (this ABCD loop) or closes on a station whose coordinates are already in the same system. Σlat and Σdep versus zero (or versus the known closing ΔN/ΔE) are the check.

Open traverse: starts on known A and ends on a different known point E (a highway centerline from a CCS83 pair to another CCS83 pair, or from a GPS control to a second GPS control). There is no Σlat ≈ 0 identity unless you insert the known A→E line as a closing course. Linear closure is the difference between computed E and published E:

E_linear = √((N_comp − N_pub)² + (E_comp − E_pub)²)

You may still Compass-adjust an open link between two fixed ends by treating the misclosure against the known end the same way you treated Σlat/Σdep against zero. You may not invent a return course you did not measure just to force a zero sum.

Civil engineering surveying under BPC 6731.1 often looks like a short closed loop around a site plus side shots to fixed works, or an open alignment traverse between two control points. It is not a PLS Record of Survey. Keep the hydrant out of the loop table either way.

Exam traps

• Applying Compass corrections in proportion to |lat| (that is Transit) or splitting Σlat equally (that is an angle-style split, not Bowditch).
• Adjusting a side shot as if it were a loop course.
• Computing side shots from unadjusted stations, then mixing them with adjusted loop points on the same staking sketch.
• Forcing Σlat = 0 on an open traverse that ends on a different published coordinate.
• Stating that BPELSG requires Compass rule, Transit rule, or a 1:10,000 ratio. Report the method the stem names; if it names none, Compass on a closed mixed-bearing loop is the usual hand calculation.