Differential Leveling and Field Notes

Anyone can read a rod. What makes someone useful on a layout crew is that their elevations can be trusted, and that they can prove it weeks later from their notes. If a slab comes in 0.2 foot low, the first thing anyone asks for is the level book.

You already know height of instrument, backsights, foresights and turning points. This guide is about running levels without a person checking your work: laying out a clean book, proving the math, testing the instrument, and tracking down errors. Sight limits and closure figures below come from the California Department of Transportation (Caltrans) Surveys Manual as a working example. Your job specification, your state and your employer can set different limits.

What You Will Be Able to Do

• Keep a level book that someone else can read and check.
• Prove your arithmetic with the sum check.
• Run a two-peg test and decide whether an instrument is usable.
• Close a loop, judge the misclosure, and spread small errors.
• Find what went wrong when a loop will not close.

A Level Book That Works

A level book records every reading, in order, so anyone can follow it. Write in it as you go, not from memory at lunch.

At the top of each page, record the date, the weather, the crew, the instrument and its serial number, the job, and the benchmark you started on with its source.

Worked example. A loop starts on BM-1 at elevation 100.00, runs through two turning points, and closes back on BM-1.

The height of instrument (HI) for each setup goes in its own column in a real book. Here it works out like this:

1. Setup 1: HI = 100.00 + 5.12 = 105.12. TP-1 = 105.12 - 3.40 = 101.72.
2. Setup 2: HI = 101.72 + 6.05 = 107.77. TP-2 = 107.77 - 4.21 = 103.56.
3. Setup 3: HI = 103.56 + 2.18 = 105.74. BM-1 = 105.74 - 5.71 = 100.03.

The Sum Check

This test catches arithmetic errors and takes one minute. The total of the backsights minus the total of the foresights must equal the change in elevation.

• Backsights: 5.12 + 6.05 + 2.18 = 13.35.
• Foresights: 3.40 + 4.21 + 5.71 = 13.32.
• Difference: 13.35 - 13.32 = +0.03.
• Elevation change: 100.03 - 100.00 = +0.03.

They match, so the math is right. That does not prove the readings were right. It only proves you added them correctly.

Book Habits

• Use pencil or a permanent pen as your employer requires, and never erase. Draw one line through a mistake and write the correct number beside it.
• Note what each point is: "TP-2, top of curb at NE corner of inlet."
• Record your sideshots too, which are extra foresights taken from one setup.
• If you use a digital level or data collector, the same rule applies. Back it up, and keep the raw file.

Sideshots are not checked by the loop. A loop only checks points that are carried through it. A sideshot could be off by a foot and the loop would still close. Read each one twice, or tie important points in as turning points.

Testing the Instrument

An automatic level can look fine and still be out. Its line of sight may tilt slightly up or down, which is called collimation error. A two-peg test finds it.

1. Drive two stakes on firm, fairly flat ground, about 200 feet apart. Call them A and B.
2. Set up exactly halfway between them. Read a rod on each. Any tilt affects both sights the same way, so the difference you get is the true difference.
3. Move the level close to A, about 10 to 20 feet away, and read both again. Now the tilt barely touches A, but it fully affects B.
4. Compare the two differences.

Worked example.

• Halfway setup: A reads 5.24, B reads 4.16. True difference = 5.24 - 4.16 = 1.08.
• Close to A: A reads 4.88. B should read 4.88 - 1.08 = 3.80. It reads 3.83.
• The error is 0.03 foot in about 200 feet, and the line of sight is tilted high.

Caltrans has crews readjust a level if the error passes 0.003 foot in 200 feet for second-order work, or 0.007 foot in 200 feet for third-order work, the class it uses for construction survey control. The example above fails, so tag the level and send it in. Do not try to adjust it yourself unless you are trained and the employer allows it.

Run the test daily on precise work, and whenever the instrument has been dropped, bumped or moved in a truck on a rough road. You can check a laser level the same way, by shooting two points from the middle and then from close to one of them.

Why Balanced Sights Save You

Take the 0.03 foot in 200 feet from the example. That is 0.015 foot per 100 feet.

• If your backsight and foresight are both 100 feet, the error is the same on both and cancels.
• If your backsight is 150 feet and your foresight is 50 feet, you pick up 0.015 foot on that one setup, and a few setups can pile it up.

So balancing your sights protects you even from an instrument you do not know is off. Caltrans third-order work keeps sights to 300 feet or less, with no more than 33 feet of difference between backsight and foresight on a setup, and no more than 33 feet of difference added up along the loop. Pace them off. Keep your line of sight at least 1.6 feet above the ground, where heat shimmer is worst. On a hot day, shorten your sights.

Getting Clean Readings

• Rod. Use a rod level. If there is none, have the rod person rock the rod slowly toward and away from the level, and take the lowest reading. That is the plumb one.
• Turning points. Use something with a definite high point and no chance of settling: a nail in pavement, the top of a curb, a firm hub. Leave them in place until the loop closes, so that you can go back. A soft spot under the rod is a common hidden error.
• Setups. Push tripod legs in firmly. Stay off the legs. Recheck the bubble before each reading.
• Parallax. Focus the crosshairs, then the target.
• Call it back. The rod person or the recorder repeats the reading aloud.
• Wait. Do not move the rod off a turning point until the instrument has moved and taken the new backsight.

Closing and Adjusting

Close on the benchmark you started on, or better, a second known benchmark. Closing on the same point can hide a bad starting elevation.

Misclosure is the gap between where you came out and where you should be. In the worked example it is +0.03. Typical construction layout accepts 0.02 to 0.05 foot on a short loop. On a longer run, a common way to set the limit is by distance. Caltrans third-order work with a compensator level uses 0.06 foot times the square root of the loop length in miles.

Worked example. A 2-mile loop: 0.06 x 1.41 = 0.085 foot allowed.

A small misclosure can be spread through the loop. One simple way is to divide it evenly by setup, and take it off a little at a time.

Only adjust an error that is within limits. A big misclosure is a mistake, and spreading it around just hides it in every point.

When It Will Not Close

Do not rerun the whole loop until you have looked for the mistake.

Check a loop in sections. Go back to a turning point you trust, and rerun only the part that is in doubt. That is why turning points stay in place.

Keep working benchmarks away from machines. Set a temporary benchmark (TBM) in solid material near the work, with its elevation carried from the main benchmark. Tie it to a second point, and check it at the start of each day. On an active site, TBMs do get hit.

Common Mistakes

Check Your Understanding

1. Your backsights add up to 21.48 and your foresights add up to 19.92. You started at 250.00. What should your last elevation be?

21.48 - 19.92 = +1.56. The last elevation should be 251.56.

2. In a two-peg test, the halfway setup reads 6.11 on A and 5.02 on B. Close to A, you read 5.60 on A and 4.48 on B. What is the error?

True difference is 1.09. B should read 5.60 - 1.09 = 4.51. It reads 4.48, so the error is 0.03 foot over the distance, and the line of sight tilts low. Have the level adjusted.

3. A loop closes perfectly, but a stake you shot as a sideshot looks wrong to the operator. Is it proven?

No. A sideshot is not checked by the loop. Reshoot it.

4. A loop misses by 0.42 foot. A coworker suggests spreading it across the five setups. Why not?

That is a mistake, not normal error. Find it first. Spreading it would put part of the mistake into every point.

5. What is the allowed loop misclosure for a 4-mile loop under the Caltrans third-order figure?

0.06 x 2 = 0.12 foot.

Key Takeaways

• A level book is your proof, so write it as you go and never erase.
• Sum of backsights minus sum of foresights must equal the change in elevation.
• A closed loop proves the loop, not the sideshots.
• Run a two-peg test after any knock, and tag a level that fails.
• Balanced sights cancel errors you cannot see.
• Only spread a misclosure that is within limits. Find a big one.