Reduced levels from a level book¶

What the program works out: the R.L. of every reading in a field book sheet, from the bench mark in row 2 and the staff readings (B.S., I.S., F.S.), by the height of instrument method. Then the arithmetic check of the level sheet. Back calculate does the reverse: the staff readings from the R.L.s.

This page explains the arithmetic. For the steps on screen, see Enter a field book.

The terms¶

The method¶

The program starts from the bench mark in row 2 and works down the sheet, one row at a time.

1. The bench mark.

H.I. = R.L. of the bench mark + its B.S.

2. A row with an I.S.

R.L. = H.I. − I.S.

The H.I. stays as it was.

3. A row with an F.S. (a change point). The R.L. comes from the F.S. and the set-up the staff was read from:

R.L. = H.I. − F.S.

Then the level moves. The row's B.S. gives the new set-up:

new H.I. = R.L. + B.S.

The rows below are worked out from the new H.I. The row gets that H.I. in its H.I. column and the Remark Change Point.

4. The end. The program stops at the first row with no B.S., I.S. or F.S. The last row, an F.S. with no B.S. after it, is also marked Change Point: its H.I. is its own R.L., because there is no new set-up.

The R.L.s are worked out in full and shown to 3 decimals.

The level check¶

Check level sheet compares the two sides of the usual arithmetic check:

ΣB.S. − ΣF.S. = Last R.L. − First R.L.

• ΣB.S. adds the bench mark's B.S. in row 2 and every B.S. on a row that has an R.L.
• ΣF.S. adds every F.S. on a row that has an R.L.
• First R.L. is the bench mark's R.L.
• Last R.L. is the R.L. of the last row that has one.

Both sides are rounded to 3 decimals. The check passes only when they are equal at 3 decimals.

The I.S. readings do not appear in the check. It proves the arithmetic from set-up to set-up, not the I.S. readings, and not the readings as they were taken in the field.

Worked example¶

This is the 13-row book from Enter a field book. Bench mark: B.S. 1.525, R.L. 150.000.

Bench mark: H.I. = 150.000 + 1.525 = 151.525

Row 10 gets H.I. 150.430 and the Remark Change Point. Row 15, the last F.S., is marked Change Point too.

The level check:

• ΣB.S. = 1.525 (bench mark) + 0.985 = 2.510
• ΣF.S. = 2.080 + 1.505 = 3.585
• ΣB.S. − ΣF.S. = 2.510 − 3.585 = −1.075
• Last R.L. − First R.L. = 148.925 − 150.000 = −1.075

Both sides are −1.075, so the panel says Level check passed.

When the readings and the R.L.s no longer match¶

A row goes with its reading when R.L. + reading (its F.S., or else its I.S.) is the H.I. of one of the set-ups: the bench mark's, or a change point's. The program allows 0.0015 for rounding. When a row doesn't go with its reading, because a reading changed after the R.L.s were worked out or an R.L. was typed, the panel warns: The R.L.s don't match the readings from row ….

Sorting (C-L-R, C-R-L) can move a reading past a change point. Its R.L. still goes with its own set-up, but working down from the top would now give it another set-up's H.I. Calculate R.L.s then asks Calculate would change … R.L.s … Calculate anyway? Click No and undo the sort.

Back calculate¶

Back calculate keeps the R.L.s and works out the staff readings, from the bench mark down. Use it for a field book that has levels only.

1. The start. The H.I. is the bench mark's: R.L. + B.S.

2. Each row. reading = H.I. − R.L. It goes in as an I.S.

3. A change point is made in two cases. The limits are under Settings › Change point settings on the Field Book panel.

• A reading off the staff: greater than or equal to If the Staff Reading Greater than (6 unless you change it), or less than or equal to If the Staff Reading Less than (0 unless you change it). The row before it becomes the change point: its I.S. becomes its F.S.
• A marked row: its Remark is the text in If the remark Column contains text (CP unless you change it). That row itself becomes the change point.

4. Its B.S. At a change point the program asks for the B.S., and offers a recommended value:

recommended B.S. = next R.L. − this R.L. + 0.050

This keeps the next reading at least 0.050 up the staff. The B.S. you type must lie within the staff limits and be no less than the recommended value; otherwise the program says so and asks again. Then new H.I. = R.L. + B.S.

5. The end. At the first row with no R.L., it stops. The last reading becomes an F.S.

Back calculate ends with the level check.

Good to know¶

• Book a change point's F.S. and B.S. on the same row, as in the example. A row with a B.S. and no F.S. is worked out from the reading on the row above it, which is rarely what was meant.
• End the book on an F.S. The level check needs the last set-up closed.
• If a row part way down has no reading, the R.L.s stop there: The R.L.s were worked out down to row …. Type its reading and calculate again.
• Each command is one step for Home › Edit › Undo.

Related¶

• Enter a field book
• Interpolated levels
• Cross-section areas