Levelling produces a column of staff readings. Turning those into reduced levels — actual heights above the datum — requires a systematic method, and two exist.
They give identical answers but differ in one important way: how thoroughly they check themselves. This post covers the terms first, then both methods.
The Essential Terms
| Term | Definition |
|---|---|
| Height of instrument (H.I.) | The elevation of the plane of sight with reference to the assumed datum |
| Back sight (B.S.) | A sight taken on a point of known elevation, to obtain the height of instrument. Known as a plus sight |
| Fore sight (F.S.) | A sight taken on a point of unknown elevation. Known as a minus sight |
| Turning point (T.P.) | A point on which both a plus sight and a minus sight are taken |
| Intermediate station (I.S.) | A point between two others on which only one sight (a minus sight) is taken, to determine its elevation |
Why Height of Instrument Is Not the Instrument’s Height
This term misleads almost everyone at first. H.I. is not how tall the tripod is.
It is the elevation of the line of sight above the datum — a reduced level in its own right. If the instrument’s line of sight happens to lie 101.450 m above mean sea level, then H.I. = 101.450 m, regardless of how high the tripod stands above the ground.
Once you see it that way, the arithmetic becomes obvious: any staff reading taken from that instrument is measured downwards from H.I., so the point’s level is H.I. minus the reading.
Why Back Sight Is “Plus” and Fore Sight “Minus”
The alternative names describe exactly what you do with them.
- A back sight is taken on a point whose level you already know. Add the reading to that known level and you get the height of instrument. Hence plus sight.
- A fore sight is taken on a point whose level you want. Subtract the reading from the height of instrument and you get that level. Hence minus sight.
Known level + B.S. = H.I.
H.I. − F.S. = Unknown level
Note that “back” and “fore” have nothing to do with direction. A back sight is not necessarily behind you. The distinction is entirely about whether the point’s elevation is known or unknown.
Turning Point versus Intermediate Station
This pair is heavily examined, and the distinction is clean:
| Turning Point | Intermediate Station | |
|---|---|---|
| Sights taken | Two — both a plus and a minus sight | One — a minus sight only |
| Purpose | To move the instrument forward | To find that point’s elevation |
| Carries the survey? | Yes | No |
A turning point is a bridge between two instrument positions. You take a fore sight on it from the old position, then move the instrument, then take a back sight on the same point from the new position. Because its elevation was established by that fore sight, it can now serve as the known point for the new setup.
An intermediate station is simply a point whose height you want along the way. Nothing depends on it, and an error in its reading affects only that one level.
This is why turning points matter so much. An error at a turning point propagates into every subsequent level, because the whole survey is carried forward through it. An error at an intermediate station stays where it is.
Method 1: Height of Instrument Method
- The height of instrument is calculated at each set-up of the instrument.
- Based on the height of instrument, the reduced levels of other staff stations can be calculated.
Where It Is Used
- Generally used for fly levelling, or to establish bench marks.
- Suitable if there are no intermediate sights.
The Arithmetic Check
ΣB.S. − ΣF.S. = Last R.L. − First R.L.
Why This Must Hold
Every back sight raises the reckoning to the line of sight; every fore sight lowers it to a ground point. Travelling from the first station to the last, the net of all the rises and drops must equal the total change in level between the two ends.
So the check is really a statement of conservation — you cannot end up at a different height than the sum of your steps says you should.
Method 2: Rise and Fall Method
- The difference between the levels of consecutive staff points is calculated.
- A higher staff reading indicates a fall, and a lesser reading indicates a rise.
Why Higher Reading Means Fall
This follows directly from how a level works. The line of sight is fixed and horizontal. If the staff has to extend further up to reach it, the ground it stands on must be lower.
So a bigger reading means a lower point — the relationship is inverse, and it is the single rule the whole method depends on.
Where It Is Used
- Generally used in contour surveys, in small areas, or for longitudinal and cross sections.
- Used when a large number of intermediate station readings are required.
The Arithmetic Check
ΣB.S. − ΣF.S. = Last R.L. − First R.L. = ΣRise − ΣFall
Note the Third Term
The rise and fall method has three quantities that must agree, not two. That extra term is the whole reason for preferring this method.
The Decisive Comparison
| Height of Instrument Method | Rise and Fall Method | |
|---|---|---|
| Basis | H.I. computed at each set-up | Difference between consecutive readings |
| Check | Two terms agree | Three terms agree |
| Intermediate sights checked? | No | Yes |
| Speed | Faster | Slower — more computation |
| Suitable when | No intermediate sights | Many intermediate sights |
| Typical use | Fly levelling, establishing bench marks | Contour surveys, small areas, L-sections and cross sections |
The Critical Weakness of the H.I. Method
This is the most important idea in the topic, and it explains the entire pattern of use.
Look at the H.I. check: ΣB.S. − ΣF.S. = Last R.L. − First R.L. Notice which readings appear — only back sights and fore sights.
Intermediate sights appear nowhere in it. You could misread an intermediate staff reading by half a metre, book a wrong level for that point, and the check would still balance perfectly. The error would pass entirely undetected.
The rise and fall method closes this gap. Because every level is computed as a rise or fall from the previous reading, each intermediate sight enters the ΣRise − ΣFall column. An error anywhere breaks the third equality.
The H.I. method checks only the back sights and fore sights. The rise and fall method checks every reading.
Why Each Method Is Used Where It Is
Everything now follows:
- Fly levelling and establishing bench marks involve almost no intermediate sights — you are carrying a level from A to B, not surveying points along the way. The H.I. method’s blind spot does not matter, and its speed is welcome.
- Contour surveys, longitudinal sections and cross sections are made up almost entirely of intermediate sights. Here the blind spot would be fatal, so the rise and fall method’s complete check is essential.
The rule reduces to one line: use H.I. when speed matters and there is little to check; use rise and fall when there is much to check.
Worked Illustration of the Two Rules
| Station | B.S. | F.S. | H.I. Method | Rise and Fall Method |
|---|---|---|---|---|
| A (R.L. 100.000) | 1.500 | — | H.I. = 100.000 + 1.500 = 101.500 | — |
| B | — | 2.300 | R.L. = 101.500 − 2.300 = 99.200 | 2.300 > 1.500, so fall of 0.800 |
Both give B as 99.200 m. Check: ΣB.S. − ΣF.S. = 1.500 − 2.300 = −0.800, and Last R.L. − First R.L. = 99.200 − 100.000 = −0.800. Also ΣRise − ΣFall = 0 − 0.800 = −0.800. All three agree.
Quick Revision Notes
- Height of instrument is the elevation of the plane of sight with reference to the datum — not the height of the tripod.
- Back sight is on a known elevation, used to obtain H.I.; called a plus sight.
- Fore sight is on an unknown elevation; called a minus sight.
- Turning point takes both a plus and a minus sight; intermediate station takes only a minus sight.
- H.I. method: H.I. computed at each set-up; used for fly levelling and establishing bench marks; suitable when there are no intermediate sights.
- Rise and fall method: difference between consecutive readings; higher reading = fall, lesser reading = rise.
- Rise and fall is used for contour surveys, small areas, longitudinal and cross sections, and where many intermediate sights are needed.
- H.I. check: ΣB.S. − ΣF.S. = Last R.L. − First R.L.
- Rise and fall check: ΣB.S. − ΣF.S. = Last R.L. − First R.L. = ΣRise − ΣFall.
- The H.I. method does not check intermediate sights; the rise and fall method does.
Mistakes Students Commonly Make
- Taking height of instrument to mean the height of the tripod above the ground. It is the elevation of the line of sight above the datum.
- Thinking back and fore sights relate to direction. They relate to whether the point’s elevation is known or unknown.
- Saying a higher staff reading means a higher point. It means a lower point, hence a fall.
- Confusing turning point and intermediate station. A turning point takes two sights; an intermediate station takes one.
- Giving only two terms in the rise and fall check. It has three.
- Claiming the H.I. check verifies all readings. It omits intermediate sights entirely.
- Using the H.I. method for a contour survey, where intermediate sights dominate and would go unchecked.
Conclusion
Both methods reduce staff readings to levels, and both give the same answers — but they do not check the same things. The height of instrument method is quicker and works from the elevation of the line of sight, yet its arithmetic check touches only back sights and fore sights, leaving intermediate readings unverified. The rise and fall method computes each level from the one before it, so every reading enters the check and all three totals must agree. That is why fly levelling uses the first and contour surveys use the second.
Frequently Asked Questions
What is height of instrument?
The elevation of the plane of sight with reference to the assumed datum. It is not the physical height of the instrument above the ground.
What is a back sight?
A sight taken on a point of known elevation, in order to obtain the height of instrument. It is known as a plus sight because it is added to the known level.
What is a fore sight?
A sight taken on a point of unknown elevation. It is known as a minus sight because it is subtracted from the height of instrument.
What is a turning point?
A point on which both a plus sight and a minus sight are taken, allowing the instrument to be moved forward while carrying the survey.
What is an intermediate station?
A point between two others on which only one sight, a minus sight, is taken to determine its elevation.
Why does a higher staff reading indicate a fall?
Because the line of sight is fixed and horizontal, so if the staff must extend further up to reach it, the ground it stands on must be lower.
What is the check for the height of instrument method?
The sum of back sights minus the sum of fore sights must equal the last reduced level minus the first reduced level.
What is the check for the rise and fall method?
The sum of back sights minus the sum of fore sights equals the last reduced level minus the first, and also equals the sum of rises minus the sum of falls.
Which method checks intermediate sights?
The rise and fall method. The height of instrument check involves only back sights and fore sights, so an error in an intermediate reading would go undetected.
When is the height of instrument method preferred?
For fly levelling or establishing bench marks, and generally when there are no intermediate sights, since it is faster.
When is the rise and fall method preferred?
For contour surveys, small areas, and longitudinal and cross sections, where a large number of intermediate station readings are required and must be checked.