Rrange finding is measuring the distance between two points, one of which, or the terrain between them, is remote or inaccessible - for example the width of a gully, or the distance of a far off point.
Like this:-

There are two methods - by stadium rod, and by triangulation. The stadium rod can be used when the remote point is accessible, and is quicker but less accurate than triangulation.


The Stadium Rod needs an assistant at the remote point. to hold the rod vertical.. The method is the same as finding the height of an object (See the Dumpy Plummet), except that in this case the vertical height is known, and the distance from the instrument to the rod is needed..

Make the rod as long as possible; it is likely to be more accurate than a short one. A range pole or measuring rod of known length is O.K.. If possible, put the rod on a stand or tripod, to keep it still. Set up the Dumpy Plummet, look through sight 1 at the stadium rod, and raise or lower arm 1 until the bottom of the rod is in line with the scale 100 mm. mark. Then read the scale number,R, in line with the top of the rod.

Then using the Dumpy Plummet arm length of 200 mm., the scale reading R in millimetres, and a 2M. stadium rod, the distance D is found from:- .
Numerical example:- Let R = 110 mm.. Then R-100 =10 mm. Divide 400 by 10. The distance D is 40 Metres.
D is not the horizontal distance, but for rough measurements it is near enough.

Triangulation. A simple method with 5 stakes & a tape measure works well if the ground is reasonably flat; drive a nail in the top of each stake to help get an accurate sight. Use a plumb line to test if the stakes are vertical.
This method does not need anyone at the remote point. Pick a prominent feature near the point you wish to measure to - a rock, a tree trunk, even a bright flower. (A flower may not be there next time you want to find it). Call this point A. If point A is higher or lower than the height of your sight lines, you can line up a plumb line with point A and sight through that.

Put a stake in the ground at B, another at point C - in line with AB & as far behind as practical; at least 3 M. -- and a third at point D, as far as practical to one side of ABC. Measure the lengths of BC and BD. Then locate point E, so that CE = BD, and DE = BC, and put in a fourth stake (you may need more than one try to get this right ). Then sighting from behind E, locate point F,. so that EF is in line with FA, and BF is in line with FD. A string line from B to D may help. Like this:-
.
Then using the method of similar triangles, . Numerical example:-
Let BC = 5 M., BD = 7M.,BF = 4M., and FD = 3M..
1. Multiply BF by DE; 4 x 5 =20.
2. Divide 20 by FD; 20/3 = 6.67 M..
The distance from A to B is 6.67 Metres.



The Crevel is a combined surveyors’ cross with measuring scale, and a wide angle dumpy level. It will do most surveying tasks, including (within its scale limits ) measuring lengths and heights by triangulation.

The design of the Crevel avoids sights on a moving arm, or alidade; while an alidade gives accurate sighting over a wide vertical angle, it needs a slow motion drive, which is hard to make with hand tools. Instead, a raised scale and tall backsight give accurate horizontal measuring over a gradient of nearly +/ - 4:1, which is enough for most work.

Provided the instructions are followed, the Crevel is the most accurate instrument in these notes. Tests gave an accuracy of 0.3% for range finding, and an optical resolution of between 1 and 3 arc minutes, depending on the target pattern and the observer’s eyes. If you do much surveying, the extra effort needed to make it and set it up is well worthwhile.

The crevel is a rectangular frame, with a scale, foresight, and crosshair mounted along one long edge, and with two tall cross sights and a unidirectional centre line backsight along the opposite edge.

The sights and the mounting plate fold flat for carrying; when unfolded, the cross sights are held erect by screws under the hinge pivots (See ‘Open Sights” in ‘Instrument Parts”), the backsight is held erect by misaligning the hinges with washers under two of the screws (See Backsight Assembly). The foresight is held with a wing nut, and the vertical mounting plate is clamped to its stop block by a 6 mm. eyebolt. Like this:-


Mounted horizontally, the Crevel will do the following tasks:- 1. With the bidirectional cross sights, set out and extend straight lines in opposite directions.
2. With the cross and centre line sights, set out right angle offsets from a datum line.
3. With the cross sights, centre backsight and scale, set out offsets at any angle to a datum line.
4. With the cross sights, centre backsight and scale, make horizontal measurements using three different triangulation methods.
5. Using the horizontal backsight slit and crosshair, give a wide angle level reference (artificial horizon).
6. Measure gradients, using the horizontal backsight slit, crosshair, and a staff and target.
7. Using the centre backsight pinhole, carry out operations 2 to 6 with more precision.

With the crevel mounted vertically, the crosshair becomes a plumb line, the vertical slits are horizontal, and the horizontal slits and the scale are vertical. The Crevel will now carry out the following tasks:-
1. Using the centre vertical backsight slit and plumb line, give a plumb reference for setting up tall structures.
2. Use the centre vertical backsight slit and plumb line, to set out straight lines in hilly country (unidirectional only).
3. Using the centre backsight slit and scale, measure vertical heights and gradients by triangulation, in three different ways, and horizontal distances with a stadium rod.

Construction of the Crevel is in six parts : -
a. The frame parts and assembly (Figs 6-4 to 6-6).
b. The scale, crosshair, centre foresight parts and assembly (Figs. 6-7 to 6-8).
c. The backsight and mount parts and assembly (Figs. 6-9 to 6-11)
d. The cross sights and mounts parts and assembly. (Fig. 6-12)
e. The bubble level indicator and multiplier table.
f. An alternative mounting method.

a. Cut out and drill the frame and brace members as in Figs. 6-4 and 6-5, and assemble the frame as in Fig. 6-6, using temporary 5 mm. and 6 mm. machine screws for the corners. The braces, sides and back use one screw at each back corner; the braces’ front ends have separate wood screws; square up the frame (this is important) and position the brace front ends before putting in the wood screws. Then cut the brace ends flush with the frame. Using the two empty holes in the front ends of the side strips as guides, drill through the front strip. These holes are for the crosshair screws, to be put in later.

Make and attach the horizontal mounting plate stop block. The thickness of the block is important; the back face must be in line with the axis of the backsight mounting screw, and the mounting plate must be flat against the front face when they are screwed together. Both the block and plate will need to be cut away for the mounting plate hinges.
Attach the mounting plate and hinges, then drill the upper 6 mm. hole in the plate, using the hole in the stop block as a guide. Small countersunk head screws in the bottom of each stop block, allow the crevel to be adjusted for level or plumb when mounted on a vertical post (See ‘Alignment’). Screw the vertical stop block on.

Attach the pendulum as in Figs. 6-4 and 6-6. It swings from two screw eyes when the frame is vertical, and shows when the frame is ‘plumb’.(See ‘Alignment’ below).

b. Cut out the scale from a 300 mm. plastic ruler, and drill 4 small mounting holes, as in Fig. 6-7. Be careful to keep the scale numbers clear when cutting and drilling. Cut , drill, and file the scale mounting strip from 25 mm. x 20 mm. aluminium angle (25 x 20 mm. timber can be used provided the scale face is straight and smooth). Stick a strip of white paper to the scale face of the mounting strip (p.v.c. wood glue will work) or paint it flat white. Screw the scale to the strip with four small wood or self tapping screws.

Try to get two cotton reels of the size shown in Fig. 6-7, or make and drill two wood blocks the same size.(If they are round, spare crosshair line can be wound on one). Remove the front temporary screws, and attach the cotton reels and scale assembly to the frame, and install the crosshair screws and locknuts as in Fig. 6-8. Make the centre foresight from 16 mm. strap iron (Fig. 5-7), and attach it to the frame front strip with a 5 mm. screw, wing nut and angle bracket. as in Fig. 6-8.

c. Make and assemble the centre backsight as in Figs 6-9 to 6-11. Screw the horizontal slit strips on first; the vertical strips cross over the horizontal ones. Counterbore the hole for the 5 mm. backsight mounting screw on the underside, to allow a 5 mm. locknut to clear the mounting plate stop, and screw the backsight to the frame with a 6 mm. panel washer between the backsight mount and the frame, so the backsight can turn smoothly. Screw the backsight to the frame as in Fig. 6-11.

d. Make the cross sights as in Fig. 6-12. Remove the frame back corner temporary screws and screw on the cross sights. Drill the holes in the bottom of the vanes to suit the holes in the hinges, and slot them so they can be adjusted to give the correct slit width. The holes in the top bracket should also be slotted for the same reason. Put two small (No. 4 or 6 gauge x 10 - 12 mm.) countersunk head screws under the hinge pivot, so the heads can bear on the moving parts, to stiffen the hinge movements (See ‘Hinge Sights’ in Chapter 1, “Instrument Parts”).
e. Another way to make the sights is to space them further apart at the top ( See ‘ Tall Sights” , also in Chapter 1).

f. Screw a bubble level indicator on the left hand side strip (See ‘Bubble Level Indicators’ in ‘Instrument Parts’). A table of scale ‘Multiplier Points’ (See Alignment”) can be downloaded, printed, and stuck on the right hand side strip.



















g. An alternative mounting is shown in Fig. 6-13. It allows the frame to sit on a flat plate, and eliminates the horizontal mounting plate, the stop blocks, pendulum, and the need for a Universal Mount. But it is harder to turn the crevel to align the sights correctly, and it can’t be used vertically.








Aligning the Crevel. Start by mounting the crevel on a firm base -e.g. the permanent tripod and universal mount - and level it according to the bubble indicator(s).

1. Aligning the cross sights. Using a 25 thou. feeler gauge or an offcut of strap iron as a feeler gauge, and holding it at right angles, adjust the slit width top and bottom. Then level the instrument, and with a plumb line, adjust the height of the screws under the hinges to bring the sight vane faces plumb, and adjust the height of the stop to bring the edges plumb. Like this:-

2. Aligning the vertical backsight slit. Level the instrument, and with a plumb line, set one vertical sight vane plumb. Using a 16 thou. feeler gauge, or a double thickness of tin can hammered flat, set the second sight vane to give the right slit width top and bottom. Like this:-

3. Adjusting the scale. Set the backsight plumb, and measure the distances from the 0 and 300 mm. points of the scale to the vertical backsight slit. Measure from the back face of the scale, and through the gap in the backsight plate; the measurements must both be exactly 250 mm.; loosen the scale mounting bracket screws a little and adjust the position of the scale mounting bracket to do this. Check that the distance from 150 mm. point to the slit is exactly 200 mm..

4. Adjusting the cross alignment. Set up an end-for-side alignment test (See Surveyors’ Cross). Adjust the cross by loosening the scale mounting screws and sliding the scale a little from side to side. Now raise the centre fore sight, set it exactly on 150 mm., and repeat the end-for-side test; if the foresight is out of line, it may not be vertical. Remove the foresight holding screw, and pack the sight out from its bracket with washers. Like this:-



4. Adjusting the Crosshair. With a bubble level, set one horizontal backsight vane level by loosening its screws. With the 16 thou. feeler gauge, set the horizontal slit width at both ends. Now set up a string line end-for-centre test (See Chapter 4 - Dumpy Levels.). and adjust the crosshair at each end by turning the crosshair screws. Check that the horizontal slit and the crosshair look parallel; if not, repeat the test.
5. Adjusting the pendulum. Mount the Crevel vertical, and adjust it plumb in the forward direction by comparing the scale with a plumb line. Loosen the bubble indicator screws a little, and set the bubble level. Adjust the crevel plumb in the side to side direction, by comparing the crosshair with the plumb line. DO NOT re-adjust the crosshair screws;.adjust the pendulum by turning the eye of the upper screw eye or bending it with pliers to bring the pendulum into line. Like this:-



The Crevel, with all sights folded for transport. When this picture was taken, the scale had additional red markings which are no longer needed.


Using the Crevel. When horizontal, the tall sights fitted to the crevel allow measurements up to +/- 13.5º from level for the scale, up to +12º -25.8º for the centre sights, and up to +/- 20.5º for the cross sights; above and below this a plumb line in front of the sights must be used.

1. To lay out a straight line AB beginning from point A.
First read ‘Measuring and Setting Up.’

(a). Mount the instrument level and with the backsight vertically above point A, using a plumb line under the stand, and the cross sights aligned with the direction you wish to go, perhaps by sighting a distant point, and the cross sights aligned with the datum line.
(b) Multiple points in a straight line can be laid down; if the terrain is undulating, this is up to the maximum vertical angle of the cross sights. (See “Laying Out”, Chapter 5.

2. . To lay out a line AB, at right angles to a datum line BC.

(a). . Mount the instrument level and with the backsight vertically above point B, using a plumb line under the stand, . and the cross sights aligned with the datum line.
(b). Raise the foresight until it is on the 150 mm. point.
The Crevel centre sights and cross sights form a surveyors’ cross, like this:-

The centre sights are unidirectional; if one arm of a cross has bi-directional sights, the other arm needs uni-directional sights only. (If the center sights are pointing in the wrong direction, just turn the crevel around).


3. To lay out an offset CD, at an angle other than a right angle, to a datum line BC.

(a). Mount the instrument level and with the backsight vertically above point B, using a plumb line under the stand, . and the cross sights aligned with the datum line BC. Then follow the diagram. Like this:-.



4. To measure the distance to a remote point A (Range Finding).

Part of the art of surveying is the ability to measure the horizontal distance between two points A and B, one of which, or the terrain between them, is remote or inaccessible - e.g. the width of a deep gully, or the distance to a far off point. Like this:-

With the Crevel horizontal, the measuring scale and vertical backsight allow measurement of the horizontal distance between two points by triangulation. There are two ways of doing this. The first involves placing the Crevel at the accessible point A, then at a third point C, from which both A and B can be seen, and solving the resultant triangle.

This method, which is almost the same as using a theodolite, has the disadvantage that the arithmetic is complicated. We must know the distance from the backsight to the point on the scale the sight line runs through; this varies with the scale reading, and in an instrument like the Crevel, with no alidade, there is no direct way of knowing it. It may be calculated however by Pythagorus’ theorem, from the scale reading, and the perpendicular distance from the backsight to the centre of the scale; this requires a knowledge of squares and square roots.

The second method needs two extra points, C and D, but the backsight to scale reading distance isn’t needed, and the arithmetic is easier to understand. Unfortunately either method usually gives awkward numbers best worked out with a hand calculator.

First Method:-
(a) Mount the Crevel on a stand, with the frame level, the backsight positioned vertically above point A by using a plumb line under the stand, and the cross sights aligned with point B. If B is at a different height than the cross sights can handle, suspend a plumb line or stand a range pole in line with AB.

(b) Choose a point C, on a sight line from the backsight through a point on the scale, and from where point B can be seen. (Move your eye up or down the backsight slit to bring C just above the top edge of the scale. If C is at a height the backsight slit can’t handle, suspend a plumb line or stand a range pole in line with BC ). Record the scale reading, R1, in line with BC.
(c) Measure the distance AC in metres. Call it D. Like this:-


(d) Set up the crevel at point C, with the frame level, and the backsight vertically above point C. Turn the Crevel until point A can be sighted in line with the scale reading R1; the scale is now parallel with the line AB. Read and record the scale reading, R2, in line with point B. Like this:-



(e) Calculate the distance between A and B
If R1 is less than 150, .
If R1 is more than 150, .
If the answer to (R1 - R2) is negative; simply ignore the - sign.

There is an easy way to work this out. In the table below, the answer is worked out for every 10 scale numbers, so if we position point C so that the sight line AC is in line with one of these numbers - generally, not hard to do - we can pick a “multiplier’ number M from the table, and work out the length of AB like this:-


With this method, we simplify the subtraction R1 - R2, avoid having to do squares and square roots, and have an easy division by 1000.


In words:- The distance from point A to point B is found like this :-
(1). Subtract R2 from R1; if the answer is negative ignore the sign.
Example:- Let AC = 5.7 Metres, R1 = 280 millimetres and R2 = 21 millimetres. Then R1 - R2 = 280-21 =259.
(2) From the table, look up the number M for the value of R1, and multiply M by R1 - R2..
Example:- The number M for R1 = 280 is 4.19. So M x (R1 - R2) = 4.19 x 259 = 1085.21..
(3) Multiply this answer by AC.
Example:- The length of AC is 5.7 Metres, so 5.7 x 1085.1 = 6185.697.
(4) Divide the answer to (3) by 1000. That is, just shift the decimal point 3 places to the left.
Example:- 6185.697 / 1000 = 6.185697 Metres.
(5) Reduce the number of digits after the decimal point; 3 are enough to give the answer to a millimetre, which is more accurate than the survey will be.
Example:- The length of AB is 6.186 Metres.

Second Method:-
(a) and (b). As in the first method (a) and (b).
(c) Without turning the Crevel, look through the cross sights backwards, and pick a point D, 3 to 5 metres behind A, so that AD is in line with AB. Like this:-

(d) Set up the crevel at point C, with the frame level, and the backsight vertically above point C. Turn the Crevel until point A can be sighted in line with the scale reading R1; the scale is now parallel with the line AB. Read and record a scale reading, R2, in line with point B, and a scale reading, R3, in line with point D. Like this:-



(e) Calculate the distance between A and B.
.
 In words:-
(1) Subtract R2 from R1. If the answer to R1 - R2 is negative, ignore the - sign.
Example:- Let R1 =210 and R2= 24. Then R1 - R2 =210 - 24 = 186.
(2) Multiply R1 - R2 by AD.
Example:- Let AD = 3 Metres. Then AD(R1 - R2) = 3 x 186 = 558.
(3) Subtract R1 from R3. If the answer to R3 - R1 is negative, ignore the - sign.
Example:- Let R3 = 270 . Then R3 - R1 = 270 - 210 = 60.
(4) Divide the answer to (2) by the answer to (3).
Example:- 558 / 60 = 9.3. So the length of AB is 9.3 Metres.
(5) Reduce the number of digits after the decimal point; 3 are enough to give the answer to a millimetre, which is more accurate than the survey will be. In this example, no reduction is needed.


5. To set up a Pole, Post or Tower Vertical .

(a) Mount the crevel vertical, and stand it a distance from the object roughly 2 to 3 times its height.

(b) Adjust it to plumb, using one bubble indicator and the pendulum.

(c) Turn the crevel until the object can be seen close to the vertical crosshair when looking through the vertical slit, and pull the object vertical by aligning it with the crosshair. (Also see the Dumpy Plummet)

6. To lay out a straight line AB beginning from point A, in rough country.

The vertical backsight slit and crosshair give a wide vertical angle sight plane similar to the Dumpy Plummet, and can be set up to project a straight line over undulations the same way. (See the same heading under ‘Dumpy Plummet).

7. To Measure the Vertical Height of an Object.

With the Crevel vertical, the measuring scale and horizontal backsight slit allow measurement of the vertical height between two points A and B (where point A is too high to be accessible - e.g. the height of a tree, pole, or wall) by triangulation.
(a). Set up the Crevel vertically, and stand it pointing at the object from a distance of 2 to 3 times the height of the object.
(b)Level the instrument, making sure the plumb indicator is in the centre of the ring.

(c). Use the centre sight line (150 mm.) to find the point on the object level with it. Mark the object at this point, and call the point C. With a tape measure, measure and record the horizontal distance from the backsight to C - not necessarily to point B, or the distance along the ground. Call it D . Like this:-




(d). Read and record the scale number in line with the top (point A) of the object. Call this reading R1.

(e) Measure the height of C above B, in Metres.
(f). Calculate the height H of the object from A to C in Metres, using the formula:- .
In words:-
(1) Subtract R1 from 150.
Example:- Let R1 = 50, so 150 - R1 = 100.
(2) Multiply (150 - R1) by D
Example:- Let D = 7 Metres. So D x (150 - R1) = 7 x 100 =700.
(3) Multiply the answer to (2) by 5.
Example:- 5 x D x (150 - R1) = 5 x 700 = 3500.
(4) Divide the answer to (3) by 100; just shift the decimal point 3 places to the left.
Example:- 3500/ 1000 = 3.5.
(5) Add BC to the answer to (4).
Example:- Let BC be 0.25 Metres. Then 3.5 + 0.25 = 3.75.
So the height of the pole is 3.75 Metres.

8. To use the Crevel as a wide angle Dumpy Level.

Set up the Crevel horizontally, level it, and use the horizontal backsight slit and crosshair as a wide angle artificial horizon, similar to the wide angle dumpy level. It may be used to measure height differences, or gradients, between ground points, with a staff and target. (See ‘Levelling’).

The Crevel is the last of the instruments covered in these notes. Chapter 7, Accessories, shows other things which may be needed to do a survey.