8/8/2019 m m Pakka Wala Hai - Copy

http://slidepdf.com/reader/full/m-m-pakka-wala-hai-copy 1/13

Angular Measurement

Instruments for Angular Measurement

Angle gaugeAngle gauge indicating a tree to measure for a BAF 10

An angle gauge is a tool used by foresters to determine which trees to

measure when using a variable radius plot design in forest inventory. Using

this tool a forester can quickly measure the trees that are in or out of the plot.

An angle gauge is a very similar tool to a wedge prism though it must be held

a fixed distance from your eye for it to work properly. Unlike the wedge prism,

which is alway held over the plot center, the surveyor's eye is kept over plotcenter when using an angle gauge.

Using the Angle Gauge

When using an angle gauge the user must count trees that are larger than the

width of the angle gauge, as viewed from the center of the plot. The angle

gauge is held a set distance away from the eye of the surveyor. Most angle

gauges have a string or chain that lets the user know the set distance. Each

angle gauge is set at a certain basal area factor or BAF. Each tree that is in

the plot represents this number, the BAF, of square footage. It is multiplied by

the number of trees on the plot to give basal area per acre. In the US BAF is

measured in units of Ft2/acre.

For example: Using a BAF 10 angle gauge a forester measures 12 trees that

are in trees. Therefore, this plot represents 120 ft2 of basal area per acre.

Borderline Trees

Some trees are on the borderline of the plot and must be checked to be sure

they are in trees. The limiting distance must be calculated to see if the trees

are in or out. The equation to calculate the limiting distance in feet is Diameter 

at breast height, DBH, in inches times plot radius factor , PRF, in feet.

Dlim=DBH*PRF

For example: Using a BAF 10 angle gauge a forester needs to know the

limiting distance for a 20-inch (510 mm) tree. The PRF using a 10 BAF angle

gauge is 2.75 feet (0.84 m) for every inch of tree diameter. Therefore, 20

inches * 2.75 ft/inch = 55 feet (17 m). This means that a 20-inch (510 mm)

8/8/2019 m m Pakka Wala Hai - Copy

http://slidepdf.com/reader/full/m-m-pakka-wala-hai-copy 2/13

tree must be over 55 feet (17 m) away from the center of the plot using a BAF

10 angle gauge to be out of the plot.

 Sine bar

A sine bar is a tool used to measure angles in metalworking.

It consists of a hardened, precision ground body with two precision ground

cylinders fixed at the ends. The distance between the centers of the cylindersis precisely controlled, and the top of the bar is parallel to a line through the

centers of the two rollers. The dimension between the two rollers is chosen to

be a whole number (for ease of later calculations) and forms

the hypotenuse of a triangle when in use. The image shows a 10 inch and a

100 mm sine bar, however, in the U.S., 5 inch sine bars are the most

commonly used.

When a sine bar is placed on a level surface the top edge will be parallel to

that surface. If one roller is raised by a known distance, usually using gauge

blocks, then the top edge of the bar will be tilted by the same amount forming

an angle that may be calculated by the application of the sine rule.

The hypotenuse is a constant dimension — (100 mm or 10 inches in

the examples shown).

The height is obtained from the dimension between the bottom of one

roller and the table's surface.

The angle is calculated by using the sine rule. Some engineering andmetalworking reference books contain tables showing the dimension

required to obtain an angle from 0-90 degrees, incremented by 1 minute

intervals.

Angles may be measured or set with this tool.

8/8/2019 m m Pakka Wala Hai - Copy

http://slidepdf.com/reader/full/m-m-pakka-wala-hai-copy 3/13

Principle

Angles are measured using a sine bar with the help of gauge blocks and

a dial gauge or a spirit level. The aim of a measurement is to make the

surface on which the dial gauge or spirit level is placed horizontal. For example, to measure the angle of a wedge, the wedge is placed on a

horizontal table. The sine bar is placed over the inclined surface of the wedge.

At this position, the top surface of the sine bar is inclined the same amount as

the wedge. Using gauge blocks, the top surface is made horizontal. The sine

of the angle of inclination of the wedge is the ratio of the height of the gauge

blocks used and the distance between the centers of the cylinders.

Types

Sine centre

A special type of sine bar is sine centre which is used for conical objects

having male and female parts. It cannot measure the angle more than 45

degrees.

sine table

Sine table (or sine plate) is used to measure angles of large workpieces.

Compound sine tableIt is used to measure compound angles of large workpieces. In this case, two sine

tables are mounted one over the other at right angles. The tables can be twisted

to get the required alignment.

clinometer 

An inclinometer or clinometer is an instrument for measuring angles

of slope (or tilt), elevation or  inclination of an object with respect to gravity. It is

also known as a tilt meter , tilt indicator , slope alert , slope gauge, gradient 

meter , gradiometer , level gauge, level meter , declinometer , and pitch & roll 

indicator . Clinometers measure both inclines (positive slopes, as seen by an

observer looking upwards) and declines (negative slopes, as seen by an

observer looking downward).

In aircraft, the "ball" in turn coordinators or turn and bank indicators is

sometimes referred to as an inclinometer.

8/8/2019 m m Pakka Wala Hai - Copy

http://slidepdf.com/reader/full/m-m-pakka-wala-hai-copy 4/13

History 

Early inclinometers include examples such as Well's inclinometer , the

essential parts of which are a flat side, or base, on which it stands, and ahollow disk just half filled with some heavy liquid. The glass face of the disk is

surrounded by a graduated scale that marks the angle at which the surface of 

the liquid stands, with reference to the flat base. The line 0.—0. being parallel

to the base, when the liquid stands on that line, the flat side is horizontal; the

line 90.—90. being perpendicular to the base, when the liquid stands on that

line, the flat side is perpendicular or plumb. Intervening angles are marked,

and, with the aid of simple conversion tables, the instrument indicates the rate

of fall per set distance of horizontal measurement, and set distance of the

sloping line.

 Accuracy 

Clinometer designed to enable indirect firecapability with a Vickers machine

gun circa 1918

Certain highly sensitive electronic inclinometer sensors can achieve an output

resolution to 0.001 degrees - depending on the technology and angle range, it

may be limited to 0.01º. An inclinometer sensor's true or absolute accuracy

(which is the combined total error), however, is a combination of initial sets of 

sensor zero offset and sensitivity, sensor linearity, hysteresis, repeatability,

and the temperature drifts of zero and sensitivity - electronic inclinometers

accuracy can typically range from .01º to ±2º depending on the sensor and

situation. Typically in room ambient conditions the accuracy is limited to the

sensor linearity specification.

8/8/2019 m m Pakka Wala Hai - Copy

http://slidepdf.com/reader/full/m-m-pakka-wala-hai-copy 5/13

The Well's clinometer 

A simple clinometer 

Sensor technology 

Tilt sensors and inclinometers generate an artificial horizon and measure

angular tilt with respect to this horizon. They are used in cameras, aircraft

flight controls, automobile security systems, and speciality switches and are

also used for platform leveling, boom angle indication, indeed anywhere tilt

requires measuring.

Important specifications to consider when searching for tilt sensors and

inclinometers are the tilt angle range and number of axes (which are usually,

but not always, orthogonal). The tilt angle range is the range of desired linear 

output.

Common sensor technologies for tilt sensors and inclinometers areaccelerometer, Liquid Capacitive, electrolytic, gas bubble in liquid, and

pendulum.

.Inclinometers are also used in civil engineering, for example to measure the

inclination of land to be built upon.

Some inclinometers provide an electronic interface based on CAN (Controller 

Area Network). In addition, those inclinometers may support the

standardizedCANopen profile (CiA 410). In this case, these inclinometers are

compatible and partly interchangeable.

8/8/2019 m m Pakka Wala Hai - Copy

http://slidepdf.com/reader/full/m-m-pakka-wala-hai-copy 6/13

Uses

Inclinometers are used for:

Determining latitude using Polaris (in the Northern Hemisphere) or the

two stars of the constellation Crux (in the Southern Hemisphere).

Determining the angle of the Earth's magnetic field with respect to the

horizontal plane.

Showing a deviation from the true vertical or horizontal.

Surveying, to measure an angle of inclination or elevation.

Alerting an equipment operator that it may tip over.

Measuring angles of elevation, slope, or incline, e.g. of an

embankment. Measuring slight differences in slopes, particularly for geophysics.

Such inclinometers are, for instance, used for monitoring volcanoes, or for 

measuring the depth and rate of landslide movement.

Measuring movements in walls or the ground in civil engineering

projects.

Determining the dip of beds or strata, or the slope of an embankment

or cutting; a kind of plumb level.

Some automotive safety systems. Indicating pitch and roll of vehicles, nautical craft, and aircraft. See turn

coordinator and slip indicator .

Monitoring the boom angle of cranes and material handlers.

Measuring the "look angle" of a satellite antenna towards a satellite.

Measuring the slope angle of a tape or chain during distance

measurement.

Measuring the height of a building, tree, or other feature using a

vertical angle and a distance (determined by taping or pacing),using trigonometry.

Measuring the angle of drilling in well logging.

Measuring the list of a ship in still water and the roll in rough water.

Measuring steepness of a ski slope.

Measuring the orientation of planes and lineations in rocks, in

combination with a compass, in structural geology.

Measuring Range of Motion in the joints of the body

Measuring the angles of elevation to, and ultimately computing thealtitudes of, many things otherwise inaccessible for direct measurement.

8/8/2019 m m Pakka Wala Hai - Copy

http://slidepdf.com/reader/full/m-m-pakka-wala-hai-copy 7/13

Optical Instruments for Angular 

Measurement (Metrology)Autocollimator.

This is an optical instrument used for the measurement of small

angular differences. For small angular measurements, autocollimator provides

a very sensitive

and accurate approach. Auto-collimator is essentially an infinity telescope and

a collimator 

combined into one instrument. The principle on which this instrument works is

given below.

O is a point source of light placed at the principal focus of a collimating lens in

Fig. 8.30. The

rays of light from O incident on the lens will now travel as a parallel beam of 

light. If this beam

now strikes a plane reflector which is normal to the optical axis, it will be

reflected back along

its own path and focussed at the same point O. If the plane reflector be now

tilted through asmall angle 9, [Refer Fig. 8.31] then parallel beam will be deflected through

twice this angle,

and will be brought to focus at O' in the same plane at a distance x from O.

Obviously 00' = x

= 26. f, where f'\s the focal length of the lens.

There are certain important points to appreciate here :

The position of the final image does not depend upon the distance of reflector 

from the

lens, i.e. separation x is independent of the position of reflector from the lens.

But if reflector 

 

Principle of working of autocollimator.

is moved too much back then reflected rays will completely miss the lens and

no image will be

formed. Thus for full range of readings of instrument to be used, the maximum

remoteness of 

8/8/2019 m m Pakka Wala Hai - Copy

http://slidepdf.com/reader/full/m-m-pakka-wala-hai-copy 8/13

the reflector is limited.

For high sensitivity, i.e. for large value of a; for a small angular deviation 8, a

long focal

length is required.

8.10.1.

Principle of Autocollimator.

A crossline "target" graticule is positioned at the

focal plane of a telescope objective system with the intersection of the

crossline on the optical

axis, i.e. at the principal focus. When the target graticule is illuminated, rays of 

light diverging

from the intersection point reach the objective via a beam splitter and are

projected from theobjective as parallel pencils of light. In this mode, the optical system is

operating as a

"collimator".

A flat reflector placed in front of the objective and exactly normal to the optical

axis

reflects the parallel pencils of light back along their original paths. They are

then brought to

focus in the plane of the target graticule and exactly coincident with its

intersection. A

 

— Reflected beam when reflector is square to beam

■ Reflected beam from tilted reflector 

proportion of the returned light passes straight through the beam splitter and

the return imageof the target crossline is therefore visible through the eyepiece. In this mode,

the optical system

is operating as a telescope focused at infinity.

If the reflector is tilted through a small angle the reflected pencils of light will

be

deflected by twice the angle of tilt (principle of reflection) and will be brought

to focus in the

plane of the target graticule but linearly displaced from the actual target

crosslines by an

8/8/2019 m m Pakka Wala Hai - Copy

http://slidepdf.com/reader/full/m-m-pakka-wala-hai-copy 9/13

amount 28 x f.

Linear displacement of the graticule image in the plane of the eyepiece is

therefore

directly proportional to reflector tilt and can be measured by an eyepiece

graticule, optical

micrometer or electronic detector system, scaled directly in angular units. The

autocollimator 

is set permanently at infinity focus and no device for focusing adjustment for 

distance is

provided or desirable. It responds only to reflector tilt (not lateral displacement

of the reflector).

This is independent of separation between the reflector and the

autocollimator, assuming no

atmospheric disturbance and the use of a perfectly flat reflector.

Many factors govern the specification of an autocollimator, in particular its

focal length

and its effective aperture. The focal length determines basic sensitivity and

angular measuring

range. The longer the focal length the larger is the linear displacement for a

given reflector 

tilt, but the maximum reflector tilt which can be accommodated is

consequently reduced.Sensitivity is therefore traded against measuring range. The maximum

separation between

reflector and autocollimator, or "working distance", is governed by the

effective aperture of the

objective, and the angular measuring range of the instrument becomes

reduced at long working

distances. Increasing the maximum working distance by increasing the

effective aperture then

demands a larger reflector for satisfactory image contrast. Autocollimator 

design thus involves

many conflicting criteria and for this reason a range of instruments is required

to optimally

cover every application.

Air currents in the optical path between the autocollimator and the target

mirror cause

fluctuations in the readings obtained. This effect is more pronounced as

distance fromautocollimator to target mirror increases. Further errors may also occur due to

8/8/2019 m m Pakka Wala Hai - Copy

http://slidepdf.com/reader/full/m-m-pakka-wala-hai-copy 10/13

errors in

flatness and reflectivity of the target mirror which should be of high quality.

When both the autocollimator and the target mirror gauge can remain fixed,

extremely

close readings may be taken and repeatability is excellent. When any of these

has to be moved,

great care is required.

8.10.2.

Laser Interferometer.

With laser interferometer it is possible to measure

length to an accuracy of 1 part in 106 on a routine basis. With the help of two

retro-reflectors,

placed at a fixed distance, and a length measuring laser interferometer thechange in angle

can be measured to an accuracy of 0.1 second. The device uses the Sine

principle. The line

 joining the poles of the retro-reflectors makes the hypotenuse of the right

triangle. The change

in the path difference of the reflected beam represents the side of the triangle

opposite to the

angle being measured. Such laser interferometer can be used to measure an

angle upto ± 10

degrees with a resolution of 0.1 second.

The principle of operation is shown in Fig. 8.33.

 

Fig. 8.33. Interferometric measurement of angle.

8.10.3.

Photoelectric Microptic Autocollimator.Photoelectric setting makes

measuring and checking by autocollimator far simpler and faster. Micrometer 

adjustment is

provided for setting, but coincidence of setting graticule and target image is

detected photo-

electrically, and shown on a meter as a null reading. This provides a high

degree of sensitivity

and repeatability, also reducing eye fatigue to a minimum. The eyepiece is

normally only used

8/8/2019 m m Pakka Wala Hai - Copy

http://slidepdf.com/reader/full/m-m-pakka-wala-hai-copy 11/13

to assist in initial setting-up.

 

Fig.8.34. Schematic diagram of Photo-electric autocollimator.

The photoelectric autocollimator is particularly suitable for calibrating

polygons, for 

checking angular indexing and for checking small linear displacements.

It can be used as a visual autocollimator, if required, and is available with a

dark field

graticule as standard.

Fig. 8.34 shows a schematic of the operation of photoelectric autocollimator. It

consists

of a vibrating slit, a photoelectric detector, electronic amplifier for magnified

viewing on a

meter.

Operating Principle.

(Refer Fig. 8.35). The photoelectric detecting unit consists of 

photocell and a vibrating slit which is attached to the micrometer screw. When

the slit is

positioned so that it vibrates about

the reflected image, the intensity of 

light received by the photocell will

vary. The output waveform is

amplified and fed to a frequency dis-

criminator and meter which, in

effect, indicates the asymmetry of 

the waveform. When the slit is posi-

tioned so that it vibrates symmetri-

cally about the image the meter 

indicates a null reading, and the

angular displacement of the target

8/8/2019 m m Pakka Wala Hai - Copy

http://slidepdf.com/reader/full/m-m-pakka-wala-hai-copy 12/13

mirror can be read from the

micrometer.

 

Fig. 8.35. Schematic diagram of Photoelectric Autocollimator.

The autocollimator, with suitable reflecting surfaces or optical gauges, is

capable of 

calibrating straightness, flatness, squareness or division of the circle.

8.10.4.

Automatic Position Sensing Autocollimators.Automatic position sensing

autocollimators provide fully automatic setting and display. Angular 

displacement of the

reflector is displayed on a digital readout—eliminating any micrometer reading

for setting or measuring.

Automatic autocollimators can be used in cramped positions where it could be

impossible

to use a visual instrument, and no handling during measurement minimises

the danger of 

accidental autocollimator movement.

Instruments measure in one plane only. For measuring in a second plane

perpendicular 

to the first, the instrument is rotated through 90°. A dark field graticule is fitted

as standard.

Accuracy is unaffected by normal mains fluctuations or lamp ageing.

Automatic autocollimators are ideal for the repetitive checking of production

com-ponents, and for continuously monitoring angular displacement of slow

moving parts.

Operating Principle :

The vibrating slit image detecting system is similar to that

described for the photo-electric autocollimator, but in addition, the slit is

electrically biased

across the field. The amplitude and polarity of the biasing signal is dependent

upon the

misalignment of the slit with the return image. By this arrangement the slit is

8/8/2019 m m Pakka Wala Hai - Copy

http://slidepdf.com/reader/full/m-m-pakka-wala-hai-copy 13/13

biased to the

position straddling the image, at which the misalignment is negligible. The

current necessary

to hold the slit biased in this position is used to provide a direct angular 

reading on a digital

readout.

8.10.5.