A goniometer is an instrument that either measures an angle or allows an object to be rotated to a precise angular position. The term goniometry derives from two Greek words, 'angle' and 'Measurement'.
The first known description of a goniometer, based on the astrolabe, was by Gemma Frisius in 1538.
Protractor
A
protractor is a measuring instrument, typically made of transparent plastic, for measuring
. Some protractors are simple half-discs or full circles. More advanced protractors, such as the bevel protractor, have one or two swinging arms, which can be used to help measure the angle.
Most protractors measure angles in degrees (°). Radian-scale protractors measure angles in radians. Most protractors are divided into 180 equal parts. Some precision protractors further divide degrees into arcminutes. A protractor divided in is normally called a "percentage protractor".
Bevel
A bevel protractor is a graduated circular protractor with one pivoted arm; used for measuring or marking off angles. Sometimes
are attached to give more precise readings. It has wide application in architectural and mechanical drawing, although its use is decreasing with the availability of modern drawing software or
CAD.
Universal bevel protractors are also used by toolmakers; as they measure angles by mechanical contact they are classed as mechanical protractors.
The bevel protractor is used to establish and test angles to very close tolerances. It reads to 5 arcminutes (5′ or °) and can measure angles from 0° to 450°.
The bevel protractor consists of a beam, a graduated dial, and a blade which is connected to a swivel plate (with Vernier scale) by a thumb nut and clamp. When the edges of the beam and blade are parallel, a small mark on the swivel plate coincides with the zero line on the graduated dial. To measure an angle between the beam and the blade of 90° or less, the reading may be obtained directly from the graduation number on the dial indicated by the mark on the swivel plate. To measure an angle of over 90°, subtract the number of degrees as indicated on the dial from 180°, as the dial is graduated from opposite zero marks to 90° each way.
Since the spaces, both on the main scale and the Vernier scale, are numbered both to the right and the left from zero, any angle can be measured. The readings can be taken either to the right or to the left, according to the direction in which the zero on the main scale is moved.
Gallery
Image:Protractor1.svg|A 360° protractor marked in degrees.
Image:Grad protractor.png|A 400 gon protractor marked in .
Image:Navigational rules types.JPG|A "Cras navigation plotter" double-protractor, in foreground, named after its inventor Jean Cras.
Image:Protractor_Rapporteur_Degrees_V3.jpg|A half circle protractor marked in degrees (180°).
Image:Set square Geodreieck.svg|Geodreieck, a special type of protractor triangle (180°).
File:Electronic protractor.jpg|Electronic protractor
File:Degree-Radian Conversion.svg|Protractor scale in degrees and radians
Applications
Surveying
Prior to the invention of the
theodolite, the goniometer was used in
surveying. The application of triangulation to
geodesy was described in the second (1533) edition of
Cosmograficus liber by Petri Appiani as a 16-page appendix by Frisius entitled
Libellus de locorum describendorum ratione.
Simple semicircle protractor or protractor triangle with a knitted small weight via pice of thread to protractor origin point (most of protractors has a thin hole at origin point) could be used as a cheap goniometr, level (optical instrument), Inclinometer and quadrant for wide range of tasks.
In military topography
There are various tools deisigned for use together with topographic maps, were some are a combination of protractor, scale ruler and grid scale for measuring azimuth, distance and coordinates (in MGRS, UTM, USNG, etc).
Most of military protractors and plotters produced to be layed ontop of detailed Topographic map, so are made from thin flexible transluent plastic intentionally to avoid parallax and optics distortion, on the other hand it mades tools less durable.
File:Exercise Aurora 23 DDC-OFFICIAL-20230509-180-103.jpg|Semicircle military protractor on map
File:2-8 scout sniper platoon begins pre-screener 151014-M-ML847-195.jpg|Square military protractor flexed on map
File:RM Military Round Protractor.jpg|Round protractor flexed in hands
File:ITX 3-15 150520-F-AH628-412.jpg|Partially broken military protractor still in use
Royal Artillery Mils Protractor
Semi circular 6in and 9in Mils protractors, produced in UK (marked R.A.), Australia (marked R.A.A.) and New Zealand (marked R.N.Z.A.) since 1960s for the
Royal Artillery, the Royal Australian Artillery and the
RNZA. Protractors, commonly used in
Vietnam War and other conflicts since then. Protractors stamped with the
Ordnance Survey product number, were some additionally stamped with a NATO Stock Number.
Instruction on its basic use described in the
Military Map Reading booklet (an excerpt from the
Manual of Map Reading and Land Navigation, Army Code 71874. Issue 1.0: Apr 2009). Identical and modified protractors commercially produced by various publishers.
[ RA 6IN Protractor Degrees/Mils/Metres/Yards. miltemptech.com.au.]
Its original design derived from 400 degrees semicircle protractor (Patent 11465 of 1916) produced by J.H. Steward Ltd. in 1935,
GTA 05-02-012 Coordinate Scale and Protractor
Since 1981, the GTA 05-02-012
Coordinate Scale and Protractor tool (initially GTA 5-2-12, which superseded GTA 5-2-10) is a standartized 125x125mm square-size military protractor (its official standard is a PDF file with a vector template for print, latest revision released in June, 2008), designed and produced by the Department of Army Graphic Training Aid for the needs of the U.S. Army. For its users published special guides and instructions: GTA 05-02-013
How To Find Your Way (old title:
How To Avoid Getting Lost), TC 3-25.26 (FM 3-25.26)
Map Reading and Land Navigation,
STP 21-1-SMCT
Soldier’s Manual of Common Tasks, Warrior Skills Level 1,
etc.
File:GTA 05-02-012, JUN 2008.svg|The GTA 05-02-012, JUN 2008 tool layout
File:GTA 05-02-012 JUN 2008 - COORDINATE SCALE AND PROTRACTOR (Army Warrior Training).jpg|Finding object's MGRS coordinates on map
File:Measuring Slope Angle with GTA 5-2-12 (Step 1).png|Knitted nut for use as inclinometer/quadrant
File:Measuring Slope Angle with GTA 5-2-12 (Step 3).png|Measuring slope or object altitude angle
File:9-11 Memorial Airborne Operation 150911-A-OK697-003.jpg|Measuring angle to airborne target
The GTA 05-02-012 protractor included in most of military and ranger students, recruits and the first responders backpack's check lists, also it's used by military personnel in NATO member states and by its allies. Identical or modified versions of this tool, based on officially released template, commercially produced by various publishers.
[ GTA 05-02-012 Jun 2008 - Coordinate Scale and Protractor. miltemptech.com.au. «The standard US Army and USMC protractor is the Graphic Training Aid (GTA) 05-02-012 dated Jul 2008. Normally these are printed on plastic so thin you can scrunch it into a ball in your hand, so it comes out of your pocket broken, scratched or unreadable.»]
Combat Mission Plotter
For the needs of combat mission planers designed special plotters for drafting special symbols on maps. Such tools combined protractors, rulers and scale plotters on a single plate.
File:Combat Mission Plotter PLU-6C.svg|U.S. Army/NATO Combat Mission Plotter PLU-6C
File:Map marking stencil.svg|Soviet/Russian combat mission plotter — Officer's ruler (rus. )
GPS Plotting Protractor
Is a special protractor used to define positions with an accuracy to 10 meters according reference grid or to measure GPS accuracy.
In 2017, in the Infantry, the magazine of the U.S. Army, was published training notes under the title of Winning in a GPS-Degrade Environment, describing military acting in severe navigational conditions, were author summed article with the next note:
Communications
The Bellini–Tosi direction finder was a type of radio direction finder that was widely used from World War I to World War II. It used the signals from two crossed antennas, or four individual antennas simulating two crossed ones, to re-create the radio signal in a small area between two loops of wire. The operator could then measure the angle to the target radio source by performing direction finding within this small area. The advantage to the Bellini–Tosi system is that the antennas do not move, allowing them to be built at any required size.
The basic technique remains in use, although the equipment has changed dramatically. Goniometers are widely used for military and civil purposes,
Crystallography
In
crystallography, goniometers are used for measuring angles between crystal faces. They are also used in X-ray diffraction to rotate the samples. The groundbreaking investigations of physicist Max von Laue and colleagues into the atomic structure of crystals in 1912 involved a goniometer.
Light measurement
measure the spatial distribution of light visible to the human eye (often luminous intensity) at specific angular positions, usually covering all spherical angles.
In medicine
A goniometer is used to document initial and subsequent range of motion, at the visits for occupational injuries, and by
disability evaluators to determine a permanent disability. This is to evaluate progress, and also for medico-legal purposes. It is a tool to evaluate Waddell's signs (findings that may indicate symptom magnification.)
Rehabilitative therapy
In physical therapy, occupational therapy, Orthotics and prosthetics and athletic training, a goniometer measures range of motion of limbs and joints of the body. These measurements help accurately track progress in a rehabilitation program. When a patient has decreased range of motion, a therapist assesses the joint before performing an intervention, and continues to use the tool to monitor progress. The therapist can take these range of motion measurements at any joint. They typically require knowledge about the anatomy of the body, particularly bony landmarks. For example, when measuring the knee joint, the therapist places the axis (point of rotation) on the lateral
epicondyle of the femur, and lines up the stationary arm with the greater trochanter of the
femur. Finally, the therapist lines up the moveable arm of the goniometer with the lateral
malleolus of the
fibula, and records a measurement using the degree scale on the circular portion of the tool. Reading
accuracy is sometimes a problem with goniometers. Issues with the intra-measure (between measures) and inter-tester (between clinicians) reliability may increase as the experience of the examiner decreases. Some studies suggest that these errors can be anywhere between 5 and 10 degrees.
These goniometers come in different forms that some argue increase reliability.
More recently in the twenty-first century, smartphone application developers have created mobile applications that provide the functions of a goniometer. These applications (such as Knee Goniometer and Goniometer Pro) use the accelerometers in phones to calculate joint angles. Recent research supports these applications and their devices as reliable and valid tools with as much accuracy as a universal goniometer.
Modern rehabilitative therapy motion capture systems perform goniometry at the least measuring active range of motion.
Surface science
Contact angle goniometer
In
surface science, an instrument called a contact angle goniometer or tensiometer measures the static
contact angle, advancing and receding contact angles, and sometimes surface tension. The first contact angle goniometer was designed by
William Zisman of the United States Naval Research Laboratory in Washington, D.C. and manufactured by ramé-hart (now ramé-hart instrument company), New Jersey, USA. The original manual contact angle goniometer used an eyepiece with a microscope. Today's contact angle goniometer uses a camera and software to capture and analyze the drop shape, and is better suited for dynamic and advanced studies.
Surface tension
Contact angle goniometers can also determine the
surface tension for any liquid in gas or the interfacial tension between any two liquids. If the difference in densities between the two fluids is known, the surface tension or interfacial tension can be calculated by the pendant drop method. An advanced instrument often called a goniometer / tensiometer includes software tools that measure
surface tension and interfacial tension using the pendant drop, inverted pendant drop, and sessile drop methods, in addition to
contact angle. A centrifugal adhesion balance relates the contact angles to the adhesion of the drop to the surface. A gonioreflectometer measures the reflectivity of a surface at a number of angles.
Positioning
A positioning goniometer or goniometric stage is a device that rotates an object precisely about a fixed axis in space. It is similar to a
linear stage—however, rather than move linearly relative to its base, the stage platform rotates partially about a fixed axis above the mounting surface of the platform. Positioning goniometers typically use a
worm drive with a partial worm wheel fixed to the underside of the stage platform meshing with a worm in the base. The worm gear may be rotated manually, or by a motor in automated positioning systems.
Knife and blade cutting edge angle measurement
The included cutting angles of all kinds of sharp edge blades are measured using a laser reflecting goniometer. Developed by the Cutlery and Allied Trades Research Association (CATRA) in the UK, a range of devices can accurately determine the cutting edge profile, including a rounding of the tip to ½°. The included angle of a blade is important in controlling its cutting ability and edge strength—i.e., a low angle makes a thin sharp edge optimized for cutting softer materials, while a large angle makes a thick edge that is less sharp but stronger, which may be better for cutting harder materials.
Doctor blade inspection
Used
, from
gravure and other
printing and
coating processes, can be inspected with a goniometer, typically with a built-in light source, to examine the blade edge for wear and correct angles. A difference in angle from that set on the machine may indicate excessive pressure, and a range of angles ("rounding") probably indicates a lack of stiffness, or wear, in the blade holder assembly.
See also
-
Sliding T bevel
-
Technical drawing tools
External links
