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WELL, BECAUSE MOST IMPORTNAT REASON IS – ALFREDO LAID TILES ON TOP of some existing tiles.. so, there is one surface – then – robert did the hole fillup because e of FLOATING vanity – thats another surface –
now, there is a a 3RD surface – that got created BECAUSE of these two surfaces –

lets say you have a mistress and you have stuff all over like fluids and then suddenly wife knocks.. what do u do?- you throw in a sheet over taht sheet right?

well, between the sheets – no matter HOWMUCH PRESSED – there WILL be a plane – no matter howmuch and how hard you try

anyway, so yeah.

these surfaces are like planes – not like but they are – planes –

and because ofmahcine tolerances – there is an AZIMUTH –

digital is NOT analog

here is the maths and stats and atcually its stats – and engineering shit



From Wikipedia, the free encyclopedia

For the band, see Azimuth (band).

The azimuth is the angle formed between a reference direction (North) and a line from the observer to a point of interest projected on the same plane as the reference direction orthogonal to the zenith

An azimuth (Listeni/ˈæzɪməθ/) (from Arabic al-sumūt, meaning "the directions") is an angular measurement in a spherical coordinate system. The vector from an observer (origin) to a point of interest is projected perpendicularly onto a reference plane; the angle between the projected vector and a reference vector on the reference plane is called the azimuth.

An example is the position of a star in the sky. The star is the point of interest, the reference plane is the horizon or the surface of the sea, and the reference vector points north. The azimuth is the angle between the north vector and the perpendicular projection of the star down onto the horizon.[1]

Azimuth is usually measured in degrees (°). The concept is used in navigation, astronomy, engineering, mapping, mining and artillery.




In land navigation, azimuth is usually denoted alpha, alpha, and defined as a horizontal angle measured clockwise from a north base line or meridian.[2][3]Azimuth has also been more generally defined as a horizontal angle measured clockwise from any fixed reference plane or easily established base direction line.[4][5][6]

Today the reference plane for an azimuth is typically true north, measured as a 0° azimuth, though other angular units (grad, mil) can be used. Moving clockwise on a 360 degree circle, east has azimuth 90°, south 180°, and west 270°. There are exceptions: some navigation systems use south as the reference vector. Any direction can be the reference vector, as long as it is clearly defined.

Quite commonly, azimuths or compass bearings are stated in a system in which either north or south can be the zero, and the angle may be measured clockwise or anticlockwise from the zero. For example, a bearing might be described as "(from) south, (turn) thirty degrees (toward the) east" (the words in brackets are usually omitted), abbreviated "S30°E", which is the bearing 30 degrees in the eastward direction from south, i.e. the bearing 150 degrees clockwise from north. The reference direction, stated first, is always north or south, and the turning direction, stated last, is east or west. The directions are chosen so that the angle, stated between them, is positive, between zero and 90 degrees. If the bearing happens to be exactly in the direction of one of the cardinal points, a different notation, e.g. "due east", is used instead.

True north-based azimuths[edit]

From North
North 0° or 360° South 180°
North-Northeast 22.5° South-Southwest 202.5°
Northeast 45° Southwest 225°
East-Northeast 67.5° West-Southwest 247.5°
East 90° West 270°
East-Southeast 112.5° West-Northwest 292.5°
Southeast 135° Northwest 315°
South-Southeast 157.5° North-Northwest 337.5°

Cartographical azimuth[edit]

The cartographical azimuth (in decimal degrees) can be calculated when the coordinates of 2 points are known in a flat plane (cartographical coordinates):

az = 90.0 - 180.0 / {pi}  {atan2  ( X2 - X1, Y2 - Y1 )}

Remark that the reference axes are swapped relative to the (counterclockwise) mathematical polar coordinate system and that the azimuth is clockwise relative to the north.

Calculating azimuth[edit]

The azimuth between Cape Townand Melbourne along the geodesic (the shortest route) changes from 141° to 42°. Azimuthal orthographic projectionand Miller cylindrical projection.

We are standing at latitude phi_1, longitude zero; we want to find the azimuth from our viewpoint to Point 2 at latitude phi_2, longitude L (positive eastward). We can get a fair approximation by assuming the Earth is a sphere, in which case the azimuth alpha is given by

tan alpha = frac{sin L}{(cos phi_1)(tan phi_2)- (sinphi_1)(cos L)}

A better approximation assumes the Earth is a slightly-squashed sphere (an oblate spheroid); "azimuth" then has at least two very slightly different meanings. "Normal-section azimuth" is the angle measured at our viewpoint by a theodolite whose axis is perpendicular to the surface of the spheroid; "geodetic azimuth" is the angle between north and the geodesic – that is, the shortest path on the surface of the spheroid from our viewpoint to Point 2. The difference is usually unmeasurably small; if Point 2 is not more than 100 km away the difference will not exceed 0.03 arc second.

Various websites will calculate geodetic azimuth – e.g. GeoScience Australia site. Formulas for calculating geodetic azimuth are linked in the distance article.

Normal-section azimuth is simpler to calculate; Bomford says Cunningham’s formula is exact for any distance. If f is the flattening for the chosen spheroid (e.g. 1/298.257223563 for WGS84) then

e^2 = f(2-f) ,1 - e^2 = (1-f)^2 ,Lambda = (1 - e^2) frac { tan phi_2}{ tan phi_1} + e^2 sqrt{ cfrac {1 + (1 - e^2)(tan phi_2)^2}{1 + (1 - e^2)(tan phi_1)^2}}tan alpha = frac {sin L}{(Lambda - cos L) sin phi_1 }

If phi_1 = 0 then

tan alpha = frac {sin L}{(1 - e^2) tan phi_2}

To calculate the azimuth of the sun or a star given its declination and hour angle at our location, we modify the formula for a spherical earth. Replace phi_2 with declination and longitude difference with hour angle, and change the sign (since hour angle is positive westward instead of east).


There are a wide variety of azimuthal map projections. They all have the property that directions (the azimuths) from a central point are preserved. Some navigation systems use south as the reference plane. However, any direction can serve as the plane of reference, as long as it is clearly defined for everyone using that system.

Comparison of some azimuthal projections centred on 90° N at the same scale, ordered by projection altitude in Earth radii. (click for detail)

A standard Brunton Geo compass, used commonly by geologists and surveyors to measure azimuth


Used in celestial navigation, an azimuth is the direction of a celestial body from the observer.[7] In astronomy, an azimuth is sometimes referred to as a bearing. In modern astronomy azimuth is nearly always measured from the north. (The article on coordinate systems, for example, uses a convention measuring from the south.) In former times, it was common to refer to azimuth from the south, as it was then zero at the same time that the hour angle of a star was zero. This assumes, however, that the star (upper) culminates in the south, which is only true if the star’s declination is less than (i.e. further south than) the observer’s latitude.

Other systems[edit]

Right ascension[edit]

If instead of measuring from and along the horizon the angles are measured from and along the celestial equator, the angles are calledright ascension if referenced to the Vernal Equinox, or hour angle if referenced to the celestial meridian.

Horizontal coordinate[edit]

In the horizontal coordinate system, used in celestial navigation and satellite dish installation, azimuth is one of the two coordinates. The other is altitude, sometimes called elevation above the horizon. See also: Sat finder.

Polar coordinate[edit]

In mathematics the azimuth angle of a point in cylindrical coordinates or spherical coordinates is the anticlockwise angle between the positive x-axis and the projection of thevector onto the xy-plane. The angle is the same as an angle in polar coordinates of the component of the vector in the xy-plane and is normally measured in radians rather than degrees. As well as measuring the angle differently, in mathematical applications theta, theta, is very often used to represent the azimuth rather than the symbol phi phi.

Other uses of the word[edit]

For magnetic tape drives, azimuth refers to the angle between the tape head(s) and tape.

In sound localization experiments and literature, the azimuth refers to the angle the sound source makes compared to the imaginary straight line that is drawn from within the head through the area between the eyes.

An azimuth thruster in shipbuilding is a propeller that can be rotated horizontally.

Etymology of the word[edit]

The word azimuth is in all European languages today. It originates from medieval Arabic al-sumūt, pronounced as-sumūt in Arabic, meaning "the directions" (plural of Arabic al-samt = "the direction"). The Arabic word entered late medieval Latin in an astronomy context and in particular in the use of the Arabic version of the Astrolabe astronomy instrument. The word’s first record in English is in the 1390s in Treatise on the Astrolabe by Geoffrey Chaucer. The first known record in any Western language is in Spanish in the 1270s in an astronomy book that was largely derived from Arabic sources, the Libros del saber de astronomía commissioned by King Alfonso X of Castile.[8]

Engineering tolerance

From Wikipedia, the free encyclopedia

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (May 2008)

Engineering tolerance is a machine’s potential to cope with changes in the following elements of its surroundings and remain functioning:

  1. a physical dimension,
  2. a measured value or physical property of a material, manufactured object, system, or service,
  3. other measured values (such as temperature, humidity, etc.).
  4. in engineering and safety, a physical distance or space (tolerance), as in a truck (lorry), train or boat under a bridge as well as a train in a tunnel (see structure gauge andloading gauge).
  5. in mechanical engineering the space between a bolt and a nut or a hole, etc..

Dimensions, properties, or conditions may vary without significantly affecting functioning of machines. A variation beyond the tolerance (for example, a temperature that’s too hot or too cold) is said to be non-compliant, rejected, or exceeding the tolerance. If the tolerance is too restrictive, the machine being incapable of functioning in most environments, it is said to be intolerant.



Considerations when setting tolerances[edit]

A primary concern is to determine how wide the tolerances may be without affecting other factors or the outcome of a process. This can be by the use of scientific principles, engineering knowledge, and professional experience. Experimental investigation is very useful to investigate the effects of tolerances: Design of experiments, formal engineering evaluations, etc.

A good set of engineering tolerances in a specification, by itself, does not imply that compliance with those tolerances will be achieved. Actual production of any product (or operation of any system) involves some inherent variation of input and output. Measurement error and statistical uncertainty are also present in all measurements. With a normal distribution, the tails of measured values may extend well beyond plus and minus three standard deviations from the process average. Appreciable portions of one (or both) tails might extend beyond the specified tolerance.

The process capability of systems, materials, and products needs to be compatible with the specified engineering tolerances. Process controls must be in place and an effectiveQuality management system, such as Total Quality Management, needs to keep actual production within the desired tolerances. A process capability index is used to indicate the relationship between tolerances and actual measured production.

The choice of tolerances is also affected by the intended statistical sampling plan and its characteristics such as the Acceptable Quality Level. This relates to the question of whether tolerances must be extremely rigid (high confidence in 100% conformance) or whether some small percentage of being out-of-tolerance may sometimes be acceptable.

An alternative view of tolerances[edit]

Genichi Taguchi and others have suggested that traditional two-sided tolerancing is analogous to "goal posts" in a football game: It implies that all data within those tolerances are equally acceptable. The alternative is that the best product has a measurement which is precisely on target. There is an increasing loss which is a function of the deviation or variability from the target value of any design parameter. The greater the deviation from target, the greater is the loss. This is described as the Taguchi loss function or "quality loss function", and it is the key principle of an alternative system called "inertial tolerancing".

Research and development work conducted by M. Pillet and colleagues[1] at the Savoy University has resulted in industry-specific adoption.[2] Recently the publishing of the French standard NFX 04-008 has allowed further consideration by the manufacturing community.

Mechanical component tolerance[edit]

Summary of basic size, fundamental deviation and IT grades compared to minimum and maximum sizes of the shaft and hole.

Dimensional tolerance is related to, but different from fit in mechanical engineering, which is a designed-in clearance or interference between two parts. Tolerances are assigned to parts for manufacturing purposes, as boundaries for acceptable build. No machine can hold dimensions precisely to the nominal value, so there must be acceptable degrees of variation. If a part is manufactured, but has dimensions that are out of tolerance, it is not a usable part according to the design intent. Tolerances can be applied to any dimension. The commonly used terms are:

  • Basic size: the nominal diameter of the shaft (or bolt) and the hole. This is, in general, the same for both components.
  • Lower deviation: the difference between the minimum possible component size and the basic size .
  • Upper deviation: the difference between the maximum possible component size and the basic size .
  • Fundamental deviation: the minimum difference in size between a component and the basic size. This is identical to the upper deviation for shafts and the lower deviation for holes.[citation needed] If the fundamental deviation is greater than zero, the bolt will always be smaller than the basic size and the hole will always be wider. Fundamental deviation is a form of allowance, rather than tolerance.
  • International Tolerance grade: this is a standardised measure of the maximum difference in size between the component and the basic size (see below).

For example, if a shaft with a nominal diameter of 10 mm is to have a sliding fit within a hole, the shaft might be specified with a tolerance range from 9.964 to 10 mm (i.e. a zero fundamental deviation, but a lower deviation of 0.036 mm) and the hole might be specified with a tolerance range from 10.04 mm to 10.076 mm (0.04 mm fundamental deviation and 0.076 mm upper deviation). This would provide a clearance fit of somewhere between 0.04 mm (largest shaft paired with the smallest hole, called the "maximum material condition") and 0.112 mm (smallest shaft paired with the largest hole). In this case the size of the tolerance range for both the shaft and hole is chosen to be the same (0.036 mm), meaning that both components have the same International Tolerance grade but this need not be the case in general.

When no other tolerances are provided, the machining industry uses the following standard tolerances:[3][4]

1 decimal place (.x): ±0.02"
2 decimal places (.0x): ±0.01"
3 decimal places (.00x): ±0.005"
4 decimal places (.000x): ±0.0005"

International Tolerance grades[edit]

Main article: IT Grade

When designing mechanical components, a system of standardized tolerances called International Tolerance grades are often used. The standard (size) tolerances are divided into two categories: hole and shaft. They are labelled with a letter (capitals for holes and lowercase for shafts) and a number. For example: H7 (hole tapped hole or nut) and h7 (shaft or bolt). H7/h6 is a very common standard tolerance which gives a rather tight fit, but not so tight that you can’t put the shaft in the hole, or turn the nut on the bolt, by hand. The tolerances work in such a way that for a hole H7 means that the hole should be made slightly larger than the base dimension (in this case for an ISO fit 10+0.015−0, meaning that it may be up to 0.015 mm larger than the base dimension, and 0 mm smaller). The actual amount bigger/smaller depends on the base dimension. For a shaft of the same size h6 would mean 10+0−0.009, which is the opposite of H7. This method of standard tolerances is also known as Limits and Fits and can be found in ISO 286-1:2010 (Link to ISO catalog).

The table below summarises the International Tolerance (IT) grades and the general applications of these grades:

Measuring Tools Material
IT Grade 01 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Fits Large Manufacturing Tolerances

An analysis of fit by Statistical interference is also extremely useful: It indicates the frequency (or probability) of parts properly fitting together.

Electrical component tolerance[edit]

An electrical specification might call for a resistor with a nominal value of 100 Ω (ohms), but will also state a tolerance such as "±1%". This means that any resistor with a value in the range 99 Ω to 101 Ω is acceptable. For critical components, one might specify that the actual resistance must remain within tolerance within a specified temperature range, over a specified lifetime, and so on.

Many commercially available resistors and capacitors of standard types, and some small inductors, are often marked with coloured bands to indicate their value and the tolerance. High-precision components of non-standard values may have numerical information printed on them.

Difference between allowance and tolerance[edit]

The terms are often confused but sometimes a difference is maintained. See Allowance (engineering)#Confounding of the engineering concepts of allowance and tolerance.

Clearance (civil engineering)[edit]

In civil engineering clearance means the difference between the loading gauge and the structure gauge in the case of railroad cars, trams or the difference between the size of any vehicle and the width/height of doors or the height of an overpass

See also[edit]