Horizontal and vertical measurements

A Linear dimensions

The web page shows the key dimensions of the Airbus A380 in metres, and the explanations below it describe how they are measured. In the explanations, the word plane means an imaginary surface (not an aeroplane). On drawings, planes are shown as lines that indicate where dimensions are measured from and to, and are positioned to strike (touch) the faces (edges or surfaces) of components. Often, they are either horizontal planes or vertical planes.

Airbus A380 dimensions:

Overall length is a measurement of how long the aircraft is in total. The measurement is taken between the two points that are furthest apart (the front and rear extremities), along the length of the aircraft. The length is measured along a horizontal plane. It is the distance between a vertical plane striking the front of the nose, and a vertical plane striking the rear of the tail.

Wingspan is the total distance spanned by both wings. The span is measured as a straight line * between the two wingtips.

Overall height measures how tall the aircraft is. The dimension is measured vertically between the underside of the wheels and a horizontal plane striking the top of the tail.

Maximum fuselage width is the external width of the aircraft’s body - how wide it is, measured horizontally between vertical planes striking the outside faces of the fuselage.

Maximum cabin width states the maximum internal width, measured between the inside faces of the fuselage. The measurement is equivalent to the external width, less the thickness of the fuselage at each side of the aircraft.20

Notes:

When written, the words dimension and dimensions are often abbreviated to dim and dims. Span is also used to describe the distance crossed by a bridge, between its supports. If a bridge has a support at its centre (as well as at each end), then it has two spans.

B Level and plumb

If a surface is described as being level, this means it is both horizontal and flat (smooth). However, a surface which is flat is not necessarily horizontal. A flat surface may be vertical, or inclined (sloping at an angle to the horizontal or vertical plane).

Faces that are vertical, such as those of the walls of buildings, are described by engineers as being plumb. Structures that are slightly inclined from vertical are said to be out of plumb.

4.1 Complete the key dimensions of the Millau Viaduct in France, using the words in the box. Look at A opposite to help you.

 

height

overall

thickness

span

width

 

1)................................ length: 2,460 m

2) Maximum...............................between supports:342 m

3)...............................of tallest support (ground to deck): 245 m

4)...............................of deck: 32 m

5)...............................of deck: 4.2 m

 

4.2 Decide whether the sentences about the viaduct are true or false, and correct the false sentences. Look at A and B opposite to help you.

1. The height of the towers is measured horizontally.

2. The overall span is measured along the width of the bridge.

3. The tops of the towers are at different levels, so a horizontal plane striking the top of one tower will not strike the tops of all the others.

4. The highest point of the structure is the top extremity of the highest tower.

5. The thickness of each tower decreases towards the top, so the faces of the towers are plumb.

6. The greatest thickness of each tower is its internal thickness at its base.

4.3 Circle the correct words to complete the text about extra-high voltage (EHV) power lines. Look at A and B opposite to help you. The first one has been done for you.

On EHV transmission lines, cables - called conductors - (1) incline /span between pylons, which are described as supports. The conductors are suspended from the supports by rods, called insulators. On straight sections of line, the insulators are (2) level / plumb, hanging vertically from the supports. At supports where the direction of the line changes, pairs of insulators are used. In this situation, the insulators are (3) inclined / striking from the vertical plane, as they are pulled (4) plumb / out of plumb by the conductors pulling in different directions. The higher the voltage being transmitted by the line, the greater the required distance between the conductor and the support, in order to provide effective insulation. The (5) length / width of insulators therefore varies, depending on the voltage. Higher voltages also mean that conductors must be located at a greater minimum (6) height / thickness above the ground, for safety. This distance is measured between the ground and the lowest point of the cable.

 

4.4 Read the text below. Can you answer the questions?

On long suspension bridges, when the distance between the vertical centres of the towers at either side of the bridge is measured horizontally, the distance between the tops of the two towers will be several millimetres longer than the distance between their bases. Does this mean the towers are out of plumb? Why is there a difference?

Over to you

Think of a product with a fairly simple shape. What dimensions would need to be specified on a drawing in order to allow the product to be manufactured?

 

Locating and setting out

A Centrelines and offsets

The drawing below shows the position of some holes for bolts. The distances between the holes can be shown as running dimensions or as chain dimensions. In both cases, the centreline (CL) - a line through the centre of the hole - is marked (drawn), and the distances between the centrelines are given. Distances between centrelines are called centre-to-centre (c/c) dimensions. The holes below are at 100 mm centres.

Centrelines are often used as reference points. These can be measured from, in order to locate - that is, give the position of - points on components. The measurements are offset from the centreline - each is at a certain distance from it, and the offsets are measured at a right-angle to the centreline (at 90 degrees to it).

 

Notes:

We can say at a right-angle to X, at 90 degrees to X, or at right-angles to X.

B Grids

In large designs, notably those of structures, grids are used for horizontal positioning. The gridlines have numbers and letters. All numbered gridlines are parallel with one another - that is, they are straight, and are regular distances apart. Lettered lines also run parallel with one another, and are perpendicular to (at a right-angle to) the numbered lines.

The plan below shows part of the floor of an office building. The perpendicular gridlines intersect at (cross at) the centres of columns. An opening (hole) in the floor is shown using coordinate dimensions. These allow the site engineer to set out (mark the position of) the opening by squaring off the gridlines - marking lines that run at a right-angle to them - and then measuring along these lines using a tape measure.

A theodolite - an optical device used for measuring angles - can be used to square off gridlines accurately. To double-check dimensions - that is, carry out an extra check - diagonal measurements can be used, as in the engineer’s sketch below. The length of diagonals can be calculated using Pythagoras’s Theorem.

 

5.1 Look at the sentences about the design of a ship. Replace the underlined words and expressions with alternative words and expressions from A opposite.

1. The handrail is fixed by 115 brackets, which are 175 mm apart, between their centres.

2. The dimensions are measured from the line down the middle of the ship.

3. How far is the widest point of the ship located away from the centreline?

4. Are the adjacent lengths of handrail at 90 degrees to each other?

5. These dimensions allow you to establish the position of the hole.

 

5.2 Look at the extracts from technical discussions on a construction site. Complete the sentences using the words in the box. Look at B opposite to help you.

Gridline

intersect

parallel

perpendicular

set

out

quare

off

1 According to this drawing......... 8 runs along the external wall of the structure.

2 The positions were marked accurately - they were.......... by our site engineer.

3 The external wall runs along gridline I, and the internal corridor wall runs along gridline 2, so the walls are.........with each other.

4 I've marked a cross on the concrete floor, showing where the two gridlines..............

5 We need to show the position of the corner of the staircase with coordinate dimensions. There should be two.......... dimensions, taken from two gridkines.

6 We'll use the theodolite to......... the gridline and mark a ninety-degree offset.

Over to you

Choose a nearby object, or part of a building. Describe it, using language from A and B opposite. (You could also give approximate measurements) Then imagine you are designing the object or the part of the building. What dimensions and lines will be needed on the drawings in order to locate its features?

Dimensions of circles

A Key dimensions of circles

An engineer is giving a training course to a group of technical sales staff who work for a tyre manufacturer. During the talk, she mentions a number of dimensions relating to circles.

‘Obviously, the outside edge of a tyre forms a circle, as you can see in this simple diagram. The outer circle in the diagram is the outside of the tyre, and the inner circle - the circle with the smaller diameter - represents both the inside of the tyre and the outside of the wheel. And, clearly, the inner circle is right in the middle of the outer circle - it’s exactly in the centre. So because it’s central, that means the inside and outside of the tyre form concentric circles. And as the tyre is circular, simple geometry tells us that measurements of the radius, taken from the centre of the circle to different points on its edge- points on the circumference - are equal. All the radii are the same. In other words, the tyre has a constant radius.’

‘But when a tyre is fitted to a vehicle, it’s compressed against the road surface. That means its geometry changes. So while the wheel the inner circle - obviously remains round, the circumference of the tyre - the outer circle - changes shape. It deforms. Before deformation, this part of the tyre forms an arc of the circle, between points A and B. So, as you can see in this diagram, it’s not a straight line - it’s a curved line. But after deformation, it’s no longer a curve. The tyre becomes deformed between points A and B. It becomes a chord of the same circle, forming a straight line between A and B. However, the length of a chord and the length of an arc, between the same two points on a circle, are different. So the design of the tyre has to allow for this change in shape - from a rounded edge to a straight edge.’

B Pipe dimensions

Specific terms are used to describe the circular dimensions of pipes. The width of the inside of a pipe is called the inside diameter (ID). It can also be called the bore. The outside width is called the outside diameter (OD). When pipes are laid horizontally, the top of the outside of the pipe is called the crown, and the bottom of the inside of the pipe is called the invert.

6.1 Complete the notes, made by a salesperson attending the engineer’s talk, using the words in the box. Look at A opposite to help you.

 

arc	circular	constant	deformed	radius
chord	circumference	curved	diameter

Before tyres are fitted to vehicles:

- shape is round - outside edge is perfectly (1)......

- distance from centre of wheel to edge of tyre = (2).......

- total distance across tyre = 2 x radius = (3)....... of tyre

- all measurements from centre to points around tyre's (4)....... are equal - tyre has (5)...... radius

- bottom of tyre is (6)..... of a circle

When fitted to vehicle, bottom of tyre is compressed and (7)......- changes from (8)..... line to straight line. Straight line is (9)....... of a circle.

 

6.2 Find words and expressions in B opposite with the following meanings. One question has two possible answers.

1. the highest point of a horizontal pipethe lowest point of the inside of a horizontal pipe

2. the maximum overall external width of a pipe

3. the maximum internal width between the pipe walls

 

6.3 Change one word in each of the sentences below to correct them. Look at A and B opposite to help you.

1. The distance travelled by the vehicle each time its wheels turn completely is equal to the radius of one of its tyres.

2. The diameter of the tyre is measured from the centre of the wheel to the outside edge of the tyre.

3. The radius of the curve in the motorway is constant, so the edges of the road follow chords of a circle.

4. The curve in the motorway has a constant radius, so the inside and outside edges of the road are arcs of two deformed circles that have the same centre.

5. The invert is on the circumference of the external face of the pipe, and therefore cannot be in contact with the liquid flowing inside the pipe.

6. The thickness of the wall at the bottom of the pipe, plus the distance between the invert and the crown of the pipe, is equal to the inside diameter of the pipe.

 

Over to you

Choose an object which has circular and/or curved shapes. Describe it using language from A opposite. (You could also give approximate measurements)

Imagine you are designing the object. What measurements and lines will be needed to define its circular/curved features?

Dimensional accuracy

A Precision and tolerance

It is impossible to produce components with dimensions that are absolutely precise, with sizes exactly the same as those specified in a design. This is because all production processes are imprecise to a certain extent. Therefore, the sizes of several components produced from the same design will vary (differ). Although the variation may only be a few hundredths of a millimetre, sizes will not be 100% accurate (exact) compared with the design.

Because engineers know that accuracy cannot be perfect, in designs they often specify tolerances - that is, acceptable variations in precision. Instead of giving one precise size, a tolerance specifies a range of acceptable sizes - an allowed amount of variation. This is often given as a deviation (difference) from a precise size.

The drawing below shows a shaft with a specified diameter of 88 mm, plus or minus (+) 0.05 mm. This means the diameter may deviate 0.05 mm either side of this size. Therefore, diameters of 87.95 mm and 88.05 mm, which are slightly inaccurate, are still permissible (allowed), as they are within tolerance. However, diameters of 87.94mm or 88.06mm are not permissible - they are outside tolerance.

When the permissible deviation in size is very small, we say it is a tight tolerance (or a close tolerance). A large permissible deviation is a loose tolerance. For example:

Machining a metal component to a tolerance of ±0.1 mm is relatively easy to do, so this tolerance is loose. But a tolerance of just ±0.01 mm is a tight tolerance in metalworking.

In a concrete structure, ±10mm is a loose tolerance. But ±lmm is tight, because it is difficult to place wet concrete accurately.

 

B Fit

When one component goes through another, such as a shaft or a bolt going through a hole, the two must fit together - their sizes and shapes must match. The key question is, how tightly (or loosely) should they fit together? There are two main types of fit:

A clearance fit allows a component to slide or turn freely, by leaving clearance (a gap) between itself and the sides of the hole. This distance must be quite precise. If there is insufficient clearance - if the gap is too small - the component will fit too tightly. As a result, the component will bind - it will not be able to slide or turn freely. In other words, there will not be enough play. However, if there is too much clearance, there will be too much play and the component will be able to move too much.

An interference fit is a very tight fit which does not allow a component to move freely inside a hole. This type of fit can be achieved by forcing the component into the hole. Alternatively, the metal around the hole can be heated so that it expands (increases in size due to heat). After sufficient expansion, the component is placed in the hole. The metal then cools and contracts (decreases in size due to cooling). The contraction results in a tight fit. An example of an interference fit is a train wheel fitted on an axle.

7.1 Find words and expressions in A opposite with similar meanings to the words and allowed exact differ exactness not exact expressions below (1-10). Sometimes there is more than one possible answer. The first one has been done for you.

1. allowed permissible

2. exact

3. differ

4. exactness

5. not exact

6. deviation between maximum and minimum

7. an acceptable deviation

8. an unacceptable deviation

9. little deviation allowed

10. large deviation allowed

7.2 Match the related sentences. Look at B opposite to help you.

1. It’ll bind.

2. It’ll contract.

3. It’ll expand.

4. There’ll be too much play.

5. It needs a clearance fit.

6. It needs an interference fit.

 

a. The bolt will have to turn in the hole.

b. The bolt won’t be able to turn freely enough in the hole.

c. The bolt won’t fit tightly enough in the hole.

d. The wheel will have to fit very tightly on the axle.

e. The hole will widen with the high temperature.

f. The shaft will shorten and narrow slightly as it cools.

7.3 Complete the article about engine blueprinting using the words in the box. Look at A and B opposite to help you.

 

clearances	minus	plus	range	variation
fit	permissible	precise	tolerances	within

 

Blueprinting for performance since they are manufactured, not to perfectly (2).......... dimensions, but to specified (3).......... Although these differences may only be (4)........ or (5)....... a few hundredths of a millimetre, they will nevertheless result in a slight performance gap between any two engines.

One way round this problem (if you have the cash) is to have your engine blueprinted. The process is perfectly legal, as the sizes of all parts remaim (6)....... the tolerances that are (7)...... for the standard engine specification. However, by carefully matching pairs or groups of parts that are all in either the lower or upper half or the tolerance (8)......, a blueprinted engine is built to (9)....... together very precisely, thanks to almost perfect (10)..... between moving parts.

Over to you

Think of a type of product or structure you're familiar with. Imagine you're designing it, and are discussing the tolerances required for different components. Say what tolerances are permissible, both for production (not too tight due to cost), and for quality (not too loose). Say which parts require the tightest tolerances, and explain why.

Numbers and calculations

A Decimals and fractions

A manufacturer is thinking about giving both metric measurements (for example, millimetres) and imperial measurements (for example, inches) in its product specifications. One of the company’s engineers is giving his opinion on the idea in a meeting.

‘One problem is, when you convert from metric to imperial you no longer have whole numbers - you get long decimal numbers. For example, one millimetre is nought point nought three nine three seven inches as a decimal.

So to be manageable, decimals have to be rounded up or down. You’d probably round up that number to two decimal places, to give you zero point zero four. Now, you might say the difference is negligible - it’s so small it’s not going to affect anything. But even if it’s just a tiny fraction of a unit - one hundredth of an inch (1/100), or one thousandth of an inch (1/1000) - and those numbers are then used in calculations, the rounding error can very quickly add up to give bigger inaccuracies.’