COP v3.0:useful-information;

18 Useful Information 

Useful tools and tables to do calculations and conversions for roof and wall cladding. Just choose the correct online caculator, input your values, and get the answer.

18.1 Conversion Factors 

 

=

18.1A Measurement Conversions

To convert from thisinto this
To convert this back
multiply by this
divide by this
atmospheremillibar1013.25
atmospherepascal101.325
cubic footcubic metre0.028317
cubic inchcubic millimetre16387.1
cubic yardcubic metre0.764555
footmetre0.3048
foot per minutemetre per minute0.3048
foot per minutemetre per second0.00508
foot per secondmetre per second0.3048
foot pound force per secondwatt1.35582
gallon (Imp)litre4.54609
gallon (US)litre3.78541
inchmetre0.0254
inchmillimetre25.4
inch mercurykilopascal3.38638
inch water gaugekilopascal0.248642
kilogramkN102
kilometre per hourknot0.539
knotkilometre per hour1.852
knotnautical mile/h1
knotft/h6080
knotmetre per second0.515
metre Head of waterkPa9.8
milekilometre1.609344
mile per hourkilometre per hour1.609344
millimetre mercurykilopascal0.133322
millimetre water gaugepascal9.78904
MPakip6.895
ouncegram28.3495
ounce per square footgram per square metre305.152
ounce per square yardgram per square metre33.9057
poundkilogram0.45359237
pound forcenewton4.44822
pound force footnewton.metre1.35582
pound force inchnewton.metre0.112985
pound force per square footkilopascal0.0479
pound force per square inchbar0.69
pound force per square inchpascal6894.76
pound force per square inchkilopascal6.89476
pound force per square inchmegapascal0.006895
pound per cubic footkilogram per cubic metre16.0185
pound per footkilogram per metre1.48816
pound per square footkilogram per square metre4.882
square footsquare metre0.092903
square foot per tonsquare metre per tonne0.091436
square inchsquare millimetre645.16
square milesquare kilometre2.59
square yardsquare metre0.836127
Steel thickness in mmWeight of steel kgs/m²7.85
tontonne1.01605
ton force footkilonewton metre3.03703
ton force per square inchmegapascal15.4443
ton per cubic yardtonne per cubic metre1.32894
ton, freight (40 ft³)cubic metre1.13267
yardkilometre0.000914

 

Water 0 ̊ – 100 ̊ increases in volume by 4.4%
1 litre    = 1 kg = 0.001 m3
1 m3      = 1000 litres
Weight of steel kgs/m2     = thickness in mm x 7.85
1 kN     = 102 kg
1 kip     = 6.895 MPa

 

18.2 Roof Pitch Tangent 

 

The relationship between the pitch, fall or rise and the horizontal, is the relationship between the opposite and the adjacent sides of a right angled triangle.

This is known as the tangent of the angle. (tan ɸ) with the opposite side being the rise and the adjacent side the horizontal distance.

Enter any two values on the illustration for live calculations.

°
1 in

 

18.2A Rafter, Hip and Rise Chart

PitchRafter lengthHip/Valley LengthVertical RiseValley Angle
 per metre spanper metre spanper metre span 
0.51.0001.4140.009179°
11.0001.4140.017179°
1.51.0001.4140.026178°
21.0011.4150.035177°
31.0011.4150.052176°
41.0021.4160.070174°
51.0041.4170.087173°
61.0061.4180.105172°
71.0081.4200.123170°
81.0101.4210.141169°
91.0121.4230.158167°
101.0151.4250.176166°
111.0191.4280.194164°
121.0221.4300.213163°
131.0261.4330.231162°
141.0311.4360.249160°
151.0351.4390.268159°
161.0401.4430.287158°
171.0461.4470.306156°
181.0511.4510.325155°
191.0581.4560.344153°
201.0641.4600.364152°
211.0711.4650.384151°
221.0791.4710.404149°
231.0861.4770.424148°
241.0951.4830.445147°
251.1031.4890.466145°
261.1131.4960.488144°
271.1221.5030.510143°
281.1331.5110.532141°
291.1431.5190.564140°
301.1551.5280.577139°
311.1671.5370.601137°
321.1791.5460.625136°
331.1921.5560.649135°
341.2061.5670.675133°
351.2211.5780.700132°
361.2361.5900.727131°
371.2521.6020.754130°
381.2691.6160.781128°
391.2871.6300.810127°
401.3051.6440.839126°
411.3251.6600.869125°
421.3461.6770.900124°
431.3671.6940.933122°
441.3901.7120.966121°
451.4141.7321.000120°
461.4401.7531.036119°
471.4661.7751.072118°
481.4941.7981.111117°
491.5241.8231.15115°
501.5561.8491.192114°
511.5891.8771.235113°
521.6241.9071.280112°
531.6621.9391.327111°
541.7011.9731.376110°
551.7432.0101.428109°
561.7882.0491.483108°
571.8362.0911.540107°
581.8872.1361.600106°
591.9422.1841.664105°
602.0002.2361.732104°

18.3 Material Density, Melting Point, Expansion And Modulus 

 

18.3A Density, Melting Point, Expansion and Young Modulus

MaterialDensity
kg/m³
Melting point
°C
Expansion
mm/10m/100°C
Youngs modulus
Gpa
Air1.29   
Air acetylene 2500*  
Aluminium, rolled27106582469
Brass833090018 
Carbon Dioxide 0°C1.99   
Cement1281   
Concrete, reinforced 2% steel2420   
Copper8938108317131
Glass27878509 
Gold19290106314 
Hydrogen 0°C0.0897   
Helium 0°C0.178   
Ice9130  
Iron, cast7208153012179
Lead, rolled113253272916
Nitrogen 0°C1.25   
Oxygen 0°C1.43   
Oxy acetylene 4400*  
Pinus Radiata609  6
Polycarbonate124413364 
Polyester129924580# 
P.V.C.146586140 
Silver1050096019 
Silver solder 735  
Easy-flo 630  
Solder Lead 50%9302210  
(Eutectic) Lead 33%/tin 67%8615180  
Snow: fresh961  
             wet compact320   
Stainless Steel 3048080142517193
Stainless Steel 3168080138516193
Steel, low carbon7850135012200
Tin728023127 
Water: fresh 4°C1000   
Water: fresh 20°C988   
Water: fresh 100°C958   
Water: salt1009-1201   
Zinc: rolled719241929 

* max flame temperature
# glass reinforced polyester GRP expansion = 22
To convert Centigrade to Farenheit.
To convert Farenheit to Centigrade.
C° = F° - 32° x .56
F° = C° x 1.8 + 32°

 

 

18.3.1 Thermal Conductivity K 

 

18.3.1A Thermal Conductivity

Material

W/mK

Copper385 
Aluminium205 
Zinc108 
Steel50 
Lead35 
Stainless Steel16 
Ice2 
Glass1.05
Concrete 0.94
Brick 0.8
Water (20°C) 0.56
Timber (Pine) 0.14
Snow 0.1
Kraft building paper 0.07
Fibreglass 0.035
Rockwool 0.035
Polystyrene 0.035
Air (20°C ) 0.025
Polyurethane (Rigidised) 0.016

18.4 Decadic Number System 

 

18.4A Decadic Numbers

SymbolDesignationLong MeasureMultiplier
TTeraBillion (Trillion  10 12
GGigaMilliard (Billion USA)  10 9
MMegaMillion  10 6
maMyriaTen thousandmamMyriametre10 4
kKiloThousandkmKilometre10 3
hHectoHundredhmHectometre10 2
daDecaTendamDecametre10
  OnemMetre1
dDeciTenthdmDecimetre10 -1
cCentiHundredthcmCentimetre10 -2
mMilliThousandthmmMillimetre10 -3
μMicroMillionth Micrometre (Micron)10 -6
nNanoMilliardthnmNanometre10 -9
pPicoBillionthpm 10 -12

18.4.1 International Symbols 

18.4.1A The Greek Alphabet

UpperLowerGreek
ΑAαaalpha
ΒBβbbeta
ΓGγggamma
ΔDδddelta
ΕEεeepsilon
ΖZζzzeta
ΗHηheta
ΘQθqtheta
ΙIιiiota
ΚKκkkappa
ΛLλllambda
ΜMμmmu
ΝNνnnu
ΞJξjxi
ΟOοoomicron
ΠPπppi
ΡRρrrho
ΣSσssigma
ΤTτttau
ΥYυyupsilon
ΦFφfphi
ΧXχxchi
ΨCψcpsi
ΩVωvomega

18.5 Geometry And Mensuration 

Enter values below for automatic calculations

= area 
= base
= diameter
= height
= length
= radius
= 3.1416 
= circumference = 2πr or 22/7d 

Areas

= πr² or 0.7854 d² 
= bh 
= .5 bh 
= .5 two parallel sides x h 
= 0.8862 d 
= 1.1284 side of square 
= .66 bh 
= 0.7854 d1 d2 
Area of any figure of four or more unequal sides is found by dividing it into triangles, finding areas of each and adding together.

Surface Area

= 6b² 
= πd² 
= .5 cbh (slant height) 
= πdh 
= πdh + 2πr2 
= ab + c of base x .5h (slant height) 

Volume

= b³ 
= 0.5236 d³ 
= .33 abh 
= .33 abh 
= πr²h 

Table of polygons

= side of polygon. 
= Radius of circumscribed circle. 
= Radius of inscribed circle. 
= Angle formed by the intersection of the sides. 
NameNo of sidesAngle
Trigon360°
Pentagon5108°
Hexagon6120°
Octagon8135°
Decagon10144°
Area of any regular polygon = Radius of inscribed circle x 1/2 number of sides x length of one side.

Right Angle Triangles

Enter any two values on the illustration for live calculations.

°
1 in
FindGiven Solution
A a, b tan A = a / b
  a, c sin A = a /c
  b, c cos A = b / c
B a, b tan B = b / a
  a, c cos B = a / c
  b, c sin B = b / c
a A, b b tan A
  A, c c sin A
  b, c √ c² - b²
b A, a a / tan A
  A, c c / cos A
  a, c √ c² - a²
c A, a a / sin A
  A, b b / cos A
  a, b √ a² + b²
Area a, b ab / ²
 

18.5B To Find a Right Angle

Draw a line ab 3x long. At point a scribe an arc 4x long.
At point b scribe an arc 5x long to intersect a c.
Join ac and b, ac and ab are at 900.

18.6 Velocities 

18.6A Velocity

18.6A Velocity

Unitm/skms/hmile/h
mile / hour
m/s
km/h
0.44704
1
0.277778
1.60934
3.6
1
1
2.23694
0.62137

 

Velocity is the distance travelled in one second (m/s).

The following speeds are approximate and are assumed to be constant and in a straight direction and therefore are also the velocity.

Description marked R are speed records.

18.6B Velocity Comparison

 m/skm/hmile/hourBeaufort Scale
Calm0<10 Smoke rises vertically
Light Air0.8321Smoke rises on angle
Man walking1.55.5.3.5  
Light breeze2.595.62Feel wind on face
Gentle breeze4.516103Flags extend
Moderate breeze72515.54Raises dust
Fresh breeze1035225Trees sway, waves
Runner 100m R103522  
Strong breeze12.545286Telegraph wires whistle
Racehorse trotting R155433  
Moderate gale15.556357Difficult to walk
Fresh gale18.567428Branches break
Racehorse R196842.5  
Ostrich207245  
Racing cyclist R227949  
Strong gale2382519Slight building damage
Whole gale26.5966010Trees uprooted
N.Z. Road speed limit2810062.5  
Skier downhill2810062.5  
Storm311116911Widespread damage
Low wind speed NZS 36043211571  
Hurricane33.51207512Severe damage
Medium wind speed NZS 36043713383  
High wind speed NZS 36044415898  
AS/NZS 117045162101  
Swift - fastest bird47169105  
Very high wind speed NZS 360450180111  
AS/NZS 1170 (Cook Strait)51184114  
Moderate cyclone55198153  
Tennis serve R66238148  
Bullet train (Japan)69248154  
Severe tropical cyclone70252157  
TGV express train77277172  
Wind R103371230  
Boeing 747256920572  
Sound in air3331199743  
Land speed R3411228763  
Rotation of earth at equator46516741040  
Concorde64923361452  
303 Bullet79228511772  
Lockheed Blackbird R98135292193  
Moon round the earth100036002237  
Sound through steel51001836011408  
To escape earth’s gravity78232816317500  
Fastest man has travelled111764023425000  
Earth round the sun2970010692066437  
Pioneer space probe66720240192149248  
Light and electric waves2993880001077614064669600000186,000 miles/sec

18.7 Cricket Penetration Patterns 

When cricket and diverter penetration flashings are used, the pitch of the cricket valley will always be less than the pitch of the roof.

To find the pitch of a roof or valley, a simple method is to use a 1m long level measuring stick and measure the rise as shown in drawing 18.7A Measuring Stick Method. The relationship between the rise and the horizontal distance is known as the tangent of the angle and is calculated by using tan f = O/A (being the opposite side divided by the adjacent side). See 18.2 Roof Pitch Tangent.

 

 

250/1000 = 0.25 = 14° (1 in 4)

N.B. Angles A and B are equal.

It is possible to obtain the length of the hypotenuse by using √ a2 + b2

Cricket flashings as described in section 6 can be made to suit any penetration width, any cricket flashing depth to width ratio and roof pitch down to 3°. For simplicity, three angles have been selected.

f X = 45°
f Y = 27°
f Z = 18°

 

VARIATION OF CRICKET VALLEY DESIGN DEPENDENT ON DEPTH AND ROOF PITCH

Penetration Width = 2A
Depth = D
Valley = V

 

 

 

f X = 45°
D = A
V = √2 = 1.42
f Y = 27°
D = 1/2A
V = √1.25 = 1.118
f Z = 18°
D = 1/3A
V = √1.11 = 1.054

 

 

To find the cricket valley pitch when the roof pitch is known, it is necessary to find the depth (D) of the cricket. If the depth of the cricket is half of the width of the penetration, as shown for 'Cricket X' the angles are at 45° and there is a defined relationship between the length of the valley of the cricket and the width of the penetration and also between the pitch of the valley of the cricket and the pitch of the roof.

This is 1 : √ 2 = 1.42, which means that to maintain the desired 3° fall in the cricket valley, the minimum roof pitch (4°) can be calculated using table 15.8.

If the depth of the cricket is a quarter or a sixth of the width of the penetration, there are also defined relationships between the pitch of the valley of the cricket and the pitch of the roof.

These are described in table 18.7C as 'Cricket Y' and 'Cricket Z'.

All figures comply with the minimum fall of 1.5°, but all the bold figures will provide a 3° cricket valley pitch. This methodology is valid for all sizes of penetration. However, there is a point at which, having a design with a wide penetration and a low pitch, it becomes uneconomic to pursue the ideal 3° fall in the cricket valley. When the roof pitch is known, the minimum allowable fall of the cricket valley pitch (1.5°) can then be read from table 15.8.

It is permissible to lower the valley pitch because 1.5° allows sufficient fall to clear debris from the valley and therefore qualifies as a warrantable flashing.

A diverter flashing without a cricket design only shifts the position of the cricket to the top over-flashing of the penetration as shown on drawing 9.7.6B Cricket Flashings, unless the penetration is rotated 45° as shown on drawing 9.7.6C Diverter Flashings.

 

18.7C

ROOF PITCH10°
TANGENT.0524.0699.0875.1051.1228.1405.15841763
CRICKET X3.5°4.5°   10°
CRICKET Y1.5°1.75°2.25°2.75°3.25°10°
CRICKET Zn/an/a1.5°2.25°2.5°3.5°

 

PROCEDURE TO MAKE A HALF PATTERN FOR A CRICKET PENETRATION FLASHING

Example:
A net penetration width is 550 mm wide and gross width to the flat of the pans is 620 mm (2A).
The back curb is required to have a fall of 3°.
The roof pitch is 7°.
From Table 18.7C . select the cricket - Type Y

Given:

Half the width of the cricket
Depth of the Y cricket from drawing 15.8.B (D=1/2A)
Height of the side curb
Height to the top of the cricket
H - Hc = Hr
From Drawing 15.8.C
Find the length of V, S and R.
Right angle triangle, therefore, the length of V.
 
A = 310mm
D = 155mm
H = 130mm
Hc = 70mm
Hr = 60mm
 
 
V = √ A2 + D2
A = 346 mm

 

Right angle triangle, therefore, the length of R.

 

Right angle triangle, therefore, the length of S.

 

R = √ Hc² + D²

R = 170 mm

S = √ A² + Hc²

R = 318 mm

 

 

 

DRAW A HALF PATTERN

 

1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
Draw a dotted line K - L length equal to A
From L draw a dotted line at right angles L - M length equal to D
Draw the line K - M (length equal to V)
With centre M scribe an arc length equal to R
With centre K scribe an arc length equal to S
From their point of intersection, N draw a line to K and also to M
With centre K scribe an arc length equal to H.
With centre N scribe an arc length equal to Hr.
Draw a line as a tangent to the two arcs
From point K, draw a line at right angles to intersect this line at O.
From O measure length A to a point P
The shape K-M-N-P-O is the net cricket pattern

18.8 Sheet Metal Work For Roofing Contractors. 

When forming various flashings in sheet-metal the Roofing Contractor is required to know how to cut his material in order to obtain the desired shape.

A basic knowledge of geometrical drawing and mensuration is required and this section explains the methods which are employed to ensure accurate results.

 


A straight line. A straight line is a line drawn in the shortest manner between two given points, so any other line between these points is a curved line.

 


Parallel lines. Parallel lines are lines which, when extended, do not touch. Given a line CD, to draw a parallel line set a compass to the required distance apart and with C and D as centres, describe two arcs. A line drawn as a tangent to both arcs will be a parallel line to CD.

 

To draw a perpendicular line. Given a straight line EF, set a compass to any distance more than half the distance EF and, with E and F as centres, describe arcs of radius EG and FH.

A line drawn through the points of intersection of these arcs is perpendicular to EF, and bisects the distance EF.

To divide a line into any number of equal parts. Given a straight line J K, draw another line J L at any suitable angle and no particular length. Set off on JL, at any reasonable distance apart, a number of equal spaces similar in number to the parts into which JK is to be divided.

Connect L and K with a line, and parallel to this draw other lines through points on JL. These divide JK into the required number of equal parts.


To bisect an arc. Given an arc AB, set a compass to a distance a little more than half that between the ends and with A and B as centres, describe arcs of equal radii.

A line drawn through the points of intersection will bisect AB. This method can be employed to divide the arc into any number of even parts by repetition. Further, the method may be used to find the centre of any given arc by further bisecting AC and CB.

Lines taken through the intersecting points of these latter arcs, when produced, will intersect at the centre of the arc AB.

 


To bisect an angle. Given an angle ABC, set off equal distances BD and BE and with D and E as centres and a compass set at any reasonable radius, describe arcs to intersect in F. A line drawn through B and F bisects the angle.

 

 


To divide a circle into six equal parts. Set a compass to the radius of the circle and step this distance off along the circumference. Further division into 12 parts may be done by bisecting one part, and again steppingoff with the radius of the circle

Development of the frustrum of a true cone.

Draw the elevation X with base diameter AB, the vertical height CD to the desired cone angle and add the section line EF to the elevation. With centre D and radius DA describe a semicircle Y on the base, and divide the circumference of this into six equal parts.

To draw the development Z: With centre C and radius CB, describe an arc AA¹ whose length equals the circumference of cone base.

This may be obtained by marking off along the arc from A spaces equal to parts in the semicircle Y but double in number.(12)

With C as centre and radius CE, draw the arc EE1 and add the line CA¹.

The figure AA1E1E is the development Z of the frustrum.

To do this, drop a perpendicular from F to F¹ and extend the base line AB.

An offset diagram is now made by measuring distances B¹F¹, B¹G, and B¹H, setting these off from F¹ on base line AB and drawing lines to F.

The lengths FF¹, FG, and FH, etc., are now true lengths.

To draw the development Z:

Draw a centre line C¹O. At right angles to C¹ draw A²B² equal to AB.

From C1, set off distance C1F1, equal to FB.

Join A² and B² to F¹. With centre A² and radius F¹G, draw a short arc to be cut by an arc of F¹G radius struck from F1 to obtain point G1.

Similarly, with A² as centre and radius FH, draw an arc, to be cut by an arc of GH radius struck from point G¹, thus obtaining point H¹.

Draw a line through, A² and H¹ and produce same to intersect the centre line C¹O at O.

Repeat the process with. B² as centre for long radii, thus completing one quarter of the whole development.

To complete the pattern, draw a curve through points H¹G¹F¹ and repeat in the other sections of the development.

Development of a square base to a circular top.

Draw the elevation X, making the base AB, vertical height CD, and diameter of top EF.

Draw a half plan Y on the base, drawing the semicircle E1F1 and dividing one half of this into a number of equal parts, F¹G, GH, HJ, and JK.

Through points F¹, G, H, J, and K, draw lines to B¹.

Before proceeding to the development it is necessary to find the true lengths of B¹K, B¹J, B¹H, B¹G, and B¹F¹.