CHAPTER 1 Fundamentalsof Measuring
25
CHAPTER 1 Fundamentals of Measuring Dr. Davut Solyalı 2017©
Transcript of CHAPTER 1 Fundamentalsof Measuring
CH
AP
TE
R 1
Fu
nd
amen
tals
of
Mea
suri
ng
Dr.
Dav
ut
Soly
alı
2017©
Ter
min
olo
gy
Dr.
Dav
ut
Soly
alı
2015©
Tru
e v
alu
e –
sta
ndard
or
refe
rence o
f
know
nvalu
e o
r a theore
tical valu
e
Accura
cy –
clo
seness to the tru
e v
alu
e
Pre
cis
ion –
repro
ducib
ility
or
agre
em
ent
with
each o
ther
for
multip
le trials
Acc
ura
cy v
s. P
reci
sio
n
•Acc
ura
cy r
efer
s to
the
agre
emen
t b
etw
een a
mea
sure
men
t an
d
the
true
or
acce
pte
d v
alue
•C
annot
be
dis
cuss
ed m
eanin
gfu
lly u
nle
ss t
he
true
val
ue
is
know
n o
r know
able
•T
he
true
val
ue
is n
ot
usu
ally
know
n o
r m
ay n
ever
be
know
n)
•We
gen
eral
ly h
ave
an e
stim
ate
of
the
true
val
ue
•Pre
cisi
on r
efer
s to
the
rep
eata
bil
ity o
f m
easu
rem
ent
• D
oes
not
requir
e us
to k
now
the
true
val
ue
Ex
amp
le ‐
Lev
er B
alan
ce –
So
urc
es o
f E
rro
r
Dr.
Dav
ut
Soly
alı
2015©
Ex
amp
le ‐
Lev
er B
alan
ce –
So
urc
es o
f E
rro
r
•Bu
oya
ncy
-Th
e d
iffe
ren
ce
in
de
nsity o
f a
ir
•Err
or
in m
ass o
f re
fere
nce
we
igh
t
•Air
gu
sts
, e
ve
n s
ma
ll o
ne
s, w
hic
h p
ush
th
e s
ca
le u
p o
r d
ow
n
•Fri
ctio
nin
th
e m
ovin
g c
om
po
ne
nts
•Se
ttlin
g a
irb
orn
e d
ust co
ntr
ibu
tin
g to
th
e w
eig
ht
•Mis
ca
libra
tio
n/ M
isa
lign
ed
me
ch
an
ica
l
•Ma
gn
etic fie
lds
actin
g o
n fe
rro
us c
om
po
ne
nts
•Fo
rce
s fro
me
lectr
osta
tic fie
lds
•Ch
em
ica
l re
activity b
etw
ee
n a
ir a
nd
th
e s
ub
sta
nce
be
ing
we
igh
ed
•Co
nd
en
sa
tio
no
f a
tmo
sp
he
ric w
ate
r o
n c
old
ite
ms
•Eva
po
ratio
no
f w
ate
r fr
om
we
t ite
ms
•Co
nve
ctio
no
f a
ir fro
m h
ot o
r co
ld ite
ms
•Gra
vita
tio
na
l d
iffe
ren
ce
s fo
r a
sca
le w
hic
h m
ea
su
res fo
rce
•Vib
ratio
n a
nd
se
ism
ic d
istu
rba
nce
s
•Ho
w a
bo
ut o
the
r e
rro
rs?
?
Ty
pes
of
erro
rs (
un
cert
ain
ties
)
Dr.
Dav
ut
Soly
alı
2015©
• G
ross (
hu
ma
n)
• S
yste
ma
tic (
de
term
ina
te)
• R
an
do
m (
ind
ete
rmin
ate
)
Hu
man
err
ors
(G
ross
err
ors
)
Dr.
Dav
ut
Soly
alı
2015©
Met
ho
ds
of
elim
inat
ion
or
red
uct
ion
Dr.
Dav
ut
Soly
alı
2015©
•Ca
refu
l a
tte
ntio
n to
de
tail
wh
en
ma
kin
g
me
asu
rem
en
ts a
nd
ca
lcu
latio
ns.
•Aw
are
ne
ss o
f in
str
um
en
t lim
ita
tio
ns.
•Use
tw
o o
r m
ore
ob
se
rve
rs t
o ta
ke
cri
tica
l
da
ta.
•Ta
kin
g a
t le
ast
thre
e r
ea
din
gs o
r re
du
ce
po
ssib
leo
ccu
rre
nce
s o
f g
ross e
rro
rs.
•Be
pro
pe
rly m
otiva
ted
to
th
e im
po
rta
nce
of
co
rre
ctre
su
lts.
Sy
stem
atic
Err
ors
Dr.
Dav
ut
Soly
alı
2015©
Sy
stem
atic
Err
ors
Dr.
Dav
ut
Soly
alı
2015©
Sy
stem
atic
Err
ors
Dr.
Dav
ut
Soly
alı
2015©
Ran
do
m E
rro
rs
Dr.
Dav
ut
Soly
alı
2015©
Ran
do
m E
rro
rs
Dr.
Dav
ut
Soly
alı
2015©
Ho
w t
o r
epre
sen
t U
nce
rtai
nti
es?
Sig
nific
ant
Fig
ure
s
How
many s
ignific
ant
dig
its in e
ach m
easure
ment
taken w
ith a
mete
r stick?
Thre
e o
r fo
ur?
40.0
5 c
m
41.2
cm
42.4
5 c
m
42.7
2 c
m
Ho
w t
o r
epre
sen
t U
nce
rtai
nti
es?
Sig
nific
an
t F
igu
res
Exp
eri
me
nta
l n
um
be
rs m
ust b
e w
ritte
n in
a w
ay c
on
sis
ten
t w
ith
th
e
pre
cis
ion
to
wh
ich
th
ey a
re k
no
wn
.
In th
is c
on
text o
ne
sp
ea
ks o
f sig
nific
an
t fig
ure
s o
r d
igits th
at h
ave
ph
ysic
al m
ea
nin
g.
1.
All
de
fin
ite
dig
its a
nd
th
e fir
st d
ou
btfu
l d
igit a
re c
on
sid
ere
d
sig
nific
an
t.
2.
Le
ad
ing
ze
ros a
re n
ot sig
nific
an
t fig
ure
s.
Exa
mp
le: L
= 2
.31
cm
ha
s 3
sig
nific
an
t fig
ure
s. F
or
L=
0.0
23
1m
, th
e
ze
ros s
erv
e to
mo
ve
th
e d
ecim
al p
oin
t to
th
e c
orr
ect p
ositio
n.
Le
ad
ing
ze
ros a
re n
ot sig
nific
an
t fig
ure
s.
3. T
raili
ng
ze
ros a
re s
ign
ific
an
t fig
ure
s: th
ey in
dic
ate
th
e n
um
be
r’s
pre
cis
ion
.
4. O
ne
sig
nific
an
t fig
ure
sh
ou
ld b
e u
se
d to
re
po
rt th
e u
nce
rta
inty
or
occa
sio
na
lly tw
o, e
sp
ecia
lly if
the
se
co
nd
fig
ure
is a
fiv
e.
Ho
w t
o r
epre
sen
t U
nce
rtai
nti
es?
Sig
nific
ant
Fig
ure
s
How
many s
ignific
ant
dig
its in e
ach m
easure
ment
taken w
ith a
mete
r stick?
• B
e c
lear
in y
our
com
munic
ation
Whic
h is it?
• 40 c
m
• 40.0
cm
• 4 x
10 c
m-1
Wh
at is
an
err
or?
• N
o m
easu
rem
ents
–how
ever
car
efull
y m
ade-
can b
e co
mp
lete
ly
free
of
erro
rs
• In
dat
a an
alysi
s, e
ngin
eers
use
• er
ror
= u
nce
rtai
nty
• er
ror
≠ m
ista
ke.
• M
ista
kes
in c
alcu
lati
on a
nd m
easu
rem
ents
should
alw
ays
be
corr
ecte
d b
efore
cal
cula
ting e
xp
erim
enta
l er
ror.
• M
easu
red v
alue
of
x =
xb
est
+ δ
x
• xb
est
= b
est
esti
mat
e or
mea
sure
men
t of
x
• δx =
unce
rtai
nty
or
erro
r in
the
mea
sure
men
ts
• E
xp
erim
enta
l unce
rtai
nti
es s
hould
alm
ost
alw
ays
be
rounded
to
one
sig. fi
g
• U
nce
rtai
nty
in a
ny m
easu
red q
uan
tity
has
the
sam
e dim
ensi
ons
as
the
mea
sure
d q
uan
tity
its
elf
Err
or!
!!!
Err
or!
!!!
Un
certa
inty
of
Measu
rem
en
ts
Err
ors
are
quan
tifi
ed b
y a
ssoci
atin
g a
n u
nce
rtai
nty
wit
h e
ach m
easu
rem
ent.
For
exam
ple
, th
e b
est
esti
mat
e of
a le
ngth
L i
s 2.5
9cm
, b
ut
due
to u
nce
rtai
nty
, th
e le
ngth
mig
ht
be
as s
mal
l as
2.5
7cm
or
as l
arge
as 2
.61cm
.
L c
an b
e ex
pre
ssed
wit
h i
ts u
nce
rtai
nty
in t
wo d
iffe
rent
way
s:
1.
Ab
solu
te U
nce
rtai
nty
Exp
ress
ed i
n t
he
unit
s of
the
mea
sure
d q
uan
tity
:
L =
2.5
9 ±
0.0
2cm
2. P
erce
nta
ge
Unce
rtai
nty
:
Exp
ress
ed a
s a
per
centa
ge
whic
h i
s in
dep
enden
t of
the
unit
s
Ab
ove,
sin
ce 0
.02/2
.59 ≈
1%
we
would
wri
te L
= 2
.59cm
±1%
Un
cert
ain
ties
in
Rea
din
g A
nal
og
Dis
pla
ys
Dr.
Dav
ut
Soly
alı
2015©
What is
the u
ncert
ain
ty o
f re
adin
g v
oltages
usin
g t
he m
ete
r show
n?
Ex
amp
le:
Un
cert
ain
ty i
n a
nal
og
vo
ltm
eter D
r. D
avut
Soly
alı
2015©
• 100 d
ivis
ions o
n s
cale
.
–voltage r
ead is 6
V a
nd
–m
ete
r has t
wo r
anges:
0 –
10 V
and 0
–100 V
• U
ncert
ain
ty =
±½
VF
SD
/ # o
f div
isio
ns
–O
n 1
0 V
range,
uncert
ain
ty =
±½
(10/1
00)
= ±
0.0
5 V
yie
ldin
g V
= 6
±0.0
5 v
olt.
–O
n 1
00 V
range,
uncert
ain
ty =
±½
(100/1
00)
= ±
0.5
Vyie
ldin
g V
= 6
±0.5
volt.
VF
SD
=V
oltage f
ull
scale
devia
tion
Rel
ativ
e &
% u
nce
rtai
nty
Dr.
Dav
ut
Soly
alı
2015©
• R
ela
tive u
ncert
ain
ty:
–on 1
0 V
range,
0.0
5/6
= 1
/120 =
0.0
083;
–on 1
00 V
range,
0.5
/6 =
1/1
2 =
0.0
83
• P
erc
enta
ge u
ncert
ain
ty:
–on 1
0 V
range,
(0.0
5/6
)x100 =
0.8
3%
, and
–on 1
00 V
range,
(0.5
/6)x
100 =
8.3
%
Ex
erci
se
Dr.
Dav
ut
Soly
alı
2015©
Dete
rmin
e t
he I
nstr
um
ent
limit o
f err
or
and least
count
For
each o
f th
e t
hre
e r
ule
rs in f
igure
, dete
rmin
e a
nd r
ecord
•The least
count
of th
e s
cale
(sm
alle
st
div
isio
n)
–scale
s a
re a
ll in
cm
•Length
of
the g
ray r
ods
•Uncert
ain
ties in y
our
readin
gs
Nex
t o
n…
Dr.
Dav
ut
Soly
alı
2015©
Err
or
Pro
pa
ga
tio
n!
