Problem 1.50 [Difficulty: 3]
Given: Lateral acceleration, a = 0.70 g, measured on 150-ft diameter skid pad; Uncertainties in Path
deviation ±2 ft; vehicle speed ±0.5 mph
Find: Estimate uncertainty in lateral acceleration; ow could experimental procedure be improved?
Solution: Lateral acceleration is given by a = V2/R.
From Appendix F, uuu
avR
=± +[( ) ( ) ] /
22212
From the given data, s
ft
1.41ft75
s
ft
2.3270.0; 2
2=××=== aRVaRV
Then uV
V
mi
hr
s
41.1 ft
f
t
mi
hr
3600 s
v=± =± × × × =±
δ
0 5 5280 0 0178..
and uR
R2ft ft
R=± =± × =±
δ
1
75 00267.
so
u
u percent
a
a
=± × + =±
=±
(.)(.) .
.
/
2 0 0178 0 0267 0 0445
445
22
12
Experimental procedure could be improved by using a larger circle, assuming the absolute errors in measurement are
constant.
For
()
[]
%4.20240.00100.00109.02
0100.0
200
2
;0109.0
8.45
5.0
mph8.45
s
ft
1.67ft200
s
ft
2.3270.0;
ft200;ft400
2
2
2
2
±=±=+×±=
±=±=±=±=
==××===
=
=
a
RV
u
uu
aRVaRV
RD