Solved

error uncertainty of equation

Posted on 2013-06-05
10
299 Views
Last Modified: 2013-06-09
What is the uncertainty dA of this equation:

A=D/(T.cosB).(C1/C2-1)

assuming each of the variables D, T, B, C1, C2 have a propagation error dD, dT, dB, dC1, dC2
0
Comment
Question by:bestnagi
  • 4
  • 3
  • 3
10 Comments
 
LVL 84

Expert Comment

by:ozo
ID: 39224202
Assuming dD, dT, dB, dC1, dC2  are infinitesimal, you can differentiate A with respect to each of  D, T, B, C1, C2, but we'd still need to know whether dD, dT, dB, dC1, dC2 are independently distributed.
0
 

Author Comment

by:bestnagi
ID: 39224214
Yes they are independently distributed
0
 
LVL 84

Expert Comment

by:ozo
ID: 39224329
in that case, the net uncertainty would be the square root of the sum of the squares of the individual uncertainties.
0
PRTG Network Monitor: Intuitive Network Monitoring

Network Monitoring is essential to ensure that computer systems and network devices are running. Use PRTG to monitor LANs, servers, websites, applications and devices, bandwidth, virtual environments, remote systems, IoT, and many more. PRTG is easy to set up & use.

 

Author Comment

by:bestnagi
ID: 39224365
No its usually derived by taking the log of each side and then the derivative
0
 
LVL 31

Expert Comment

by:GwynforWeb
ID: 39224499
Is the term ( C1/C2-1 )  

( (C1/C2) -1 )   or  ( C1/(C2 -1) )

Also is the term in the denominator or numerator? The parentheses of the whole equation are ambiguous..

By taking logs of both sides, expanding out and then differentiating gives the result fairly quickly. The A term substitutes out and the log terms go with the differentiation. I won't do the differentiation until I am sure what the equation is, as it is lengthy.
0
 
LVL 84

Expert Comment

by:ozo
ID: 39224612
By individual uncertainties, I was referring to the individual contributions to dA, which can be derived from the derivative process
0
 
LVL 31

Expert Comment

by:GwynforWeb
ID: 39225751
I will illustrate the process for A=D/(T.cosB), as I am not sure of the parentheses for the rest of the equation. This clearly extends to the full equation.

A=D/(T.cosB)

ln A = ln( D/(T.cosB) )

ln A = ln (D) -ln(T) -ln(cosB)

Now perturbing D, T and B by dD, dT, dB; through differentiation we get

  dA/A = dD/D - dT/T + dB.tan(B)

      dA =A( dD/D - dT/T + dB.tan(B) )

This may be the form you need, however you can continue further and substitute A = D/(T.cosB) to get

  dA = dD/(T.cosB)  - dT. D/(T²cosB ) + dB.D.tan(B)/(T.cosB)
0
 

Author Comment

by:bestnagi
ID: 39226435
Thanks. The full equation is
A=[D/(T.cosB)].[(C1/C2)-1]
0
 
LVL 31

Accepted Solution

by:
GwynforWeb earned 100 total points
ID: 39227368
A=(D/(T.cosB))((C1/C2)-1)

   =(D/(T.cosB))((C1-C2)/C2)

ln A = ln( (D/(T.cosB))((C1-C2)/C2))

ln A = ln (D) - ln(T) - ln(cosB) + ln(C1-C2) - ln(C2)

Now perturbing D, T, B, C1 and C2 by dD, dT, dB, dC1, dC2; through differentiation we get

  dA/A = dD/D - dT/T + dB.tan(B) + dC1/(C1-C2) -  dC2/(C1-C2) -  dC2/C2

      dA =A( dD/D - dT/T + dB.tan(B) + dC1/(C1-C2) -  dC2/(C1-C2) -  dC2/C2 )

This may be the form you need, however you can continue further and substitute

  A = (D/(T.cosB))((C1-C2)/C2) .

I am sure you can do the rest if required
0
 
LVL 31

Expert Comment

by:GwynforWeb
ID: 39230828
A 'B'? Which part of it did I do wrong?
0

Featured Post

3 Use Cases for Connected Systems

Our Dev teams are like yours. They’re continually cranking out code for new features/bugs fixes, testing, deploying, testing some more, responding to production monitoring events and more. It’s complex. So, we thought you’d like to see what’s working for us.

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

Suggested Solutions

Title # Comments Views Activity
springs 9 271
Table function 6 52
Permutation and Combination 9 87
Coordinate Geometry-Finding ratio of a point splitting a line 4 68
Complex Numbers are funny things.  Many people have a basic understanding of them, some a more advanced.  The confusion usually arises when that pesky i (or j for Electrical Engineers) appears and understanding the meaning of a square root of a nega…
How to Win a Jar of Candy Corn: A Scientific Approach! I love mathematics. If you love mathematics also, you may enjoy this tip on how to use math to win your own jar of candy corn and to impress your friends. As I said, I love math, but I gu…
This is a video describing the growing solar energy use in Utah. This is a topic that greatly interests me and so I decided to produce a video about it.
Although Jacob Bernoulli (1654-1705) has been credited as the creator of "Binomial Distribution Table", Gottfried Leibniz (1646-1716) did his dissertation on the subject in 1666; Leibniz you may recall is the co-inventor of "Calculus" and beat Isaac…

770 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question