Solved

error uncertainty of equation

Posted on 2013-06-05
10
300 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
[X]
Welcome to Experts Exchange

Add your voice to the tech community where 5M+ people just like you are talking about what matters.

  • Help others & share knowledge
  • Earn cash & points
  • Learn & ask questions
  • 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
Industry Leaders: We Want Your Opinion!

We value your feedback.

Take our survey and automatically be enter to win anyone of the following:
Yeti Cooler, Amazon eGift Card, and Movie eGift Card!

 

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

Free Tool: Path Explorer

An intuitive utility to help find the CSS path to UI elements on a webpage. These paths are used frequently in a variety of front-end development and QA automation tasks.

One of a set of tools we're offering as a way of saying thank you for being a part of the community.

Question has a verified solution.

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

Suggested Solutions

Introduction On a scale of 1 to 10, how would you rate our Product? Many of us have answered that question time and time again. But only a few of us have had the pleasure of receiving a stack of the filled out surveys and being asked to do somethi…
When we purchase storage, we typically are advertised storage of 500GB, 1TB, 2TB and so on. However, when you actually install it into your computer, your 500GB HDD will actually show up as 465GB. Why? It has to do with the way people and computers…
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.
I've attached the XLSM Excel spreadsheet I used in the video and also text files containing the macros used below. https://filedb.experts-exchange.com/incoming/2017/03_w12/1151775/Permutations.txt https://filedb.experts-exchange.com/incoming/201…

733 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