got stuck in equation

[ptc-4899011]

hi . . my name is usama khan
i am the student of civil engeering and we got assignment to make a project program on flexible pavement design using python.

i know very litle about programing. still learning from tutorials. u can call me a beginner.

now i need to solve this equation so that i can put this in python but the formula of design is very complex

Formula is :

log(W18) = (Z)(S)+9.36log(SN+1) -2.0+(log(dpsi/(4.5-1.5))(/(.40+1094/(SN+1)^2.5)+2.32log(Mr-)-8.07

every thing is constant except this SN. . i want to seperate SN like SN= rest of the stuff. how can i seprate it because manualy its impossible to take SN out.

so plz help me out.
log(w18)=Esals=50x10^6
Z=-1.645

S=0.45

dpsi=2.5

Mr=5800
these all are variables depending upon some factors. . but for ideal case we take these values. .
now i hope u got my question.
plz help

[ptc-4899011]

" +2.32log(Mr) - 8.07 "

[RogerYeh]

I imagine something like this:

[ptc-4899011]

thanks for responding sir. .
did u iterate it ??
secondly i just want that SN= all other variables. .means how could get SN formula??
Regards

[Werner_E · Accepted solution]

usama khan schrieb:

thanks for responding sir. .
did u iterate it ??
secondly i just want that SN= all other variables. .means how could get SN formula??
Regards

What you are asking for is a symbolical solution. As the variable SN is argument of log AND also exists outside in the term (SN+1)^2.5 you could not expect to get a closed solution. So the numerical approach shoen by Roger is the best Mathcad will be able to deliver. The steps necessary to find a numeric solution are done automatically by Mathcad. You may want to look for "solve block" in the built in help.

@Roger: I think Esals should be 50*10^6, not the logarithm of it

[ptc-4899011]

one last thing sir. .
as u say sn canot be seperated the way i want. .
then how would i use it while making the program on python. .

actually the program shud calculate the SN number wit hall these other dependable constants. .
in normal life we calculate Sn number using a bunch of graphs. . .i want to make a program in which no graphical work willl be used. .

is it possible with this equation. .if yes then how. .?? if no then what to do. . ??

following is the graph that is used to determine the SN number. .

initialy i thought it would be easy job. . but now it seems that i will losen up my grades
thanks for the concern sir. .

[Werner_E]

As you have to write the program yourself from scratch I think you will have to program yourself whats behind Mathcad's built-in solve block. That is you have to chose a numerical approximation method and implement it. I have no expertise on numerical methods so I can not recommend a specific method.

In Mathcad you can chose methods between "linear" and "non-linear". Non-linear methods to chose from are "Levenberg-Marquardt", "Conjugate Gradient" and "Quasi Newton".

Maybe you try at first to implement something simple like a bisection or Newton and then go ahead for faster and more stable algorithms. But it sure is going to be more work than you expected - there seems to be a reason for the nomogram 😉

Probably it would be a good idea to ask in Python forums as I could imagine that there are already some free python libraries for numerical methods out there which you could use without having to reinvent the wheel. Maybe you are able to find an implementation of the well known Numerical Recipes (http://www.nr.com/).

Good luck!

[ptc-4899011]

THanks sir for the concern nd wishing me luck. .:)
yeah now i come to know why this nomogram is made but still there would be a round about of this nomogram. .
i hope i would make that milestone as a begineer. .:)
thanks

[Werner_E]

i hope i would make that milestone as a begineer. .:)

All the best for Your efforts.

Some libraries which could be helpful are e.g. "numeric" (http://qwone.com/~jason/python/numeric/) or the famous "NumPy" with or without "SciPy" (http://www.scipy.org/). May be https://sites.google.com/a/aims-senegal.org/scipy/ is woth a look, too.

[Fred_Kohlhepp]

The example does not satisfy the equation. Well, since Z_R is not defined it could, but . . .

[Werner_E]

Fred Kohlhepp schrieb:

The example does not satisfy the equation. Well, since Z_R is not defined it could, but . . .

Yes, we have R=95% but Z.R is missing. Using the values and the formula of the scan (the poster had some numbers in his formula different in his first post) you have to chose Z.R=-1.688 (a value near the one the poster had given) to get the result 5 from the example.

WE