Discussion in 'Home Power and Microgeneration' started by Curbie, Jul 2, 2009.

1. ### CurbieGuest

I went back after the math behind calculating loads exerted on wind
turbine tower masts and I'm still having trouble converting the
formulas to a spread-sheet so the results match the examples given.

The formula I'm having trouble converting is:
(34,000/1.9)[1 - (1/2)(101.8/132)^2] = 10,994

My question is how do I convert the contents of the left square
bracket "[" and right square bracket "]" to spread-sheet expression?
Or maybe just what is the purpose of the brackets.

Thanks for any help.

Curbie

2. ### vaughnGuest

Just change those square brackets to round ones. They were probably only
made square to help us humans keep track of things. Computers (even cheap
scientific calculators) can handle multiple nested round brackets just fine.

Vaughn

3. ### CurbieGuest

Vaughn,
That worked for me in the past but using this spread-sheet expression:
(34000 / 1.9) * (1 - (1 / 2) * (101.8 / 132)^2) = 12,573

where their example is:
(34,000/1.9)[1 - (1/2)(101.8/132)^2] = 10,994

Different results, and since these formulas where taken from some
college physics department, I have to be interpreting that formula
incorrectly.

http://physics.uwstout.edu/StatStr/Statics/Columns/colse62c.htm

I always look for examples with results so I can check my math for
just this sort of mis-interpretation.

Curbie

4. ### Neon JohnGuest

I worked this out by hand on a calculator to make sure I got my
get 10,994 using any combination of the numbers, even abusing
precedence rules.

I ran the formula using square root instead of square, figuring that
the guy might have hit the wrong key on his calculator. That produces
10,037. Closer but no cigar. I think that he made a math error. Why
not drop him a note and ask?

John

5. ### CurbieGuest

I'm sorry John, I didn't mean for anyone to run the calculations, just
explain the use of the "[ ]".

Do you think those "[ ]" could be replaced with "( )", it seems there
has to be more than that and that one of the students would have run
the math and gleefully pointed out the error (seems that would to be
worth some extra credit)?
I'll try, I've never had any luck doing that, their pretty busy.

Thanks,

Curbie

6. ### vaughnGuest

You have been rare lately John. Good to see you back.

Vaughn

7. ### CurbieGuest

z,

On a side note, have you ever visited OtherPower.com hydro page?

I read over there a lot and someone asked if anyone was using a
WindBlue generator, so I pointed him at your site and you.

Vaughn,

You where right about just replacing the square brackets with
parentheses (see below) thanks for your help.

Neon John,

You where right about the formula being wrong, I was really wrong in
thinking a university physics department couldn't post simple math
errors, I can't believe one of the student haven't pointed that out.

The next example that they give uses a larger column with the same
formula:

(34000 / 1.85) * (1 - (1 / 2) * (69.3 / 132)^2) = 15,845

My spread-sheet agrees those results using the same formula with new
variables so it seems that the results given for the first formula
(the one you hand calculated) was wrong. I sent the instructor an
email like you suggested before I ran into this latest discovery. Be
interesting to see how they handle this?

Thanks Neon John,

Curbie

8. ### CurbieGuest

So:
(34,000/1.9)[1 - (1/2)(101.8/132)^2] = 12,578 and NOT 10,994

and

(34,000/1.85)[1 - (1/2)(69.3/132)^2] = 15,845

2:36 and I'm still at it too.

Get sleep that's what I'm going to do. zzzzzzzzz

Curbie

9. ### Neon JohnGuest

Kewl. Be sure to post the reply. Interesting to see if he weasles or
You be welcome.

10. ### daestromGuest

Working it backwards to find the 'error',

(34000/1.9)*(1-0.5*X) = 10994
-.5*X = 10994*(1.9/34000)-1

X = .771259

Which is almost exactly 101.8/132

So in order to get the 'answer' of 10994, the original calculation would
have to have been...

(34,000/1.0)(1 - (1/2)(101.8/132)) = 10994.42

Without the square.

So now you'll have to decide if the 'error' was in the calculation and
the right answer should have been 12,573, or the 'error' was in putting
the superscript '2' indicating the quotient of (101.8/132) is supposed
to be squared.

Probably the person working the example simply forgot to square the
quotient and came up with the wrong answer and the right answer is
12,573. Does the rest of the text show that that term is supposed to be
squared?

daestrom

11. ### CurbieGuest

z,
When it come to DIY wind turbines OtherPower has some people with lots
of experience, big brains, I've read the posts there for years (good
wind forum) although I rarely post there, my first two posts where
pulled there I E-mailed both times to fine out why, but they never
told me what I was doing wrong.

They have a hydro forum I was hoping you aware of, I can't really tell
how good it is, but alternative energy forums are so rare I read it
anyway.

Have fun.

Curbie

12. ### CurbieGuest

daestrom,
The next two examples that they give uses a larger columns with the
same formula (Ys / FS) * (1 - (1 / 2) * (S / SC)^2)
Ys = Yield Strength
FS = Factor of Safety
S = Slenderness Ratio
SC = Slenderness Ratio Critical

My spread-sheet agrees those results using the same formula with their
new variables so it seems the results given for the first expression
was wrong.

I'm easily confused so when something doesn't make sense my mind seems
to fixate on it to the exclusion of all else that is related. I
generally don't pursue information posted on a site that contains an
error; my mind fixates on the error and questions the validity of
everything else. I've decided to press on with that site, the subject
has such specialized and limited interest that I've only found four
other sites with examples (and issues of their own) to learn from
(beggars can't choosers).

Hopefully between the four incomplete spread-sheets I'll be able to
fill in the blanks to make one complete sheet that both make sense to
me and can be verified with on-line calculators?

Neon John suggested I email them and ask for clarification (this was
before I knew it was an error), hopefully they can clean it up for