Assignment A1, Exc 2
2. While basking on Seba beach of Wabamun lake (just west of Edmonton),
in the distance I can just barely see the very top of the three power plant
chimneys over at the eastern end of the lake. Determine the height
of the chimney's with error margins. Assume the earth radius r=6366km,
and make appropriate measurements with error margins in the map below.
Let r= the earth radius and a the distance to the chimney.
When resting on the beach our ray towards the chimney will
be grazing the surface. The precense of water between ourselves
and the powerplant ensures that the surface is curved as a
circle. Using geometry we can derive the following expression for the
height:
What term in the above formula causes a numerical instability?
Subject: Re: Assignment 1 Question
Jarett Hailes writes:
> I have some questions regarding question 2 of assignment 1.
>
> I am not sure how to compute the error margins for this question. Here's
> the list of potential errors I've found:
>
> - Error in measuring the distance between Seba Beach and Kapasiwin on the
> map (ie. error in variable 'a')
> - Error in computation of variable alpha, due to floating point precision
> - Error in computing cosine(alpha), due to floating point precision and
> unexact input (carrying error from value of alpha)
> - Error in computing h, due to floating point precision and inprecise input
> (carrying error from value of cosine(alpha))
You have identified many different sources of potential errors (Good).
Now, which one of these is going to be the dominating? Explain
your reasoning, and explain how you measured and arrived at a reasonable
error bound.
Then pick the dominating error cause and derive/compute it's effect on
the answer h so you can give h with error bounds.
>
> How can we quantify these errors within bounds? Also, when we are able to
> assume things, does this mean that these values are precise/exact? Ex: the
> radius of the earth is exactly 6366, so there's no error there.
If four significant digits are given usually you can expect that those
are correct, ie r=6366 +-0.5 km.
/Martin
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Paul Cartledge writes:
> I'm not exactly sure how to compute the error margins for the distance. I
> could try to find the true value of the distance between Seba Beach and
> Kapasiwin, but no doubt, any values I find via Internet are probably
> estimated as well.
Exactly. Just about any "numbers" we use in computations with real
data have some error.
>
> If that is not what is meant, then I'm not exactly sure how to determine
> the error margins. Measuring the distance between the 2 towns on the
> given map will give me a value, but to what precision should I have, the
> nearest millimetre, with the error margins being 2 mm?
Good start. The assignmnet spec says:
" make appropriate measurements with error margins in the map below.
Consider how accurately each "tool" (ruler or similar) measures.
To translate into kilometers you also need to measure the "scale
bar" on top with error margins, then figure out how those translate
into the solution.
> It would seem that we are attempting to estimate the height of the tower
> as precisely as possible. Accordingly, if I could get a very precise
> answer, that would be much appreciated.
The absolute precision is not the issue here. (If I wanted to know
I could presumably call transalta and ask them) What matters is that
you show how to make use of the presented means (the map) and arrive
at a reasonable estimate *and* error bound from it.
/Martin
Let r= the earth radius and a the distance to the chimney.
When resting on the beach our ray towards the chimney will
be grazing the surface. The precense of water between ourselves
and the powerplant ensures that the surface is curved as a
circle. Using geometry we can derive the following expression for the
height: