Math Is Fun Forum

FiggelHorn

Member

Registered: 2011-05-21

Posts: 13

Mathematical model (Extended modeling and problem solving assignment)

Hey guys and girls

I just started my second semester of year/grade 11. I just recently received my new math assignment.

So basically our task is to analyse the daylight hours in two cities and make recommendations about whether these cities would be able to sustain a solar electricity power plant

We needed to make a couple of graphs and models etc. all of which I have completed without incident. Now I am up to the discussion So the question asks "Explanation of the strengths and limitations of the mathematical model in terms of what the model can/cannot be used for and why"

These are the ones I could think of;
strengths
- Ease of access/dont need to gather a lot of raw data
Limitations
- Cannot predict things such natural disasters, sandstorms etc.
- Very reliant on data ie. if data is wrong the model will be wrong.
- Not 100% accurate
- Cannot predict things such as cloudy days etc . . .

It could be used for large scale predictions such as daylight hours over the period of a year where error of + or - 30 min are not catastrophic but on smaller scales such as on a day to day basis those errors would become apparent . . .

If anybody has any suggestions ie things I could add etc. please let me know I realy want to get into those A's B's are just mediocre

PS If you would like any further information please let me know I wouldn't mind scanning in the task sheet or uploading my graphs etc.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Mathematical model (Extended modeling and problem solving assignment)

Hi;

How much data was collected to make the models?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

FiggelHorn

Member

Registered: 2011-05-21

Posts: 13

Re: Mathematical model (Extended modeling and problem solving assignment)

Yeah I forgot about that, it was the monday of every second week. So the sunrise and sunset times for those days

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Mathematical model (Extended modeling and problem solving assignment)

Did you make a few scatterplots of the points you collected? How well does your model go through those points? Is there a correlation. How close to 1 is it? Why was data only collected on Monday?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

FiggelHorn

Member

Registered: 2011-05-21

Posts: 13

Re: Mathematical model (Extended modeling and problem solving assignment)

Yeah we had to do a couple of scatter plots + models ( I attached them to the message)  We were told to do the Mondays simply because some raw data had already been collected for this day in the year 2000.

2000 model - 1.72 * cos(0.121*X) + 12.13     (I don't think I need to fiddle with the C value but I'm not sure)
2010 model - 1.73 * cos(0.121*X) + 12.15

Last edited by FiggelHorn (2011-08-11 12:09:23)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Mathematical model (Extended modeling and problem solving assignment)

Hi;

What method and software was used to fit the data?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

FiggelHorn

Member

Registered: 2011-05-21

Posts: 13

Re: Mathematical model (Extended modeling and problem solving assignment)

I'm not sure what you mean . . . I used excel to plot the data and then I just used the longest and shortest days from the collected raw data to find the ampitude (max-min/2) and the midpoint (max+min/2)  and then I just used (B=2*Pi/52) I used 52 as my Period because 52 weeks . . .  and then I just subd those values into my equation to find the model. I put the actual formulas in excel so that it didn't round it.  I just used the right click select data function in exel to add the model to the graph

Last edited by FiggelHorn (2011-08-12 20:24:06)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Mathematical model (Extended modeling and problem solving assignment)

Hi;

That is what I meant. Looks like to me that you have enough to go with it.

Just one more thing:

I do not see the residuals, because I do not have your data but how did you decide on this equation:

- 1.72 * cos(0.121*X) + 12.13

Or did excel pick it for you.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

FiggelHorn

Member

Registered: 2011-05-21

Posts: 13

Re: Mathematical model (Extended modeling and problem solving assignment)

I was given the specific formula by my tutor. I'm not even sure how I would get excel to do that . . . Would it be worth figuring that out and then comparing my formula to that of excel?

Thank you for the help

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Mathematical model (Extended modeling and problem solving assignment)

Hi;

As I said from the graph I can not tell how well that formula is doing. So I can not know if another formula will do better. Generally unless you have an exact fit ( a formula that exactly matches the data ) you can always do better!

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

FiggelHorn

Member

Registered: 2011-05-21

Posts: 13

Re: Mathematical model (Extended modeling and problem solving assignment)

Just another quick question I wasn't sure if I should of started a new post or not . . .

Why do we use a cosine graph instead of a sine graph is their a particular reason when talking about daylight hours? Does it even matter which we use because a sine graph is just a shifted version of a cosine graph?

Last edited by FiggelHorn (2011-08-20 22:03:20)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Mathematical model (Extended modeling and problem solving assignment)

Hi;

Why do we use a cosine graph instead of a sine graph is their a particular reason when talking about daylight hours?

When data is periodic we do a fourier fit of it. This consists of terms of sine and cosine just as a polynomial fit consists of powers of x. This interpolating process determines which terms are included and which terms are zeroed out.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Mathematical model (Extended modeling and problem solving assignment)

hi Figglehorn

Why do we use a cosine graph instead of a sine graph is there a particular reason when talking about daylight hours? Does it even matter which we use because a sine graph is just a shifted version of a cosine graph?

No it doesn't matter for the reason you have given already.  As you are looking at the amount of light from the Sun, there are good astronomical / physics reasons why the figures might be expected to follow a cosine (/ sine) curve.  If you want to research this further look up 'the equation of time' and the 'inclination of the Earth's rotational axis to the ecliptic' (plane of the Earth's orbit around the Sun).

Bob

Last edited by Bob (2011-08-21 01:35:33)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob