Eco Home Math Problem

[Daniel Durrant]

Greeting All,

 

I am nearly 42 and haven't had to do any algebra for 26 years. I am studying to become an Eco Home assessor. I have an exam on 14/11/07 and could do with some help with a couple of calculations.

The people running the course have not replied to my emails asking for help so I am on my own.

Is this the kind of thing your forum could help with?

 

If so, the one I am struggling with at the moment is understanding the formula for calculating energy used appliances in Zero Carbon Homes.

 

kg CO2/year from appliances and cooking:

 

99.9 x (TFA x N)0.4714 - (3.267 X TFA) + (32.23 x N) + 72.6

Where TFA is the Total Floor Area and N is the Number of Occupants

For TFA < 43m2; N = 1.46

TFA ≥ 43m2; N = 2.844 x (1 - exp(-0.000391 x TFA2))

 

I have cut and pasted this and the figure 0.4714 is written in smaller numbers as is 2 in m2 so I asume this means 0.4714 squared

 

I am using 70.98m2 as the floor area so need to understand what exp means to calculate number of occupants.

I also don't understand how to apply 0.4714

 

Hope this wasn't too long for an Intro :phones:

 

Any help would be greatly appreciated.

 

Kind regards

 

Daniel

[Buffy]

kg CO2/year from appliances and cooking:

 

99.9 x (TFA x N)0.4714 - (3.267 X TFA) + (32.23 x N) + 72.6

Where TFA is the Total Floor Area and N is the Number of Occupants

For TFA < 43m2; N = 1.46

TFA ≥ 43m2; N = 2.844 x (1 - exp(-0.000391 x TFA2))

 

I have cut and pasted this and the figure 0.4714 is written in smaller numbers as is 2 in m2 so I asume this means 0.4714 squared

 

I am using 70.98m2 as the floor area so need to understand what exp means to calculate number of occupants.

I also don't understand how to apply 0.4714

 

We can do math equations here using 6576 which you don't need to know, but it will let you see if what we think you're saying is the same as what your problem is! So translating, it looks like your equation is:

[math]CO_2 produced = (99.9 \times (\rm TFA \times N)^{0.4714})

- (3.267 \times TFA) + (32.23 \times N) + 72.6

[/math]

Where:

[math]\rm TFA < 43m^2 \Rightarrow N = 1.46[/math]

[math]\rm TFA \geq 43m^2 \Rightarrow N = 2.844 \times (1 - exp(-0.000391 \times TFA^2))[/math]

Now, "exp(x)" is normally the natural logarithmic value [imath]e[/imath] (which is approximately 2.71828...), so translating, that last line would be:

[math]\rm TFA \geq 43m^2 \rightarrow N = 2.844 \times (1 - e^{(-0.000391 \times TFA^2)})[/math]

On a calculator built to do these kinds of computations, you need two operations. The first one is a key labeled something like [imath]y^x[/imath], and that's used for the part:

[math](\rm TFA \times N)^{0.4714}[/math]

or in English "TFA times N to the 0.4714 power".

 

The other key you need is usually labeled [imath]e^x[/imath] and is used for the

[math]e^{(-0.000391 \times TFA^2)}[/math]

or in English "e to the -0.000391 times TFA squared power", and what you need to do is square TFA, multiply times -0.000391 and then hit the [imath]e^x[/imath] key.

 

This may or may not have answered your question, but keep asking if it didn't!

 

Cooking with powered arrowroot,

Buffy

[Daniel Durrant]

Thanks for your help

 

I think I have got the hang of this one now.

 

If TFA = 70.98 Kg CO2/year =1055.61

 

Thanks again

Daniel

[sanctus]

I actually find 1055.7023, if you copy the following into an excel sheet for example you see how I did it:

=99.9*(70.98*(2.844*(1-EXP(-0.000391*70.98^2))))^0.4714-3.267*70.98+32.23*(2.844*(1-EXP(-0.000391*70.98^2)))+72.6

[C1ay]

I got the same result as Sanctus using the Windows Calculator in scientific mode...

[modest]

I actually find 1055.7023, if you copy the following into an excel sheet for example you see how I did it:

=99.9*(70.98*(2.844*(1-EXP(-0.000391*70.98^2))))^0.4714-3.267*70.98+32.23*(2.844*(1-EXP(-0.000391*70.98^2)))+72.6

 

rounding N to 2.447 gives you 1055.613649

 

I'm sure that's how Daniel got 1055.61

 

But really - with only four significant digits in 70.98 you could round to 1056.

[C1ay]

rounding N to 2.447 gives you 1055.613649

 

Why would you round N to begin with? Why round intermediate calculations at all?

[modest]

Why would you round N to begin with? Why round intermediate calculations at all?

 

No, you misunderstand. I'm not saying that's a good thing to do at all. I'm just saying that's how it happened to him. No, you wouldn't want to round an intermediate calculation.

 

-modest

[sanctus]

I thought it might be due to rounding up, but since Daniel said it is ages he doesn't touch this stuff I thought it is more likely that he made a mistake somewhere.