February 27th, 2018, 03:37 AM  #1 
Member Joined: Feb 2018 From: England Posts: 38 Thanks: 0  Formula / roof
Hi all, Norman from England. Any help would be much appreciated. Produce a model of the maximum power output as a function of the roof size. Show that a general formula for the area of the roof (Atot) can be written as: Atot = a² + ½ b (d₁ + d₂) Using variables a, b, d₁ and d₂ shown in the figure explain each step in obtaining this formula, stating how you have split the roof into different shapes. Thanks. Last edited by skipjack; February 27th, 2018 at 04:30 AM. 
February 27th, 2018, 04:25 AM  #2 
Senior Member Joined: Jun 2015 From: England Posts: 891 Thanks: 269 
It is conventional with a diagram to state whether it is a plan or an elevation or perhaps a slope view? Further I am just guessing but is this an exercise in solar panels or what do you mean by the power output of a roof? 
February 27th, 2018, 04:45 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 19,958 Thanks: 1845 
The diagram comprises a square (hence the first term on the RHS of the equation) and a trapezium (or trapezoid for those in the US or Canada). This assumes that the angles that appear to be right angles are precisely right angles.

February 27th, 2018, 04:55 AM  #4 
Senior Member Joined: Jun 2015 From: England Posts: 891 Thanks: 269 
The ending oid comes from the Latin and means similar to or resembling. It has many wider uses in English see here. Oid is the rootword for many other words. In mathematics the term cuboid refers to a block that resembles a cube, often with 3 pairs of parallel rectangular sides. So I would hesitate to use trapezoid in the way skipjack describes. 
February 27th, 2018, 05:12 AM  #5 
Member Joined: Feb 2018 From: England Posts: 38 Thanks: 0 
Thanks for the replies. Yes 'studiot' this is an exercise in solar panels, you done something similar before? Hopeless with these type of formulas. It further gives the peak output of the photovoltaic material then asks for maximum power output etc. Many thanks. 
February 27th, 2018, 06:58 AM  #6  
Senior Member Joined: Jun 2015 From: England Posts: 891 Thanks: 269  Quote:
Otherwise it is impossible to calculate the area. In any case solar panels come in fixed sizes so there is the issue of how do these best fit a given roof shape, as they are most unlikely to cover all of it.  
February 28th, 2018, 01:37 AM  #7 
Member Joined: Feb 2018 From: England Posts: 38 Thanks: 0 
Hi Studiot Please see attached pic of the building/roof area. The question unfortunately does not give any sizes of the photovoltaic panels, I think it wants me to give a detailed description of splitting the roof into different shapes with the given formula. Show that a general formula for the area of the roof (Atot) can be written as: Atot = a² + ½ b (d₁ + d₂) Using variables a, b, d₁ and d₂ shown in the figure explain each step in obtaining this formula, stating how you have split the roof into different shapes. It later asks for many other variables including maximum power, average power etc Many thanks. 
February 28th, 2018, 07:43 AM  #8  
Senior Member Joined: Jun 2015 From: England Posts: 891 Thanks: 269  Quote:
You did not answer it.  
February 28th, 2018, 08:10 AM  #9 
Member Joined: Feb 2018 From: England Posts: 38 Thanks: 0 
Hi Studiot. It says the projected shape of the roof and later describes the variables in a plan view. May make sense to you? Finding this question too difficult at the mo. Many thanks. 

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