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Building Shape 

Out of many concepts and aspects of energy efficient design, building size and shape is at the base of any design, and it determines the limit of what can be done to optimize thermal performance of the house. Some houses are easy to make energy efficient, others will require a lot of effort and expense. So when designing new home a good consideration should be given to the shape of the house because its something that cannot be easily changed after the house was built. And in existing homes it can help understanding why the building performs as it does. 

The heat transfer between interior and exterior occurs on the boundary between these two environments, which means external walls, roof and ceiling and the floor. The bigger the area the more heat gets transferred. But since in a single-storey house walls have usually the same height throughout we can simplify our consideration to examining the floor plan. 

The principle is simple - of the two shapes with the same area, the one with smaller perimeter is more efficient. Or, given the same perimeter, the shape enclosing larger area is more efficient. Of all geometric shapes, the circle has the smallest perimeter, but, unless we are designing a light house, our floorplan shape will be a combination of squares and rectangles. Of the two, square is the next best thing to a circle while rectangle efficiency depends on it's length and width. The longer the rectangle is (proportionally) the less efficient it will be. In the drawings below we can see three shapes, square, long rectangle and a more complex shape. All three have the same area with different perimeters. The external walls corresponding to the square are in colored in black, while the walls in pink represent additional perimeter length due to less efficient shape. 

From the pictures we can see that the more complex the shape, the more heat transfer through external walls and less efficient the shape is.

This principle applies to all buildings but in a building with multiple levels we need to know how the levels are aligned in relation to each other, that is, consider floors and ceilings in addition to walls. The two shapes below have the same size and shape floor plans on both levels except one has 1st floor plan rotated 90 degrees. The rotation makes the shape more complex by creating additional roof space (at the front) and a floor facing the exterior (on the side), both highlighted in pink.  

It could be argued that while the square or cube (in 3d) shape is more efficient, more complex designs are also more esthetically pleasing. So does it come down to the choice of either dull cuboid blocks or higher energy bills?

Pretty much, but it doesn't have to be dull. Rather than physically dividing the shape, we can divide visually by using different cladding materials, different color paint or render or by adding external shading and other features 

The shape pictured on on the right is exactly the same as the left one except for different color of the walls. It already looks more interesting and I am sure that professional building designer can do much better job.  

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