Geometry and parameters of Mashrabiya
Geometry of Mashrabiya
Perforation Ratio (PP): This is the ratio between the area of the opening and to the whole area of the screen (Sherif et al., 2012).
Depth Ratio (DR): It is the ratio between the depth and the width of each perforation opening (Sherif et al., 2012).
Parameters of the Mashrabiya
After learning about the importance of functions and patterns of Mashrabiya, it is necessary to understand what are the determined terms of its parameters relating to length, angle and section of each baluster, along with the sectional layers and baluster offset (Figure 3.33).
Samuels (2011) offered a number of rules and mathematical formulae for the optimal design of the Mashrabiya lattice, by analyzing traditional construction methods. This constituted an important step towards catching up with the variable production methodology nowadays, as we will see in next chapter. These rules can be used to design the perfect lattice of Mashrabiya to ensure the optimum internal conditions, regardless of the geographic location or programmatic requirements.
Figure 3.33: Traditional Mashrabiya Typology. (Samuels, 2011)
Baluster Diameter/Length ratio
The ratio between the baluster (Figure 3.34) diameter and length (D/L Ratio) was traditionally used to determine two important issues:
The functional features of the Mashrabiya, and the porosity of the lattice are directly influenced by this.
The exact time of year in which direct sunlight enters the internal space, which defines the critical moment when the temperature of room switches from cool to hot.
If this is too soon in the year, the internal space will become dramatically overheated and uncomfortable. If it is too late, the internal space will be bitterly cold during the winter – and equally uncomfortable.
It is well known that direct sunlight controls the thermal environment of a building, and the porosity of the lattice adjusts it. The porosity is subservient to the D/L Ratio which is calculated through the formula [D/L =Cosθ1]; a sun altitude angle is (θ1) (Figure 3.35) (Samuels, 2011).
Figure 3.34: Illustration of (D/L Ratio) (Samuels, 2011)
Figure 3.35: Illustration of the formula [D/L =Cosθ1] for baluster design (Samuels, 2011)
Baluster angle
Mornings are generally a lot cooler than the rest of day, so it is necessary to introduce sunlight into the room during the morning. The calculation of the precise angle on both the horizontal and the vertical balusters determines what time of day the sunlight enters the room, thus ensuring the correct daily solar gain. But the determination of the established angle was not something that was possible or easy to achieve in the traditional construction of the Mashrabiya, as it depended on the skills of the craftsman and ‘trial and error’ testing.
Samuels in his research explored exactly what angle is required, providing an accurate example in his case study (information coming from the Giles Weather Station in Australia), by using shading masks, which he changed from a symmetrical shape to one that favors the morning or evening sun, then he applied this to the stereographic temperature graph (Figure 3.36).
“ .. and by incorporating the established D/L ratio an accurate shading diagram can be formed which will precisely map the times of the year in which complete shading is provided by the Mashrabiya.”
Figure 3.36: Baluster angle analysis in Samuels’s study (in Giles Weather Station- Australia) (Samuels, 2011)
Baluster section
According to traditional construction, the section of the baluster should be circular for many functional requirements which are related to the adjustment of glare and airflow (Fathy, 1986). Therefore any alterations in the shape of the baluster section should be derived from the circular section to provide the same important requirements. It should be noted that changing the section of each baluster alters the angle at which sunlight enters the room, meaning modifications must be made to the D/L ratio calculations in order to compensate.
“A reduction in the baluster width will increase the PF value, increasing the amount of ambient light and air passing through the screen. The PF value has to be high enough to allow adequate ambient light to enter the space for normal activities to occur.”
As mentioned before, the porosity of the Mashrabiya lattice controls the solar gain, glare and the airflow. In addition, this porosity factor (PF or φ ) describes the ratio of open lattice to that which is filled with balusters (Figure 3.37).
“PF can be calculated by dividing the total area of the opening by the total area of the interstices. A PF of 1 is equivalent to an opening without a Mashrabiya, i.e. 100% porosity.”
Figure 3.37: Baluster section analysis (Samuels, 2011)
Sectional layers
Traditionally Mashrabiya consisted of just one layer of lattice, but nowadays (Figure 3.38) with contemporary processes of construction, it has become possible to produce new models of Mashrabiya with double layers using a computer numerically controlled (CNC) router. After many tests, much research, 3D modeling and computer simulations, it became apparent that:
The optimal number of layers is two.
The important benefits of the extra layer are:
1 - An increase in the amount of solar gain within the building:
It alters the way light passes through the lattice during winter, although it is still possible to use the previously defined D/L ratio, baluster angle and sectional shape as a basis for the lattice.
“in winter there are points at which the interstices of each layer directly line up with the angle of the sun.”
2- A reduction in glare
“The first layer of balusters, that which is closest to the outside, benefits from light reflected off the second layer of balusters, thus reducing the amount of shadows across its surface. This creates a two-tiered transition between the interior and exterior, greatly reducing both the visual contrast and the glare.”
3- Creation of a more visually dynamic surface
“The intricacy and delicacy of the screens were a visual wonder, and any contemporary interpretation must express those qualities to do any level of justice to the original form. The use of additional layers within the Mashrabiya comfortably achieves that by adding to the visual intrigue and spectacle of the screen.”
Figure 3.38: Sectional layer analysis (Samuels, 2011)
Baluster offset
This describes the degree to which the two layers of the lattice line up. The possible offset of the layers is a way in which the airflow or lighting in the room is not directly affected, in contrast to the privacy matter; the offsetting gives more or less control to the designer. Whereas the visual porosity in this case changes, relying upon the position in which a person stands and the angle at which he looks at the lattice (Figure 3.39).
“For the offset to ensure that the direct light is not affected precision is required. The vertical offset needs to be matched by a horizontal offset, the ratio of which has been found to be determined by the equation [X1 /X2= 2Y1 /(Y1+Y2)] , ensuring that the solar gains are kept constant.”
Figure 3.39: Baluster offset analysis (Samuels, 2011)
Supplemental parameters of Mashrabiya related to the potentiality of reflected sunlight
Aljofi (2005) published a research study concerning the effects of the Mashrabiya screen on reflected sunlight. The results of the experiment were:
The effect of the baluster shape in the screen:
The light is lower in the case of the rounded shape than in other complicated shapes.
The effect of the size of the screen baluster:
In both vertical and horizontal positions of the balusters, the contributed reflected light is increased in the lattice with large diameter balusters, than in the lattice with smaller diameter balusters. This is due to the ratio of open to closed parts of the lattice.
The effect of surface reflection of the screen:
The contributed light from the light Oak wood lattice is more than in other types of wood, by an average of 17% .
