__Objective__

In this assignment, the framework to design the arrangement of sprinklers is created.

**Framework**

**Framework**

This framework has 3 variables, the number of sprinklers in X direction, those in Y direction, and the radius the sprinklers can cover. As for evaluators, efficiency, covered area, and cost are established. If the areas each sprinkler can cover do not overlap, this arrangement is thought to be the most efficient. For the good fire prevention, the total area sprinklers can cover is expected to be larger. Although installing more sprinklers leads to the safety, owners care about the cost to install sprinklers.

The concept of this framework is shown in the pictures below. The area a sprinkler can cover is represented by a circle. If the circle overlaps other circles, the actual covered area can be calculated by subtracting the overlap area. To evaluate correctly, the area of circles outside the room is ignored. The efficiency of the arrangement can be calculated by dividing the total area of circles without overlap by those with overlap. When the figure equals to 1.0, there are no overlap, which means efficient. To evaluate the covered area, the ratio the covered area is divided by the area of the room is computed. In the ration, the larger number is thought to be the better for the fireproof. The total cost of the sprinkler installation can be determined by multiplying the number of sprinklers by a cost per sprinkler. The cost per sprinkler depends on the function of the sprinkler; therefore, the cost is thought to be proportional to the radius and assumed as 50 USD x the squire of the radius.

__Dynamo__

The flow in Dynamo is shown in the pictures below. The length of the room in X and Y direction are designated in the gray part, and the number of sprinklers in the green part. The areas such as the total area, the overlap area, the area outside the room are computed in the purple part. Based on the areas, The efficiency and covered area are calculated in the pink and bule area. In the orange part, the calculation of the installation cost is conducted.

__Results__

As the diagram is shown below, there is no option that has the highest efficiency and covered area and the lowest cost. In the results, there cases shown below are thought to be well-balanced in terms of efficiency and covered area.

Case 1 Efficiency 0.963, Cost 62500, Covered area 0.860

Case 2 Efficiency 0.841, Cost 122500, Covered area 0.951

Case 3 Efficiency 0.722, Cost 87500, Covered area 0.968

From the data above, the option that has more efficient and covered area than case 1 requires higher expense.