Design Tool Name: Setting the Stage
Purpose and Methods of Setting the Stage (Read Me):
This design tool was created with the intention of helping concert stage architects develop a stage design that is aesthetically appealing, cost efficient, properly sized, and optimizes the decibel volume for concert attendees.
This tool uses Dynamo to generate the visual design of a stage with a panelized colorful roof that uses sine wave logic to generate the shape, side panels that will help cover the artist from natural elements during performances, and a stage with panelized walls and a vinyl floor. The tool takes inputs from the user to generate a Revit model visualization and Generative design study through the developed Dynamo logic to explore alternatives.
As inputs, the user inputs their desired stage and roof width and height, their desired stage height, the cost estimate for the panel and stage flooring costs in dollars ($) per feet squared, and the estimated decibels that the sound system would create during a concert.
The outputs of the generative design are the stage floor area, the stage volume, the decibels that a person would hear at a specific location, and the total stage material cost. I chose these elements as outputs with the assumptions that the designer and owners of the stage project would want to create a stage that has a large enough floor area to host a performer with backup performers that is also cost efficient, and will create a pleasant decibel range for concert goers.
There are many alternatives that can be explored with this design, and I hope that architects and designers who are passionate about music can use this tool to properly size their stage and sound output.
Generative Design Interface Tool Preview:
Preview of Model Design Generated:
Dynamo Logic Preview:
Setting the Stage: In-Depth
The Setting the Stage tool starts with Dynamo nodes that create the stage, roof, and side panel design. All elements of the design are linked together through these nodes so that many design alternatives and aesthetics can be explored at once with just 6 user inputs.
The six user inputs are:
- Stage and roof width (ft)
- Stage and roof height (ft)
- Stage height (ft)
- Cost estimate range for the panel costs ($/ft^2)
- Cost estimate range for stage flooring costs ($/ft^2)
- Decibels that the sound system would create (dB)
Generative Design Inputs and Constants
There are other constant inputs that could be changed if needed, but are kept constant throughout each test to compare alternatives more accurately. Those constant inputs are the height offset of the roof, the number of waves in the roof design, and the location and height of a person attending the concert to help simulate the decibels they would experience from a certain location with different stage design alternatives.
Previous Design Logic
In this design, I used some logic from a previous design to create curves for the roof that are based on the variable inputs of stage and roof width and height. The roof changed from the previous design in that it now implements sine wave logic to create the curves that are then lofted together to create a surface:
Along with the surface lofting logic used from the previous design, this design also implements ribs and panel logic used previously. First the curves are lofted and then the surface is divided equally so that 3 point ribs can be placed. The surfaces are also divded into a UV grid and calculated into quads so that panels can be placed onto the surface. I chose to use the same colorful image as used previously to map onto the surface of the roof.
New Design Logic
The new design logic uses a “build down” approach where profiles are created by transposing points that were generated through the roof surface.
The 4 edge points of the roof surface are extracted to create the 4 points that will create the rectangular profile of the stage as well as the profiles that will create the rectangular profiles of the side panels.
Side Panel Generation
Side panels of the model are created by generating curves that connect the 4 edge points of the roof to 4 transposed points that create the 4 points of the top of the rectangular stage. The side curves are then lofted together to create the side panel surfaces.
The side panel surfaces are then lofted into 2 separated side surfaces on the left and right side of the stage and divided into UV grids accordingly. The UV grids are then made into a list of quads where adaptive components are places.
Stage Generation
The stage is generated using similar logic as the roof and side panels where two rectangular profiles are lofted together by extracting and transposing 4 points that are based on the top of the stage. The bottom points are generated by subtracting the stage height from itself This time however, the profiles are made into a solid so that surfaces can be chosen individually in output calculations.
A choose building wall surfaces node is implemented to separate the floor of the stage, stage ground, and the stage wall surfaces. The ground surface is not used in the calculations, but the other surfaces are. For this model, the “roof” surface refers to the top of the stage, which is the floor of the stage. The stage floor and wall surfaces are then divided similarly to other surfaces into a UV grid and into a list quads.
Adaptive components are placed into the stage wall and floor.
Generative Design Outputs
The stage floor area is calculated using the resulting stage floor area and the Surface.Area node. The total volume of the stage is calculated by using the resulting stage solid form generated and implementing the Solid Volume node. Both of these values are outputs of the generative design.
The surface area of the roof, side panels, and stage walls are then obtained using the Surface.Area node. The values are added together to calculate the total area of panelized surfaces of the design. The total area of panelized surfaces is then multiplied by the the cost estimate range for the panel costs ($/ft^2), resulting in the total cost for panelized surface material. The stage floor area is also obtained and multiplied by the cost estimate range for stage flooring costs ($/ft^2), resulting in the total cost for stage flooring material.
The total cost of panelized surface material is then added to the total cost of the stage floor area material to obtain an output of total material costs for the stage.
The final design output, decibels a person of an average height experiences at a set distance away from the stage, is calculated using simplified acoustic equations and the Geometry.DistanceTo node. I am assuming the following:
- The stage speakers are modeled as a point source so that a single distance to the stage can be calculated using the distance of a person model to the stage.
- The person model is also modeled as a point with a horizontal grid position, vertical distance away from the stage, and an average height of 5’6”. Their height is meant to simulate the position of their head.
- The point source follows can inverse square law of sound and intensity, meaning that decibel power will decrease with increased distance, so a person further away from the stage will experience less sound intensity.
- The sound threshold of human hearing is 10^-12 Watts/m^2.
- The equations are correct to the best of my ability, but my area of study is not formally sound engineering.
I assumed sound level in decibels can be converted into watts/m^2 using:
where SL is the original point source sound level in decibels. In this example, it is the user input of the speaker and performer decibel amount that they expect. Io is the threshold of human hearing and I is the value needed to understand the power of the sound at the person’s location away from the stage.
I assumed that the decreasing intensity of the sound can be found using:
where P is the power from the original point source (the stage sound) and r is the total distance of the person to the speaker calculated using the Geometry.To node.
Equation Sources:
1. http://online.cctt.org/physicslab/content/Phy1HON/textbook/Set10_QuesAns.asp
2. https://www.animations.physics.unsw.edu.au/jw/waves_power.htm
3. http://hyperphysics.phy-astr.gsu.edu/hbase/Acoustic/invsqc.html#c1
So the person’s location and height area calculated based on their location relative to the stage.
The equations are then implemented to simulate the decibels a person would experience from the stage at their set height and location. The nodes implement the equations and also convert the intensity at the person’s height and location back into decibels so that the decibel amount can be analyzed given different stage dimensions.
The decibels a person experiences at a location is then outputted as a part of the generative design. Calculating the decibels a person experiences at a given location away from the stage is important to consider because there is a balance between having a sound quality that fits the “loud concert” feel versus making sure that listener’s are not experiencing hearing damage by being exposed to loud music for long periods of time.
Generative Design Study Inputs and Ranges:
Sources:
I assumed that the following ranges applied using cost estimator resources and a general understanding of what stage dimensions are reasonable.
Sources:
Flooring material cost ranges: https://www.westernstatesmetalroofing.com/blog/metal-siding-cost
Stage floor material cost ranges: https://www.angi.com/articles/how-much-should-my-new-floor-cost.htm
Design Inputs Continued:
Generative Design Study
As seen in this graph, the total stage cost is on the x axis, the decibels at a person’s location is on the y axis, the sound level coming from the stage as the size of the dot on each point, and the stage floor area as the volume. The user can explore different alternatives about properly sizing speakers and volume coming from the stage along with the dimensions of the stage and what they would approximately cost.
Generative Design Study Alternatives Graph:
Realistic Revit-Generated image of the resulting stage:
Stage and simulated distance from stage point in Revit:
