Big Bang Theory

A reoccurring theme is Sheldon Cooper’s spot on the sofa, which nobody else is allowed to occupy. When questioned why, he states that “In the winter that seat is close enough to the radiator to remain warm and yet not so close as to cause perspiration. In the summer it’s directly in the path of a cross breeze created by opening windows”. But what if the science is wrong and this is not the optimum position in the room? With SOLIDWORKS HVAC Flow Simulation Model, we can find out.    

Initially a simplified CAD model of the apartment was constructed, keeping the key geometry as accurate as possible.

To fully determine the optimum position for both winter and summer seasons, two studies will have to be run. The following presumptions had to be made:

Additional parameters include a draft of 0.001m3/s draft under the door, Environmental Pressure to simulate an accurate window opening and Static Pressures on the bedroom doors.

Below is a plan view of the apartment, showing all heat sources and conditions.

The two different studies were run, totalling a combine solve time of 4 hours.

Below are image of the two studies, showing a temperature cut plot and flow trajectory from the draft under the front door. Notice the air flow across Sheldon’s spot:

At this point, we can establish exactly where Sheldon should sit to experience the optimum comfort. This will be utilising SOLIDWORKS Heating Ventilation & Air Conditioning (HVAC) module.

The plot that we will be using to evaluate the study will be the Predictive Mean Vote (PMV). The PMV was developed by Povl Ole Fanger at Kansas State University as an empirical fit to the human sensation of thermal comfort and has been adopted by the ISO standards.

It predicts the mean response from a large group of people on a seven-point thermal scale between -3 and +3. Below is an annotated scale:

• +3 hot
• +2 warm
• +1 slightly warm
• 0 neutral
• -1 slightly cool
• -2 cool
• -3 cold

Comparing the above PMV plots, we can see that seat X would actually be suitable for Sheldon to sit on. It scores a score of zero, for both the winter and summer plots.  

We could further look into the problem and actually suggest an alternative room layout to provide an optimised seating position. As there is a greater degree of fluctuation in the summer plot, we shall use this as our basis. Repositioning the sofa, moving it slightly forward would provide a better comfort level (pictured below). Any alterations however would most definitely have to be put through the Roommate Agreement.