Dear Harimi,

In the described situation:

the foot in the oven: 100% uncomfortable.

the foot in the ice bucket: 100% uncomfortable.

Correct using of percentage: (100% uncomfortable + 100% uncomfortable) / 2 = 100% uncomfortable.

Best,

Aryan

Dear Harimi

If you apply the Fanger Theory (ISO 7730), the average temperature may be comfortable (e.g oven at 50°C and ice at 0°C), but the same standard also has limits to temperature gradients, such as 100% dissatisfied for a temperarure difference of 10 K between head and and feet, or 100 % dissatified if the ceiling radiant temperature is 30 K above that of the the soil. Therefore, it is not comfortable.

However, you may have some momentary pleasure to drip a hand in an ice bucket if you are in a hot bath! But it is clearly not comfortable on the long term to have one hot and one cold foot!

Regards

Claude-Al.

Thank You Prof Claude-Alain Roulet and Thank You Aryan Shahabian, I do hope there will be further discussion as well when using regression analysis.

That reminds me somehow of the joke about all kinds of different professional trying to shoot/capture an elephant. There it says: "... And the statistician shoots once one meter left from the elephant and one meter right from the elephant and thus has hit the elephant on average." Yes, if the "average" is the mean displacement MD from the target, which is in this case zero. It allows deviations in different directions to cancel out each other. The root mean squared displacement RMSD however does not allow that and is in this case exactly one meter, which means on average you missed by one meter, which is what you want to know in this situation.

That was always a nice story to remind oneself the difference between these two means.

Why do I tell you that? Well, if you have an optimally comfortable temperature, then it is probably more important for the wellbeing how much you deviate in the RMSD kind of sense (rather than the MD sense). If you deviate into two different uncomfortable directions, these should not allowed to cancel each other out.

I guess in general one has to be careful with averages. One has to make sure to average the right quantity.

An extreme example in which averaging horribly went wrong was the following: I heard once about some quantity that was relative equally distributed over the days of the week and then someone said: "If monday is the 1st day and sunday the 7th day of the week, then the average day for that quantity is thursday." That did not make any sense. The average day highly depended on the definition of the week.

Sorry for the long story. I hope this could at least somewhat help. I also think, it would be alot more comfortable, if you had one foot inside an ice bucked, which itself is inside an oven.

Thermal comfort depends on a lot of parameters, the main ones being air temperature, radiant temperatures of surrounding surfaces, relative humidity, air velocities relatively to the naked parts of the body. For sake of simplicity, O. Fanger defined the operative temperature, which is the temperature of an isothermal room in which the body has the same global heat exchange rate than in the actual room, where the air and radiant temperature may be different in each part. Again for sake of simplicity, a first approximation (at low air velocity) of that operative temperature is the average of the mean radiant temperature and the air temperature. This is why people studying thermal comfort tend to use averages and not root meann squares. However, as I said before, there are limits to this method, since it is well known that large thermal gradiants are not comfortable.

Thank You Prof Claude-Alain Roulet for your insights and interesting information relvant to PMV model.

I observed that you referred only to the PMV-Fanger thermal comfort model. What about the determination of the optimum temperature from simple linear regression analysis. This is widely used in thermal comfort field studies. For instance, in some cases, it is used to validate the PMV model under various situations and in other cases; it is also used for the adaptive thermal comfort model…

Thank you Patrik Poschke for sharing your thinking and useful knowledge with us. I quote the following from your comments: “In general one has to be careful with averages. One has to make sure to average the right quantity”.

What about the selection of air temperature or operative Temperature range? Operative temperature is widely used as an independent variable for predicting neutral temperature. So, how does it affect the results in the determination of the optimum neutral temperature?

I do hope there will be further discussion…

Thank you

Indeed it is now generally accepted that the FANGER PMV model is valid in conditionned rooms only, since it is based on experiments in climatic chambers. In naturally ventilated, non conditionned spaces the so-called adaptive comfort model is applicable. This model, based on field studies, relates the optimal operative temperature (or temperature range) to the outdoor temperature averaged over several days. For further details, see for example the Annex A2 of the EN 15251 standard, Indoor environmental input parameters for design and assessment of energy performance of buildings addressing indoor air quality, thermal environment, lighting and acoustics, and several papers from de Dear, Brager and Gail, or Fergus Nicol. This model however does not handle the problem of acceptable temperature gradients !

About your second question, the adaptive model provides the optimum, neutral operative temperature, because, the operative temperature is more closely related to the comfort temperature than the air temperature.

This is just to express my very Sincere Appreciation and Gratitude for Prof Claude-Alain Roulet for his interesting answers as an expert in the field. Thank You Prof.

Thank you and have a good week!