Rossi Lugano/early demo's revisited. (technical)

Quote from Paradigmnoia

The real input power, in my opinion, is very close to what was reported. I

My feeling (For what it is worth) is otherwise, so let's wait for the recalculation and see who was right

Quote from Paradigmnoia

If you don't believe the electrical data, (such as it is) then the rest of the calculations are a waste of time.

I think that the electrical data is about right, otherwise I could not have compared the convective and radiated power with the electrical power.

If I do a recalculation based on assumed inflated temperatures, then I convert those temperatures to their assumed correct ones.

I then do a new calculation of the convected and radiated thermal power.

If this newly calculated power differs much from the electrical power, then that is another argument that the temperatues where not inflated.

I don't see where in such a calculation I don't accept that the reported electrical power in the Lugano report is about right as you suggest.

And I disagree about the fact that calculations can be a waste of time. It has given me a lot of additional insight in the issues involved. You learn from it !

But let's have a real discussion if we have some data to discuss about

Recalculating inflated temperatures when wrong emissivites where used

As a first approach to recalculate the Lugano dummy run for the case that the reported temperatures where inflated due to using wrong emissivity settings on the Optris thermal camera, we need to recalculate the temperatures to their real ones.

The procedure which can recalculate the temperatures is based on the following formula published by Optris which can be found on page 9 of their IR-basics document.

U = C · [ε Tobjⁿ +(1 – ε) · Tambⁿ – Tpyrⁿ]

The meaning of the parameters is as follows :

---------U-----------The voltage from the thermal camera sensor

---------C-----------A constant

---------ε-----------The in band emissivity set on the Optris

---------Tobj------The temperature of the measured object in degree K

---------Tamb----The ambient temperature

---------Tpyr------The temperature of the camera sensor

---------n-----------A constant depending on the used sensor frequency band

We can use this formula for two situations, the first with the wrongly used emissivity ε1 and the accompanying measured temperature Tobj1, the second case with the correct emissivity ε2 to be used with the Optris and the correct temperature Tobj2.

Since the measured sensor voltage U is only dependent on the amount of radiation coming from the object under observation, this value is the same for both situations.

Thus we can fill in the above formula for both situation and then equate them.

This is written out below

C · [ε1 Tobj1ⁿ + (1 – ε1) · Tambⁿ – Tpyrⁿ] = C · [ε2 Tobj2ⁿ + (1 – ε2) · Tambⁿ – Tpyrⁿ]

Simplifying this gives :

ε1 Tobj1ⁿ + (1 – ε1) · Tambⁿ = ε2 Tobj2ⁿ + (1 – ε2) · Tambⁿ

Or

ε2 Tobj2ⁿ = ε1 Tobj1ⁿ + (ε2 - ε1) · Tambⁿ

Tobj2ⁿ = (ε1/ε2) Tobj1ⁿ + (1 - ε1/ε2) · Tambⁿ

Tobj2 = [(ε1/ε2) Tobj1ⁿ + (1 - ε1/ε2) · Tambⁿ ] 1/n

The last formula above will be used in a spreadsheet to recalculate the assumed inflated temperatures to the assumed real temperatures.

Note :

For high temperatures the term (e1/e2)Tobj1ⁿ is much larger then the term

(1 - ε1/ε2) · Tambⁿ and the last term can in that case be discarded.

(Note that the term with Tamb can not be discarded for lower temperatues since the errors become quite large)

This leads the to the following formula also used by the MFMP to be used for high temperatures :

(Tobj2/Tobj1) = (ε1/ε2)1/n

The MFMP verified this formula at higher temperatues to be working with a value of n=3.

Quote from LDM

Recalculating inflated temperatures when wrong emissivites where used

As a first approach to recalculate the Lugano dummy run for the case that the reported temperatures where inflated due to using wrong emissivity settings on the Optris thermal camera, we need to recalculate the temperatures to their real ones.

The procedure which can recalculate the temperatures is based on the following formula published by Optris which can be found on page 9 of their IR-basics document.

U = C · [ε Tobjⁿ +(1 – ε) · Tambⁿ – Tpyrⁿ]

The meaning of the parameters is as follows :

---------U-----------The voltage from the thermal camera sensor

---------C-----------A constant

---------ε-----------The in band emissivity set on the Optris

---------Tobj------The temperature of the measured object in degree K

---------Tamb----The ambient temperature

---------Tpyr------The temperature of the camera sensor

---------n-----------A constant depending on the used sensor frequency band

We can use this formula for two situations, the first with the wrongly used emissivity ε1 and the accompanying measured temperature Tobj1, the second case with the correct emissivity ε2 to be used with the Optris and the correct temperature Tobj2.

Since the measured sensor voltage U is only dependent on the amount of radiation coming from the object under observation, this value is the same for both situations.

Thus we can fill in the above formula for both situation and then equate them.

This is written out below

C · [ε1 Tobj1ⁿ + (1 – ε1) · Tambⁿ – Tpyrⁿ] = C · [ε2 Tobj2ⁿ + (1 – ε2) · Tambⁿ – Tpyrⁿ]

Simplifying this gives :

ε1 Tobj1ⁿ + (1 – ε1) · Tambⁿ = ε2 Tobj2ⁿ + (1 – ε2) · Tambⁿ

Or

ε2 Tobj2ⁿ = ε1 Tobj1ⁿ + (ε2 - ε1) · Tambⁿ

Tobj2ⁿ = (ε1/ε2) Tobj1ⁿ + (1 - ε1/ε2) · Tambⁿ

Tobj2 = [(ε1/ε2) Tobj1ⁿ + (1 - ε1/ε2) · Tambⁿ ] 1/n

The last formula above will be used in a spreadsheet to recalculate the assumed inflated temperatures to the assumed real temperatures.

Note :

For high temperatures the term (e1/e2)Tobj1ⁿ is much larger then the term

(1 - ε1/ε2) · Tambⁿ and the last term can in that case be discarded.

(Note that the term with Tamb can not be discarded for lower temperatues since the errors become quite large)

This leads the to the following formula also used by the MFMP to be used for high temperatures :

(Tobj2/Tobj1) = (ε1/ε2)1/n

The MFMP verified this formula at higher temperatues to be working with a value of n=3.

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LDM - the basic physics means that the value of n is highly temperature dependent. MFMP verified this n ~ 3 at just one temperature (where indeed numerically n ~ 3), and if you talk to them they will say they did not validate at other temperatures because they broke the camera. That is why their high temperature results were wrong (though much less wrong than the Lugano authors).

Remember the key equation here (T=temp, Pb = power in a given passband) is the Planck curve, and this changes as Pb ~ T^1 (in extreme low frequency approx) to Pb ~ T^n where n -> infinity as frequency increases for the high frequency (above hump) case.

The LF case, n=1, is well studied as the Rayleigh - Jeans approximation.

the high frequency case (n -> infinity) is also studied as the Wien approximation. That shows:

Pb ~ exp(-C/(kT)).

that goes up faster than an exponential in T where C >> kT (the high frequency case). Unfortunately it is not a nice expression to deal with algebraically.

There are a whole load of simple approximations of which S ~ T^A is the least accurate:

https://en.wikipedia.org/wiki/…%E2%80%93Hattori_equation

You can easily validate how n changes with T yourself numerically from the Planck curve.

Quote from THHuxleynew

LDM - the basic physics means that the value of n is highly temperature dependent. MFMP verified this n ~ 3 at just one temperature (where indeed numerically n ~ 3), and if you talk to them they will say they did not validate at other temperatures because they broke the camera. That is why their high temperature results were wrong (though much less wrong than the Lugano authors).

Thanks THH,

Will investigate this further.

If you have more info how to calculate n, then I would be gratefull to receive it

Quote from LDM

Thanks THH,

Will investigate this further.

If you have more info how to calculate n, then I would be gratefull to receive it

You can do a numerical integration of the Planck curve spectral power over the camera frequency passband, and note how that changes with T. Specifically Accuracy would require knowing the Optris spectral response which may be difficult to find data on. Or you could get an approximate answer by evaluating the Planck function at just one frequency - say the mid-point of the stated response band. A good compromise would be to integrate uniformly over the stated band. Clarke used integration over a typical IR bolometer response graph found by Higgins (referenced in link). The results are not VERY dependent on what you use for this.

Her eis how you do the (reasonably good) uniform rectangular passband response calculation. For the more complex version you multiply by the bolometer response inside the integration. The idea is that B(T) is the total power received by the detector. there is also a constant (independent of T or nu) factor but this does not matter, it drops out when you calculate n.

EDIT multiply by T to get n

Here nu1 - nu2 are the bounds of the bolometer quoted response (converted to frequency nu2 > nu1).

n for a given value of T can be found by (numerically) integrating to get a function B(T). Then numerically differentiating B to get its polynomial in T approximation at any given T, note that n, dB/dT, and B are all functions of T (I've omitted the explicit dependence as in normal).

EDIT - sorry I've lost the latex source, but n should be T(dB/dT)/B (multiply by T). Sorry for the typo.

THHuxleynew

Thanks again

I wrote in the past already a VB program which integrates the Planck function over a bandwith range.

Will play with it or adapt it to find n for the Optris band as a function of the temperature

Quote from LDM

THHuxleynew

Thanks again

I wrote in the past already a VB program which integrates the Planck function over a bandwith range.

Will play with it or adapt it to find n for the Optris band as a function of the temperature

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Note typo now corrected with edit.

Recalculating inflated temperatures when wrong emissivites where used- Determining n

Inresponse to my previous post on the subject THH correctly mentioned that the factor n, used in the Optris forumla (see previous post #406) is as he stated highly temperature dependent.

He also supplied the basics for calculating n, which in hindsight is logically.

So I updated my VB program which integrates the Planck curve at a certain temperature between two frequencies, in our case the low and high limit of the Optris thermal camera.

The updated program does this calculation for a user defined temperature range and temperature step. The resulating data is written out to a text file which I then imported in Excel.

In Excel the derivative was calcualted at each temperature and using the derivative, the in band power B(T) and the temperature the factor n was calculated.

The Excel file with the data is supplied as an attachment to this post.

The calculated value of n as a function of the temperature is shown in the following figure :

There are two things standing out.

Optris stated that the value of N would be between 2 and 3, but the figure shows a larger range.

Especially at low temperatures the value of n is much higer.

Other point is that the MFMP used a fixed value of 3 to convert their measured temperatues to the supposedly inflated ones.

As we can see from the figure above this is incorrect since the factor n is very dependent on the temperature.

Having found the value of n as a function of the temperature aloows us to recalculate supposedly inflated temperatures of the Lugano dummy run to their approximate real ones.

Recalculated Lugano temperatures when temperatures where inflated

In post #406 the formula to be used for recalculating temperatures between two emissivity value settings on the Optris thermal camera has been established.

The factor n needed in that formula was as a function of the temperature determined in post #412.

With both we can now recalculate the reported Lugano temperatures if we assume that these temperatures where inflated.

For a recalculation of a temperature we start with the inflated incorrect temperature.

That causes a problem since we can not use this temperature for determining the value of n. This because n is based, by the use of the Planck curve integration,on the real temperature, not the wrong inflated one.

To solve for the correct temperature and the value of n belonging to that temperature we have to apply an iterative procedure for finding the correct temperature and it's value of n.

By applying such an iterative approach the supposed Lugano inflated temperatures where recalculated.

The results are presented in the Excel file supplied as an attachment ot this post.

Besides the recalculated temperatures I also added for each recalculated temperature in the Excel file the found value of n.

As a last remark, the recalculation assumes that the proper in band emissivity setting of the Optris is .95.

While this value give good approximate values, we also know that the Optris in band emissivity for Alumina is somewhat temperature dependent.

Using a fixed value is in my opinion however adequate for calculations if we take into account that the results of those calculations is a (close) approximation.

Quote from Paradigmnoia

LDM ,

I just compared a couple of those temperatures to the Optris software results for the same emissitivty-temperature.

Your n results are really close to the software with a heated MFMP dogbone.

I would like to test a higher temperature to make sure that it holds together.

Optris:

451.0 @ 0.695 ---> 374.0 @ 0.95 (LDM 377.66)

412.1 @ 0.731 ---> 353.4 @ 0.95 (LDM 355.95)

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Thank's for your checking that theory and practice are about in line, at least for the lower temperatures.

Really appreciate it because I was not sure if we where overlooking something.

What I do not understand is how Optris determines what value of n to use when converting their received heat flux to a temperature.

Maybe you know ?

I now intend to do a new Lugano dummy run recalculation, now based on inflated temperatures.

Have to find some time to work on that.

Quote from Paradigmnoia

Chapter 11 (from link below) has some handy calculations and a cool table of BB radiation functions (page 570, PDF page 10)

http://mechfamilyhu.net/downlo…ss.Trafer%20by%20chapter/

That one I didn't know !

Thank's for the link