## Main Question or Discussion Point

Howdy all,
I am developing a high altitude weather balloon project and I am thinking of using HDPE as a lens material for THz optics. I need to know the total heat transfer on the sheet of HDPE to see if it will reach critical temperatures. Since I am only looking for critical temperatures I can take an upper maximum on the heat transfer. To do this I am using the solar constant=1360W/m^2. However my results are crazy.

The question is, how do I determine the heat transfer due to solar radiation on my material?

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It depends on a lot of parameters so taking only the solar constant will yield to a huge error deviation as you mention.

Sun radiates in a wide spectrum and the radiation is exposed to a bunch of phenomena till it gets to earth and after it interacts with the atmosphere. You can start from tracking the radiation signature from it's origin (sun) to your target (object in the atmosphere) or you can make an acceptable (depending on your precision requirement) approximation.

An HDPE will do the trick for you but again there are a lot of parameters. Position of the lens will probably be towards the ground and it will not directly interact with the sunlight. If you can provide more information I might introduce a more precise solution.

On the other hand, if you have communication channel between the baloon and ground, why not use a LM35 at baloon side and directly get the temperature information ? You probably have a microcontroller on the baloon, it will take only one port and a couple of lines in your code to get real time temperature data.

Actually we will be pointing directly at the sun for the entire flight. Our max altitude will be about 90kft. Currently I am not trying to make an accurate approximation only an upper limit to find the temperature on the HDPE. How can I begin to calculate the radiation signature at some altitude? Also thanks for the suggestion on the LM35 I will definitely look into it.

Now we may be getting somewhere. Try to answer the following.

If the lens is towards the sun, how are you planning on communicating with the device via an optical channel through HDPE lens?

Are you trying to determine the max temperature to protect optical and electronic components or is it the purpose of your baloon ?

Are you trying to find the point (environmental) temperature on the lens or are you interested in the heat transferred to lens by the sunlight ?

Very roughly speaking ; you will be hanging approximately at 27km, there will be a ~3 degree (celcius) decrease in each km from ground to baloon, so roughly your baloon will be ~75 degrees less than ground.

We are using a thermal detector located at the focal point of the HDPE lens.

What I am trying to determine now is if HDPE is an appropriate material to use.
We are trying to filter most unwanted radiation out before focusing it to prevent overheating of the detector/electronic system which is in a housing.
So first I want to determine max temperature of the HDPE sheet because it will be in flight on the order of hours. So yes I am looking for heat transfered from the sun to the lens.

Next I will want to determine the max temp inside my housing system.

Solar constant 1.3~kW/m² is calculated for the distance between the sun and earth's surface. Amplitude of radiation is inversely proportional to the square of the distance so you just need to calculate the solar constant for 27km.

This is without any filtering due to the atmosphere is that correct?
If this is so then I need to find the atmospheric filtering as a function of altitude. Any ideas where I can find this?

Not filtered completely but you can be sure that you are far from the region that contains heaviest particles which are close to ground and which can cause additional heat. As I mentioned earlier (or not, don't remember) you need to model the atmosphere as a 7 layer medium with corresponding dispersion parameters. After that you can see the radiation at any point throughout the atmosphere. You can assume that there is no filtering at 27km (like the edge of the atmosphere) and make your calculations. Result will give you the worst case (highest exposure to sunlight) that can be encountered at 27km height from surface.

I am not aware of any chart or etc regarding altitude-filtering data, but you can simulate it yourself using computational electromagnetics softwares such as FEKO, HFSS or CST Microwave Studio.