Dust down those orbital power plans

Keith Henson wrote:
[...]

Assuming the radiator and collector mass per square meter is about the
same, then you can see from the graph that the minimum occurs a bit
above 100 deg C, which is far below the 370-650 deg C quoted in an old
paper he

http://contrails.iit.edu/DigitalColl...2article42.pdf


I'd use something like 1,000 K as Tl. High efficiency and high rate heat
radiation in space is problematic unless the temp is high. Radiative
heat dispersal is about 100 kW/m^2 for the low temp radiator.

Incident radiation on the collector is 1.1 MW/m^2, the mirror (which
weighs 0.005 kg/m^2 excluding support) concentrates sunlight from 1.33
kW/m^2 to 1.1 MW/m^2, approximately 820 times at 80% efficiency.


Th is 1800 K, Carnot efficiency is 44%, assumed overall efficiency to
local electricity is 29%.


I can't say for sure what the mass per unit area of radiation or
collection are. I need to analyze a canvas tube (like an air
mattress) radiator filled with low pressure gas and air float
charcoal, Buckey balls or BeO. Assuming they are both around a
kg/m^2, a kW should come in around 3.2 kg.


I do not understand that. Ignoring the mirror, which I think - actually,
I don't know what you are doing -

In my example design the single sided collector has a mass of 5 kg/m^2,
the double sided radiator 1 kg/m^2.

The gas contact areas are 15 times the collecting or radiating areas.
The coefficients of convective heat transfer are 800 and 80 W/m^2 K (the
gas in the high temperature one is at twelve times the pressure of the
low temperature one). The temperature difference across each is 100 K -
the collector surface is at 1900K, the radiator surface at 900 K.

One m^2 of collector produces 400 kWe at the station, and needs 8 or 10
square meters of radiator, so 15 kg of collectors and radiators are
needed to produce 400 kWe, or 0.0375 kg/kW.

My numbers might be a little hard to achieve, though they are meant to
be only medium-tech at best, so let's be very generous and say 150 grams
per kW. That's still 20 times less.


Turbines and generators
are around 0.1 kg/kW based on Boeing 777 engines. Transmitters have
been analyzed at less than a kg/kW. So giving room for such parts as
power conductors and the joint to the transmitter, it *might* come in
at 5kg/kW.

If anyone has some spare web space to hang a small xls file, I can
send it to you.


Yes please. I seem to be missing something in your argument. Will put it
up too.

-- Peter Fairbrother



Keith

-- Peter Fairbrother

On Jul 21, 10:47 am, Peter Fairbrother wrote:
Keith Henson wrote:

[...]

Assuming the radiator and collector mass per square meter is about the
same, then you can see from the graph that the minimum occurs a bit
above 100 deg C, which is far below the 370-650 deg C quoted in an old
paper he

http://contrails.iit.edu/DigitalColl...2article42.pdf

I'd use something like 1,000 K as Tl. High efficiency and high rate heat
radiation in space is problematic unless the temp is high. Radiative
heat dispersal is about 100 kW/m^2 for the low temp radiator.

That's not what the minimum mass calculation show, at least for the
assumption that collector surface and radiator surface have about the
same mass per unit area. I am assuming about a kg/m^2 for both,
taking into account the supporting structure.

What you want is for the sum of mass for the collector and radiator
per kW, and taking into consideration the Carnot efficiency to be at a
minimum.

Here is the graph. http://www.htyp.org/Space_radiator

The minimum came out 130 C with not much penalty between 75 C and 200
C.

Of course, there could be an error in the spread sheet. If you can
find one, please let me know.

Keith

Incident radiation on the collector is 1.1 MW/m^2, the mirror (which
weighs 0.005 kg/m^2 excluding support) concentrates sunlight from 1.33
kW/m^2 to 1.1 MW/m^2, approximately 820 times at 80% efficiency.

Th is 1800 K, Carnot efficiency is 44%, assumed overall efficiency to
local electricity is 29%.

I can't say for sure what the mass per unit area of radiation or
collection are. I need to analyze a canvas tube (like an air
mattress) radiator filled with low pressure gas and air float
charcoal, Buckey balls or BeO. Assuming they are both around a
kg/m^2, a kW should come in around 3.2 kg.

I do not understand that. Ignoring the mirror, which I think - actually,
I don't know what you are doing -

In my example design the single sided collector has a mass of 5 kg/m^2,
the double sided radiator 1 kg/m^2.

The gas contact areas are 15 times the collecting or radiating areas.
The coefficients of convective heat transfer are 800 and 80 W/m^2 K (the
gas in the high temperature one is at twelve times the pressure of the
low temperature one). The temperature difference across each is 100 K -
the collector surface is at 1900K, the radiator surface at 900 K.

One m^2 of collector produces 400 kWe at the station, and needs 8 or 10
square meters of radiator, so 15 kg of collectors and radiators are
needed to produce 400 kWe, or 0.0375 kg/kW.

My numbers might be a little hard to achieve, though they are meant to
be only medium-tech at best, so let's be very generous and say 150 grams
per kW. That's still 20 times less.

Turbines and generators

are around 0.1 kg/kW based on Boeing 777 engines. Transmitters have
been analyzed at less than a kg/kW. So giving room for such parts as
power conductors and the joint to the transmitter, it *might* come in
at 5kg/kW.

If anyone has some spare web space to hang a small xls file, I can
send it to you.

Yes please. I seem to be missing something in your argument. Will put it
up too.

-- Peter Fairbrother



Keith

-- Peter Fairbrother

Keith Henson wrote:
On Sat, Jul 23, 2011 at 10:41 AM, Peter Fairbrother

Ok, the problem is that the spreadsheet ignores the mirror.

You have the collection and radiating areas at approximately the
same mass per unit area. This is wrong. The collector is very much
lighter than the radiator per unit area, at least 20 times lighter
and maybe 100 times lighter.

You have calculated the minimum total area of collector and
radiator, but not the minimum mass.


Your collector is collecting at 1.33 kW/m2, and weighing 1 kg/m2,
but that's ridiculously heavy. For a start, the collector cannot
collect at 1400 K without a concentrating mirror, it's
thermodynamically impossible.

The mirror is presumably thin aluminium or metallised mylar, and
weighs in at about 0.005 kg/m2.

I agree with you *if* you can tell me how to support accurate
pointing mirrors over km scales without structure. Virtually all of
the collector mass is structure,

Agreed. I allowed 0.005 kg/m2 for the mirror itself, the same for the
high temperature bits, and 0.15 kg/m2 for structure.

The obvious ways to do this include gas-filled tubes, spinning a round
mirror, and a double very low pressure envelope, but I don't have a
specific design in mind.

Anyway, no matter what the structure is, it isn't going to weigh 1
kg/m2, or anything like that much.

The pointing doesn't have to be that accurate - I have the pointing
ratio [1] at 1 in 60, so a fairly easy pointing accuracy of 1 in 600
would give 90% efficiency.

[1] the distance between mirror and pickup, divided by the width of the
pickup.

The high temperature part of the collector can be very much smaller
than sunlight collecting area, and thus the overall mass of the
collector can be very much less than 1 kg/m2, or the mass of the
radiator.
I'd use something like 0.025 g/m2 for the collector mass, and 1
kg/m2 for the radiator mass.

This gives a minimum mass at about 720K, see:

http://www.zenadsl6186.zen.co.uk/minimum_mass.xls

I *think* I can make a 1kg/m2 self sealing, radiator surface at ~130
deg C. I don't know how at 450 C. Any ideas? Also are you counting
the heat transfer fluid?,

Two sheets of thin alloy, about 1 meter by 2. say 0.2mm Ti alloy, that's
1.8 kg/m2, and the radiator is double sided.

High surface area on the insides for good transfer between the fluid and
the metal. The sheets are roughly roller-welded in lines at say 2cm
intervals along the 2m axis. The welds do not have to be leak-free, they
are only there to keep the sheets from moving apart under pressure
(0.4MPa). This gives a relatively low initial leakage.

There are two cutoff valves so that if punctured the section is
isolated. Larger sub-sections of the whole also have cutoffs. The cutoff
valves could be pyro, pyro melting, chemical or other things.

I am ignoring the mass of the transfer fluid, it's a couple of litres of
argon at 0.4MPa, weighing 7 grams per square meter, or 0.7% of the
radiator mass.


You may also notice that the total mass is now about 0.07 kg/kW,
rather than 1.5 kg/kW.

Actually, my estimate of the total mass was 5 km/kW, but that was
after taking a 50% transmission loss, so the power at the satellite
including transmitter and the structure that keeps the antenna flat
to 1/4 wave is 2.5 kg/kW.

Agreed the transmission loss to Earth is about 50%.

However trying to keep the huge main power Tx antenna flat to 1/4 wave
sounds like a .... bad ... idea.

It makes the electronics a little easier, but the penalty in structure
mass is so huge that it isn't really even worth considering.


-- Peter F


You should perhaps talk to the Solaren people, they are down in that
region.

I hope you are right.

Keith

-- Peter Fairbrother










Keith Henson wrote:
Here you go.

Keith

On Sat, Jul 23, 2011 at 6:46 AM, Peter Fairbrother
wrote:
If you could send me ac opy of the spreadsheet please?

-- Peter F


Keith Henson wrote:
On Jul 21, 10:47 am, Peter Fairbrother
wrote:
Keith Henson wrote:

[...]

Assuming the radiator and collector mass per square meter
is
about the
same, then you can see from the graph that the minimum
occurs a bit above 100 deg C, which is far below the
370-650 deg C quoted in
an old
paper he


http://contrails.iit.edu/DigitalColl...2article42.pdf
I'd use something like 1,000 K as Tl. High efficiency and
high rate heat radiation in space is problematic unless the
temp is high. Radiative heat dispersal is about 100 kW/m2
for the low temp radiator.
That's not what the minimum mass calculation show, at least
for the assumption that collector surface and radiator
surface have about the same mass per unit area. I am
assuming about a kg/m2 for both, taking into account the
supporting structure.

What you want is for the sum of mass for the collector and
radiator per kW, and taking into consideration the Carnot
efficiency to be at a minimum.

Here is the graph. http://www.htyp.org/Space_radiator

The minimum came out 130 C with not much penalty between 75 C
and 200 C.

Of course, there could be an error in the spread sheet. If
you can find one, please let me know.

Keith

Peter Fairbrother wrote:


Keith Henson wrote:
On Sat, Jul 23, 2011 at 10:41 AM, Peter Fairbrother

Ok, the problem is that the spreadsheet ignores the mirror.

You have the collection and radiating areas at approximately the
same mass per unit area. This is wrong. The collector is very much
lighter than the radiator per unit area, at least 20 times lighter
and maybe 100 times lighter.

You have calculated the minimum total area of collector and
radiator, but not the minimum mass.


Your collector is collecting at 1.33 kW/m2, and weighing 1 kg/m2,
but that's ridiculously heavy. For a start, the collector cannot
collect at 1400 K without a concentrating mirror, it's
thermodynamically impossible.

The mirror is presumably thin aluminium or metallised mylar, and
weighs in at about 0.005 kg/m2.

I agree with you *if* you can tell me how to support accurate
pointing mirrors over km scales without structure. Virtually all of
the collector mass is structure,

Agreed. I allowed 0.005 kg/m2 for the mirror itself, the same for the
high temperature bits, and 0.15 kg/m2 for structure.


Ooops. 0.015 kg/m^2, typo. Sorry.

The obvious ways to do this include gas-filled tubes, spinning a round
mirror, and a double very low pressure envelope, but I don't have a
specific design in mind.

Anyway, no matter what the structure is, it isn't going to weigh 1
kg/m2, or anything like that much.

The pointing doesn't have to be that accurate - I have the pointing
ratio [1] at 1 in 60, so a fairly easy pointing accuracy of 1 in 600
would give 90% efficiency.

[1] the distance between mirror and pickup, divided by the width of the
pickup.

The high temperature part of the collector can be very much smaller
than sunlight collecting area, and thus the overall mass of the
collector can be very much less than 1 kg/m2, or the mass of the
radiator.
I'd use something like 0.025 g/m2 for the collector mass, and 1
kg/m2 for the radiator mass.

This gives a minimum mass at about 720K, see:

http://www.zenadsl6186.zen.co.uk/minimum_mass.xls

I *think* I can make a 1kg/m2 self sealing, radiator surface at ~130
deg C. I don't know how at 450 C. Any ideas? Also are you counting
the heat transfer fluid?,

Two sheets of thin alloy, about 1 meter by 2. say 0.2mm Ti alloy, that's
1.8 kg/m2, and the radiator is double sided.

High surface area on the insides for good transfer between the fluid and
the metal. The sheets are roughly roller-welded in lines at say 2cm
intervals along the 2m axis. The welds do not have to be leak-free, they
are only there to keep the sheets from moving apart under pressure
(0.4MPa). This gives a relatively low initial leakage.

There are two cutoff valves so that if punctured the section is
isolated. Larger sub-sections of the whole also have cutoffs. The cutoff
valves could be pyro, pyro melting, chemical or other things.

I am ignoring the mass of the transfer fluid, it's a couple of litres of
argon at 0.4MPa, weighing 7 grams per square meter, or 0.7% of the
radiator mass.


You may also notice that the total mass is now about 0.07 kg/kW,
rather than 1.5 kg/kW.

Actually, my estimate of the total mass was 5 km/kW, but that was
after taking a 50% transmission loss, so the power at the satellite
including transmitter and the structure that keeps the antenna flat
to 1/4 wave is 2.5 kg/kW.

Agreed the transmission loss to Earth is about 50%.

However trying to keep the huge main power Tx antenna flat to 1/4 wave
sounds like a .... bad ... idea.

It makes the electronics a little easier, but the penalty in structure
mass is so huge that it isn't really even worth considering.


-- Peter F


You should perhaps talk to the Solaren people, they are down in that
region.

I hope you are right.

Keith

-- Peter Fairbrother










Keith Henson wrote:
Here you go.

Keith

On Sat, Jul 23, 2011 at 6:46 AM, Peter Fairbrother
wrote:
If you could send me ac opy of the spreadsheet please?

-- Peter F


Keith Henson wrote:
On Jul 21, 10:47 am, Peter Fairbrother
wrote:
Keith Henson wrote:

[...]

Assuming the radiator and collector mass per square meter
is
about the
same, then you can see from the graph that the minimum
occurs a bit above 100 deg C, which is far below the
370-650 deg C quoted in
an old
paper he


http://contrails.iit.edu/DigitalColl...2article42.pdf
I'd use something like 1,000 K as Tl. High efficiency and
high rate heat radiation in space is problematic unless the
temp is high. Radiative heat dispersal is about 100 kW/m2
for the low temp radiator.
That's not what the minimum mass calculation show, at least
for the assumption that collector surface and radiator
surface have about the same mass per unit area. I am
assuming about a kg/m2 for both, taking into account the
supporting structure.

What you want is for the sum of mass for the collector and
radiator per kW, and taking into consideration the Carnot
efficiency to be at a minimum.

Here is the graph. http://www.htyp.org/Space_radiator

The minimum came out 130 C with not much penalty between 75 C
and 200 C.

Of course, there could be an error in the spread sheet. If
you can find one, please let me know.

Keith

Keith Henson wrote:
On Sat, Jul 23, 2011 at 10:41 AM, Peter Fairbrother

Ok, the problem is that the spreadsheet ignores the mirror.

You have the collection and radiating areas at approximately the
same mass per unit area. This is wrong. The collector is very much lighter
than the radiator per unit area, at least 20 times lighter and
maybe 100 times lighter.

You have calculated the minimum total area of collector and
radiator, but not the minimum mass.


Your collector is collecting at 1.33 kW/m2, and weighing 1 kg/m2,
but that's ridiculously heavy. For a start, the collector cannot
collect at 1400 K without a concentrating mirror, it's thermodynamically
impossible.

The mirror is presumably thin aluminium or metallised mylar, and
weighs in at about 0.005 kg/m2.

I agree with you *if* you can tell me how to support accurate
pointing mirrors over km scales without structure. Virtually all of
the collector mass is structure,

Agreed. I allowed 0.005 kg/m2 for the mirror itself, the same for the
high temperature bits, and 0.15 kg/m2 for structure.

The obvious ways to do this include gas-filled tubes, spinning a round
mirror, and a double very low pressure envelope, but I don't have a
specific design in mind.

Anyway, no matter what the structure is, it isn't going to weigh 1
kg/m2, or anything like that much.

The pointing doesn't have to be that accurate - I have the pointing
ratio [1] at 1 in 60, so a fairly easy pointing accuracy of 1 in 600
would give 90% efficiency.

[1] the distance between mirror and pickup, divided by the width of the
pickup.

The high temperature part of the collector can be very much smaller
than sunlight collecting area, and thus the overall mass of the
collector can be very much less than 1 kg/m2, or the mass of the radiator.

I'd use something like 0.025 g/m2 for the collector mass, and 1
kg/m2 for the radiator mass.

This gives a minimum mass at about 720K, see:

http://www.zenadsl6186.zen.co.uk/minimum_mass.xls

I *think* I can make a 1kg/m2 self sealing, radiator surface at ~130
deg C. I don't know how at 450 C. Any ideas? Also are you counting
the heat transfer fluid?,

Two sheets of thin alloy, about 1 meter by 2. say 0.2mm Ti alloy, that's
1.8 kg/m2, and the radiator is double sided.

High surface area on the insides for good transfer between the fluid and
the metal. The sheets are roughly roller-welded in lines at say 2cm
intervals along the 2m axis. The welds do not have to be leak-free, they
are only there to keep the sheets from moving apart under pressure
(0.4MPa). This gives a relatively low initial leakage.

There are two cutoff valves so that if punctured the section is
isolated. Larger sub-sections of the whole also have cutoffs. The cutoff
valves could be pyro, pyro melting, chemical or other things.

I am ignoring the mass of the transfer fluid, it's a couple of litres of
argon at 0.4MPa, weighing 7 grams per square meter, or 0.7% of the
radiator mass.


You may also notice that the total mass is now about 0.07 kg/kW,
rather than 1.5 kg/kW.

Actually, my estimate of the total mass was 5 km/kW, but that was
after taking a 50% transmission loss, so the power at the satellite
including transmitter and the structure that keeps the antenna flat
to 1/4 wave is 2.5 kg/kW.

Agreed the transmission loss to Earth is about 50%.

However trying to keep the huge main power Tx antenna flat to 1/4 wave
sounds like a .... bad ... idea.

It makes the electronics a little easier, but the penalty in structure
mass is so huge that it isn't really even worth considering.


-- Peter F


You should perhaps talk to the Solaren people, they are down in that
region.

I hope you are right.

Keith

-- Peter Fairbrother










Keith Henson wrote:
Here you go.

Keith

On Sat, Jul 23, 2011 at 6:46 AM, Peter Fairbrother
wrote:
If you could send me ac opy of the spreadsheet please?

-- Peter F


Keith Henson wrote:
On Jul 21, 10:47 am, Peter Fairbrother
wrote:
Keith Henson wrote:

[...]

Assuming the radiator and collector mass per square meter
is
about the
same, then you can see from the graph that the minimum
occurs a bit above 100 deg C, which is far below the
370-650 deg C quoted in
an old
paper he


http://contrails.iit.edu/DigitalColl...2article42.pdf
I'd use something like 1,000 K as Tl. High efficiency and
high rate heat radiation in space is problematic unless the
temp is high. Radiative heat dispersal is about 100 kW/m2
for the low temp radiator.
That's not what the minimum mass calculation show, at least
for the assumption that collector surface and radiator
surface have about the same mass per unit area. I am
assuming about a kg/m2 for both, taking into account the
supporting structure.

What you want is for the sum of mass for the collector and
radiator per kW, and taking into consideration the Carnot
efficiency to be at a minimum.

Here is the graph. http://www.htyp.org/Space_radiator

The minimum came out 130 C with not much penalty between 75 C
and 200 C.

Of course, there could be an error in the spread sheet. If
you can find one, please let me know.

Keith

On Jul 24, 2:18 pm, Peter Fairbrother wrote:
Keith Henson wrote:
On Sat, Jul 23, 2011 at 10:41 AM, Peter Fairbrother
Ok, the problem is that the spreadsheet ignores the mirror.

You have the collection and radiating areas at approximately the
same mass per unit area. This is wrong. The collector is very much
lighter
than the radiator per unit area, at least 20 times lighter and
maybe 100 times lighter.

You have calculated the minimum total area of collector and
radiator, but not the minimum mass.

Your collector is collecting at 1.33 kW/m2, and weighing 1 kg/m2,
but that's ridiculously heavy. For a start, the collector cannot
collect at 1400 K without a concentrating mirror, it's thermodynamical
ly
impossible.

The mirror is presumably thin aluminium or metallised mylar, and
weighs in at about 0.005 kg/m2.

I agree with you *if* you can tell me how to support accurate
pointing mirrors over km scales without structure. Virtually all of
the collector mass is structure,

Agreed. I allowed 0.005 kg/m2 for the mirror itself, the same for the
high temperature bits, and 0.15 kg/m2 for structure.

The obvious ways to do this include gas-filled tubes, spinning a round
mirror, and a double very low pressure envelope, but I don't have a
specific design in mind.

Gas filled tubes . . . . how do you keep the from being punctured?

Spinning round inflated mirror, same problem. Plus you need to
precess the mirror over a year to keep it pointed at the sun. Now we
are talking bearings.

Anyway, no matter what the structure is, it isn't going to weigh 1
kg/m2, or anything like that much.

The pointing doesn't have to be that accurate - I have the pointing
ratio [1] at 1 in 60, so a fairly easy pointing accuracy of 1 in 600
would give 90% efficiency.

[1] the distance between mirror and pickup, divided by the width of the
pickup.

It's an optics problem.

The high temperature part of the collector can be very much smaller
than sunlight collecting area, and thus the overall mass of the
collector can be very much less than 1 kg/m2, or the mass of the ra
diator.

I'd use something like 0.025 g/m2 for the collector mass, and 1
kg/m2 for the radiator mass.

This gives a minimum mass at about 720K, see:

http://www.zenadsl6186.zen.co.uk/minimum_mass.xls
I *think* I can make a 1kg/m2 self sealing, radiator surface at ~130
deg C. I don't know how at 450 C. Any ideas? Also are you coun
ting
the heat transfer fluid?,

Two sheets of thin alloy, about 1 meter by 2. say 0.2mm Ti alloy, that's
1.8 kg/m2, and the radiator is double sided.

I am not sure you grok the scope of a power sat. For 2.45 GHz, the
smallest practical size is 5 GW on the ground, 10 GW into the
transmitter, even for 60% efficient, 16.7 GW sunlight in and 6.7 GW
waste heat. 12-13 square km of reflectors into the heat cavities.
It's worth working out the flow of heat sink fluid.

High surface area on the insides for good transfer between the fluid and
the metal. The sheets are roughly roller-welded in lines at say 2cm
intervals along the 2m axis. The welds do not have to be leak-free, they
are only there to keep the sheets from moving apart under pressure
(0.4MPa). This gives a relatively low initial leakage.

There are two cutoff valves so that if punctured the section is
isolated. Larger sub-sections of the whole also have cutoffs. The cutoff
valves could be pyro, pyro melting, chemical or other things.

I am ignoring the mass of the transfer fluid, it's a couple of litres of
argon at 0.4MPa, weighing 7 grams per square meter, or 0.7% of the
radiator mass.

And how fast does the argon need to be moving to transfer the waste
heat?

Keith

You may also notice that the total mass is now about 0.07 kg/kW,
rather than 1.5 kg/kW.

Actually, my estimate of the total mass was 5 km/kW, but that was
after taking a 50% transmission loss, so the power at the satellite
including transmitter and the structure that keeps the antenna flat
to 1/4 wave is 2.5 kg/kW.

Agreed the transmission loss to Earth is about 50%.

However trying to keep the huge main power Tx antenna flat to 1/4 wave
sounds like a .... bad ... idea.

It makes the electronics a little easier, but the penalty in structure
mass is so huge that it isn't really even worth considering.

-- Peter F





You should perhaps talk to the Solaren people, they are down in that
region.

I hope you are right.

Keith

-- Peter Fairbrother

Keith Henson wrote:
Here you go.

Keith

On Sat, Jul 23, 2011 at 6:46 AM, Peter Fairbrother
wrote:
If you could send me ac opy of the spreadsheet please?

-- Peter F

Keith Henson wrote:
On Jul 21, 10:47 am, Peter Fairbrother
wrote:
Keith Henson wrote:

[...]

Assuming the radiator and collector mass per square meter
is
about the
same, then you can see from the graph that the minimum
occurs a bit above 100 deg C, which is far below the
370-650 deg C quoted in
an old
paper he

http://contrails.iit.edu/DigitalColl...2article42.pdf

I'd use something like 1,000 K as Tl. High efficiency and
high rate heat radiation in space is problematic unless the
temp is high. Radiative heat dispersal is about 100 kW/m2
for the low temp radiator.
That's not what the minimum mass calculation show, at least
for the assumption that collector surface and radiator
surface have about the same mass per unit area. I am
assuming about a kg/m2 for both, taking into account the
supporting structure.

What you want is for the sum of mass for the collector and
radiator per kW, and taking into consideration the Carnot
efficiency to be at a minimum.

Here is the graph. http://www.htyp.org/Space_radiator

The minimum came out 130 C with not much penalty between 75 C
and 200 C.

Of course, there could be an error in the spread sheet. If
you can find one, please let me know.

Keith