Temperature of satellite

[lavalamp]

The following only really matters for active satellites with electronics on board, because if they get too hot or too cold, they can break.

Everyone knows that space is cold (~3K), but it can be hard to dump heat because you can only radiate it away. At the same time you also need to keep your heat while in shade. With the satellite being so small, you're pretty much screwed in terms of relative surface area, so storing heat is quite tricky.

So I conducted an analysis for which I will only post the assumptions and conclusions. There are lots of assumptions but they are all reasonable so I believe the conclusions to be fairly accurate.

Assumptions:
1) The satellite is 20 grams, extreme upper end of the range.
2) The specific heat capacity of the satellite is 1.5 kJ/kg/K.
3) The satellite is a cuboid with dimensions 1*4*5 cm (20 cm^3 volume, 58 cm^2 surface area).
4) The average frontal area is (20-4)/sqrt(2) + 4 ~= 15 cm^2.
5) The intensity of sunlight near earth is 1360 W/m^2 and the intensity of radiation from the Earth while in orbit is 220 + 100sin(theta) W/m^2 on the day side and 220 W/m^2 on the night side.
6) The satellite is in a circular orbit at ~ 275 km (90 min period, 40.8% of time in shadow of earth).
7) The satellite has a battery power output of 0.05 W (on the high end I expect).
8) The satellite is deployed at midday at a temperature of 290 K.

I'll spare the equations in this post, but if anyone would like them let me know.

I concentrated on the emissivity of the satellite, it's ability to emit (or absorb) radiation, as a passive method of controlling temperature. I have attached a graph from simulations of a satellite with ε = 0.2, 0.4, 0.6, 0.8, 1.0. Note that the emissivity of a material varies over the electromagnetic spectrum, however for simplicity I assumed a constant value over the whole range. The simulation was run for the first 9 orbits only, but as you can see, the temperatures got into a fairly steady pattern quite quickly. The vertical axis is temperature in Kelvin (but does not go all the way down to 0) and the horizontal axis is time in seconds.

As is clear from the graph, the lower the emissivity, the better, as it results in a far lower fluctuation in temperature. However, going extremely low would similarly be bad, as then not enough energy can escape and everything inside is slowly roasted thanks to the battery. Depending on the power of the battery, an emissivity of 0.05 is probably about as low as you'd want to go.

Handily, Aluminium foil has a low emissivity and is very light. Covering the above satellite (1x4x5 cm) with a single layer of Al foil would add less than 0.25 g, just 1.25% of the weight limit.

If anyone would like to suggest any improvements to the list of assumptions, I'm open to that. Additionally, if anyone would like me to run some simulations for their specific satellite, I can do that too.

[rick m]

[lavalamp]

That should be more durable, and even lower mass (approximately half I suspect), than straight-up Aluminium foil. If it's allowed for in the budget then go for it. I believe that for aluminised mylar, ε = 0.03 to 0.04.

To expand on what I said in my previous post though, with low emissivity and/or low surface area, the satellite can potentially get too hot from being unable to dump heat from the battery if the power output is too high, so that could be a concern.

Taking an extreme case, suppose that ε = 0, or as close as makes no difference to it. Then for the satellite in my first post (power of 0.05 W, running for 13.5 hours, 9 orbits, and s.h.c = 30 J/g/K), the temperature would rise by 81 K.

I'm curious about the specifics of the satellite if you'd be willing to share. Particularly basic dimentions and shape, power output of the battery and total mass, as well as predicted orbit, if you don't think that wouldn't be giving too much away. Then I could run a much better simulation for your satellite, which of course I'd be willing to share (either in public or private as you wish).

If you'd be willing to share the exact layout and specifications of the satellite and its of components, I could have a go at performing a more detailed simulation and record the temperatures of the individual parts to make sure they don't go out of spec.

[rick m]

Have not decided on static charging a small battery or capacitor via long fine trailing wire (or using solar cells). We will only be transmitting short burst two or three times per orbit.

Rick

[DaveHein]

As we discussed in another thread, transmitting two or three times per orbit decreases the chances that anyone will actually receive the signal. The satellite will be traveling over oceans and unpopulated areas during most of its orbit. It seems like the repeat rate should be at least a few times per minute.

[lavalamp]

For the power source, would it not be a lot simpler to use an AAA battery? The Energizer Ultimate Lithium AAA battery seems like a real good candidate, it's the lightest AAA battery with prices on Amazon from £4.70 for 4 (0.12% of the budget for a single battery). It also performs quite well, here's the datasheet:
http://data.energizer.com/PDFs/l92.pdf

The following figures are for 294 K but the battery spec allows for operation between 233 and 333 K, likely performance will vary slightly with the temperature.

~ 15 hours at greater than or equal to 1.4 V with constant current draw of 50 mA (70 - 75 mW power).
~ 21 hours at greater than or equal to 1.3 V with constant current draw of 50 mA (65 - 75 mW power).
~ 24 hours at greater than or equal to 1.0 V with constant current draw of 50 mA (50 - 75 mW power).

9 orbits should only take about 13.5 hours, so there's some overhead if the circuit needs 1.4 V and 50 mA, albeit marginal. Also marginal is the ability to dump heat when coated with aluminised mylar and a battery power output of 70 - 75 mW, simulations put the peak temp around 335 K, slightly out of spec for the battery but probably still safe.

The mass of the battery is 7.6 grams, which although a significant chunk of the mass budget seems OK since the rest will likely be a very simple circuit and transmitter, however I'm not the person building it.

I did look at button cell batteries too, but they could only be used for very low current draw. Unfortunately Energizer don't make any Lithium batteries of size N, and the Alkaline batteries at that size have a higher mass and a lower energy storage than these AAAs.

[cpooley]

lavalamp's post on satellite temp control: Caution about metal surfaces: they can get very hot. The emissivity at infrared wavelength is lower than that at visible wavelength, so it can absorb visible light but radiated infrared poorly.

A plan could be to have active radiation controls like those on the early Telstars, etc. A small rotating cover over a pattern of black high emissivity areas, which is either moved by a bi-metal strip or electronic actuator.

I plan on using actuators like those used for rudders of the sub-gram model planes (smallest I've seen is 225 mg for 2 channel RC electric)

Temp control for LEO is more difficult than escape because the Earth occupies a large area and is a significant radiator. Away from Earth all energy comes constantly from one direction.

[pauldear]

If there's a need to stabilise temperatures, another option is to vary the transmission rate (if this is one of your main power drains) during the orbit - ie, more frequent transmissions when the electronics are cold, fewer when they're hot. Would that help?

I'm also curious as to what temperatures can be withstood by various electronics, and what the failure modes are. It seems like cold is as much of an issue as heat - but is cold-related failure irreversible (eg, due to cracks caused by differential contraction), or just a temporary shutdown (like a battery fading in the cold, or maybe a semiconductor changing its behaviour)?

[cpooley]

Paul's temperature range question: I think if electrolytic capacitors and batteries are avoided the range could be -50 to +100 C, and would be easy to test with a homemade controlled hot box.

But with the active control mentioned in my last post, the internal temp can be held to within 10 degrees or so. IC temp sensors in a SOT-23 package can be used to move covers with actuators like those for the rudders of 1 gram model planes (you can buy them or DIY).

The power for the magnetic actuators is within what CMOS logic gates can provide. Piezo benders could be used, but they are more temperature sensitive.

[lavalamp]

I'm curious what the effect of a vacuum on batteries is. I would think swelling/bursting/leaking might be a problem. Anyone have any information on that?

cpooley, I like the idea of a bimetallic strip moving a cover over or away from an area with high emissivity, controlling the extent to which the satellite is allowed to radiate. It's a good, but passive, method of temp control that only relies on the laws of physics to work. It has the same elegance to it that the pebbles in a pebble bed reactor have where the fail safe is literally the laws of physics.