I've been trying to reconcile various crumbs of data regarding the Solar power systems on the MER's and have come to a point where I'm more or less stumped.

I've found the following papers that are repeatedly referenced in the many documents on the Web that evaluate solar power for martian exploration:
"Photovoltaic Array for Martian Surface Power" J. Applebaum, G.A. Landis, 43rd Congress of The International Astronautic Federation August 28-Sep 5 1992.
"Solar Radiation on Mars - Update 1991" J. Applebaum, G.A. Landis. NASA Technical Memorandum 105216

These provide a model for predicting insolation on the Martian surface taking into account Latitude, Tau and Mars orbit (ie LS, declination and distance from the Sun). The latter also gives some a pair of useful models for Tau by date and latitude during a major global storm.

Michael Allisons "Telling Time on Mars" Geophysical Research Letters Vol 24 No 16, Pages 1967-1970, August 15 1997. Gives some handy formulas for calculating time and the relevant orbital elements.

Between the lot I have a model that can replicate the examples provided in a bunch of MER documents (in particular the MER Environmental Requirements Document) and plots out nice daily\annual insolation data for any chosen site.

In order to be a bit more accurate I included the MER-A and MER-B actual Tau values for Sols 1-360 from the MER Analyst Notebook site.

What I want to do is establish what the initial theoretical power output from the panels should have been (to see how accurate the theoretical model is) and for that I need to know the actual surface area of the cells. Rupert Scammels site MER Technical Data says they consist of 55 strings of 20 cells, each measuring 4x2cm (ie 0.88m^2). If the cells are GaInP/GaAs/Ge triple junction cells at ~23.8% efficiency things look a bit low but pretty good (see the chart below). If I look at the rover self portraits though I count 501-505 individual cells and they look bigger than 4x2 to me. I reckon they are 4x6cm which gives a cell area of 1.2m^2, which is a number often listed on NASA sites. Unfortunately that value leads to power values that are waay to high - initial power ~ 1200wHr/sol for Opportunity.

Can anyone give me some definitive data on the efficiency of the cells used and their physical dimensions. Or give me some other explanation for the difference between what my calculations yield and reality.

http://gltrs.grc.nasa.gov/reports/2004/TM-2004-213367.pdf doesn't answer your specific questions but might be useful to look at anyway.

http://pdsimg.jpl.nasa.gov/Atlas/MER/documents/insthost.cat says

"The solar panel provides 30 strings of triple junction cells (gallium indium phosphorus, gallium arsenide, and germanium) covering 1.3 square meters, which produced about 800 to 900 W hours per sol at the beginning of the MER mission. Each rover had two reference solar cells, one that measures short circuit current and another that measures open circuit voltage. Due to the change in season from late southern summer to early southern autumn, and the degradation in performance due to dust deposition, the energy produced by this array dropped to about 600 W h per sol, 90 sols after landing."

Thanks. The Mars Solar power is another of Geoffrey Landis' papers I'd used to get my head around the calculations. I was able to match the charts on page 7 with my model so I'm happy with that part (the charts are labelled incorrectly - diffuse and beam insolation are swapped). However this made me go back and re-examine the ratio between direct and diffuse insolation on each Sol. It seems I have some error, my diffuse component seems to be about 50% too high.

Off I go to find the bug.

Thanks again.

I know is slightly OT, did someone ever asked about the unusual high-gain antenna shape?
Isn't the classical dish (no illuminator or focal plane receiver/reflector) and I strongly suspect is something like a phased array... this should give enough precision and tracking speed needed to communicate with relay satellites (probably impossible using only the two axis orientation motors)
Incredibly, I never found infos about this important technical detail!

I don't think the HG antenna is used to communicate with relay satellites. The UHF antenna is used for that, the HGA is used to communicate directly with Earth.

Yep - the HGA is only for X-Band direct to earth. There's not much real information on it on the web but I doubt that it's a phased array design, the 2 axis gimbal positioning system is sufficient for earth tracking from the Martian surface at least according to this Machine Design article The only referencesI can find for phased array antennas on planetary exploration missions is on Messenger.

Assuming it's similar to the Mars Pathfinder HGA, it's a microstrip array. I couldn't find much about this either, but DS-1 used the MPF spare antenna (see http://smallsat.org/proceedings/12/ssc98/4/ssciv1.pdf ). "A 32-GHz Microstrip Array Antenna for Microspacecraft Application" describes a similar antenna but for Ka rather than X-band -- see http://tmo.jpl.nasa.gov/tmo/progress_report/42-116/116p.pdf

I think such antennas can be phase-steered to an extent, at the cost of including delay elements in the path, but these weren't.

I'm still confused. The chart my model produces for Spirt Sol 1 is attached.

My code produces a value for total watts per sq m. If I compare the equivalent charts to the 7 samples I've gotten elsewhere from JPL\Nasa documents my curves match to within about 3% so I'm pretty happy with those as a sanity check now. One of those uses data that is very close to the Spirit at Sol 1 example so the numbers should all tie up.

For Spirit Sol 0, Tau=0.902, Albedo 0.23, Lat -14.57. I get total insolation at the surface of 3779 watt hours/sq m, (1515 beam and 2263 diffuse). Those are Martian watt hours so we need to increase them by a factor of 1.0275 to give us Earth watt hours.

If the actual cell area is 1.21sqm (my best estimate from counting the cells) and the cell efficiency is 23.8% then the total amount of power generated would be 1118 (earth) watt hours. The numbers from JPL above are 20% and 29% lower than that number.

So there must be an efficiency factor that I'm missing. I've been trying to find numbers for the conversion efficiency of the power system which has to be less than 100%. Also the 23.8% efficiency factor of the cells is just the efficiency of the cells themselves and that must be slightly lower on Mars due to the change in spectrum. ESA have an interesting 2002 presentation that gives some idea of the power system efficiency that the MER's should have :Future Space Power Systems. That states that current power management and distribution efficiencies are 80-90%. 80% would do nicely.

Does anyone know what the PMAD efficiency is for MER? I think I can make a stab at the change in cell efficiency due to the spectrum of Martian light on my own.

One thing to remember about Spirit and the tau of the atmosphere above it at any given time is that, up in the hills, Spirit is above the top of the local haze layer. This is very, very obvious when you look at images of the plains -- there is a definite haze layer that sits nearly on top of the surface, a layer that does not extend as far in height as the present height of Spirit.

Since this haze layer cannot be caused by humidity, it *must* be caused by dust particles entrained in the air. This is probably caused by the extreme thin-ness of the Martian atmosphere, surface-air heat exchange (the primary method of heating the air, as opposed to direct solar heating of the air itself), and the swiftness with which the air thins and cools as you rise above the surface.

I think perhaps the only reason we're seeing higher currents from Spirit's solar arrays now than at the beginning of the mission is that, unlike on Earth, rising only a few tens of meters above the plains has taken Spirit above the main haze layer and increased tau above what would be expected. And since we still have enough air above us to create about the same amount of diffuse light as we would see on the plains, we get the best of both worlds -- low tau and average diffusion.

And, by the way -- Steve Squyres in his book "Roving Mars" gives a lot of detailed information about the solar cells. During the initial design phase, the number of strings of solar cells they could fit on the rovers was a critical factor, and Squyres gives a lot of detail on how much energy they expected to get out of their original configuration, how the solar panel guys goofed and could only get 30 strings (or less!) onto the vehicle instead of the 33 strings defined as the "absolute minimum" for meeting primary mission power requirements, and how each square centimeter of solar cell was going to affect the MERs' power budgets (and thereby, any chance of a mission extending past 90 days). The culmination of this story is how the designers ended up with the delta-wing-shaped array, which wasn't exactly how the arrays were originally designed...

-the other Doug

I've noticed that as well and it something that could have a measurable effect. I'm very anxious to get the next release of Tau data (due on the 28th) that will give me a bunch of solid data points to cross reference. I suppose if I was adventurous I'd try to calculate them on my own but I haven't gotten around to that yet.

Another thing that I'm sure the planners have been thinking about is that in the depths of winter low Tau can be a bad thing, below about 0.3 there is no real net power gain but the orientation of the panels becomes much more critical and it allows night time ambient temperature to drop a bit more.

The problem that I have right now is that at the start of the mission I have the published Tau numbers, the direct insolation is straightforward and the diffuse insolation is supposed to be well modelled by the Applebaum & Landis formulae but I have an undetermined loss factor that I need to account for the 25%+-5% difference between the value I calculate that comes off the cells and the numbers being reported.

Thank you mcaplinger and others for HGA infos!

When I was thinking about this problem before getting up this morning (I don't know what that says about me!) the only thing I could come up with would be shadowing from all the stuff on the rover deck, particuarly the PMA. I'm sure it's not 20% but it probably makes a significant difference to the total power generated by the arrays.

Cheers,

James.

Old topic, I know, but here's a great nearly full online Google Book preview look at a book that contains exact details of the MER antennas and radio systems, truly fascinating:

http://books.google.com/books?id=BZ7qMnpX5...;q=&f=false

There's a more specific MER article here http://descanso.jpl.nasa.gov/DPSummary/sum...orce_external=0

http://descanso.jpl.nasa.gov/DPSummary/MER...cmp20051028.pdf