I have a fairly generic (mathematical) answer, but can only find some of the actual numbers.
After finding the 2010 Mac Mini Environmental Report from Apple, there are four important numbers:
- Tbooting = The time taken to boot up and shut down (s)
- Pbooting = The power consumption while booting or shutting down (W)
- Psleep = The power consumption while sleeping (W)
- Poff = The power consumption while off (W)
The last is actually stated in the Mac Mini's environmental report, and for very low sleep power usage can't just be ignored!
The total energy used during a period of sleep is:
Esleep = time * Psleep
The total energy used from shutting down, being off for a time and booting up is:
Eshutdown = (time * Poff) + (Tbooting * Pbooting)
Requiring that Eshutdown < Esleep
, we can rearrange the inequality to give:
time > Tbooting * ( Pbooting / (Psleep - Poff) )
The Mac Mini's environmental report provides Psleep and Poff, and if we assume say 90 seconds total booting/shutting-down time and about 35W during said times, this would give an answer of 45 minutes.
I've yet to find similar values for the laptops (they make a big deal about the Mac Mini being so energy efficient), and the booting power/times would really need to be measured to provide accurate figures. But it surprised me that it was only 1 hour (I was expecting somewhat longer based on claims I've read in the past, that went along the lines of this discussion).
As @mankoff points out, there's another option which is to hibernate using something like DeepSleep. In my experience this is usually faster than a full shutdown, and of course it uses the same (incredibly low) power while off/hibernating. So to compare mathematically, you can consider it a "shutdown" of sorts and use the same equations (with the time taken to enter and recover from hibernate as Tbooting and the power usage while it swaps between RAM and disk as Pbooting). More than likely, this will reduce the the time answer since Tbooting should have been reduced somewhat.
A final thought is that laptop batteries seem to lose voltage over time, even when off, at a higher rate than the Mac Mini's advertised Poff. So the Poff value might actually be quite a bit higher for a computer with a battery, which may significantly lengthen the threshold between standby and shut-down/hibernate (however the battery and charging circuitry will complicate measurements of Poff). And to further complicate things (and possibly ruin the whole argument!), more recent Mac laptops will write the contents of RAM to the disk even when they go to sleep, in case your battery runs flat while sleeping (effectively preparing for a hibernate in case it's forced).
This is a very common problem and has happened to me twice in the past -- unfortunately the adapters are very fragile at the tip.
Apart from getting it replaced, you can try gently wiggling the thin wire connection right where it meets the metal adapter tip. Pushing it in towards the computer can also help. Sometimes it will start working again if it's in just the right position, but it's easy to knock out of place again. Either way, it will be difficult to live with for two weeks. :[
EDIT: In case it wasn't clear, the gentle wiggling/pushing should be done while the adapter is attached to the computer. You can judge your success by whether or not the computer starts/stays charging. Keep the computer on a stable surface while you do this, and if you get it working, don't touch it -- or it will likely stop working again.
Best Answer
I've worked as far afield as Northern Nigeria as a technologist (Infrastructure & Network Engineering), where reliable power is always an issue. Indeed, reliable energy is a problem endemic to many lesser developed nations across the globe. Closer to home, many folks are looking to go off-grid to escape the rat-race but still want to stay connected to the wider world.
Since powering a Mac (my solution can be used to power any AC device) seemed of broader utility to a wider audience, figured I'd share my documentation on design considerations & physical connectivity to save others solving the same-very complex - problem. Lots of annotated pictures are included at end of post to visually detail the physical connectivity between the components.
The connections should look as follows:
That may seem a lot, but trust me: this is a huge subject and to condense all the key detail into this was a huge effort. Hope it helps others trying to work off-grid tapping away happily on their MacBooks (or Min-Macs, iMacs, etc....). I'll post the link to accompany this post which shows me charging my 85 watt MacBook 2014 using solar panels shortly. Video is done, just have to render it and upload to YouTube, but thin connectivity at the 'mo.
UPDATE:
Having returned from the Omani Desert and sourcing a 5 meter extender cable to allow placing the battery and the inverter in the shade away from the solar panels, I've had a moment to pictorially document a more ideal configuration.
To avoid any ambiguity or confusion, everything is expressly labelled.
The Grounding Rod & cable for the inverter cost me the princely sum of £6.50:
If you still require further clarification, I've also created a companion video implementing my portable Solar Power solution in Oman which should fill in any questions about how confguring a portable solar power system-