If you look at the page for the Goal0 Nomad 7M (click "Tech Specs") It's rated for 7 Watts.
I don't where you got the "~7 amps @ <22V DC on a regular day."
So the sort answer is - That panel won't even keep the MacBook Air running at idle, let alone charge the battery.
Your post got me curious, so I broke out a Kill-A-Watt power meter.
11" MacBook Air Power Draw, battery already fully charged, measured at the wall:
- Idle, screen backlight completely off: ~4.7W
- Idle, Minimum Screen Brightness: ~4.9W
- Idle, Half Screen Brightness: ~5.4W
- Idle, Maximum Screen Brightness: ~8.0W
For the active tests, I have the screen set to half-brightness, where I usually use it:
- Moving the mouse in circles with the trackpad: ~6.5W
- Scrubbing the Dock (with magnification): ~11.2W
- HD Video Decoding, GPU accelerated: ~15.6W
- SD Video Decoding, GPU Accelerated: ~11.2W
- Flash SD Decoding (not sure if it's accelerated): ~12.7W
Ok, these figures are VERY approximate (the Kill-A-Watt is not a high precision instrument), but they do put things in the ballpark.
The theoretical approach -
Insolation is the term for the amount of energy that falls on a set area per set time.
Basically, we can calculate the amount of solar energy which falls on a specific area.
The Photovoltaic array wikipedia page gives us a ballpark figure of ~1Kw/M².
Then, you have to take the efficiency of the Photovoltaic Panel into account.
Wikipedia gives us a best-case mono crystalline panel efficiency of ~25%, shich means that only 25% of the light which falls on the panel is converted to electrical energy, while the rest is dissipated as heat, reflected away, etc...
Therefore, a 1m² panel will, at the equator and with a mechanism that points it directly at the sun, manage ~250 W.
From this, we can tell that a 154W panel would have to be ~0.616 m² (154/250 = 0.616), far larger than what you have.
Examining the 7W panel you have - How big does a panel have to be to produce 7W?
7/250 = 0.028 m², or 280 cm² or about 14*20 cm, which seems pretty accurate, judging from the pictures on the product page.
Anyways, I went of on a bit of a tangent here, because you mentioned you're an EE, which is one of my main interests.
I looked into the amount of current available from a USB charger when investigating how to charge multiple iPhones / iPads simultaneously. Below is something I learnt that might be relevant.
There are several different ways that a charger can "tell" an iPod how much current it can provide - the iPod can't determine this directly. If the charger is a computer, it will communicate this through a data transfer (similar to transferring MP3 file data).
But a simple charger won't use this method. Instead, there are various standards (some proprietary, I believe!) which specify how much current can be provided, by providing certain voltages at the data lines. USB has four pins: one ground, one power, and two data. For example, apparently 2.8V on one of the data pins and 2.0V on another means "you can draw up to 1 amp". See this link for some detail, although I think some of that is out-dated.
I'd guess that the LG adaptor doesn't provide the signalling that the iPod expects. I don't know a way to resolve this, other than to try a different adaptor - sorry.
Best Answer
What I would recommend is going iPad Pro and keep a Mac mini somewhere else for things you simply cannot do locally. Since you are looking at the new models that accept USB C charging, you have lots more flexibility to use solar / iOS type chargers than before. The early 2017 lineup has 4W to 35W processors instead of the much higher wattage ones from 2016 and older.
Even so, running LTE network and remote access to where you have AC power for your Mac keeps your bicycle build light and reduces your cost for solar 10x or more.
I personally wouldn't bike with anything bigger than the MacBook with USB-C charging or iPad, but you could be thinking of a trailer where 35 pounds of gear and Arizona type sunlight would make a MacSafe MacBook possible. Also, the MacBook come with 29W, 61W, or 87W USB-C Power Adapters so you can pick a solar panel that would mimic those recharge rates. It's possible you could get away with a 29W charge on the biggest MacBook if you didn't run down the battery but 1/5 of the way each day and had good times to charge it (i.e. all day on the back of the bike in clear conditions).
I have heard of people using the 13" and 15" MBP for light work and running all day on a 10W range iPad charger. They lost battery charge all day and watched CPU intensive tasks, but for email, light web, no video or no encoding work - they made it most of the day with less than 10% battery loss and regained 25% battery charge with the Mac sleeping all night on the iPad charger. Now you have USB-A to USB-C charge capability with a small cable instead of lugging a MagSafe AC to DC transformer.