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.