To get FF coverage from this design of lens (throughout the zoom range without vignetting or possibly painfully soft corners), you'd need to fit a mythical 1.6x TC to it. That same quantity of light from the small projection of a crop sensor is spread a bit dimmer over a larger area. So with a 1.6x conversion, you multiply focal length and aperture by 1.6, and you get a 29-56/2.88 FF lens.
Really??? Wow! I want an FF equivalent (with constant F1.8 aperture, not F2. at sub-1K. Hopefully it's possible.
Most likely not, if this were stretched to full frame coverage it would be 2.8 due to light magnification and such like, so unfortunately this is just a full frame 2.8 zoom with a smaller image circle
What? That doesn't make any sense.
This is not a f/2.8 zoom, it's f/1.8, regardless of which body it's mounted to. Someone has already mounted this lens to a 5D2 and the images exposed at f/1.8 like all other f/1.8 lenses (of course, there was heavy vignetting around the edges because of the smaller image circle).
If they kept the design the same and scaled it up it would be a 1.8 zoom for full frame... the problem is that it would most likely be too large and heavy after being scaled up to fit a FF image circle.
If the 'same quantity of light from the small projection of a crop sensor is spread a bit dimmer over a larger area' is confusing, imagine a projector with a zoom option - due to compression, a small image is brighter than a large image, yet both have the same quantity of light.
And yes, the FF sensor with a slower lens will need a higher ISO to get the same exposure.
Well that's not an FF equivalent to a 18-35 f/1.8, that's a 18-35 f/1.8 mounted to a teleconverter.
If you scale the design of the lens up by a factor of 1.6, then you'll have a 28-55 f/1.8 lens for full frame, which is what we want. The question is whether or not such a lens would be reasonable in size, weight, and price.
EDIT: I suppose we could try to calculate the answer to that question by scaling the size, weight, and price up by a factor of 1.6 as well. In which case, our full frame 28-55 f/1.8 zoom lens would be 125mm diameter x 194mm length, and weigh 1296g, and cost $1280. That's larger in diameter, nearly equal in length, and slightly less weight than a Canon 70-200 f2.8 IS II.
I'm guessing that rather than simply upscaling the design and leaving it completely unchanged, Sigma would want to modify this new full frame lens design to be more efficient, increasing the cost but reducing the size and weight. Would the size/weight reduction be significant enough? Would the cost increase be too high? Perhaps Sigma engineers have already answered these questions with prototype lenses.