GM will show off the all-new 2015 Corvette Z06 Convertible at this week's New York International Auto Show. Photo credit: General Motors Co.

The last month has been a rough one for General Motors (NYSE:GM), as the company has faced tough questions and withering criticism over a long-delayed recall that may have contributed to a dozen fatal accidents.

But meanwhile, life at the General goes on. GM has a few new products to show off at this week's New York International Auto Show, including this particular bit of madness: a convertible version of the white-hot, supercharged Corvette Z06.

It's "insanity" in the best sense, explains the Motley Fool's John Rosevear in this video. John will be in New York to see the latest Vette variant up close, and in this video he explains what he expects to see -- and the implications for other upcoming high-performance models from GM.

A transcript of the video is below.

John Rosevear: Hey Fools, it's John Rosevear, senior auto analyst for The New York International Auto Show starts this week. Media days are Wednesday and Thursday, and we're expecting the automakers to unveil a bunch of new models. I'll be there with my Foolish colleague Rex Moore.

We'll bring you a video report of the show's highlights at the end of each day, Wednesday and Thursday, and we'll have a bunch of more in-depth reports for you over the next week or so after that.

As of right now General Motors doesn't have any media events on the official auto show schedule, but they are bringing a couple of interesting things to New York, and one of those things is a new Corvette variant.

Rex and I were at the unveiling of the new Corvette Z06 in Detroit in January, we heard GM president Dan Ammann and product chief Mark Reuss talk about it, we brought you some of that on video back in January, and in New York they're going to unveil the convertible version of the Z06.

Now, this is an insane product, and as a former Corvette ZR1 owner I say that with great affection. This is a convertible Corvette with a supercharged 6.2-liter V8 engine, what GM calls the LT4 engine, and they haven't released official ratings for that engine yet but they are saying it'll have "at least 625 horsepower and 635 lb-ft of torque". In a convertible.

This is madness. But it's 21st century madness, and what I mean is that GM's press release for this thing also talks at length about its fuel efficiency. This new LT4 engine will have direct injection and cylinder deactivation and continuously variable valve timing and this high tech supercharger system they've been using and again they aren't yet releasing official numbers but they promise it will be, and I quote, "surprisingly fuel-efficient".

Like the Z06 coupe it'll offer a choice of the seven speed manual transmission they pioneered in the new Corvette Stingray last year, or a new eight-speed paddle-shifted automatic that apparently is quite nice to drive. We expect that paddle-shifted automatic to show up in some of GM's other V8-powered high performance cars, it'll likely appear in the Camaro and it seems like a slam dunk for the upcoming new version of the Cadillac CTS-V as well, I just hope they keep offering the manual transmissions in those cars too.

So we'll be checking out the new Corvette Z06 convertible, this is a minor debut as these things go, but it's a wild product and we'll be sure to get a close-up look at it on video for you at the show later this week. Thanks for watching.