Can Groupon take to the skies with its first airline deal?

From laser waxing to fusion barbecue, it seems there’s nothing Groupon can’t — or won’t — sell. But the email discount offers service could be on to a lucrative new market with its latest discount.

If you wanted to get on board Virgin America’s $70-off sale for new service between San Francisco or Los Angeles and Chicago, too bad. In typical Groupon fashion, the offer — the service’s first ever deal with an airline — sold out in 8 minutes in Chicago and 45 minutes in San Francisco and Los Angeles.

The avid demand suggests that Groupon, which so far has only dabbled in travel offers, could be on to a lucrative new business, and disrupt the online-travel marketplace with its innovative marketing model.

Let’s break down the offer: Groupon is selling a $77 voucher for $7. Based on typical Groupon deals, let’s assume Groupon is keeping the entire $7 it’s charging consumers. A roundtrip to Chicago might typically go for $350, so the consumer is getting a flight for $280 ($273 plus the $7 he or she paid). With those numbers, Groupon’s take ends up looking more like a 2.5 percent commission on the sale of a ticket.

Airlines hate paying commissions to online travel agents, however — look no further than American Airlines’ feud with Expedia and Orbitz. But Groupon, which has perfected the art of creating consumer frenzies through a combination of deep discounts, witty marketing copy, and exploitation of viral sharing (whether by forwarded emails or links posted on Facebook and Twitter), could offer far more value to airlines.

The ever-shifting prices consumers see for airline tickets are a result of yield management, the practice of charging different fares at different times based on a host of factors. Groupon, one could argue, is bringing this same idea of yield management to Main Street, tapping latent demand for a business by allowing it to temporarily lower its prices for a limited number of customers.

The airline business, saddled with constant price wars, could turn to Groupon as a way to fill empty seats without permanently lowering its prices on routes. (Rival airlines constantly monitor and usually match changes in prices, but a Groupon discount is harder to detect and compete with. For example, United and American would have to simply drop their fares by $70 to match Groupon’s discount — but then they’d lose money on people who might have paid the higher price.)

By the way, Groupon president Rob Solomon used to run SideStep, a fare-search site, so he’s intimately familiar with the industry’s Byzantine pricing practices — and how Groupon can best profit from them.

Updated with more precise numbers on the time it took for Groupon to sell out the offer in individual cities.