Major U.S. airlines say they expect to lose tens of millions of dollars in revenue each month because of flight delays and cancellations caused by the FAA’s furlough of air traffic controllers, which began April 21.

Many carriers also say they are cancelling hundreds of flights to try to mitigate delays. Delta Air Lines, for example, says the additional cancellations will range from about 150 on a good weather day to nearly 400 on a bad one.

The carriers provided their estimates and flight cancellation plans to support a lawsuit filed with the U.S. Appeals Court in Washington April 19 by Airlines for America, the Regional Airline Association and the Air Line Pilots Association to reverse the furloughs, which will amount to a 10% reduction in controller work hours at every airport.

The FAA insists the furloughs are unavoidable because of the budget-cutting requirements of sequestration, but the lawsuit argues that the agency’s plan is damaging, unnecessary and incorrectly applied.

In a declaration filed in conjunction with the lawsuit, Delta says its potential daily loss from the disrupted operations could exceed $575,000, based on the delay projections the FAA has provided. But the revenue damage is greater than that, it adds, because the airline expects some customers will choose not to fly “to avoid the widely publicized delays and cancellations.”

“Our revenue management and finance teams estimate that this negative impact upon demand could result in the loss of up to 2% of our domestic passenger revenue, i.e., up to $40 million in lost revenue per month,” says David Holtz, Delta’s VP-operations control.

Holtz says Delta expects to implement “aggressive, proactive” cancellations at LaGuardia Airport, John F. Kennedy International Airport, Newark Liberty International Airport, Chicago O’Hare International Airport and Philadelphia International Airport to “manage connectivity and preserve the integrity of our peak schedules.”

Those additional cancellations are expected to amount to about 22 mainline flights and 130 Delta Connection flights a day in good weather, and about 80 mainline flights and 300 regional flights on a poor weather day, the airline says.

United Airlines says it expects the furlough-driven delays to cost it at least $2 million a day, or about $60 million each month, although it notes that “these estimates are rough and based on the available information as of today.”

United says it will “aggressively cancel” flights, particularly at its hubs at Newark, O’Hare, Los Angeles International Airport and San Francisco International Airport.

Service to smaller communities will be disproportionately impacted, United adds, because the airline will be “forced to focus on canceling flights operated with smaller aircraft in order to reduce the total number of passengers impacted.”

The airline estimates that it will cancel an incremental 269 flights per day, more than half of which will be United Express regional aircraft flights.

American Airlines says it expects its daily revenue losses to total $1 million and that the furloughs will result in an additional 335 daily delays, adding significantly to the 247 delays the carrier experiences on a “typical day.”

US Airways, meanwhile, is estimating its annual revenue loss will total $249 million, and Southwest Airlines is “conservatively” estimating a cost of more than $200 million per year. Southwest worries that customers for its short-haul flights will shift to cars or other travel alternatives.

Southwest also says it will have to defer a plan it was going to implement this year to reduce the amount of surplus fuel its aircraft carry on good weather days, as well as the amount of fuel carried for taxiing. The airline expected that change to save it more than $40 million a year, but says it cannot implement the plan because of the uncertainty created by the furloughs.

It likely will take days, if not weeks, to determine the full impact the furloughs will have on airline operations. On April 22, through mid-day, the worst flight delay impact from the controller cutbacks was on New York shuttle flights and numerous airports in Florida, according to MasFlight, which analyzes flight delay patterns every day.

FlightStats, a real-time flight tracker, noted a slowdown at certain airports such as the Florida locations, but said the impact on the system as a whole as of mid-day did not seem severe.

The FAA implemented ground stops or ground delays at a handful of airports, including some it identified as related to staffing or “traffic management” issues at Baltimore-Washington International Airport and Charlotte Douglas International Airport.