It's been nearly a week since U.S. bombs began raining down on ISIS (aka "Islamic State," aka "ISIL," aka "Daesh") in Syria.

According to Pentagon news briefings, U.S. forces began the fusillade by launching some 47 Tomahawk missiles, and conducted air raids by 48 combat aircraft on the first day of bombing. And the White House tells us this is just the beginning of what could be a long campaign against ISIS in Syria.

All systems were go for airstrikes on ISIS, as this U.S. KC-135 Stratotanker took off to refuel U.S. warplanes over Syria. Photo: Wikimedia Commons

But while the White House admits that airstrikes will be ongoing, there's one question they're not eager to answer: How much will these airstrikes cost U.S. taxpayers?

Asked this question last week, White House press secretary Josh Earnest replied: "I don't have an estimate on that." But by reverse-engineering what we do know about the cost of various U.S. weapons systems, we think we might be able to give you a rough estimate of the cost.

Let's give it a try.

Follow the money
According to The Wall Street Journal (and other sources), the first day of airstrikes against ISIS in Syria began with 47 Tomahawk missile strikes launched from the guided missile destroyer USS Arleigh Burke (DDG-51) and the guided missile cruiser USS Philippine Sea (CG-58).

USS Arleigh Burke. First of its line, this is the original "DDG-51-class" guided missile destroyer. Photo: Wikimedia Commons

This was followed by by 48 "U.S. and allied planes" conducting airstrikes. Of these, the Journal notes that 16 warplanes hailed from the allied Persian Gulf nations of Saudi Arabia, Bahrain, Qatar, the United Arab Emirates, and also Jordan. That leaves 32 warplanes to make up the U.S. contingent.

The Journal notes that the U.S. warplanes involved in these strikes included Boeing (NYSE:BA) F-15 Strike Eagles and B-1 Lancers, F-22 Raptors and F-16 Fighting Falcons from Lockheed Martin (NYSE:LMT), and General Atomics MQ-1 Predators and MQ-9 Reapers. Combined, these warplanes are said to have struck ISIS forces with 160 missiles and bombs of various types.

Unarmed RQ-4 Global Hawks from Northrop Grumman (NYSE:NOC) may have performed a supporting surveillance function. Indeed, various sources say that the U.S. is now conducting about 60 surveillance flights (by various types of aircraft) over Syria daily.

Breaking down the numbers: What we know ...
According to U.S. Air Force data, the costs of the various aircraft deployed in the fight against ISIS in Syria break down like so. For every flight hour than aircraft is deployed, it costs U.S. taxpayers:

  • MQ-1B Predator drone: $3,679
  • MQ-9A Reaper drone: $4,762
  • F-16 Fighting Falcon: $30,357
  • F-15 Strike Eagle: $36,343
  • RQ-4 Global Hawk: $49,089
  • B-1 Lancer: $57,807
  • F-22 Raptor: $68,362

At "just" $3,679 per hour of flight time, General Atomics' Predator drone is one of the most cost-effective aircraft in the U.S. Air Force's arsenal. Photo: Flickr

Now, flying at different airspeeds and departing from different airbases, it's hard to say precisely how many flight hours these various aircraft actually log per mission. At least one source is guesstimating six hours flight time on average. That doesn't seem unreasonable, given the amount of ground that needs to be covered just to reach a target (it's more than 1,200 miles from Abu Dhabi to Damascus, for example), loiter until the right time to strike, and then return to base. Assuming six hours' average mission length, therefore, we can estimate that each airstrike against an ISIS target in Syria is costing U.S. taxpayers anywhere from $22,000 to $410,000 -- and about $215,000 as the average cost across all airframes. Times 32 missions per day, that average works out to about $6.9 million per day.

To this you can add the cost of the bombs and missiles dropped and fired during these strike missions -- roughly $175,000 per sortie, according to website DoDBuzz. Multiplied by 32 aircraft flying on the first day of operations, that's an additional $5.6 million.

Finally, add the cost of surveillance-only missions, which DoDBuzz estimates at approximately $57,900 per mission. Across the Pentagon's stated 60 "ISR" (intelligence, surveillance, and reconnaissance) missions daily, that works out to an additional $3.5 million per day.

Total cost for strike missions, ordnance, and ISR: Roughly $16 million per day.

... and what we can guess
Last month, Pentagon press secretary Rear Adm. John Kirby revealed that U.S. operations against ISIS positions in Iraq were costing the U.S. about $7.5 million per day, or less than half the cost of air missions over Syria on Day 1. The Pentagon has noted that operations over Syria will probably decline in tempo, however, as the Air Force and Navy run out of targets to shoot at. Certainly, the first day wave of 47 Tomahawks -- costing taxpayers in excess of $75 million at $1.6 million apiece -- is unlikely to be repeated on a daily basis.

But still, at an average cost of $16 million, or even just $7.5 million per day, the costs of this air war over Syria will add up. Since the U.S. began its intervention in Iraq on June 16, dispatching 275 U.S. special forces troops to Baghdad, then gradually ramping up to begin an air war there as well, three months of combat have probably cost U.S. taxpayers upward of $787 million. An air war over Syria of equivalent duration could cost as much as $1.7 billion -- and combined, airstrikes over Iraq and Syria could easily top $10 billion per year.

Result: The White House has already asked Congress to approve $5 billion in additional funding for "counter-terrorism operations." They could easily need twice that.

Like the $400 million-a-pop F-22 Raptor stealth fighter, the cost of fighting ISIS is going up, up, and away! Photo: Flickr

This article represents the opinion of the writer, who may disagree with the “official” recommendation position of a Motley Fool premium advisory service. We’re motley! Questioning an investing thesis -- even one of our own -- helps us all think critically about investing and make decisions that help us become smarter, happier, and richer.