One hundred and fifty years ago, in 1866, the town of Waterloo, NY, celebrated the first Memorial Day, remembering the fallen of the Civil War. Fifty years ago, President Lyndon B. Johnson honored Waterloo and reaffirmed the Memorial Day celebration, then centered around the heroes of World War II.

This Memorial Day, we’re fighting a different kind of war — one that would be unrecognizable to our forefathers.

Though it involves thousands of Americans, and a good chunk of our economy, the war against the Islamic State is fought mostly in front of computer screens, in places like Langley, Va., and upstate Syracuse.

It is, in many ways, a surreal conflict, one where some combatants can get a latte after the battle.

For that reason, it can be easy for Americans to forget we’re even fighting a war. Though our airmen and women fly hundreds of missions a day, it’s not uncommon for the conflict to go unmentioned on the news for weeks.

But the stakes are just as high, as ISIS brutalizes the people of Iraq and Syria and preaches global jihad. Also, while the United States mostly conducts airstrikes at a remove, there are still 4,000 US troops in Iraq. Three have lost their lives in this war that we don’t call a war. It’s called Operation Inherent Resolve.

Through visits to some of the nerve centers over the past few months, and more than three dozen interviews in person or by phone, The Post pieced together a mosaic that portrays what a typical 24 hours looks like in this battle against ISIS.

Combined Air Operations Center (CAOC)

Al Udeid Air Base, Qatar

Lt. Gen. Charles Q. Brown Jr., a veteran fighter pilot, runs the air war against ISIS from the Combined Air Operations Center (CAOC, pronounced “KAY-ock”) at Al Udeid Air Base in Qatar, a sandy peninsula adjacent to Saudi Arabia that juts 100 miles north into the Persian Gulf.

Housed in a building as big as a barn, the CAOC resembles NASA Mission Control. On the floor, dozens of US and coalition officers sit at rows of computer consoles holding two to six monitors. Three walls around them sport theater-size screens displaying digital maps or imagery. Looking over the consoles from behind are a balcony and offices, including Brown’s.

The CAOC produces the daily Air Tasking Order, a detailed master schedule of missions for every US and coalition aircraft in the fight — bombers, fighters, tankers, drones, manned spy planes, cargo aircraft. In a 24-hour day, 500 or more will crisscross the skies.

Each day’s Air Tasking Order takes three days to prepare. Officers around the region and at intelligence centers and remote control drone bases around the world take part by secure phone, e-mail and video teleconferences.

“It’s a constant dialogue and then, based on that, we step to a process to identify the aircraft, identify the missions, whether it’s air refueling, whether it’s intelligence, surveillance and recognizance, or if it’s a strike capability,” Brown said by phone from the CAOC.

Operation Inherent Resolve strikes are flown by three types of Air Force fighter jets, F-15E Strike Eagles, F-16 Fighting Falcons and F-22 Raptors; two kinds of bombers, the B-1B Lancer and B-52; plus armed MQ-1 Predator and MQ-9 Reaper Unmanned Aerial Vehicles (UAVs, a k a drones).

Navy F/A-18E Super Hornets, Marine Corps AV-8B Harrier jump jets and the warplanes of a few allied nations also are taking part.

In 2015, at least one bomb was dropped or one missile was fired in 9,914 Operation Inherent Resolve sorties. As of March 31 this year, the most recent tally available, the number of strike sorties was 2,781.

Such sorties come in two varieties: “deliberate” and “dynamic.”

Deliberate strikes are those launched against targets chosen well in advance, studied by “targeteers” and included in the Air Tasking Order. These include “their cash-collection points, some of their very important leadership targets, their command and control, against their IED factories, against oil targets to impact their revenue,” Brown said.

Dynamic strikes — the majority — are conducted on short notice by aircraft assigned to “overwatch” missions, meaning they fly near enough to answer calls from Iraqi ground forces for strikes on ISIS positions during combat or to hit unanticipated “targets of opportunity,” often spotted by drones.

Targeting section, 36th Intelligence Squadron, 363rd Intelligence, Surveillance and Reconnaissance Group Joint Base

Langley-Eustis, Virginia

Senior Airman Shana, a four-year Air Force veteran, and other members of the 36th Intelligence Squadron sit in a small rectangular room in a big brick building at the former Langley Air Force Base, studying satellite images of places the CAOC wants to bomb.

They are “targeteers.”

Their job is to sort out what types of bombs should be dropped on a target at what precise point or points, from what exact angle and with what duration of timing fuse to achieve “the commander’s objective and intent” while avoiding collateral damage.

Choosing munitions and their fuses, officially Advanced Target Development, is known as “weaponeering” and done with attention to both the power and the price tag.

“We weaponeer with economy of force in mind,” Shana explains by phone. “It’s basically biggest bang for your buck.”

An early version of a computer program that calculated the collateral damage of a bomb was called “Bugsplat.” The area the explosive would take out was represented by a blob on the screen.

Choosing where to strike is called dropping a JDPI — Joint Desired Point of Impact — on a target. This is done partly by using 3-D glasses to calculate the longitude, latitude and elevation of the target, a step called Precision Point Mensuration. For each target, the targeteers also conduct CDE — Collateral Damage Estimation.

They do all this with computer programs developed since the 1990s. An early version that represented a bomb’s impact with blob-shaped images showing the effects of particular munitions dropped at particular angles was called “Bugsplat.”

Today the targeteers use the more antiseptically named JWS, an acronym that contains an acronym. JWS stands for JMEM Weaponeering System. JMEM stands for Joint Munitions Effectiveness Manual, a computerized catalog of air-to-surface weapons and their effects.

“The CAOC sends us a target — they want to hit it because it’s a high value target for instance,” Shana says. “They need a point dropped on it because they don’t know how many munitions they need to drop.”

The CAOC tells the targeteers what weapons they have available. With their software and satellite photos that provide various views and angles of the target, the targeteers build a precise computerized image from the ground up, then calculate how to destroy it. They study the target for an hour or a day or even a week, adding information to their model as it comes in. Then they send the results to the CAOC in a Target Package.

Aboard the USS Harry S. Truman

In the Persian Gulf

The USS Harry S. Truman is a seagoing airfield, with four runways for nearly four dozen F/A-18E and F Super Hornet fighter-bombers. The ship carries 75 aircrafts in all and a crew of 5,000 — more than the number of US troops on the ground in Iraq.

The Truman and an escort of destroyers arrived in the Persian Gulf region Dec. 14. By April 15, her jets had dropped 1,118 bombs, partly thanks to the hard work of 127 sailors led by Michael Bracero of Brooklyn.

Aviation Ordnanceman Chief Bracero and his sailors are “magazine rats.” They work in the Truman’s ammunition magazine and rarely get above decks or see the sun. Many work nights to prepare the bombs F-18s carry, mainly 1,000-lbs. or 2,000-lbs. precision JDAMs — Joint Direct Attack Munitions, known as “JAY-dams.”

JDAMs are “smart bombs” but the fish-shaped munitions start out “dumb” — unguided. Bracero, 35, and the younger crew he leads fit them with the guidance kits that make the bomb smart. They add tail fins, aerodynamic control surfaces along the bomb’s body, an Inertial Guidance System and a GPS receiver. Then they send the JDAMs up an elevator to another deck, where other crews add timing fuses and fit the weapons onto aircraft.

“Think of it like a McDonald’s, where one person does the fries, one person does the burgers,” Bracero said. “Same concept.”

“We have a bomb assembly crew, and then we have personnel whose specialty is in testing missiles and other personnel that deal with the small-arms ammunition. The JDAM kit comes all in one container and the bomb body comes separately, the fuse comes separately. Everything comes separate. You can’t stow them together either because it’s just a hazard. When it’s time to go, we just use weapons elevators and weapons support equipment to move everything to one location, forklifts, etc. It’s a real dangerous job, but everyone is highly trained. You have 18-year-old kids out here moving 2,000 pound bombs.”

Bracero’s typical “day” at war begins at night, when he meets with other chiefs and officers to learn what missions are to be flown in the next 24 hours and how many bombs and missiles of what types are needed. Bracero assigns crews to get the bombs ready, works out the logistics of getting all the necessary parts and materials together, then supervises as his crews do their work.

Midway through the night, he lets his sailors go to chow while he makes a quick run to Starbucks. “We have a Starbucks on board,” Bracero says. “That’s pretty much a highlight of my day. It’s sort of a way to keep connected to the outside world.”

US Air Force 37th Bomb Squadron

Al Udeid Air Base, Qatar

As the Truman’s magazine rats are getting their night of work started, the four-member crew of an Air Force B-1B Lancer bomber are awake in their dormitory at Al Udeid Air Base.

A B-1B needs a pilot, a copilot and two weapons system officers, known as “Wizzos” for their job’s acronym, WSO. One WSO takes charge of the B-1’s defensive weapons, the other manages its bombs.

On this mission, Capt. Greg will be the WSO handling the bombs. After showering and donning his desert sand-colored flight suit, Greg calls his wife back in the States via Skype, then goes downstairs to join the other three members of his plane’s crew for breakfast.

The B-1 can carry more guided and unguided weapons at one time than any other plane in the Air Force stable, as many as 84 500-lbs. “dumb” bombs — 21 tons of destruction. But the rules of engagement for Operation Inherent Resolve place tight limits on how much collateral damage can be risked, so in this war, the B-1 usually carries 24 2,000-lbs. JDAMs.

Greg and his crewmates from the 37th Bomb Squadron, headquartered at Ellsworth Air Force Base, SD, will fly this mission under the radio call sign Tiger 37.

After breakfast, each crew member straps on an ejection seat harness and a combat vest. Each is also loaded down with radios, a sidearm, a GPS receiver, a flight helmet in a bag and a small backpack loaded with food and drinks for what will be a long flight. Then they head to their squadron building.

Inside, after a lengthy Step Briefing to verify that their training and qualifications are current and check the status of their aircraft, the four officers enter a secure room, where a US Army officer awaits them. The Army officer describes what is happening on the ground in the war, displaying maps on a computer screen.

The briefing over, Tiger 37’s crew gather up their gear, go out to their jet and climb up a ladder into the B-1’s belly through a hatch behind the nose gear. This will be home for the next 14 hours or so, depending on what targets they’re ordered to strike, so the first thing each does is “build your nest,” as they joke.

“The deceptive thing about the B-1 is, it’s a fairly large looking jet, but you climb inside and it’s kind of like four little fighter cockpits crammed into a small space, so there’s actually not a ton of room,” pilot in command Capt. Brian explains later. “Everybody has their own technique of getting things set up for your liking for that next 12 to 14 hours.”

They strap on their helmets and connect their headsets and other devices to the aircraft. The ladder comes up, the pilots call the tower for clearance to taxi, the B-1’s four engines roar and Tiger 37 rolls out onto the runway for takeoff.

432nd Wing

Creech Air Force Base, Nevada

The air crews of Creech Air Force Base’s 432nd Wing also begin their work day with a Step Briefing, and then an intelligence briefing, but the cockpits they take seats in afterward aren’t inside aircraft.

These pilots fly MQ-1 Predator and MQ-9 Reaper drones by intercontinental remote control.

From a Ground Control Station in the United States, these Remotely Piloted Aircraft (RPA) operators, as the Air Force prefers to call them, fly their drones over other continents by sending signals that travel via fiber-optic cable to Europe, then by satellite to their aircraft. The drones take flight from somewhere in the Middle East, a small crew there getting them airborne before turning them over to the remote crew in the United States.

Sitting beside the pilots at the GCS control console, enlisted sensor operators manipulate the drone’s daylight and infrared video cameras, its radar and other devices to gather information about what is happening on the ground from five or more miles above it. Each crew member faces three screens. One shows where the aircraft is. One shows what the sensors are seeing. A third displays information about the aircraft’s performance. Each has a joystick, pedals and a computer keyboard used to input commands to the drone, its sensors and its weapons.

The drones stay aloft as much as 24 hours or more, so their crews work in shifts, spending most of eight hours at a time “in the box,” as they call their freight container-style GCSes.

It’s often an ice box, for with lots of electronic equipment to cool, GCS air conditioners run hard. Crew members often wear flight jackets. Some GCS chairs now have seat heaters.

In any given 24 hours, officer pilots and enlisted sensor operators at more than a dozen Air Force and Air National Guard bases in the United States have 60 Predators and Reapers flying Combat Air Patrols (CAPs) over trouble spots around the world. An undisclosed but significant number patrol the skies above ISIS-held Iraq and Syria.

The latter include Reapers flown by the 174th Attack Wing at Hancock Field in Syracuse, whose members logged 7,300 combat hours and 365 MQ-9 combat sorties last year, according to the Air National Guard website.

The slow-moving drones are a key component of Operation Inherent Resolve, their video cameras, radars and other sensors providing ISR — intelligence, surveillance and reconnaissance — to US and allied forces. Drones find, assess, monitor and often strike targets. Deliberate strikes often are based on their daily monitoring of “patterns of life” in a particular area that turn up ISIS activity. Dynamic strikes rely on the drones to provide “eyes” on the target.

“We’re basically just painting the battlefield for . . . partners we’re working with on the ground,” says Lt. Andrew, a Predator pilot. “We’ll get guidance daily on where our mission is going to be at. We just provide persistent ISR coverage for that specific area. We have multiple CAPs in the AO (Area of Operations), so we’re basically covering the whole area.”

The Predator carries two AGM-114 Hellfire missiles. The larger Reaper, a Predator derivative, typically carries four Hellfires and two 500-lbs. GPS- and laser-guided bombs. When ordered, the drone crews can launch missiles or drop bombs on targets themselves. Often they use their laser designators to “paint” targets for manned aircraft.

Technical Sgt. Mike, a sensor operator, spends most of his eight-hour shift aiming the Predator’s cameras and laser designator, all carried in a “sensor ball” under the drone’s chin.

Sometimes, Mike “lases” the target for a manned aircraft like a B-1 bomber. Sometimes, he lases a target for one of the Predator’s Hellfires, whose trigger must be pulled by the pilot.

Special purpose Marine Air Ground Task Force Crisis Response Central Command

Al Jaber Air Base, Kuwait

Col. William F. McCollough arrived in the region last October with the third rotation of Special Marine Air Ground Task Force Crisis Response Central Command (MAGTF), a unit with 2,300 marines scattered around the Middle East positioned to take part in Operation Inherent Resolve.

A few hundred marines are at the air bases Al-Taqaddum and Al Asad inside Iraq protecting US forces, moving cargo or assisting and advising Iraqi forces. Another group of Marines is in Jordan training troops from that nation’s army.

This MAGTF also includes AV-8B Harrier jump jets based at an undisclosed location and a squadron of MV-22B Ospreys, tiltrotor transports that swivel two wingtip rotors up to take off and land like a helicopter and forward to fly like an airplane.

The Osprey squadron keeps at least two or more of the aircraft, their four-member crews and a team of Marines with Navy corpsman medics on alert around the clock, ready to fly into the war zone if necessary to pick up any US or allied aviators who go down from enemy fire or some other bad luck. A KC-130J aerial refueling tanker is assigned to fly with them if needed.

The Harriers, meanwhile, fly overwatch missions nearly every day, carrying up to six 500-lbs. JDAMs.

“We’re like the firehouse in the sky,” said their commander, Lt. Col. Benjamin Hutchins. “So if they need the fire engine, the fire engine comes.”

US Air Force 94th Fight Squadron

Al Dhafra Air Base, United Arab Emirates

Air Force Lt. Col. J. has known for close to 24 hours that this will be an important night for him and his wingman. Their famous “Hat in The Ring” squadron flies the F-22 Raptor, the most capable and controversial fighter plane in the world.

Built at a cost of more than $100 million per aircraft and seen by critics as an unnecessary “air superiority” stealth fighter of limited utility, advocates say the F-22 is proving its value in Operation Inherent Resolve.

“If this goes bad, we’re going to be the goat.”

The F-22 was declared operational in 2004 and saw its first combat a decade later, flying over Iraq in September 2014 in what one general called an “aerial quarterback” role and dropping 1,000-lbs. JDAMs as part of Operation Inherent Resolve.

Now J. and his wingman have been given a sensitive new mission. Tonight they are targeting an HVT (High Value Target) using a weapon newly adapted to the F-22. They are to drop 250-lbs., GPS-guided Small Diameter Bombs (SDB) on a house in Mosul where a top ISIS leader is believed to be.

Shown imagery of Mosul prior to the mission, J. recalled later, “I remember seeing the target, and seeing that it was an in urban environment, and seeing how close it was, literally tens of feet away from other buildings, and thinking, ‘This is the first time that I’ve ever dropped one of these weapons. This is the first time that the F-22 has ever dropped one of these in combat, and we’re going big first. This is no cream puff. We’re going after an HVT in an urban environment a few hundred feet from a hospital.’ I remember thinking, ‘If this goes bad, everyone is going to know about it and we’re going to be the goat.’ ”

But J. also knows that targeteers back home and one deployed with his squadron have determined it can be hit without unacceptable risk of collateral damage.

Their Step Briefing complete, J. and his wingman go for their mission briefing to a small portable shelter behind barbed wire, a Secure Compartmented Information Facility, or SCIF (pronounced “Skiff”), where matters at high levels of classification can be discussed. The SCIF is cramped, not much bigger than a tent on wheels, but there is a whiteboard and a map and computers in all corners. Here they are told where they will find the tankers that will refuel them in flight and other vital information.

By the time J. and his wingman drive to their F-22s on the other side of the airfield, the maintainers have their Raptors ready to go — full of fuel and loaded with bombs. Two 1,000-lbs. JDAMs is the Raptor’s normal load but tonight, each of the F-22s holds eight 250-lbs. SDBs in its weapons bay.

Soon the Raptors roar into the air, the sound of their afterburners reverberating for miles across the darkened desert. The flight to Mosul will take hours, so the first thing the pilots do is find the first tanker that will refuel them tonight.

497th Intelligence, Surveillance and Reconnaissance Group

Joint Base Langley-Eustis, Virginia

Senior Airman Herbert, 28, an imagery analyst with the 497th ISR Group, likes to get to work early so he can get up to speed on what’s happening in the war. Herbert is on the night shift this month, so that means arriving about 4:30 p.m. at the big brick building at Langley Air Force Base that houses Distributed Common Ground System 1, a major intelligence facility.

Here at DCGS-1 — the Air Force has other four other such intelligence nodes worldwide — Herbert and dozens of other imagery analysts, multi-source analysts, screen managers and other experts go to war in the information age. They pull three eight-hour shifts a day, 24/7, 365.

“We don’t have the luxury of being bored in our job. We’re responsible for important things — lives — so we have to make sure we’re on our game every night.” - Senior Airman Herbert

Behind a door labeled “United States Central Command,” on the DCGS-1 Operations Floor, a dark room lit by the glow of computer screens and air conditioned to a wintry chill to keep them running, Herbert and his peers sit at boomerang-shaped “pods” of gray tables holding multiple monitors displaying imagery and information of all sorts.

Some of the imagery they process and distribute to military commanders and units in the fight comes to them from the drones controlled by operators at Creech and other bases. Some imagery is supplied by manned U-2 surveillance jets, satellites or other military vehicles that carry sensors, from helicopters to high-altitude RQ-4 Global Hawk drones.

Much of the analysis involves sifting through gobs of data that arrives in real time and turning it into information those in the field can use as quickly as possible. The analysts record and annotate still images of snapshots or screen grabs, create short videos out of long ones, then send them to their “customers” electronically.

In some cases, the analysts may watch locations “down range” for extended periods to detect enemy activity, such as terrorists planting the infamous homemade bombs known as IEDs, Improvised Explosive Devices. If necessary, they can get on the phone to units that need such information in a hurry.

“We don’t have the luxury of being bored in our job,” Senior Airman Herbert reflects. “We’re responsible for important things — lives — so we have to make sure we’re on our game every night.”

For that reason, while the men and women of the 497th ISR Group are in no physical danger as they do their mission, their work is uncommonly stressful. One occupational hazard: They suffer an uncommonly high rate of tooth decay from constantly sipping energy drinks.

These days, a great deal of what DCGS-1 does for Central Command plays an active role in combat operations.

When Iraqi forces request an airstrike on ISIS positions, for example, the analysts at DCGS-1 may be asked to gather information from all their sources and put together a coherent picture that will help targeteers and commanders at the CAOC in Qatar decide whether the target is valid and whether the collateral-damage risk falls within the rules of engagement.

Tonight, Senior Airman Herbert will find himself looking for sensor information to pass directly to a B-1 bomber.

Task Force Summit

Headquarters, Nineveh Operations

Makhmour, Iraq

Lt. Col. Edward Hollis of the 10th Mountain Division, headquartered at upstate Fort Drum, leads Task Force Summit, deployed to northern Iraq to advise and assist Iraqi forces. Today he is up at 0500 and anticipating action.

Task Force Summit advises the 15th Iraqi Army Division at its Nineveh Operations Command near Makhmour, a front-line town controlled by the Kurdish Peshmerga militia on the edge of what separatists call Kurdistan. The Kurds and Iraqis here tolerate each other only because ISIS is their common enemy.

Today, elements of the 15th IAD plan to assault ISIS-held Al-Nasr, a village east of the Tigris River roughly 45 miles south-southeast of Mosul and 10 miles west of Makhmour.

Operation Valley Wolf will be a tough affair. The aim is to kill or chase away dozens of ISIS who are well dug in, protected by berms, trenches, tunnels, bunkers and VBIEDs — Vehicle-Borne Improved Explosive Devices. In plain English, car bombs.

The Iraqis have tried to take Al-Nasr before and failed, retreating in the face of ferocious fire.

Al-Nasr is tactically important, located on high ground from which Iraqi troops should be able to cut off key routes ISIS has been using to move fighters and supplies. This battle is part of shaping the future fight for Mosul. The 15th IAD is one of the Iraqi divisions earmarked for the Mosul counterattack, anticipated at earliest late this year. ISIS is thought to have 10,000 fighters there.

Hollis will spend his day behind reinforced walls topped with razor wire that protect the Joint Operations Center, a sort of miniature CAOC with far less elaborate equipment, where he and Iraqi officers will nervously watch the battle unfold on flat-screen TVs. Hollis can also watch video feeds from US drones or manned aircraft and share them with the Iraqis.

The Iraqis have what Hollis calls “significant access to human intelligence” — eyes and ears among a populace willing to pass on information that can help target ISIS positions. When they request airstrikes, Hollis can ask higher headquarters for a drone to take the proposed target under surveillance and check the geographic coordinates the Iraqi troops have provided.

Capt. Diego Hill, a 10th Mountain Division artilleryman from West Orange, NJ, is the direct link between Lt. Col. Ed Hollis’ advise and assist team and the 15th Iraqi Army Division. Hill spends 10 to 12 hours a day talking to Iraqi officers and doing what he can to fulfill their needs.

It’s indoor work, but not without risks. The other day, a rocket landed nearby, and Hill has bonded with his Iraqi counterparts. “We’ve become so close with our partners that the losses they feel are losses that we feel,” he says. “It definitely feels like a war out here.”

By late afternoon, Lt. Col. Hollis and his Iraqi colleagues have reason to celebrate. Operation Valley Wolf, the assault on Al-Nasr, has succeeded, in no small part thanks to air strikes by US planes and artillery fire provided by Marines at Firebase Bell, a location nearby.

“At the end of the day, the Iraqis were successful, extremely successful, and they’re making progress,” Hollis says.

Asked what happened to the ISIS fighters in the village, Hollis replies: “Most of them were killed by either direct fire from the Iraqi army or from air strikes or artillery provided by the coalition today.”

B-1B Lancer

Bomber “Tiger 37”

Somewhere over Iraq

At hour 10 in-flight, after being granted a two-hour extension of their mission by leaders at the CAOC, Tiger 37’s Capt. Greg checks in from over northern Iraq with the Joint Tactical Air Controller (JTAC, pronounced “JAY-tack”) working with Iraqis at Makhmour. The B-1 crew has been awake 16 hours, taken on more than 200,000 lbs. of fuel in midair while flying overwatch in multiple areas of Syria and Iraq, and still faces a multi-hour return to Al Udeid, where thunderstorms over the Persian Gulf are predicted. But Tiger 37 has bombs left.

“Tiger 37 is established overhead with two hours of time on-station, ready for situation update,” Capt. Greg tells the JTAC over the radio.

JTAC: Tiger 37, we have a troops-in-contact situation where friendly forces are receiving heavy machine-gun and rocket fire from three adjacent buildings. The ground commander requests you employ two times 2,000 pound GBU-31 smart bombs on each building. I’ve got Lookout 11, a UAV, established below you at 8,000 feet, ready to lase the center building of the apartment complex. Call ready.

Capt. Greg: Lookout 11, laser on.

Lookout 11: Lasing.

Capt. Greg: Good spot. Laser off. My crosshairs fall on an east-west-oriented, rectangular, three-story building and I’m seeing muzzle flashes directed south from the second story.

JTAC: Tiger 37, that is your target. We’ll call that “Building Alpha.” You should see two additional L-shaped buildings directly east and west of Building Alpha. Call contact.

Capt. Greg: Contact with two L-shaped buildings, one on the east of Building Alpha and one on the west. Confirm all buildings are on the north side of the U-shaped river opening to the south.

JTAC: Tiger 37, affirm. Those three buildings are your targets. We’ll label the east building “Bravo” and the west building “Charlie.” Say when ready nine-line.

The “nine-line” is a standard briefing procedure US air forces of every service use to guide an attacking plane’s crew to its target. It runs down the location of the target, where friendlies are and the route the aircraft will take after the bombing.

Capt. Greg: Ready.

JTAC: This is a Bomb on Target attack. Your target buildings are Alpha, Bravo and Charlie. I need you to derive your own coordinates for each building. Friendly forces are 1,000 meters south.

Capt. Greg: Ready remarks and restrictions.

JTAC: Looking for two GBU-31s per building, delayed fusing at your discretion, attack direction: Zero-nine-zero, plus or minus 10 degrees. Ground commander is requesting a single pass for all six weapons and your earliest TOT [time on target].

Capt. Greg: Copy. Target buildings Alpha, Bravo and Charlie from my sensor. Friendly forces 1,000 meters south. Two GBU-31s per building and zero-nine-zero heading plus or minus 10 degrees. Expect three minutes to derive coordinates and update our system.

JTAC: Good readback. This strike has been approved. Call in with direction and expect clearance on final.

Capt. Greg: Wilco. I want to confirm friendlies are still 1,000 meters south. I’m seeing a convoy of five vehicles directing fire north across the river towards target building Alpha. That convoy is approximately 500 meters south of the target buildings.

JTAC: Tiger 37, standby for ground commander coordination. Expect a new Line 8.

After a few seconds:

JTAC: Tiger 37, update to line 8: nearest friendlies now 500 meters south.

Capt. Greg: Copy. Line 8 now 500 meters south.

JTAC: Tiger 37, you’re approved an immediate TOT. Lookout 11 will be holding north of the target area.

Capt. Greg: In from the west.

JTAC: Tiger 37, cleared hot.

With “cleared hot,” the JTAC has just given Tiger 37 permission to release weapons. Capt. Greg pushes buttons. The B-1’s bomb bay doors open. A rotary launcher begins releasing bombs, spinning after each release to bring another bomb into drop position. Pistons moved by explosive charges punch each 2,000-lbs. bomb earthward. With each release, the crew feels as much as hears a thump, as if the big plane had hit a speed bump.

Capt. Greg: Six weapons away, 45 seconds to impact.

Forty-five seconds later:

Capt. Greg: Splash. Looks like all weapons went high order.

JTAC: Tiger 37, Bomb Damage Assessment from Lookout 11: Those buildings were completely destroyed and ground forces are reporting firing has ceased from all locations. Ground commander’s intent met on the strike. Thanks for the extension. This strike wouldn’t have happened without you guys. You’re cleared to return to base and good working with you, as always.

Capt. Greg: Copy on the BDA [Bomb Damage Assessment]. We’re clear of your airspace to the east. Stay safe and talk to you next time.

After meeting another air refueling tanker and gassing up, Tiger 37 heads back to Al Udeid. The B-1 crew lands after being awake nearly 20 hours, then return to their squadron building. They spend two more hours there, reviewing video recorded by their Sniper Advanced Targeting Pod for each bomb released and writing a detailed report of their mission. Then they go to their rooms to get some sleep so they can fly another mission tomorrow.

F-22 Raptor Flight

Somewhere above northwestern Iraq

Some Operation Inherent Resolve airstrikes involve a lot of participants, both on the ground and in the air. Tonight, as Lt. Col. J. and his wingman pilot their F-22s toward Mosul, where their mission is to drop Small Diameter Bombs on an HVT downtown, they are on their own. The commanders who designed the mission don’t want jet noise over Mosul to spook the HVT and make him flee before the 250-lbs. SDBs arrive.

Before takeoff, J. and his wingman entered into their bomb guidance kits the geographic coordinates of the house where the HVT is believed to be. They have checked and rechecked the coordinates repeatedly in the hours they have been airborne. The trip has been so smooth, J. thinks it almost surreal.

As he and his wingman come off the last tanker they will need before their strike, J. looks down at Mosul from 20,000 feet or more. “Wow,” he thinks, “this is a city. There are lights and there’s a lot of women and children down there. I hope that these things go to the right place.”

Maneuvering his F-22 so that its Synthetic Aperture Radar creates a precise picture of the neighborhood that includes the target house, J. can see exactly where their bombs should land.

When released, their SDBs will quickly deploy tiny wings, which will pop out of the sides of the bombs to increase their glide and range. J. and his wingman push the small red “pickle” button on their joysticks and release four SDBs each. They feel the weapons bay open and the bombs thump off their rack. Then they turn their F-22s in a circle to fly behind the bombs and record their flight and impact with onboard sensors.

Warning: The following video may be disturbing to some

“Good weapons impact times four,” J. tells his wingman over the radio in a matter-of-fact tone of voice as his bombs find their mark.

“Good weapons impact times four,” his wingman echoes, reporting on his own bombs.

Now they head for home.

Days later, intelligence analysts will conclude that the strike successfully destroyed the target house and killed several senior ISIS figures.

The HVT they were after, though, was not among them.

Combined Air Operations Center

Al Udeid Air Base, Qatar

From where Operation Inherent Resolve air commander Lt. Gen. Charles Brown sits, the campaign against ISIS is succeeding. It’s estimated that ISIS has lost 40% of the Iraqi ground the terrorist group conquered in 2014 and 10% of what it held in Syria.

“We have [ISIS] on their heels,” Brown says. “The work that we’ve been doing against some of their more lucrative targets that we’ve been able to go against, their cash-collection points, some of their very important leadership targets, their command and control, against their IED factories, against oil targets to impact their revenue, in my opinion, that is having a huge effect on their ability to actually execute and operate.”

“We have [ISIS] on their heels.” - Lt. Gen. Charles Brown

Still, what comes next is a formidable question. The US is bringing the most powerful air force in the world to bear on ISIS, but it depends on the Iraqi army to finish the job, and what comes next — what fills the vacuum in northern Iraq and Syria, remains a mystery.

Just as Operation Inherent Resolve is waged unlike any war we’ve fought before, what constitutes “success” will be just as different.

Richard Whittle is the author of “Predator: The Secret Origins of the Drone Revolution” (Henry Holt and Co.) and “The Dream Machine: The Untold History of the Notorious V-22 Osprey” (Simon & Schuster), available now.