The flight coridors are seperated by altitude. Flights going east keep to odd hundreds of feet and flights going west keep to even hundreds of feet. They all use a barometer calibrated to the same value for sea level and a magnetic compass. Even if these technically show wrong compared to true altitude and true heading any fancy GPS, radio navigation or innertial navigation instruments need to calculate what a simple barometer and magnetic compass would show because this is the standard. So as long as everyone follows these rules there are always at least a hundred feet between airplanes flying in different directions.
There’s lot of different methods and instruments pilots use. First off, they have very detailed compasses. They don’t just go North East, they go exactly 42.5 degrees. That is slightly North of North East for reference. There’s no roads so they can just go this same direction almost the whole flight.
They also can maintain a consistent speed. If they are going 500 miles per hour, and flying the same rate for hours, and are traveling at a specific direction, you can calculate where they will be before they get there. You can say that even though Plane 1 is currently in Buffalo, it will be over the Illinois-Indiana border at exactly 4:13 AM.
An air traffic controller will get this information from all the planes in an area of the country and run these calculations. If they see that any two planes are on pace to be in the same exact point at the same time they will tell one of them to change their speed or angle so they don’t hit each other.
Air traffic control tracks every plane flying in FAA controlled airspace in the US. They use radar combined with an interrogator to track aircraft. Radar tells the FAA where the plane is at and the interrogator sends out a pulse to every radar return. The interrogated aircraft replies with a unique ID and it’s altitude. This information is then correlated with the radar return. Every plane that flies in FAA controlled airspace must file a flight plan that tells the FAA what the unique ID of their aircraft is and where it’s going. Air traffic control gives directions to each pilot.
Modern aircraft have traffic collision avoidance systems that allow each aircraft to interrogate each other and send information about their range and position. It will alert the pilot of they encroach on each other’s airspace.
There’s a *lot* to this. Here are a few:
1. There are a lot fewer planes than cars, and there’s a lot more sky than roads, so the odds of a collision are very small. If you flew 100 miles in a straight line with your eyes closed you probably wouldn’t hit another plane, while if you drove 100 miles in a straight line with your eyes closed you’d *definitely* hit something with your car. But the consequences of a midair collision are so bad that many other precautions must be taken.
2. Planes contain a *ton* of technology to help them figure out where they are. They do have GPS, but they also can track a set of radio direction beacons on the ground — radio “lighthouses” designed for planes to use. Many of the big ones have radar that can detect other planes. They have radios to keep in constant communication with each other, and/or with a ground controller who can steer them away from other planes. And finally, there’s a new technology called [ADS-B](https://en.wikipedia.org/wiki/Automatic_Dependent_Surveillance%E2%80%93Broadcast) where each plane constantly sends out data giving its position, so it can be tracked by the ground and other planes even without radar.
3. There are a *ton* of rules to ensure safety. Planes are divided up into several categories based on whether the pilot is navigating visually or whether they have navigation instruments and the training to operate them, and there are tons of rules and controllers on the ground to make sure that pilots with imprecise navigation don’t come anywhere near passenger jets.
4. Training and paperwork. To drive a car, all you need to do is pass a simple test of basic driving skills, and a check to make sure the safety systems in your car work. Airplane pilots need hundreds or thousands of hours of training, constant checks and rechecks to make sure they’re qualified to fly, their aircraft have to be inspected and tested for mechanical problems constantly, and the penalty for even a minor break in the rules isn’t a traffic ticket, it’s they take away your license and you never fly again.
A ton of ways.
First, as you said, commercial aircraft fly in designated “sky highways,” which are separated both horizontally and vertically, so at cruising altitude, planes in the same “highway” don’t cross each other. Planes follow their designated flight paths by some combination of GPS, inertial guidance, radio beacons, and other waypoints.
Second, crowded airspace is monitored by air traffic control. Controllers can see the locations of all the planes in their designated areas and can make sure planes keep proper separation and alert pilots to be aware of other planes or to make heading or altitude adjustments to avoid getting to close.
Third, pilots can talk to each other on radio to keep each other aware of their locations, headings, altitudes, and speeds.
Fourth, most planes have some sort of collision warning system that can automatically detect other nearby aircraft and in some cases, even maneuver the plane by itself to avoid a collision.
In addition to the other answers, I’ll add in a bit more information from a somewhat “technical” perspective… maybe closer to ELI10 level.
When flying, pilots are governed under one of two flight rules:
* Visual Flight Rules (**VFR**)
* Instrument Flight Rules (**IFR**)
When flying under **Visual Flight Rules**, the pilot has the primary responsibility to “see and avoid” other aircraft — mostly by looking outside, scanning for other traffic, and using the radio to self-announce their location (and listen to other pilots announcing their positions).
Pilots flying VFR have a lot of freedom to fly where they want to go, and don’t have to follow the “sky highways” (typically, [Victor airways](https://en.wikipedia.org/wiki/Victor_airways) in the US & Canada). Sometimes VFR pilots navigate by simply flying above local roads, Interstate highways, heading towards known landmarks (big lakes, stadiums, etc.), or even just fly a compass direction (using [dead reckoning](https://en.wikipedia.org/wiki/Dead_reckoning)).
Since they may not follow any airways, and don’t have to fly according to any set flight plan, it is their responsibility to visually see where they’re going and not collide with other planes. Nowadays there are [systems such as ADS-B](https://en.wikipedia.org/wiki/Automatic_Dependent_Surveillance%E2%80%93Broadcast) that can map the positions of nearby aircraft, but not all planes have them so by and large the pilots need to literally look out of the window.
When flying under **Instrument Flight Rules**, the pilot must file an [IFR flight plan](https://en.wikipedia.org/wiki/Flight_plan) and coordinate the flight with Air Traffic Controllers (ATC). The flight must then precisely follow the flight plan and be conducted under [ATC clearance](https://skybrary.aero/articles/atc-clearance). ATC will then ensure that IFR aircraft remain safely clear from other aircraft within [controlled airspace](https://en.wikipedia.org/wiki/Controlled_airspace).
These days, there are many aids to air navigation used in IFR flying — including GPS and collision avoidance systems like [TCAS](https://en.wikipedia.org/wiki/Traffic_collision_avoidance_system) — but strictly speaking IFR planes don’t crash into each other because they all fly under ATC control and [ATC has the responsibility to provide separation](https://www.faa.gov/air_traffic/publications/atpubs/aim_html/chap5_section_5.html) between them.
TL;DR: pilots can fly under VFR or IFR rules. VFR pilots must “see and avoid” other airplanes, while under IFR the Air Traffic Controller is responsible to keep airplanes clear from each other.
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