A headwind will make you go slower first and foremost, requiring either more fuel or a longer flight time. Planes try to avoid this whenever possible.
Aerodynamically a strong headwind can make a plane gain or lose altitude more rapidly than expected for a given pitch. Not a huge issue but something pilots must be aware of.
Strong winds in general also increase the chances of significant turbulence.
Headwinds are actually very useful in certain circumstances. When taking off or landing, the aircraft will do so at the side of the runway opposite to the wind direction so that it will have headwinds, so that effectively it will have more airspeed. Actually doing it with tail winds is rather dangerous, exactly because the wing takes away from your airspeed, reducing your lift at the same ground speed, making both takeoff and landing rolls dangerously long.
But when you are in cruise, it acts against you, because it slows you down relatively to the ground.
Planes are designed to be able to provide enough lift to stay airborne above very low airspeeds. In fact the wings are designed to change shape to increase lift at low speed by moving the flaps down.
Go too slow and the wing stalls, and the plane starts falling. This is why planes take off and lane into the wind as much as possible.
But anything above the upper limit of what is needed for lift ceases to be a benefit. At this point the airspeed creates excessive drag on the plane, slowing it down, and requiring more fuel and time to reach the destination.
Well it’s not “bad” it just makes travel slower in cruise.
A headwind does push more air over the wings like you said, which creates more lift. This is good for takeoffs, as the plane can takeoff at a lower speed and use less of the runway, as well as climb to altitude faster. It’s also good for landing for the same reasons.
But in cruise, the extra lift doesn’t really do anything. Going against the wind makes the plane’s ground speed slower, so the flight will take a bit longer. Where as a tail wind in cruise is effectively helping push the plane forward, so the flight will be shorter.
I assume you’re just talking about cruise flight. Think of it this way: you’re traveling in a mass of air. If the mass of air you’re traveling in is moving backwards compared to the direction you want to fly in, it is like walking the wrong way on a moving walkway, or rowing upstream in a river. You will get there eventually but it will take longer.
Because planes aren’t the on the ground, they are in the air. This means that an aircrafts engines move it relative to the air, _not_ relative to the ground. A plane in the air will always going the same speed relative to the surrounding air, no matter what the wind is, sort of like you running in a moving train, you’re always going the same speed relative to the train, but your speed relative to the ground changes depending on if the train is going the same or opposite direction as you running.
So if the plane is going 100 km/h in the air, but the air is moving backwards at 50 km/h, then the plane would be moving across the ground at only 50 km/h, which means it will have to spend twice as long flying to get where it’s going.
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