Wind is generally formed by a vacuum sucking air in rather than a force pushing the air. Hot air rises and leaves a vacuum that pulls air toward it, on the global scale this forms wind.
But also there is relativity. The atoms of gases are moving at the same speed as all the gas atoms surrounding them.
The speed of air molecules is about 500m/s at room temperature, that’s over 1000mph. Colder air isn’t that different as the speed scale with the square root of temperature (in K). You don’t feel it because the direction is random for each individual molecule, so the total average, or collective speed is zero.
Wind refers to the collective speed, and rarely go over 100 mph (or you won’t survive anyway over that). So it’s really make very little difference in our daily life. But if the “wind” is strong enough, yes you do heat up on the surface blocking the air, but we call that air resistance/ friction.
The feeling of cold air is simply your body’s perception of air that is lower than the ambient temperature and your body losing heat as a result of that.
You’re conflating two separate things as far as the motion goes. Heat isn’t how fast something is moving, it’s how fast the individual molecules moving around in amongst each other. Think of it like a party bus full of people. The people are the molecules. When they move around more, it’s hot inside the bus. When they aren’t, it’s cool inside the bus. But this is separate from whether or not the bus is moving. The speed of the bus and the energy of the “molecules” inside the bus are two unrelated things.
As others have said, cold is not a thing. Cold is just less hot and anything warmer than absolute zero will have molecules that move. So look at absolute temperature in Kelvin. The lowest recorded temperature on earth is -89.2°C = 183.95 Kelvin. Highest temperature is 56.7C = 329.85 K. Earth average temperature is about 15C =288K
So there are no cold winds just more or less warm winds. We can heat up air cooler than our bodies, so a cold wind could just be one that can reduce out temperature. Our body core temperature is about 37C =310K, quite a lot over absolute zero.
You can calculate the average speed of particles in the air, that is the [https://en.wikipedia.org/wiki/Thermal_velocity](https://en.wikipedia.org/wiki/Thermal_velocity) For air at 20C it is 464m/s, the speed of sound at the same temperature at sea level is 343m/s.
464/343= 1.35 This means the average speed of molecules in air is Mach 1.35
(1.35 times the speed of sound)
You can compare that to a category 5 hurricane that requires sustained wind speed above 70m/s. A storm on the Beaufort scale is 24.5–28.4 m/s. the higher measure wind speed was 113m/s in a guse in a tropical cyclone. So the wind speed you are used to is tiny compared to the speed at which the particles ait move because of the temperature.
The wind is not the average speed of the molecules increase, it is that the direction in which molecules move is not random but slightly more in one direction.
We do not experience this motion of air as a win, what we experience is as pressure because molecules hit us evenly from all directions. According to Bernoulli’s Principle if there is a net motion of a fluid the pressure drops. Wind do this you can show it for yourself by blowing air and having two pieces of paper https://youtu.be/ORd2pgKbM6M?t=65
Compared to people walking all at the same speed in random directions in a large room, when something or someone is in the way they change direction randomly. There will be no net motion of people.
Compare that to the same people walking in at the same speed but all in the same direction you have the net motion of people. But the kinetic energy of the people is the same because their mass and speed are the same.
Wind is more like people prefer to walk in one direction but not just walk in that direction.
So-net motion do not require an increase in average speed, only a change in direction is required if there was motion to begin with.
This all means you can have a wind that moves a bit over the speed of sound without changing the average speed of molecules, That would mean the temperature has not changed. That is in theory, in practice that would not happen, all molecules will not move in the same direction. But it can and do happen at a lot lower air speed like the one we experience in wind on earth.
If have the wind at Mach 2, you likely get it from singing moving through the air like a jet fighter. The speed of the molecules in the air will indeed result in air that gets warmer from the point of view of the airplane.
Heat is a problem for supersonic airplanes. The airplane bodies get heated up and expand. An SR-71 that cruised at Mach 3.2 had a skin temperature of around 300C. It was made of metal that could handle that. There is one common way to get rid of heat for a supersonic airplane, use the fuel at cooland and heat it up with heat exchangers before you pump it into the engine and burn it.
During atmospheric reentry, spacecraft travel at a speed of around Mach 25. It compresses the air in front of it that heated up. It is the kinetic energy of the spacecraft that is transferred to heat in the air and that slows it down.
So how high wind speed is possible depends on temperature. It ic possible to have the wind at the speed of the temperature we have on Earth by just changing the average direction of motion of molecules. It is when you stare to move at speed greater then Mach 1 that you start to have significant heating of airplanes from wind.
I think the main misunderstanding is that you’re thinking of “hot” and “cold” only in human terms. To an imaginary alien living on a planet with 1000 degree weather, even the warmest summer breeze on Earth would feel freezing cold.
“Cold” wind has plenty of heat energy in it. It’s just that our bodies happen to be hotter.
The other misunderstanding is that there are different types of energy. Heat is the vibration of atoms, roughly speaking. But it’s entirely possible for a cold thing to be moving very fast. Satellites in orbit are moving incredibly fast, but they don’t really heat up just because of that motion. And why should they?
To prevent confusion: fast moving things on Earth *do* tend to heat up, but only because they rub against the air or ground, and that rubbing creates heat. Also cars get heated up by the engine and bullets get heated up by the gunpowder explosion that shoots them.
If there were no air or ground (like in space) and no hot thing creating the motion (like an engine or explosion) then a very cold thing can move very fast indeed in space. Like a comet, which travels very fast but is made of ice.
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