Humber...
Since you seem to think that heating the air in a hot-air balloon somehow affects the balloon's velocity, let's assume that we're talking about a hydrogen (or helium) balloon, such as a zeppelin.
If the balloon is unpowered, and moving through still air, the balloon will slow down due to drag, and eventually come to a complete stop.
The balloon will be stationary; no difference between velocity of the the air and the balloon. The balloon is stationary, and the air is stationary too.
But what if you look down at the ground, and notice that the ground is moving?
Sure, there might be some turbulance in the air near the ground, but up where the balloon is, nothing is changed. The air remains still, and the balloon remains still. The fact that the ground is moving has no effect at all on the balloon.
And what of someone on the ground? From their perspective they are standing still, the ground isn't moving, but the air is moving and the balloon is moving along with it.
So who is correct?
Is the person in the balloon, who thinks the air is still and the ground is moving?
Or the person on the ground who thinks the ground is still, and the air is moving?
The answer is: They both are.
Well, you are indeed a glutton for the
same punishment, Brian_M.
My genuine answer is; So what?
The laws of physics are symmetrical. It makes no difference which is moving and which is still; in fact, the distinction is essentially meaningless.
Here we go again. Yes, that is correct. However, it is NOT maintained on the treadmill.
From the balloonist's perspective the balloon is sitting still, and there is no wind, even if from his perspective the earth is rolling along below him, like a planet-sized treadmill.
OK. I take the idea, but not the wording. To say it's
like something is not valid. You can say that it
appears to you that the ground is passing under you. Not a trivial point when making a model.
But if you're right, and a balloon can't travel at windspeed, then that means that the balloon sitting in still air will be slowly dragged through the air in the same direction as the ground is moving (relative to the air).
You are assuming the conclusion. If the conditions you suggest are correct, then the balloon would not be dragged back.
Can you describe any plausable mechanism that would cause the balloon to move like this? What force would prevent the balloon from slowing down to a stop (relative to the air)? After all, the drag from wind resistance is acting to stop the balloon from moving (relative to the air).
The balloon will not get there, so there can be no plausible mechanism.
The closest answer I can give you is to say that if the balloon were held at windspeed, then it would indeed be dragged back, but to below windspeed.
This is because the force driving the balloon, the downstream wind, is not enough over come the drag of the balloon
through that medium.
There is the 'downwind' drag, propelling the balloon, but there is also the opposing drag of the balloon through the air. It's not a free ride. The air ahead of the balloon is going to oppose the motion.
There is a
turbulent wake in
front of the balloon, just like there is an equivalent trail
behind an object being dragged through a still medium. It's the wake of the medium over the balloon.
Large diameter objects such as a balloon, have a big area to offer to the wind, and so gather a lot of force. They have a smooth profile, so the turbulence ahead is
relatively low. That means that the ratio of the driving and retarding forces is high, so the balloon can approach windspeed.
The opposing drag can never be zero, so true windspeed, in a constant homogeneous medium can never be achieved. With real world objects, you have to be careful about jumping to conclusions. If the balloon spins, that will unbalance the drag force, creating a shear force. If it has gained momentum by falling, then that must be considered too. These details matter.
I will say it again. This is the 21st Century, don't expect to find a pot of gold.
Wind is complicated, hot air balloons have been designed to exploit the conditions, to become refined. However, even they do not work in all winds. What do you expect? Weather balloons collapse in high winds...
It's a huge and erroneous step to conclude that not only all, but even some objects, can behave the same as a balloon. Balloons are like bubbles, they are perhaps unique. Sediment is in a class of its own, and so are canoes, which are different from barges. I am afraid that it is
useless to argue from example.