It appears that humber has indeed ignored my quiz about the Japanese baseball gun, so spork is right again. Not surprising.
Well jjcote, if it is as easy as this little canard, it won't be a problem.
Okay, we have a smoke generator sitting on the ground. There is a 10 m/s wind blowing out of the south, and we are approaching the smoke generator at 10 m/s, northbound (i.e. at windspeed) in some sort of conveyance (not necessarily wind powered). When we are 10 m from the generator, it emits two puffs of smoke, one at eye level, the other at ankle level. What do we see? The puff that is at eye level travels northward at 10 m/s, and remains 10 m in front of us, while the one at ankle level, in the boundary layer, moves forward at only 6 m/s, so we close the distance to it at 4 m/s, and we pass by it in 2.5 seconds.
Yes, yes, get on with it...
Now we have a smoke generator attached to a (sufficiently large) treadmill belt that is moving from north to south at 10 m/s. It is in a room with still air, and we are maintaining our position with respect to that air (and to the "floor") by moving relative to the belt at 10 m/s in some sort of conveyance, so the smoke generator is coming toward us at 10 m/s. When the smoke generator is 10 m in front of us, it emits two puffs of smoke, one at eye level, the other at ankle level. What do we see? The puff that is at eye level stays put relative to the air (and to the "floor"), and remains 10 m in front of us., while the one at ankle level, in the boundary layer, is dragged back by the belt at 4 m/s, and we pass by it (or it passes by us) in 2.5 seconds. Exactly the same.
Oooh, no, JJcote, you are using the apparent closing distance, but ignoring the direction. In real wind, the difference between the flows is constant regardless of traveler velocity.
Try this using the same situations that you have described.
Stand in real wind while holding a paddle device, so that the axle is above the boundary layer, with the top and bottom blades driven by the wind and boundary respectively. This should yield a difference of '4m/s' (CW) and then again at windspeed. (10 - 6 = 4).
The belt is not the same. At windspeed, (taken from he cart) the paddle will turn ( 0 - 6) -6m/s (CW). Going with the belt will be ( 10 - 6)
6m/s (CCW) ETA:4m/s (CCW)This is tricky. If you stand on the belt, the air right next to the belt will be at 0 w.r.t you, so the slower flow of 6ms, can be said to move away from you at 4m/s. The air over the top (from your back) is coming to the paddle at 10m/s, so the difference is
6m/s (CCW.) ETA: 4m/s (CCW)
ETA:
If the lower paddle touches the belt, the paddle will stop, and so for a flow going at the speed of the belt. A flow of 6m/s will therefore be 4m/s slower, turning the paddle 4m/s (CCW)
You have to agrees that at
some point when moving up the belt, the flows will be equal and opposite, so the paddle will stop. This will not happen in the wind.