Missa said:
...snip...
However, this was not the questions asked. The question has the converyer controlled by speed, not force/power. The only way to have a speed without translational motion is angular speed, since I don't think anyone is visualizing the airplane turning nose over tail, the entire plane can not have an angular speed. Because the problem controls the conveyer speed based on the airplane (assumed translational) speed, it means the plane is moving forward developing the necessary airspeed to fly.
Missa
I just take speed at face value...nothing fancy...change in distance/unit of time, dx/dt. If you travel down the runway at 30 kts you cover roughly 50ft/sec. If the conveyor moves you backward at 50ft/sec. you still have 30kts relative to the moving runway but 0kts relative to an outside observer. If those 50ft you traveled in any second are ALWAYS offset by moving the runway in the opposite direction at 50ft/sec...you don't move forward with respect to an outside observer. As long as your wheels are on the runway, it is the SAME 50 ft of runway. Your wheels have traveled 50ft down the runway, the runway is moved back 50ft. Whenever you say that you are moving forward with respect to a stationary observer, we just haven't moved the runway/treadmill backward fast enough, therefore the backward speed is NOT matching your speed. When it does, you have no forward motion/speed with respect to the stationary observer.
I don't think that the "free wheeling" idea works (not your comment Missa, just including it here). If the plane moves one foot forward, the wheels have traveled exactly one foot too. If the runway is moved back that SAME one foot, we have a stationary aircraft. The only time we can "free wheel" is when the plane lifts off, then you can spin the wheels all you want, otherwise they are connected to the runway by a ton of aircraft above them. The aircraft "speed" is measured by movement down that runway and as before, if we match the "speed", with a backward displacement it remains stationary.
I gave an earlier example of an airboat stationkeeping in a moving stream. If we can always advance the stream speed, the airboat goes nowhere. It seems that some don't buy the example because it is an airboat and not a plane, therefore somehow different. What if we take a floatplane (we know that they fly) and put it in the moving stream. If we set the speed stream to be 60 kts, the floatplane could stationkeep at that speed just like a fast airboat or speedboat but would have 0 airspeed and would hence remain on the water. If we can always match the speed, there is never any airspeed/lift/takeoff. Replace the floatplane with a powered parachute on floats so we don't have to go so fast. If the powered parachute could normally take off at a more realistic speed, say 20 kts and yet we put it in a stream flowing 20 kts, the chute would never fill because there's no forward motion/airspeed. Don't like the stream, put the powered parachute back on the moving runway...the cockpit could be going 20kts down our imaginary treadmill/runway but the chute would still not fill.
Let's now get Evel Knievel on a bike with a powered parachute engine and prop on a backpack (no chute necessary this time but you can picture it both ways). Now place Evel and his contraption inside a giant rat treadmill, a 100 ft high wheel with steel floor all the way around. Of course we can rotate the treadmill at any speed to match Evel's speed. Let Evel fire up the engine/prop on his backback to provide forward motion (purposely chose prop to avoid the whole motive force stuff). He moves a foot forward, we rotate the treadmill 1 foot. No matter how fast Evel goes, we rotate the treadmill at the same rate and Evel will stay perfectly centered on this thing. Why? Because regardless of speed, for every foot forward he and his wheels move, we rotate the treadmill a foot in the opposite direction. As long as we keep Evel centered, his airspeed is zero but even the Great Evel wouldn't want to jump off the bike while we have it spun up because he has considerable "ground speed" with respect to the inside of the giant rat treadmill (GRT), right. Of course, if he lept off and outside the GRT, he would land with ease, except that backpack/engine/prop thing would be awkward, right? Now, I've kept the prop, the wheels and the treadmill in the picture in an attempt to sway the formidable challengers from the "other side". I hope this helps you understand why I feel that all forward motion of the aircraft could be off set by backward motion of the treadmill, just like Evel in the GRT. Flame on
Final wild example...take a parasail behind a boat. Send the boat into a stream going 40kts and assume the boat is going 40kts, and thus now stationkeeping in the stream. What happens to the person in the parasail 500ft up in the air behind the boat? Splashdown!! Just like this thread, huh
Sorry to pile all this on your post Missa, just happened to go through my mind once I got started. I know,...bizzare mind, but hey, it is winter in Montana...no flying for the past month. This is a good indoor activity while I'm not on the slopes. Thanks to you and everyone else for all the inspiring, challenging discussion. Ciao!
