A paradoxical thought experiment
in [Motorcycles]
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From: sean_q_ on 7 Jul 2010 16:08 Imagine an extremely lightweight (but very strong) sidecar mounted on the right-hand side of the bike (meaning no offence to Brits, Kiwis, Ozzies, Sri Lankans and others). Make a hard left turn; the chair lifts because it lacks enough weight to keep the bike from leaning into the turn. Then make a sharp right turn. Once again it lifts because the rig's center of mass is offset above the wheels' contact patches (where the turning forces are applied), creating longitudinal torque. So the chair flies no matter which way the bike turns! Surely I'm not the first to discover the Massless Sidecar Paradox. Perhaps I should qualify this by saying, "Above a certain speed the chair flies no matter what the turn." However, it gets more even more paradoxical. The turn (and the lean) to the left would be by counter-steering -- ie, turning right -- towards the chair! But then, why wouldn't it just turn that way? So -- turn the bars left. Without the chair, that would be counter steering for a right turn. But the chair prevents a lean to the right, so I suppose the whole rig turns left. Then turn the bars right. That's countersteering to the left, and with a weightless chair there's nothing to stop a lean (and a turn) to the left. So (above a certain speed) the machine will only turn left!!?? SQ [being intentionally dense just for the fun of it]
From: ? on 7 Jul 2010 16:27 On Jul 7, 1:08 pm, sean_q_ <nos...(a)no.spam> wrote: > Imagine an extremely lightweight (but very strong) sidecar > mounted on the right-hand side of the bike (snip) Isn't the function of a sidecar to carry a female pasenger? I'm trying to imagine a female passenger which wouldn't negate your entire thought experiment by weighing 110~140 pounds or so...
From: Bob Myers on 7 Jul 2010 16:54 sean_q_ wrote: > So (above a certain speed) the machine will only turn left!!?? > Well, sure. You've described a situation which can be equally well described by saying you have a motorcycle (all by itself, since the mass/weight of the sidecar has been eliminated from consideration) which is simply somehow prevented from leaning to one side, so countersteering cannot be employed symmetrically. It'll lean (and steer) normally in one direction, but not the other - so any attempt at a sharp turn in that "other" direction (where "sharp" is dependent on speed) becomes an instant highside/roll/whatever-you-wanna-call-it. So above a certain speed, it will only SUCCESSFULLY make a quick turn one way and not the other. Bob M.
From: Bob Myers on 7 Jul 2010 17:04 Bob Myers wrote: > So above a certain speed, it will only SUCCESSFULLY make a > quick turn one way and not the other. Which, just to reply to myself, is true of a sidecar rig anyway, to a different extent, right? The thing is by its very nature always going to be asymmetrical in its handling. Bob M.
From: Bob Myers on 7 Jul 2010 17:35
sean_q_ wrote: > Isn't there some kind of plane with no wings? Where the fuselage > is designed to create its own lift? It must have a fairly high > stalling speed. And I've never seen one of these things flying > in or out of at any airport I've ever been at. A "lifting body" - the most famous example being the M2-F2, through being the craft shown crashing in the title sequence of "The Six Million Dollar Man" TV show. Also see X-24 and HL-10 for other examples. As a bit of trivia, the Space Shuttle is designed to derive some lift from its body shape. You won't see one flying in or out of any airport because they're pretty useless unless you've got (a) either a really big engine to play with - and no real reason to econonmize on fuel, or you're not worried about powered flight (i.e., it's just a glider), and (b) some reason not to want to have conventional wings (for instance, it needs to go REALLY fast at some point, as in the case of a re-entry from orbit). Since you have no real wings (and hence no wing-fuselage joint to worry about), they can be really, really strong craft for their weight. The downside, of course, is that they fly just a bit better than the standard issue brick. And yes, since they're barely "flying" in the first place, stalling and other problems are always right there... Bob M. |