Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!watmath!clyde!caip!ll-xn!cit-vax!elroy!smeagol!usc-oberon!sdcrdcf!lwall From: lwall@sdcrdcf.UUCP (Larry Wall) Newsgroups: net.puzzle,net.sci Subject: Re: A heavy problem (results) Message-ID: <2939@sdcrdcf.UUCP> Date: Wed, 6-Aug-86 19:50:17 EDT Article-I.D.: sdcrdcf.2939 Posted: Wed Aug 6 19:50:17 1986 Date-Received: Sat, 9-Aug-86 04:16:59 EDT References: <1033@mmm.UUCP> <3093@ism780c.UUCP> Reply-To: lwall@sdcrdcf.UUCP (Larry Wall) Organization: System Development Corporation R&D, Santa Monica Lines: 72 Xref: watmath net.puzzle:1954 net.sci:1469 In article <1033@mmm.UUCP> cipher@mmm.UUCP (Andre Guirard) writes: >>In fact, the raven says he can't think of _anything_ that would be >>taller and thinner under higher gravity. If anyone can think of >>something, or can refute the raven on some point, I'd be happy to hear >>of it. In article <3093@ism780c.UUCP> tim@ism780c.UUCP (Tim Smith) writes: >Visitors from another planet. Only when dangling from a tree limb. A spring would serve as well. Or anything else that stretches when it hangs. Also, I think the raven is wrong about things that are buoyant, such as balloons and flames. The higher gravity would induce a bigger gradient of pressure from the top of something to the bottom, causing more vertical force. I'm not sure how this would affect the shape of the balloon envelope proper, but the cables would certainly stretch more. The higher air pressure might well collapse the balloon partially, like a stratospheric helium balloon looks at sea level. The flame should rise faster, creating a lower pressure due to the venturi effect, resulting in a narrower flame. Atomic mushroom clouds might be taller and skinnier for the same reason, and also because the initial fireball would be smaller and hotter in a denser atmosphere. Buoyant but cohesive objects will also have greater tidal effects. This might tend to stretch out the shape of the balloon envelope, if ever so slightly. Thinking a bit more about the flame in 0 g being round--surely you believe that the transition from a round flame at 0 g to a long flame at 1 g is continuous? I doubt there's some amount of gravity at which the flame suddenly springs from being round to being long (catastrophe theory notwithstanding). Given this presumption, is there any reason to suppose the the transition from round to long flame stops at 1 g? Maybe the length of a flame peaks or plateaus out at 2g. Here are some other, rather esoteric, candidates: * An arch of a given mass, cross section, and lateral force. * A rocket of a given mass with a given amount of drag, due to denser air. * A valley, whether carved by water or ice (presuming the rock is strong enough to support steep sides), because it is carved faster at the bottom in proportion to the weathering of stone on the sides, which is more related to the annual freeze/thaw cycle. * Certain trajectories, optimized for certain things, AND taking into account air resistance. I'm not sure about this, but how about something like a minimum energy trajectory necessary to put a cannonball over a cube. The increased air resistance would tend to truncate the flight, so the minimum energy trajectory might involve blasting it higher and letting it drop straight down the other side, a shape more approximating a right triangle than a parabola. I don't have the math, and could be all wet. A rough sketch: . . . . . . . . ._________. ._________. . | | . . | |. (NB: Dot spacing does . | | . . | |. NOT represent speed.) . | | . . | |. . |_______| . . |_______|. Thin Air Thick Air (Note when I say minimum energy trajectory, I don't mean that the energy would be the same on both planets. It would obviously take more energy to get over the cube on the planet with higher gravity.) Enought of this. Anybody want to give me a ride to such a planet so I can check it out? Larry Wall {allegra,burdvax,cbosgd,hplabs,ihnp4,sdcsvax}!sdcrdcf!lwall