Haydn said: explain how some of this really does work? Like just what are the
speeds of different points on the track?
This can be done at many levels but lets not get too microscopic and include vibrations, standing waves, or any of the esoterica that is beyond the minimum required to explain the "gross" behavior. Gross behavior? If someone throws a rock at your head, you are interested in speed, direction, density, distance, and like that, not in vibrations in the rock in flight.
Now to the speed of the track. With a minimum of detail, the speed of the track is everywhere constant (same assumptions begining mech eng and physics types use with pulleys and ropes. sure, real world ropes stretch between pulleys and deform going around one under load and not all of that energy is returned to the system because of interfiber friction etc. but most pulley and rope problems neglect friction, first couple yrs of courses anyway.
Track's speed is constant but not velocity. Speed is scalar, velocity is a vector. Pick a point on the track and paint it red for ID. As it lies still, with respect to the ground from the mid point of the front wheel (tangent point under front wheel) till it is directly beneath the rear wheel (of course we are assuming flat ground constant vehicle speed etc.) it has zero speed and velocity (With respect to the ground). From the rear tangent point then up around the rear half of the rear wheel it is under acceleration (constant speed but changing direction). We are probably visualizing this last bit as circular motion around circumference of rear wheel. In that case it is constant speed and the acceleration is due to changing direction. If you reference this last bit to the ground as well it gets a lot more complicated. It is equivalent just more dificult to deal with. Consider a wind up kiddie toy bear playing a drum. Bear's drum sticks in 3D are fairly easy to visualize and not to tough a motion to describe. Now take the toy up in an Aerobat being put through its paces. The actual motion of the tips of the drum sticks, with respect to the ground is complicated by the motion of the aircraft but doesn't actually change the motion of the sticks re the bear (assuming bear can take the g's and they are negligible to his drumming.)
From the mid point above the rear wheel to the mid point of the front wheel the track travels forward at constant speed and velocity of twice the speed of advance of the vehicle (ref to the ground). This is the same speed as vehicle ref to the vehicle.
It is difficult to go into greater detail without either stating a huge s--t load of assumptions or barging ahead in hope everyone will make the same assumptions. Lets barge ahead.
The above description of gross motion is mute on the topic of belt thickness and inherently assumes that the belt, although it may distort, principly maintains the same thickness during a full circuit around the wheels. With respect to the original sugested overbelt this is probably good enough. Even if the belt was distorted, stretched thinner in some part of the circuit, compressed a bit on the inside while rounding a wheel or whatever, it would still have an effective thickness and that might not be enough different from the manufacturers specs molded on the edge of the belt to warrant discusion. Tires are thinner on the bottom, and have a sort of flat spot at the ground contact point yet it doesn't cause too much difficulty in discussions about tire size changes causing changes in speedometer vs road speed be careful you don't get a ticket. The real nitnoids practically get down to the molecular level when discussing tread squirm but most of us don't care.
Haydn asks: why doesn't a drive wheel lose it's lever arm (or maybe more accurately why doesn't the lever arm "break" as the track departs the wheel surface?
The lever arm in question is a static construct for simplification but is probably good enough. Who wants to have to think of an infinite number of infintesimally small thingies coming one after another. The lever arm acting from the center of the axel to the earth/track contact point directly beneath the front axel makes torque easier to visulalize and effective gear ratio changes with changes in track thickness easy to calculate but doesn't rotate past the vertical (tangent point of contact with ground). What is really happening (well slightly more detail) is a shear force acting tangent to all the points on the leading half of the front wheel transmits force to the track in the form of tension in line with it. This pulls the top run of track toward the front wheel (assuming the front wheel is driving not idling). A similar force on the back half of the rear wheel puts tension on the part of the track in contact with the ground (in either case - 2wd or 4wd). I think I have noticed something while discussing this that is of interest. 2wd vs 4wd tracked veh. Unless transmission of engine power and torque was too difficult due to lack of strength of materials there would be litle or no advantage to 4wd tracked vehicles unless redundant power delivery was an issue (being able to press on if one end's power transmission failed). Of course everyone else knew this last week.
Haydn said: The outer surface must expand as the track goes around the wheel,
right? Basic geometery. Etc etc etc.
Well, there has to be a bit of finagling with respect to the inner and outer track dimensions as we go from horizontal
to going around the half circle of contact with a wheel. It could be inner contraction, outer expansion, both or something else. In actual practice this probably also involves the "ground" being run across. This is comparable to the round tire on the flat road. The tire flexes, squirms, displaces dirt (off road) and on and on when transitioning to or from the contact patch to or from the rest of its rotation.
Some tracks are overlapping like fish scales and expand and open up on the leading wheel near top front then lay flat on the ground as they contact it and are closed up during the run to the rear. Some tracks look like dominoes strung on a couple strings (linkages actually) and are of steel so they don't expand or contract. Wanna get complicated? Consider the effective diameter of one of those as the edges of the dominoes sink a variable depth into the traversed terrain depending on the PSI of supportability available. Complication abounds but may not be a requirement for the level of understanding required.
For many folks the water analogy for electricity is just fine. Amps is gallons/unit time, volts is pressure, Ohms is the friction of turbulent flow through orifices or the friction inside a length of pipe. Capacitors are tanks, batteries or generators can be pumps. Check valves are diodes. Works for wiring a house or trailer lights,or an electric fence, understanding a flashlight schematic and like that. It gets complicated with three phase brushless generators. Real tough with quantum tunnelling in solid state devices or a Pentium chip or a CCD digital camera sensor.
I think for most pratical purposes, not to include designing tracks for long wear characteristics, the don't-worry-about-track-expansion-contraction level of detail is like the water analogy for electricity, good enough for most folks most of the time. Ever see a high speed movie of the motion of an engine block in a high output situation? It is quivering, squirming, vibrating, distorting in virtually every imaginable and some that probably aren't ways but in most discussions about engines, their rebuild, hot rodding, repair, etc. this level of detail is not mentioned or needed. Track expansion-contraction-distortion is important at some level but I think not at ours. Not wimping out on yoiu regarding previous debate, I really don't think it is crucial to the discussion. Not saying it might not be an interesting topic though. Pretty much beyond my level of interest though.
Off topic examples of potential interest. We are all pretty much taught the additive and subtractive theories of color as we grow up and go to school. You know, blue and yellow make green. Red, blue and green like in a RGB color monitor reproduce the full rainbow of colors visible to the human receptors. Or you can go the Cyan Magenta blah blah blah route. OK, a thought experiment. If a picture of a color scene is taken using black and white transparency film (positive film rather than negative, likek a slide but in B&W) exposed through a green filter and the exact same scene is photographed also with B&W transparency film through a red filter. The frames are developed and the resulting transparencies are projected onto a screen one at a time. First lets project the red image through the original red filter.
What do we see? A picture with contrast and rendition based on the amount of red in various objects. The picture could be said to be black and red rather than black and white when viewed on the screen. Now project the picture originally taken through the green filter on the screen but don't use a filter.
What do we see? A black and white image with contrast dependent on the green content of the original scene.
Project the two versions of the scene superimposed on the screen. What do we see?
What indeed. Maybe a pink and black picture. We have red light painting a picture on the screen through a positive transparency and white light painting the same scene through a different transparency. Shouldn't what we see on the screen at any given "POINT" be composed of from 0-100% red mixed with 0-100 white. Shouldn't that be a pink and white picture or black and pink or something like that?
Well I guarantee that it isn't The results are quite surprising. Unless you are as weird as me or have followed the career of Dr. Land of Polaroid Land Camera fame, I promise you will be surprised, astounded or something of a close resemblance.
This statement of the thought experiment is posted also under the "Off topic and just for fun" heading under the thread title of "We been lied to about color!" Go there to learn the amazing truth of how we have been lied to about color.
Another old chestnut for provoking a spirited discusion is "Why we can't reach the speed of light." Yet another new thread in the "Off topic and just for fun column" Don't get me wrong, I am a dyed in the wool treckie but separate my science facts from fiction.
I hope you all may drop by either or both threads and put in your two cents worth or just be entertained watching some of us (like me) get pummelled for our heretical beliefs.
Patrick
