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RE: Tom?

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Posted by tom@digitalmoon.net on September 15, 2000 05:52:31 UTC

perhaps i should just list some charicteristics for you . lets assume that you had a bare 12 foot long 6 inch (standard,sch 40) pipe pier sticking up out of your concrete block. if you applied an 850 pound load sideways at the top of the pipe, it would deflect 1 inch, and cause a bending stress at the base of the pipe of 14,000 pounds per squair inch stress, about 1/2 of the yield stress of the pipe. unless you are into some sort of astronomical bondage, you can see that the pipe alone is strong enough for about anything that you are likely to do, also quite stiff. the rotation at the top of the pier would be about 0.6 degrees. if you could suddenly let go of the end it would vibrate at a natural frequency of about 1.7 vibrations per second, well below the threshold of human hearing, about 25 cycles is the lowest that we can hear. now, take the same pier and apply a 100 foot pound torque at the top of the pier (equivalent to hanging a 50 pound weight on a 2 foot cantilever sticking out sideways from the top of the pier). the angular rotation of the top of the pier would be 0.0117 degrees(42.22 seconds of arc). notice that this is the change due to the application of a new weight. and if you were looking through the telescope with crosshairs on one side of jupiter, the crosshairs would move roughly to the other side of jupiter. in actual practice, you are unlikely to be making these chnges while photographing, and the change would go largely unnoticed while viewing. with these parameters defined, you can now make your own calculations concerning the changes that you might make while taking a long exposure. remember, you will be making guiding corrections an order of magnitude larger than this anyway.
a few words about vibration damping, since you seem to want more info. a sprung mass will have a natural frequency of vibration in a given vibration mode. in your case, the primary vibration mode is to have the top of your pier vibrate sideways in response to an impact. without damping, the vibration will go on for ever. but all systems have friction which eventually stops the vibration. us tricky humans have figured out formulae that allow us to quantify both the vibration frequency, and the effect of damping. without shock absorbers, automobiles would be leaving the pavement far more frequently than they do(mode 1, mass of the automobile sprung by the suspension system), and the (mode 2, wheel mass would vibrate up and down uncontrollably on the suspension springs). we fix this by introducing the shock absorbers, which are chosen such that when the wheel mass is nocked up by a bump the wheel is eased back into the neutral position without rebounding further (critically damped) . under- damped, there would be some rebound, and over- damped, the wheel would return to the neutral position so slowly that it would not be ready for the next bump. auto shock absorbers use fluid damping, which produces a damping force which is a function of the square of the velocity of the wheel mass movement. on many older cars, the damping in mode 1 was very underdamped, and one would often see those huge cars almost leaping off the road under some driving conditions. ok, the concrete and sand damping that you have is sandpaper type friction damping, and is not a funcion of velocity squared, it provides a constant friction force. note that a sand runway is used to stop runaway trucks on steep downhill grades. here the mass of the sand plays some part in mireing the truck to a stop. i do not recommend trying to determine if your system is critically damped, it is adequate to understand what is going on, and just use common sense. for example, if you grossly change your parameters with new instrumentation and projects, yu may decide to use the sonotube,which would put you into a whole new category of strength , stiffness, and immunity from vibration. i hope that you do not live near a mainline raliroad track,otherwise all bets are off. good luck, tom leech

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