Strange Behaviour in Equation library
in [HP48]
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From: Harold A. Climer on 3 Sep 2008 19:32 I teach lower level Physics labs and today we were doing a projectile motion lab. We fire a Spring Gun horizontally to find the Muzzle Velocity. Then we set the gun to a fixed angle and predict the distance the projectile will go before the gun is actually fired. I use the Equation Library to check the projectile motion results of the students. Lately however I have been getting some strange results. I have been plugging the values for Xo,Yo,Yfinal, theta, and the value of Vo. When I solve for t, etc I keep getting negative values for t, which is impossible. Is there a flag that I have forgotten about that I need to set to get the positive value for the time? Could other variables be confusing the solver? HELP!!! This has happened with both my GX and my HP50G Harold A Climer Dept. Of Physics Geology, and Astronomy U.T, Chattanooga Rm. 406A Engineering, Math & Computer Science Building 615 McCallie Ave. Chattanooga TN 37403 Harold-Cimer(a)utc.edu
From: John H Meyers on 3 Sep 2008 22:03 On Wed, 03 Sep 2008 18:32:16 -0500, Harold A. Climer wrote: > projectile motion... When I solve for t, etc. > I keep getting negative values for t D�j� vu? http://groups.google.com/group/comp.sys.hp48/browse_thread/thread/624a3ed6fcbfd75b/ > This has happened with both my GX and my HP50G Verification against the venerable and reliable HP48GX suggests that no doubt the equation solution is unfolding as it should :) http://www.fleurdelis.com/desiderata.htm Even the simplest quadratic equation often has both positive and negative mathematical solutions, whether or not each one makes "physical sense," and a purely numerical solver stops at the first number found which zeroes the equation, without interpreting the physics behind the equation (that's the user's responsibility, rather than the calculator's). Left-over data (or settings) from previous problem solutions could also play a role (see older thread above and more below), as suggested by your observation that clearing the calculator (or perhaps just all ten variables and the initial problem state) may be helpful to inspiring better "guesses" in new solutions, or else to carefully marking known vs. unknown variables, which is important to MES functioning. The detailed operation of the Equation Library and MES is covered in Chapter 25 of the 48G series Users Guide, where at the bottom of page 25-10 is found this sentence: "If any solutions seem improper, check for the following problems:" The topic continues on subsequent pages of the guide, including paragraphs about "Multiple roots," "Wrong variable states" (known vs. unknown variables), "Inconsistent conditions," "Not related," "Wrong direction," and notes about units (are we in DEGgrees mode?) If you'd like others to compare results with yours, a specific input set could be useful. @ Clear all variables and [re]start "Projectile Motion" \<< { R t vy vx v0 \Gh0 y y0 x x0 } PURGE DEG 8 3 1 SOLVEQN \>> 'projm' STO The Equation Library menu (EQNLIB) also clears variables by pressing [VARS] [NXT] [PURG] [EXIT] before [SOLV] "HP 48G Series User's Guide" [scanned PDF] http://www.hpcalc.org/search.php?query=hp48gug The above guide may contain the only truly complete reference for the operation of both the Equation Library and MES, except possibly a manual for the original HP48SX card (which I've never seen), indicating that older manuals were better constructed, as well as older calculators :) Best wishes. [r->] [OFF]
From: Harold A. Climer on 3 Sep 2008 23:22 On Wed, 03 Sep 2008 21:03:26 -0500, "John H Meyers" <jhmeyers(a)nomail.invalid> wrote: >On Wed, 03 Sep 2008 18:32:16 -0500, Harold A. Climer wrote: > >> projectile motion... When I solve for t, etc. >> I keep getting negative values for t > >D�j� vu? >http://groups.google.com/group/comp.sys.hp48/browse_thread/thread/624a3ed6fcbfd75b/ > >> This has happened with both my GX and my HP50G > >Verification against the venerable and reliable HP48GX >suggests that no doubt the equation solution >is unfolding as it should :) >http://www.fleurdelis.com/desiderata.htm > >Even the simplest quadratic equation often has >both positive and negative mathematical solutions, >whether or not each one makes "physical sense," >and a purely numerical solver stops at the first number found >which zeroes the equation, without interpreting the physics >behind the equation (that's the user's responsibility, >rather than the calculator's). > >Left-over data (or settings) from previous problem solutions >could also play a role (see older thread above and more below), >as suggested by your observation that clearing the calculator >(or perhaps just all ten variables and the initial problem state) >may be helpful to inspiring better "guesses" in new solutions, >or else to carefully marking known vs. unknown variables, >which is important to MES functioning. > >The detailed operation of the Equation Library and MES >is covered in Chapter 25 of the 48G series Users Guide, >where at the bottom of page 25-10 is found this sentence: > >"If any solutions seem improper, check for the following problems:" > >The topic continues on subsequent pages of the guide, including >paragraphs about "Multiple roots," "Wrong variable states" >(known vs. unknown variables), "Inconsistent conditions," >"Not related," "Wrong direction," and notes about units >(are we in DEGgrees mode?) > >If you'd like others to compare results with yours, >a specific input set could be useful. > >@ Clear all variables and [re]start "Projectile Motion" >\<< { R t vy vx v0 \Gh0 y y0 x x0 } PURGE >DEG 8 3 1 SOLVEQN \>> 'projm' STO > >The Equation Library menu (EQNLIB) also clears variables >by pressing [VARS] [NXT] [PURG] [EXIT] before [SOLV] > >"HP 48G Series User's Guide" [scanned PDF] >http://www.hpcalc.org/search.php?query=hp48gug > >The above guide may contain the only truly complete reference >for the operation of both the Equation Library and MES, >except possibly a manual for the original HP48SX card >(which I've never seen), >indicating that older manuals were better constructed, >as well as older calculators :) > >Best wishes. > >[r->] [OFF] I appreciate your suggestions, and eventually I will figure out what is actually going on. I have taught this same lab experiment for at least ten years in one form or another and we have used the same settings during the whole time, so I have a pretty good idea as to what the results should be. However since I sometimes can't remember what I ate for dinner the night before, I like to check things out to see if I really remember things as well as I tell my students. So the numbers I was plugging into the calculator were fairly well known to me. Vo was 3.00 m/s (PASCO Spring Gun Short Range setting) Xo = 0.0m, Yo = 0.25m above the table top. Theta 15 degrees and the final Y position is 0.0 m. This should give a time of flight of 0.318 s and an X distance of 0.922m. This what I get when I do a clear memory before I try the problem. When I use ALL soft menu key to clear the variables and re-enter the same values I get a -0.16s time of flight and a X distance of -0.463m Try this example on for size: Xo =0.0m Yo =2000.0 m Y final = 0.0m Vo = 139.76 m/s Theta = + 15 degrees This is a problem in the physics text we use for the lecture. It applies to a jet flying at an angle of 15 degree to the horizontal with a velocity of 139.76 m/s and an altitude of 2000m The question asks. 1.How far ahead of the planes present position will it's drop tank land if it is released? 2 At what velocity will the drop tank strike the ground? Assume no air friction After I clear memory and plug in the values above I get time of flight -16.84 s and a X distance of -2273.56 m The X velocity is 134.99 m/s The Y velocity is 201.39 m/s There is obviously something screwy going on here. Or maybe I have been teaching physics labs for too long. Harold A Climer Dept. Of Physics Geology, and Astronomy U.T, Chattanooga Rm. 406A Engineering, Math & Computer Science Building 615 McCallie Ave. Chattanooga TN 37403 Harold-Cimer(a)utc.edu
From: John H Meyers on 4 Sep 2008 04:29 On Wed, 03 Sep 2008 22:22:30 -0500, Harold A. Climer wrote: [re "Projectile Motion" or DEG 8 3 1 SOLVEQN ] > Vo was 3.00 m/s, Xo = 0.0m, Yo = 0.25m > Theta 15 degrees and the final Y position is 0.0 m. > This should give t=0.318 s and x=0.922m It does! > When I use ALL soft menu key to clear the variables... [ALL] doesn't actually clear the variables; it only clears their solution status, i.e. "user supplied" [dark label] vs. "calculate" [white label], while the stored values remain unchanged. Therefore, "solutions" left over from previous problems can perturb your next unrelated problem, if you don't also actually reset the stored values! Means of resetting stored values were mentioned in prior post. > and re-enter the same values I get > t=-0.16s and x=-0.463m > There is obviously something screwy going on here. "Something is happening here, but we don't know what it is, do we, Mr. Jones?" :) So let's see whether we can "get our heads around it": With no intervening use for any other problem, if I repeat the entry of the same values, then solve specifically for 't' and then for 'x' I get the identical original (positive) results. However, your new answers are valid _mathematical_ solutions, given a certain order of using the equations (did you just press R.S. [ALL] and leave it up to MES to decide which order?) The factors which can vary between answer sets are: o Stored initial values of variables. o Sequence of which unknown to solve for. o Sequence of choosing equations which have only the desired unknown yet undetermined. By leaving previously calculated values in place, particularly if they are from unrelated cases, the first of these factors has varied. If you did not specifically solve for one chosen variable at a time, but let R.S. [ALL] give the MES liberty to "walk whichever way it wants," then the next two factors may also vary. Even when you actually select which variable to solve for, the fact that MES internally "rotates" the original equation list to the position of the most recently used equation as it performs each single numerical solution may lead to subsequent selection of a different equation to solve for the same variable during the next solution, because the first equation in the rotation having only the desired variable as yet undetermined will (I think?) be the one selected, which can stir further illusory "randomness" into the results! You can see which equations were used to solve each variable in your most recent solution set via R.S. [ALL] (showing values) then [EQN] shows which specific equation was employed to numerically solve for each variable (press ENTER to further display a complete single equation). My last solution set (which I even "seeded" by storing some negative guesses :) shows that my t=-0.16s was obtained using a complete quadratic equation in variable 't'; well, no surprise that there might be both a positive and a negative value that could mathematically suffice; in fact, it might also even make perfect physical sense, if we consider that we could have been observing a projectile simply passing us where we are now, which was at another place some seconds ago, rather than that we just launched it from where we are now, is that not so? The "black dots" in menu labels also show which variables simply "took part" in the latest solution set (though not indicating which equations were used), as described further in the User's Guide. By the way, _user_ flag +63 changes the meaning of right-shifted MES menu keys (clear: variables recall; set: variables toggle state; the MUSER and MCALC functions only appear when the flag is clear). The Equation library nonetheless contains rather "tame" equation sets. If we want to exhibit an environment really so badly suited to using MES that it's like "forcing a square peg into a round hole," try "solving general triangles" with a set of equations left up to MES to more or less arbitrarily choose from to automatically solve for each variable (also in arbitrary sequence). Despite its being quite a nightmare, that very application was chosen for the latest "AUR," apparently taking little notice of how badly it actually works when put to real life use, as we once dug into at length: http://groups.google.com/group/comp.sys.hp48/browse_thread/thread/fe7f00f27c83410d/ I started my rant around January 20 2007 in that thread, and by the last post on January 23, it was getting quite clear why an MES triangle solver is a pretty horrible idea :) Another randomly selected principle of equation set design, introduced for no particular rhyme or reason: "No one remembers variables' names when they're strange" :) http://www.lyricsdomain.com/2/bob_dylan/ballad_of_a_thin_man.html http://www.lyricsdomain.com/4/doors/people_are_strange.html [r->] [OFF]
From: John H Meyers on 4 Sep 2008 04:52
Erratum: > If you did not specifically solve for one chosen variable at a time, > but let R.S. [ALL] give the MES liberty to "walk whichever way it wants..." L.S. [ALL] is "solve all"; R.S. [ALL] is "Progress catalog" (post-mortem). Maybe "Errata" applies, but as being awake right now is a bigger error, I'll correct that one next :) G'night! .. |