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  1. #1

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    Why is there a jog in the trolley track? The math, the practical issues

    This started in the DCA project tracker thread, but I wanted to explore the math and practical issues more, so started a new thread for it. I hope nobody finds this too math-y.

    Why is there a little jog in the Red Car Trolley tracks as it transitions from the Carthay Circle to the straight Hollywood street?

    The aesthetic answer is that it makes things more interesting. The common sense (and I played with model trains) answer is that too tight a turn would "crowd" guests on the inside of the turn as well as "poke" guests on the outside of the turn. But what is the actual math? How much extra crowding/poking would we get if the turn radius was tighter?

    I think the only variables needed are the radius of the turn and the wheelbase of the trolley. The width of the trolley carriage is important from a practical standpoint, but doesn't change the math (how many extra inches the trolley would crowd on one side, protrude on the other).

    I've done my own little bit of math. Hopefully mycroft16, flynnibus and TreoFred can all chime in.
    Last edited by Mojave; 09-01-2011 at 11:57 AM.

  2. #2

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    Re: Why is there a jog in the trolley track? The math, the practical issues

    I think it's as simple as this: the minimum radius of curvature the trolley can navigate is being applied in the layout of the track. The geometry of the street in this area could not accommodate not having that "bump"...any attempts to eliminate the "bump" would push the track onto the curb in front of the carthay (the area of minimum clearance mentioned previously by Fred). They chose to keep the curbs where they wanted them and adjust the track.

    Btw, any attempts at math are going to get very complicated. Those aren't just circular arcs (assuming this is like train tracks)...there is a spiral transition at the end of each arc.

    EDIT: Any vehicle fixed to a train track cannot safely or comfortably negotiate the transition from a straight line to a circular arc. The vehicle will experience a sudden increase in centripetal force and either cause discomfort to its passengers and damage the mechanics of the vehicle or simply derail. The spiral eases the vehicle into experiencing centripetal force, avoiding the jarring. Think being launched on Rock n Roller Coaster vs. accelerating your car to 60 mph normally.

  3. #3

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    Re: Why is there a jog in the trolley track? The math, the practical issues

    Quote Originally Posted by John Goodman View Post
    Btw, any attempts at math are going to get very complicated. Those aren't just circular arcs (assuming this is like train tracks)...there is a spiral transition at the end of each arc.
    Rule #1 of math and physics and science in general really: "Assume that the chicken is a sphere." It makes the math easier. In essence, boil the question down to the simplest form and solve that then extrapolate back up the more complicated situations.

    Our revels now are ended. These our actors, As I foretold you, were all spirits and Are melted into air, into thin air: And, like the baseless fabric of this vision, The cloud-capp'd towers, the gorgeous palaces, The solemn temples, the great globe itself, Yea, all which it inherit, shall dissolve And, like this insubstantial pageant faded, Leave not a rack behind. We are such stuff As dreams are made on, and our little life Is rounded with a sleep. mycroft16 on Twitter

  4. #4

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    Re: Why is there a jog in the trolley track? The math, the practical issues

    I'm not a math or trolley expert, but I think this is fairly common.

    It might be unclear in the following example, but this is the cable car line that runs down Market St in SF.



    It makes a left onto Embarcadero (bottom right) and pretty much straightens out (top center). BUT, you can see how it kind of dips out and sways back in. It must have something to do with turn clearances, but the example I've used here is much more subtle due to the space available. The one in DCA is a smaller, more confined area so it's just more noticeable.

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    Re: Why is there a jog in the trolley track? The math, the practical issues

    Quote Originally Posted by mycroft16 View Post
    Rule #1 of math and physics and science in general really: "Assume that the chicken is a sphere." It makes the math easier. In essence, boil the question down to the simplest form and solve that then extrapolate back up the more complicated situations.
    Oh, I know. I have a degree in civil engineering...we ignore theory in favor of empirical constants. Why solve a third order differential equation, we argue, when you can slap a 1.2 on some elementary physical relationship?

  6. #6

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    Re: Why is there a jog in the trolley track? The math, the practical issues

    Quote Originally Posted by John Goodman View Post
    Btw, any attempts at math are going to get very complicated. Those aren't just circular arcs (assuming this is like train tracks)...there is a spiral transition at the end of each arc.
    Awesome, we have someone even more qualified to help answer this question!

    Spiral transitions? Goes to look this up... But will that have a significant difference in the calculation?

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    Re: Why is there a jog in the trolley track? The math, the practical issues

    Nope! You can do it with circles with...eh...98% accuracy. I do not, however, feel like solving this problem. I'll upload some useful info for whoever wants to do the math in a bit.

  8. #8

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    Re: Why is there a jog in the trolley track? The math, the practical issues

    Get at it!

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  9. #9

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    Re: Why is there a jog in the trolley track? The math, the practical issues

    Please excuse the crudity of this model, I didn't have to time to build it to scale or to paint it...

    So, we have our Jolly Red Car Trolley Thingie (I've taken the liberty to extend the lines from the side view of the bogies to extrapolate, at a high level, the actual position of the rotational axis of each bogie):



    And let's place it on the tracks (Yes, this old blueprint is no longer truly accurate but that'll do for now... I hope !)

    Notice, as was mentioned by Flinnybus, John Goodman and others, that the trolley being largely a rectangular shape with two independent bogies rolling tangentially to the track, it's position can be extrapolated as being in alignment with the two center points of said boogie. And because it is squarish, it doesn't exactly follow the contour of the curve.



    Now notice that within the circle per se, the body of the vehicle tends to go INSIDE the circle (which could be a problem if you had intented to place, say, a trolley stop somewhere on the curbs and, to support people in wheelchairs, you wanted to have a gap as small as possible so as to allow your vehicle to be accessible.) Now, getting into the circle is not the problem thanks to the Euler Spiral used in devising said access. (Obviously, right? I mean come on, I totally called it! )



    So, at that point, you might want to check how far you are from the various curbs and determine for yourself where the clearance might be a problem . Tada. done.... for part 1 !!!!

    And now, for the part 2 reason: the physics and the need for authenticity in a Fantasy Land (because, no matter how much pixie dust you use, it seems that some laws don't like to be bent)

    As you're clearing the bend and doing your 90 degree (tangentially again, considering how you'd be exiting the circle to make that turn), you end up on the following path.


    Now, you have forward momentum of course. But a second ago, that forward was in a another direction entirely (in fact, at the beginning of your turn, that forward was quasi 90 degrees away from where you want to go now). If we zoom in on that situation and add some vectors (equally not to scale because come on I DO have a life AND a job, I assure you, outside of this forum! promise!), we could show the following:


    In Red is your current direction and thus, the force vector of your movement. In Green is where you ultimately want to go. In Blue is the counteracting direction you will take momentarily. And yes, vectors should have arrow heads but I have a very lousy paint program. Called paint. So there. Just imagine for a second that the Alamo is replacing the Hyperion and it becomes painfully obvious in which direction all arrows are flying to.

    As you can see, throughout the curb, the trolley not only wants to move forward, it pretty much wants to leave its rails. The reason it stays there is the good old application of Newton law of action and reaction which states that as the trolley is pushing on its rail to leave them and go vacationing towards Award Weiners, the rails seriously deny said motion and apply a concerted push back for the trolley to stay on track (pun intended). This is often call Centrifugal Force (incorrectly) by trivia geeks trying to impress others and random people having been squished by their significant others while riding the Tea Cups.

    The force applied is in direct relation of the kinetic energy of the body in motion, aka the body of the trolley and the many bodies inside (Note: the body of the trolley should represent most of the mass but lets remember Professor Al Lutz Theory of Theme Park Patron Body-Mass Expansion, which states that Small_world_boat_bottoming_out is a derived function of the Fast Churo Transform). In our case, the kinetic energy can be expressed as Ec= 1/2 m*v2 (sorry, best I can do formulawise unless I draw them too !) This formula of course is non relativistic and as such only applies if the trolley is traveling at speed much less than the speed of light of which, although build out of BVS is not complete, I will gamble on. If said gamble is wrong though, I shall recommend to avoid walking on the street at all cost. I would also recommend upgrading the status of the Red Car Trolley to that of an E-ticket immediately.

    It's been a while since I put a picture so I'll add one now.


    I've added in yellow the projected vector of force that tries to derail the trolley and this conversation, yellow being the international color of fear, jaundice and most people with acute liver issues. I know that these are not the right angles but I still don't have any decent paint program for illustrating and I will choose any inertial frame of reference I may please, thank you very much. Now, if we remember our kinetic equation, speed shouldn't be too high so a large part of the energy is coming from the large mass in motion. At that point, not only does the trolley want to take a detour and go see the Muppets (and frankly, who could blame him? Muppets are awesome!) but while most people seating towards the fountain are feeling increasingly pressured by the extraordinary forces currently placed on them, people seating in front of them on the other side of the trolley are suddenly contemplating forcefully jumping on their laps (Note: since we're potentially going very slowly, please consult a lawyer on the validity of your case before suing the park for excessive pressure or forceful jumping... unless the person seated in front of you stubbornly refuses to share their churro... in which case the use of forceful jumping is not only legitimate, I believe it is in fact covered in the Bill of Rights (to Churro) ).

    What could possibly save us from said disaster? Tune in next week for our climatic ending to this tale, or keep on reading, but really it's your choice, ok?

    The bodies in motion feel the force being applied to them which triggers acceleration and eventually momentum. HOWEVER, there's is inertia (the tendency of an object to resist any change in its motion or rest, and also the reason why I stay and watch Oprah sometimes if the remote control is too far from the couch). As they start accelerating in a given direction, Imagineer simultaneously forcing the trolley into the aforementioned JOG of this thread's name's fame, save the day! Immediately, counter force is being exerted, counter body motion is being felt and 'permanecer sentado por favor' is once again fully available to everybody in the cabin ! This would be the little blue arrow projection that negates most of the yellow one

    And since yellow and blue make green (in subtractive color, but once again my pictures, my referential, my rules !), we're all go and lined up with our little green path we originally intended to commit to (however short of a commitment this maybe of course).

    At this point, I sure hope this has brought you all the answers you were currently looking for on this particular issue. And by I hope, I mean for your own best interest... Because if it hasn't... I will hunt you... and I will find you... and then...

    mwahahahaha
    Last edited by TreoFred; 09-01-2011 at 04:42 PM.

  10. #10

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    Re: Why is there a jog in the trolley track? The math, the practical issues

    I love this thread.
    "And after a long time or a short time, Ivan and the Wolf came at last to the home of the Firebird..."

  11. #11

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    Re: Why is there a jog in the trolley track? The math, the practical issues

    um... what? lol

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