Roller Coaster - B

Original Authors for NSO Summer Camp

Patrick Chalker

CeAnn Chalker

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December 3rd Construction

Presentation

Jeff Anderson

MSO Board Member

NSO Tech Committee Member

Former National Roller Coaster ES

Current National Flight ES

Retired Ford Engineer

janderson@twmi.rr.com

248-476-6341

Disclaimer

• Devices picture in this presentation are not all legal for the current year’s rules.

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• Currently there are no rule clarifications for Roller Coaster. www.soinc.org/events/rules-clarifications

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• I’ve added to this presentation a focused section on design and construction. I’ll focus on that, not the original materials, though I’m happy to answer questions as I can.

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What is Roller Coaster?

• A Device that guides a ball/sphere using gravity.
• Has a specific target time
• Can have both jumps and loops.

Construction Rules

• Dimensions - Max 30 cm wide x 60 cm long x 60 cm high sitting flat

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• The ball/sphere must be visible at all times

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• All power for the device must be from position due to gravity
• No rubber bands, no springs, no added energy, no magnets

Construction Rules – Cont’d

• Start & Finish Lines –
• Only 1 Clearly labeled Start Line
• Only 1 Clearly labeled Finish Line
• Both lines must be perpendicular to the direction the ball/sphere travels on the track
• The position of the start and finish lines cannot change after impound

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• Height is measured at the end of each run

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• Track can be swapped or modified before each run

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Gaps

• Open horizontal span of at least 5 cm

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• Gap must be clearly labeled Start and End

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• The labeled track must be at least 0.5cm above the next surface below it

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• Up to 2 gaps in the device can earn points

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• Gap can not end at a wall

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• Must be a minimum of 5 cm of unbroken track at the end of every gap

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Gap Measurement

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• Measurement boundaries of the Gap are from the physical edges of the Gap

Loops

• A Loop is a continuously concave section of track
• May contain 1 loop for Loop Score

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Point of Intersection – POI

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• The POI is defined as the point where the entry to the loop and the exit of the loops appear to self-intersect

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• The POI must be clearly labeled point that can be measured from

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• The height of the loop is from the POI to the highest inside point of the loop.

Not Allowed

• Magnets, springs, rubber bands, electrical and electronic devices

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• Moving or adjusting the position of the start and finish lines

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• Bouncing the vehicle as a part of the gap

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Data & Design Log

• Data Log
• Recorded Data for at least 10 previous test runs prior to competition
• Required parameters
• Run Time in seconds
• Gap and Loop Score(s), in centimeters, if attempted
• Qualitative or Quantitative observations on an aspect of the device that, once modified, changes the time of the run
• Design Log
• List of materials used to construct the device
• Labeled Diagram or picture identifying the Start Line, Finish Line, and if included Gaps and Loop and how they are measured.
• Identifying information for the team
• Additional requirements if a 3-D printer, laser cutter, CNC machine or similar device was used

Data & Design Log �Labeling & Units of Measurement

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• Front Cover on the Log
• Must have a front cover labeled with the team name and team number for the current tournament

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• Numerical values
• All values should be labeled with standard units (e.g. SI or English) appropriate to the dimension being measured.
• SI units should be the default standard.

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Competition

• Impound at every Competition
• Target Time between 30s and 60s
• Regionals/invitationals – 5s intervals
• State – 2s intervals
• National – 1s intervals
• During the 8-Minute Competition Time
• May do as many practice runs as the competitors want
• may adjust the device, swap track, change the ball/sphere, practice
• Scoreable Runs must be declared prior to the start of a run (up to 2)
• Participants may not touch the device during a scorable run

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Where is the end of this gap?

• The 8-Minute Competition Time stops while the Event Supervisor measures the device
• the Scorable Run is included in the Competition Time
• If the second Scorable Run begins before the 8 minutes is up, the run is allowed to go to completion
• There are no Failed Runs
• if a ball/sphere does not cross the finish line the team does not get a time score.
• The still receive a height score and scores for any gaps/loops completed.

Competition – Cont’d

Scoring

Run Score

Height Score + Time Score + Gap Score + Loop Score

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Height Score

2 x (60 – Roller Coaster Height in whole cm)

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Time Score

Time Bonus + Time Penalty

Time Bonus:

5 points for every whole second up to Target Time

Time Penalty:

-5 points for every whole second after Target Time

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Gap Score

4 points for every whole horizontal cm

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Loop Score

6 points for every whole vertical cm measured from the POI to the highest inner point of the loop

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Note, there are no gaps on this device!

Data and Design Log

• Data Log Penalties

Incomplete 10% - Missing 20%

• Design log Penalties

Incomplete 5% - Missing 10%�

Tiers

• 1 - run with no violations
• 2 – construction or competition violation
• 3 – Roller Coaster or ball/sphere not � impounded during impound period

Scoring – Cont’d

Construction - Slowing Methods

Speedbumps

• flaps, notches, different textures

Alternate track paths

• Skipping sections of track

Alternate track parts

• whole sections of track swapped out

Funnels or half pipes

• back and forths

Swap vehicle

Materials & Construction

Scrap!

• Paper, wood, tubing, toy parts, cardboard, PVC pipe, aluminum rails, anything students can find
• Try to keep consistency in entire coaster

Strength in Transport

• Reliable and sturdy transportation box
• Avoid overly sensitive parts

Construction, �an engineers approach.

Warning:

• This is everything I can think of to maximize score, top results.
• If you have a beginning or small team, you will need to pick and choose which portions you take on. I will discuss where those opportunities are

Before you build ANYTHING, analyze/ understand the problem!�EXPLICITLY AND WITH NUMBERS!

• Note, I’m going to guide you through this. YOU should guide your students to figure this stuff out! Don’t give them ‘answers’, help them discover the answers!
• Goal: Move a ball through a sequence of tasks.
• Constraints:
• Limited energy, only gravitational potential energy available to accomplish all tasks.
• Limited size available, 30.0 cm wide by 60.0 cm long by 60.0 cm high. Note, by convention, this is a rectangular prism, becomes important when measuring.
• Max run time, twice the target time, up to two minutes.
• Start device is ES provided #2 pencil
• One loop, two gaps within available space and with initial energy

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Analyze/understand the problem (cont)

• Tradeoffs:
• The rules and scoring algorithm against the constraints REQUIRE you to think about tradeoffs
• Max Height Score: zero height roller coaster, 60*2=120 points, but you won’t get ANY time, gap or loop points. So, you want to consider trading it off for additional points
• Time Score: between 30*5=150 and 60*5=300 points.
• So, you need enough height to get at least 600 seconds.
• From past tournaments I can tell you that it is around 10 cm to accomplish that reliably.
• Is that a good tradeoff? (60-10)*2=100 points, loss of 20 to gain 150 to 300 points, pretty easy decision. YES!

Analyze/understand the problem (cont)

• Tradeoffs (cont):
• Gap Score:
• Physically, you are limited by the available space. The longest path to jump in your device is along the diagonal of the base. The base is 30 by 60 cm. From the Pythagorean Theorum, diagonal = sqrt(30*30+60*60)= 67 cm
• You need 5 cm at the end (per rule), plus some distance at the beginning, say 10 cm (this is an approximate, your team will need to determine this experimentally). For 50 cm max gap.
• Query: Do you have enough energy to do two 50 cm jumps within 60 cm? I don’t know, that will take experimentation, I’ll get to that later. I have seen such jumps in previous years with similar dimensions.
• Two of those gives 2*50*4=400 points
• Tradeoffs:
• Height: Jumping gaps requires energy to accelerate your ball, which requires height. 400 points vs possible 120, net 280 if you have to give up all the height score seems like a path to pursue
• Time: Turns out you DON’T need to trade this one off. Though the reason isn’t immediately obvious and depends on your design. IF you put the timer at the beginning, you will trade height for gap jumping energy. BUT, if you put it at the end, there should be enough energy remaining to accomplish most timing designs. Again, more about this later.

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Diagonal layout

Analyze/understand the problem (cont)

• Tradeoffs (cont):
• Max loop score:
• Again, physically, you are limited by the available space. But this time, no math, its just the height.
• BUT, you can’t use all that height because you need the marble going fast enough across the top to be held to the track by centrifugal force. Since height energy plus velocity energy must be constant, if you loop back to the top of the device you’ll be going zero speed and fall out of the loop.
• So, how much height DO you need to complete a loop? I don’t know, but here is an experimental approach to figure it out: https://www.sciencebuddies.org/science-fair-projects/project-ideas/Phys_p036/physics/marble-roller-coaster-loop-the-loop or https://www.scientificamerican.com/article/make-a-marble-roller-coaster/ Note, the answer will vary depending on track materials, more on that later too.
• Just for an example, lets suppose it takes 10 cm of height above the top of the loop to complete the loop. This leaves 50 cm for a loop maximum for 6*50=300 points.
• Tradeoffs:
• Height: Jumping gaps requires energy to accelerate your ball, which requires height. 300 points vs possible 120, net 280 if you have to give up all the height score seems like a path to pursue
• Time: Again, turns out you (probably) DON’T need to trade this one off. Though the reason isn’t immediately obvious and depends on your design. IF you put the timer at the beginning, you will trade height for looping energy. BUT, if you put it at the end, there should be enough kinetic energy remaining to accomplish most timing designs. Again, more about this later.
• Gaps: Hmm, this one isn’t so obvious and really deserves some thought/experimentation to determine. BOTH have kinetic energy remaining at the end of the task, is it enough to either follow a loop with a jump or jump with a loop. Probably SOME, but how much will very much depend on details and experiments your students will HAVE to run!

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Analyze/understand the problem (cont)

• Why are gaps, loops and time not clear tradeoffs like height is?
• Kinetic energy (velocity energy) plus potential energy (height energy) is a constant.
• At the beginning of the run all you have is potential energy. Ball isn’t moving.
• At the end, all you have is velocity, a calculatable amount from the starting height. It is this velocity that lets you jump gaps & loop loops.
• In an ideal world, the velocity you use for a loop is all recovered, same for gaps. So, there shouldn’t be a tradeoff.
• Timers work by either slowing the ball (waste energy) or lengthening the path (which increases drag loses, again wasting energy). Which is why you want them last.
• Except that is an ideal! In real world there is DRAG which constantly steals energy from the system.
• ENERGY CONSERVATION IS EVERYTHING to get more tasks done.

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Enough analysis (for now, you’ll never actually be done!) Time for testing.

• First, as an engineer, I NEVER start by testing the whole system. SO DON’T leap into building a complete system!
• FIRST, test subcomponents to understand them thoroughly and build up a complete system piece by piece. Testing each subsystem along the way MANY times.
• Where to start. Remember I said energy conservation is everything? Well, that means we start with determining what track cross section and ball which causes the minimum drag.

Testing: Track configuration

• Track cross sections:
• Three characteristics desired:
• Minimum drag
• Ease of construction
• Accurate running (ball not jumping out, consistent jumps, consistent timing.
• Possible cross sections (not exhaustive):
• V, should be accurate, should be low drag, straight easy to build, curves harder
• Parallel bars, should be accurate, should be low drag, harder to build consistent gaps
• Half tube, probably less accurate, may be lower still drag, straights easy to build, curves harder
• Full tube (not allowed for loop), probably less accurate, since must be clear, I suspect higher drag, easy to build
• Square/flat bottom, much less accurate, not sure about drag, easy to build
• Other?
• Track material, important because it has effect on drag, soft is bad

Rails

V-Section

Half Tube

Tube

Flat Bottom

Ball position variable

one or two contact points

Only one ball position

Two contact points

Ball Position variable

One contact point

Testing: Ball Selection factors

• Ball selection:
• Characteristics desired:
• Minimum air drag points to denser material and larger size
• Minimum track drag points to harder materials
• Fast Acceleration points to Solid balls, not hollow spheres & smaller balls
• Size, larger size to minimize air drag effect is offset by practical considerations, a bowling ball might be better otherwise, but wouldn’t fit through the device!
• Where to start, engineering judgement says
• Marbles, hard surface good for drag, convenient sizes available
• Ball Bearings, hard surface good for drag, convenient sizes available, denser than marbles
• Wood balls, too light, probably high drag.
• Rubber balls, depends a lot on the ball. Harder, denser balls like super balls better than soft. But probably more drag than metal or marbles.

Testing: How do you sort that all out, test alternatives and decide based on DATA!

• Make a test device:
• Obtain/make a number of straight, equal sections of track, varying materials and cross sections. Say 1-2 meters long.
• Prop them all up side by side say 10-20 cm on one end. Not too high, you want the balls rolling slow enough to time them and tell differences
• Now, get a bunch of balls of different types. Preferably as many of each type as you have track alternatives.
• Now, start racing the balls down the tracks.
• Start by racing all ball bearings of one size down each track, record times from start to finish. Oh, make sure you release them like in the event, not adding energy!
• Now race another size ball bearing. Then some marbles. Etc. Look at your data, see if one track configuration is consistently fastest for a given ball type.
• And of course you should repeat each configuration 2-3 times to average out variability or uncertainty.
• Once you have a good track, do the same with the ball types on that track to pick the fastest.
• From all this data you can now select a track cross section and ball with minimum drag losses to start designing your next level tasks (or in engineering terms, subsystems).

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Testing Alternative Tracks and Balls

Testing: Loop sub-system

• I’m going to refer you back to those links from earlier:
• https://www.sciencebuddies.org/science-fair-projects/project-ideas/Phys_p036/physics/marble-roller-coaster-loop-the-loop
• https://www.scientificamerican.com/article/make-a-marble-roller-coaster/
• But we’re going to change some things.
• First, don’t use the foam tubing from those examples. Use the track and ball combination you found previously to have the lowest drag!
• Second, don’t vary the height for a fixed loop, vary the loop size for a fixed (60 cm anyone?) starting height. Find the largest loop you can do from that height for your track and ball.
• Note, don’t assume a circular loop is best, see https://www.youtube.com/watch?v=zLQuf8N-mGw But remember how the loop is measured! From POI to top! This video claims such a loop loses less energy, which may give higher total height, or more remaining energy for other tasks, don’t lose this info on YOUR system.
• And as always, don’t take data from one run! Take data from many runs in each configuration, make sure your results are consistent and predictable.

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Loop Test Fixture

Start

Acceleration Ramp

Curve into loop

Test Loop Sizes

On to Timing or Gap?

Testing: Gap sub-system, first gap

• Here is an interesting discussion on exactly this problem:
• https://www.physicsforums.com/threads/what-shape-ramp-for-maximum-marble-jump.644609/
• Not a full answer, but things to consider as you run this experiment!
• Setting up the gap experiment
• You should use the same kinds of disciplines and thought processes as the examples from the loop testing links
• Again, you are going to use YOUR track and ball for best efficiency.
• You are going to start with targeting that max geometrically available jump from earlier. Start with ONE 50 cm gap. Trial different height start points and launch angles angle to just cross the gap.
• Note, you may want to try different height landing zones from launch point.
• Note also, this is where accuracy of ball path, especially the launch point, is CRITICAL to make sure you hit the launch zone EVERY time.
• If you just CAN’T get a 50 cm gap, try 45 cm. Shorten until you have a gap you CAN hit consistently (multiple trials always!) within the allowable space,

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Trial different lengths until you can make gap

If can’t make this gap, shorten

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Launch and Land at 45 degrees

65 cm wide to fit diagonal

60 cm tall

Turn back around

to next task

Testing: Gap sub-system, second gap

• All the things said previously about methods and practices of testing still apply!
• Setting up the gap experiment
• Here’s where things get harder, because what you do here depends on what you learned and decided about on the first gap. In fact, it may require you to go back and redesign the first gap.
• Starting condition. You can no longer start from an arbitrary point. Your starting point MUST be your first gap! You won’t be able to consistently recreate the starting conditions for the second gap without a LOT of sophisticated equipment, much easier just to use the first gap to start the second.
• Note, you’ve probably used all of the device space with the first gap, so you’ll need to turn the ball 180 degrees maintaining as much speed as possible. Again, trial different launch angles, possible further height loss to gain speed, etc to hit that theoretical 50 cm. If not possible, again, shorten target. Also, consider changing the first jump to increase exit speed for use on the second gap!
• And, as usual, you have to run each configuration multiple times to results against variability.
• And again, accuracy of launch is critical to hitting the landing.
• Finally, consider landing space design to not lose speed for next task. Don’t land on a flat, land on a down slope.

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Testing: Timing sub-system

• I’m aware of four approaches to timing:
• For all of these, don’t stop testing until under full run conditions, you can hit your target time multiple times in a row!
• Long, low ramp.
• Typically, a flat board with bars across it to cause the ball to zig-zag back and forth slowly.
• Time controlled by changing ramp angle
• Doesn’t take much height, but starts with a slow ball
• One BIG drawback from my observations as an ES.
• The ball rolls so slow that it is highly likely to be stopped by any bump, bit of grit, or other irregularity in the track!
• I do NOT advise this approach.
• If you do, run it LOTS and make sure you have NO stoppers.
• Seriously, don’t consider it good until you can run successfully at all times between 30 and 60 seconds consecutively 10, 20, 30 times with NO stops!
• Funnel
• Ball enters at the top of the funnel at an angle causing it to spin around many times until it exits the funnel at the bottom.
• Can use a ball at speed coming out of gaps or loops so no height required
• Time controlled primarily by changing the angle of entry. You could change out funnels of different diameters, or different slopes for discrete time changes.
• Generally placed at END of all other tasks, calibration strongly dependent on up stream conditions, so if you change those, you’ll need to calibrate funnel time all over again. As a result, it is typically designed and calibrated LAST.
• Consistent performance requires an accurate way of introducing the ball to the funnel.

Testing: Timing sub-system (cont)

• I’m aware of four approaches to timing:
• For all of these, don’t stop testing until under full run conditions, you can hit your target time multiple times in a row!
• Half Pipe
• Essentially a distorted funnel, split open. Ball enters at top at angle to pipe, causing it to roll back and forth across the pipe many times until it exits at the bottom.
• Can use a ball at speed coming out of gaps or loops so no height required
• Time controlled by angle of entry, point of entry along pipe, width of pipe, or curvature of pipe
• Generally placed at END of all other tasks, calibration strongly dependent on up stream conditions, so if you change those, you’ll need to calibrate funnel time all over again. As a result, it is typically designed and calibrated LAST.
• Consistent performance requires an accurate way of introducing the ball to the half pipe.
• Independent ball delay system
• This may be controversial, so use at own risk. I’ve allowed it in past, and under these rules I’d still allow it. BUT, I’m NOT your ES!!!
• I’ve seen devices that were operated by separate system to hold the ball at the start and then release it after a given time. I can’t give much design guidance, except when it releases the ball it MUST NOT ADD energy! Also, it must be triggered by the ball itself after release by the ES provided #2 pencil.
• The advantage, engineered properly, it is easy to calibrate, costs little to no height energy, and is entirely independent of the other sub-tasks (which is generally strongly desirable in engineering!)

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Integrating your subsystems

• Here, I can only give you general guidance. Only your creativity, verified with data can tell you what is best.
• Do you want a simple, but reliable device. Consider only using one-subsystem, or maybe two. I’d suggest in this order.
• Loop only: give up all height and time points, but easy to build consistently. Max score in 300 range
• Timer only at minimum height: Best possible score around 250 to 400 points depending on time target. BUT, hard to get consistent.
• Gaps only: consistent score in 400 possible, but construction challenging, and consistency harder than loop.
• Loop and timer: easy, consistent combination. 450 to 600 points depending on time target.
• Gaps and timer: more challenging, but 550 to 700 points possible.
• Gaps, loop and timer: All out, most challenging, most points possible, 850 to 1000 points.
• Note, I quickly drop any consideration of height. It has so few points, that you only need 30 cm of gap score or 20 cm of loop to ignore it. Either is easy to achieve

Integrating your subsystems (cont)

• For loop and gap combinations, you have several possible ways to lay them out.
• Gap-Gap-Loop
• Gap-Loop-Gap
• Loop-Gap-Gap
• I have no guidance on which to choose, but seat of pants... From what I’ve seen with gaps previously, you can have a lot of speed left after the gaps to do a loop, so I’d start with the first alternative. But without data, that is worth what you paid for it!

General construction considerations

• As for all size limited events, DO NOT PUSH THE BOUNDARIES HARD!
• An extra couple of millimeters in the device will not give enough points to recover from being tiered.
• I strongly recommend you build your device 0.5 cm under the limits.
• Be careful of fasteners sticking out of sides!
• Remember, the dimensions are a rectangular prism. At the highest levels, the ES will use a square frame to check your box.
• Don’t just measure along the edges, make sure the edges are square to each other!
• Better, since the longest dimensions are the diagonal, don’t build a rectangular structure at all. The best devices I’ve seen are a vertical board oriented along the diagonal of the allowed dimensions.
• Build a rectangular box gage yourself and have the students check their device so they understand how it fits!

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Previous Year Gage

Twisted Device

Corners outside gage!

General construction considerations (cont)

• Build leveling feet into your device. Floors are uneven, the ball WILL run differently if the device is tilted. Particularly the time, but also the gaps.
• BUILD STURDY!
• Once dialed in, you DON’T want the device twisting or changing shape.
• Biggest problems I’ve seen with failed runs both gaps and timers, has been device twisting out of shape from when tested at home.
• There is NO way to fix that within the 8 minute run time.
• Make sure your foundation is STIFF. It should not move or flex under transport.
• Make sure you anchor the track so it does not move. Particularly the beginning and ends of gaps, and start of timers. If it needs to be adjustable, make sure the adjustments lock solidly. Consider screw adjustments, not pushing or pulling.
• The track itself should be stiff. You can’t get consistent results if the track is moving around.

General Testing considerations

• Testing approach. This slide should be in bold, underline, highlighted and repeated throughout this presentation, but space prohibits.
• You must test LOTS to get consistent repeatable results, which is critical for performance at competitions, and is the real lesson of this event!
• Take data EVERY time. Lots, write it down in an organized fashion.
• As stated already, test the subsystems independently first until you can get consistent performance.
• When you integrate the subsystem, test the first task until it performs consistently. Consistently means MANY times, not 1 or 2, but 10, 20, 30 or more. Do not even look at the down stream tasks until you have consistency with the first task
• Then, move on to the second task. BUT, it MUST be started by running the first task. You cannot test the second gap by starting the ball at the end of the first!! The initial conditions are all wrong. And that is why the first task must be consistent BEFORE you bother with the second!
• And so on through the tasks. All upstream tasks must be run every time, and all must be consistent!
• If you find a downstream task really needs to change an upstream task, you have to back up and start that cascade again!!!

Printable designs.

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• Paul wants me to point you to printable paper designs, so here you go:
• https://paperrollercoasters.com/

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• What, you detect some reluctance in my tone? Yep, here’s why:
• You can get a score, but not consistently, and you reduce learning opportunities considerably.
• They meet NONE of the above engineering considerations I’ve just spent time on.
• No analysis or thought on the problem by the students
• Definitely not low drag track and ball choice
• NOT sturdy or consistently controllable
• As a result, your students will struggle to get consistent results.
• I would only consider them for teams with little direct coaching available, no one to supervise proper construction (power tools and/or sharp-edged hand tools are almost a must), and little time to invest.
• If you do chose paper, I’d still suggest you have your students go through a design analysis as I’ve outlined, and be aware of the build and test considerations as much as possible.

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Example Paper Device