Roller Coaster

Roller Coaster is a Division B build event. Before the tournament your team designs, builds and tests a track that guides a single ball from a Start Line to a Finish Line, powered only by the ball's own gravitational potential energy. At the tournament the event supervisor announces a Target Time between 30 and 60 seconds, and you have a few minutes to tune the coaster so the ball crosses the Finish Line as close to that time as possible. Because only full seconds count, the best place to land is just over the target, not under it.

Time is only part of the score. The 2027 rules also reward a small device, up to two Elevators (lifts built from specific simple-machine combinations that raise the ball at least 10 cm) and one Loop (scored by its height). A strong team treats the coaster as a points optimization problem: how much height, footprint and risk to spend on each of the four score components. This guide covers the 2027 rules in plain language, the scoring math with worked examples, the physics of a slow run, how to design legal Elevators and a Loop, and how to calibrate to a target you only learn minutes before your run.

Event format

Because your tools must be non-electronic and the rules name no calculator class for this event, plan on doing all calculations before the tournament. Your impounded data and notes are where your calibration tables live (see "Calibrating to an unknown Target Time" below).

Category B eye protection means impact-rated goggles, marked Z87+ on the frame. Ordinary safety glasses marked only Z87, face shields and regular prescription glasses do not meet it. A participant without proper eyewear is told and may get a chance to fetch some if time allows, but cannot compete without it.

What the rules cover

The 2027 Roller Coaster rules (Division B manual, Roller Coaster section) fall into five areas. The table summarizes each one; the subsections below explain what each means for your design.

You must also be able to answer the supervisor's questions about how your device was designed, built and operated, under Science Olympiad's general Building Policy. Build it yourselves and know why every part is there.

Device limits in practice

The 30 x 80 x 60 cm box applies at all times during competition, not just at measurement. An Elevator arm that swings above 60 cm at the top of its stroke, or a counterweight that hangs past the edge, puts the device out of bounds during the run. The coaster's height is measured again at the end of each scorable run, so whatever position your moving parts finish in is the position that gets measured.

The ball must stay visible. Open track (rails, channels, ledges) is the simplest way to satisfy this; if any section is enclosed, such as a tube, the tube must be clear. The Loop is stricter: no part of it may be fully enclosed, so the supervisor could lift the ball out anywhere along it.

Track materials must not create a safety hazard, and an unsafe device will not be allowed to run until the supervisor is satisfied. Sharp metal edges, unstable tall towers and heavy counterweights that could fall off the table are the usual concerns.

Run procedure and timing

After you collect your coaster from impound, the 8-minute clock starts. You may make as many practice runs as you like and up to two scorable runs. Time the supervisor spends measuring does not count against your 8 minutes, and a scorable run that starts before time runs out may finish.

Between runs you may adjust the coaster: change or add or remove track pieces, swap the ball, level the base. You may not move the Start or Finish Line. You must announce a scorable run before you start it, and nobody may touch the device during a scorable run.

For each scorable run:

1. You place the supervisor's pencil on the Start Line so it holds the ball, with the ball completely behind the line.
2. The supervisor checks that the timers are ready and counts down "3, 2, 1, Go".
3. On "Go" you lift the pencil away without pushing the ball, and timing starts.
4. Timing stops at the first of these: the ball completely crosses the Finish Line; twice the Target Time has passed; the ball leaves the device; or the ball stops moving and does not start again within 3 seconds.

Three timekeepers are suggested, and the median of their times is the Run Time, recorded to the precision of the timers.

If the ball never crosses the Finish Line, the Time Score is zero for that run, but the run still earns its Size Score and any Elevator or Loop points completed before timing stopped. How long the ball ran before stopping or leaving the device is used only as the last tiebreaker.

Scoring

Tiers and tiebreakers

Every run lands in a tier, and any team in a higher tier beats every team in a lower one regardless of points.

Ties are broken in this order: highest Loop Score, then highest Size Score, then highest Time Score, then the longest time the ball ran before leaving the device or stopping. A Loop is therefore worth more than its points: at a tournament where several teams max out time and Elevators, the Loop decides the tie.

How the score really works

Before you design anything, look at what each component is worth, because the numbers decide where your effort should go.

Three conclusions follow.

The time window is lopsided. Because only full seconds count, a run anywhere from exactly $T$ up to just under $T + 1$ s earns the maximum Time Score. A run 0.1 s short loses 5 points; a run 0.9 s long loses nothing. So the real goal is to land in the one-second window above the target, and your aim point should be about $T + 0.4$ s, the middle of that window. Remember the timers have their own precision and three humans react differently, so a target of exactly $T$ is a coin flip between full marks and minus 5.

A working Elevator is worth 10 seconds of timing error. 50 points equals 10 full seconds of miss. Two Elevators (100 points) outweigh almost any amount of time fine-tuning. But an Elevator that jams can stop the ball, and a ball that never reaches the Finish Line scores zero for time, which costs 150 to 300 points. The better-of-two-runs rule softens that risk: one clean run is all you need.

Size is the smallest lever but the most certain. Size points never fail mid-run. Each centimeter you shave off is 1 point, and Size is the second tiebreaker. Do not shrink the coaster so much that you lose the height you need for time, Elevators or the Loop, but do not waste space either.

The physics of a slow run

Most physics problems ask how fast a ball rolls. This event asks the opposite: how to make a ball take 30 to 60 seconds to travel through a box less than a meter long, using nothing but the height it starts at. The tools are the same, energy and rolling motion, but you use them to waste speed in a controlled way.

Energy budget

Near Earth's surface a ball of mass $m$ at height $h$ stores gravitational potential energy, which turns into kinetic energy as it drops.

The coaster is at most 60 cm tall, so the ball can never drop more than about 60 cm in total, unless an Elevator lifts it again. Every Elevator adds at least 10 cm of height that the ball can spend a second time. Every Loop spends height quickly, because the ball needs real speed to get around it. Plan the run as a height budget: where the ball starts, where each drop, lift and loop happens, and how much height is left for slow travel.

Rolling slows the ball down

A rolling ball stores energy in two places: forward motion and spin. For a solid sphere rolling on its full radius, the spin takes $\tfrac{2}{7}$ of the energy, so it moves slower than a sliding object would after the same drop.

Rails make it slower still

Many teams run the ball on two rails instead of a flat surface or a groove. A ball resting on two rails rotates about the line through its two contact points, which sits closer to its center than its full radius. That effective rolling radius $r_{\text{eff}}$ makes the ball spin faster for the same forward speed, so more energy goes into spin and less into forward motion.

Rail spacing is a powerful time control, and it gets more sensitive as the ball sits lower between the rails. If the rails are almost as wide as the ball, a fraction of a millimeter changes the time a lot, and the ball may drop through. Pick a spacing where the time is slow enough but not on that knife edge.

Time on a gentle incline

For a ball starting from rest on a straight slope of length $L$ with constant acceleration $a$:

Two things in that example matter for design. First, one leg uses only about 2.4 cm of height for over 3 seconds of time, so a stack of legs can stretch 25 to 35 cm of height into most of a minute. Second, time depends on slope through $1/\sqrt{\sin\theta}$: at small angles, a 10% steeper slope makes each leg about 5% faster. That square-root relationship is what makes fine tuning possible.

Friction, stalls and losses

Real tracks also lose energy to rolling resistance (the ball and track deform slightly at the contact), rubbing against guides, air drag and impacts at joints and turnarounds. On the very gentle slopes this event uses, rolling resistance is no longer a small correction. Below some minimum slope, which depends on the ball and track materials and has to be measured, the ball slows down instead of speeding up, and it can stop.

A stall is the worst failure in this event. If the ball stops and does not move again within 3 seconds, timing ends and the ball has not crossed the Finish Line, so the Time Score is zero. Find the minimum slope your ball and track will reliably roll on, then build every leg comfortably steeper than that.

Designing a 30-60 second track

Switchbacks

The common way to get a long time out of a short box is a switchback track: a series of gently sloped legs running back and forth along the 80 cm length, each a little lower than the one before. At the end of each leg the ball turns around, either around a curve or by hitting a bumper and dropping onto the next leg. A turnaround that brings the ball nearly to rest resets its speed, so each leg behaves like the "from rest" example above and the leg times add up.

This calculation is a starting point, not a prediction. Its job is to tell you whether a design is in the right range (12 legs, not 3 or 40) before you build.

Turnarounds

Turnarounds are where runs go wrong. A curved turnaround keeps some speed and adds little time; a bumper turnaround kills speed and adds a repeatable pause but can bounce the ball off the track. Whichever you use, make every one identical, so their effect is consistent, and make sure the ball can never stop in a dead spot where the 3-second stall rule ends the run.

Joints and alignment

Each joint between track pieces is a small bump that costs energy and adds scatter. Align joints carefully, fasten sections so they cannot shift during transport from impound, and favor long continuous rails over many short pieces. A section that flexes under the ball adds random losses that no calculation can model.

Leave room for tuning

Because the target is not known until just before your run, the coaster must be able to produce any time in the 30-60 s range on short notice. Build in at least one tuning element whose effect on time you have measured. Good candidates are:

• a removable or swappable track section (the rules allow adding or removing track pieces between runs);
• a hinged leg whose slope can be set with a pin or shim at marked positions;
• a set of balls of slightly different diameters, which roll at different speeds on the same rails;
• leveling shims under the base, which tilt every leg slightly.

The best tuning elements change the time in small, predictable steps, and you should know each step's size from testing.

Elevators

An Elevator lifts the ball from a lower level of the coaster to a higher level. The 2027 rules allow up to two, each of a different type, and each earns 50 points the first time it works.

The types may come in either order. Counterweights are allowed, track sections may be reused by the ball after a lift, and gates or barriers may move into place as part of an Elevator's action. Each Elevator must be clearly labeled.

Ideal mechanical advantage

Ideal mechanical advantage (IMA) is the ratio of the distance the effort moves to the distance the load moves, assuming no friction:

An IMA greater than 1 trades distance for force: you push a long way with a small force to move a heavy load a short way. An IMA less than 1, which the rules require, does the opposite. A short, strong effort motion moves the load (the ball) a longer distance and faster. The price is that the effort force must be larger than the ball's weight. In practice that effort comes from a counterweight, because nobody may touch the device during a scorable run and the coaster has no other energy source.

Levers

• A first-class lever can have any IMA. Put the fulcrum closer to the effort than to the load and its IMA is below 1, like a catapult arm.
• A second-class lever always has IMA greater than 1, because the load sits between the fulcrum and the effort, so the effort arm is always the longer one. A wheelbarrow is the classic example.

That second fact is the trap in the Type 2 Elevator. The lever alone pushes the IMA above 1, so the pulley stage must bring the total back below 1.

Wheel and axle, and pulleys

A fixed pulley alone cannot rescue a Type 2 Elevator, because $\text{IMA}_{\text{lever}} \times 1$ is still above 1. You need a pulley arrangement with IMA below $1/\text{IMA}_{\text{lever}}$, such as the reversed movable pulley.

Real machines have friction, so build in a healthy margin, often 50% or more, and test it.

Making an Elevator work in a scorable run

• The ball must trigger it. You cannot touch the coaster during a run, so the usual pattern is a cup or platform that the ball rolls into, whose weight releases a latch and lets the counterweight drop. Test the latch hundreds of times; a sticky latch is the most common Elevator failure.
• The ball must leave onto track. Points require the ball to reach the track at the top and keep traveling. Design the top so the cup tips or a gate opens and the ball rolls out onto the next section.
• Stay inside the box. The arm and counterweight must stay within 30 x 80 x 60 cm through the whole motion, and the coaster's height is measured after the run with the Elevator in its final position.
• Lift at least 10 cm. Measure vertical rise of the ball, not the length of the arm's arc, and leave margin above 10 cm.
• Label it. Mark each Elevator clearly with its type and keep a labeled diagram with arm lengths, radii and the IMA calculation in your notes, so you can show the supervisor the IMA is below 1.
• Use it for time. An Elevator gives the ball at least 10 cm of new height to spend on slow track, and the lift itself takes time. A lift slowed by friction or a damped counterweight adds time, but its duration must be repeatable from run to run.

The Loop

A Loop is a section of track that keeps curving in the same direction until it appears to cross over itself. The place where the two pieces of track meet is the Point of Intersection (POI); the Loop begins and ends when the ball reaches it. The two track sections must actually touch at the POI and carry a clearly labeled measuring point.

The rules add four conditions:

• the Loop may not be fully enclosed anywhere; the supervisor must be able to lift the ball out;
• the ball must stay in contact with the track all the way around;
• at the top, the ball must be completely unsupported from below, riding on the inside of the track, held there only by its motion;
• the Loop height (POI to the highest inner point) must be clearly labeled to score.

At most one Loop counts. It scores 3 points per whole centimeter of height and is the first tiebreaker.

How much height a Loop needs

At the top of a loop the track pushes down on the ball. The ball stays on the track only if gravity alone is not enough to provide the centripetal force, which means it needs a minimum speed at the top.

Combining that with energy conservation from the release point gives the minimum drop above the bottom of the ball's path:

Two lessons follow. First, ride the ball in a channel through the Loop rather than on widely spaced rails, because rails raise the required height. Second, a Loop spends a lot of height fast and leaves the ball moving quickly, so plan what happens afterward. The ball must be slowed safely, for example by a climb, a bumper turnaround, or an Elevator that lifts it back up to the slow track.

Start, finish and stopping the ball

Start. The ball sits completely behind the Start Line, held by the supervisor's pencil, which you hold in your hand. Build a short, nearly level start area with a guide where the pencil can rest across the track and lift straight up. A start on a steep slope makes the pencil hard to lift cleanly and invites an accidental push.

Lines. Exactly one Start Line and one Finish Line, each clearly labeled and crossing the track at right angles to the ball's path. They must be in place before the Target Time is announced and are fixed relative to each other once you impound, so every tuning change must happen between them.

Finish. Timing stops when the ball completely crosses the Finish Line, so the whole ball, not just its front edge, has to pass. Put the line where the ball is still moving steadily.

Stop. After the finish the coaster needs a mechanism that safely stops the ball, such as a padded cup or a short uphill dead end with a backstop. The stopping mechanism is a construction requirement, so a coaster without one has a violation and its runs fall to Tier 2.

Calibrating to an unknown Target Time

The whole event comes down to the minutes after the target is announced. You learn the target, collect the coaster from impound, and have 8 minutes for setup, practice runs and both scorable runs. A 50-second run plus resetting the ball takes over a minute, so you may only get four or five runs in total. You cannot tune by trial and error at the tournament; you must arrive already knowing which settings produce which times.

Build a calibration table

Before the tournament, run the coaster many times at each setting of your tuning element(s) and record the median time. The result is a table like the one below, kept in your impounded notes.

The numbers above are illustrative. Your table must cover every target your level can produce: every 5 s at Regionals (7 targets from 30 to 60), every 2 s at State, every second at Nationals. For each target, pick the setting whose median sits about 0.4 s above the target.

Separate drift from scatter

When you test, look at two things: the median (where the coaster sits) and the spread (how repeatable it is). A consistent offset from your prediction means something systematic changed, such as humidity, a shifted joint, or a dusty rail. A wide spread means the release, a joint or a turnaround is inconsistent. The fixes are different, so diagnose before you adjust.

Plan the 8 minutes

1. On collection, check transport damage: joints, rail spacing, Elevator latches, labels.
2. Level the base and set the tuning element from your table for the announced target.
3. One practice run, timed by your partner. Compare with the table.
4. Make at most one adjustment from the table, then declare scorable run 1.
5. Use run 2 to correct based on run 1, or to attempt something riskier if run 1 already scored well.

Strategy

• Divide the work. One partner owns the track and the calibration table; the other owns the Elevators, the Loop and the label/diagram set. Both should be able to run the start and answer design questions.
• Reliability first. A coaster that finishes every run inside the 1-second window with both Elevators working beats a fancier one that works three times in four. Take your two scorable runs seriously as insurance, not as two lottery tickets.
• Spend height deliberately. Write a height budget: start height, Loop drop, Elevator lifts, slow legs. If the Loop costs 20 cm of height, make sure an Elevator gives some of it back.
• Keep the box small but useful. Find the smallest footprint that still fits the legs you need. A 70 cm long coaster gives 10 Size points over an 80 cm one; that is equal to two seconds of timing error.
• Test in tournament conditions. Practice with someone else counting "3, 2, 1, Go", three timers, the median rule and a #2 pencil exactly like the one the supervisor will hand you.
• Bring spares. Impound spare balls, a spare counterweight, spare track pieces and non-electronic tools (screwdriver, shims, tape, pliers). Anything not impounded cannot be used.
• Label everything. Start Line, Finish Line, each Elevator and its type, the POI and the Loop-height measurement. Missing labels can cost the Elevator or Loop points or create a violation.

Common pitfalls

How tournaments test this

Roller Coaster has no written component, and the site has no archived test questions for it. What tournaments test is the device and your ability to explain it:

• The run itself. Two scorable runs, judged on Run Time against a target you learn just before setup, plus Size, Elevator and Loop points. The best run counts.
• Rule compliance. Supervisors measure the box at the end of each run, check labels, watch for touching during a run, and check that Elevators and the Loop meet their definitions. Any violation drops the run to Tier 2.
• Design questions. Under the Building Policy, the supervisor may ask how your coaster was designed, built and operated. Expect questions such as "what is the IMA of this Elevator and how did you calculate it?", "which lever class is this?" and "why does the ball stay on the track at the top of the Loop?"
• Level differences. The only level difference in the 2027 rules is the Target Time step: 5 s at Regionals, 2 s at State, 1 s at Nationals. Finer steps reward a coaster with finer, well-calibrated tuning.

Test yourself

There are no archived tournament questions for this event, so these practice problems were written for this guide. Work each one before reading the answer.

References and further reading

• Science Olympiad, Roller Coaster event page and the 2027 Division B Rules Manual (the official rules; read them in full): https://www.soinc.org/
• Science Olympiad policies on eye protection and building events: https://www.soinc.org/
• OpenStax, University Physics Volume 1, chapters on conservation of energy, rolling motion and circular motion: https://openstax.org/details/books/university-physics-volume-1
• OpenStax, Physics, section on simple machines and mechanical advantage: https://openstax.org/details/books/physics
• SciOly Wiki, Roller Coaster (community summary, not a rules source): https://scioly.org/wiki/index.php/Roller_Coaster
• Related guides on this site: Scrambler, Mission Possible, Boomilever