Science Olympiad Trajectory Event Guide: Physics, Device Design, and Scoring

Trajectory is one of Science Olympiad's most consistently popular build events. Teams construct a device that launches a projectile — typically a golf ball or tennis ball — at a target at a specified distance, which is revealed on the day of competition.

Because the target distance is unknown until competition day, Trajectory rewards calibration and prediction over raw power. Your device does not need to launch perfectly every time — it needs to be consistent enough that you can calculate how to hit any target distance within the event's range. If you are new to Science Olympiad and still deciding which events to take on, the Science Olympiad beginner roadmap and our breakdown of build events vs. study events are good starting points before committing to Trajectory.

For the current season's specific target distances, allowed materials, and scoring formula, always consult the official Science Olympiad rules. This guide covers the underlying physics and methodology that apply year to year.

The physics: what you actually need to understand

Trajectory is grounded in projectile motion — one of the clearest applications of kinematics in high school physics.

A projectile launched at angle θ with initial speed v₀ from the same height as the landing surface follows a symmetric arc. The three quantities that matter most are:

• Horizontal range: R = (v₀² × sin(2θ)) / g
• Time of flight: T = (2 × v₀ × sin(θ)) / g
• Maximum height: H = (v₀² × sin²(θ)) / (2g)

The range equation R = v₀² sin(2θ) / g is valid only when the projectile launches and lands at the same height. In that case, the angle that maximizes range is exactly 45 degrees. The sin(2θ) term reaches its maximum of 1.0 when 2θ = 90°, meaning θ = 45°. Angles on either side of 45° — say 35° and 55° — produce equal range because sin(70°) = sin(110°).

When launch height and landing height differ, the 45-degree rule does not hold. If your launcher sits on a table and the target is on the floor, the projectile has extra height to travel. The extra fall time adds horizontal distance, which shifts the optimal angle below 45 degrees. The exact optimal angle depends on how much higher the launch point is relative to the landing surface, and on the launch speed. In practice, Trajectory events often place the launcher at table height with the target on the floor, so your device's actual maximum-range angle may be closer to 35–42 degrees rather than 45. Run test launches at several angles and let the data tell you where your device's effective optimum is — do not assume 45 degrees is correct.

The range equation also shows that range scales with v₀². Double the launch speed and you quadruple the range. This means small changes in stored energy produce large changes in distance — which is exactly why consistency in your energy delivery mechanism matters so much.

Air resistance is a real factor that your theoretical calculations will ignore. At the velocities typical of Trajectory devices, drag reduces actual range by 5–15% compared to the vacuum-physics prediction. You cannot remove drag from the equation, but you can make it consistent across every launch — which is what your data-gathering process accounts for.

How launchers store and deliver energy

Every competitive Trajectory launcher must do two things well: store a controlled amount of energy, and release that energy the same way on every shot. The second requirement is harder than it sounds.

Elastic (bungee or surgical tubing): Energy is stored by stretching the tubing to a fixed, repeatable draw length. The adjustable parameter is usually the draw length or the attachment point of the tubing. Elastic launchers are compact and easy to vary across a wide range of distances. The main failure mode is tubing aging — surgical tubing stiffens and loses elasticity over a season, so a calibration table built in October may be wrong by March. Keep spare tubing of the same brand and lot, and recalibrate whenever you replace it.

Gravity (pendulum or counterweight): A dropped mass swings an arm that strikes or slings the projectile. If the release mechanism is consistent, gravity-powered launchers can be extremely repeatable because the energy input (mass × height drop) does not degrade over time. Distance adjustment is typically done by changing the launch angle rather than the energy input. The tradeoff: adjusting for different distances is less fine-grained than changing a draw length on an elastic launcher.

Spring-loaded: A compressed spring drives a plunger or throwing arm. Springs allow compact, fast-resetting designs. The drawback is that springs compress slightly differently depending on how quickly you cock them, and spring constant can drift with heavy use. If you use a spring design, build in a consistent cocking procedure — same hand, same feel, every time — and recheck calibration after every 50 launches.

Regardless of mechanism, every launcher needs a reliable, low-friction release. Any sticking or slippage at the release point adds random variation to your launch velocity, which shows up directly as scatter in your landing positions.

Building a calibration curve

Calibration is where Trajectory is won or lost. You are not trying to memorize a list of distances — you are building a model of your device's behavior that lets you interpolate for any target distance you have never practiced at.

The cleanest approach is to define one primary adjustable parameter on your device. For an elastic launcher, this is typically the draw length measured in centimeters or to a numbered stop position. For a gravity launcher, it is the launch angle. Hold everything else constant — same ball, same release procedure, same surface.

Then systematically vary that parameter and measure the resulting distance. A usable calibration table looks like this:

Draw length (cm)	Mean distance (ft)	Std deviation (ft)
12	7.4	0.3
14	9.1	0.2
16	10.8	0.3
18	12.5	0.4
20	14.1	0.3

Each row should be the average of at least five launches — ideally ten. With a table like this, if the competition reveals a target of 11.5 ft, you interpolate between the 16 cm and 18 cm rows and set your draw to approximately 17 cm. You do not need to have practiced at exactly 11.5 ft to hit it.

The density of your data points matters. If your table has entries every 2 cm and the relationship between draw length and distance is approximately linear in that range, interpolation is accurate. If you have sparse data (entries 5 cm apart), you are extrapolating assumptions about linearity that may not hold. Aim for data points every 1–2 cm or every 2–3 degrees across the full competition range.

How many total launches does this take? Competitive teams typically do 80–150 test launches over a season. That sounds like a lot. It is not — you need enough data to build a reliable table, identify which settings have low variance, and verify that the table remains accurate after you reassemble or transport the device.

Sources of variability and how to reduce them

Variance is the enemy of a good Trajectory score. A device that averages 5 cm short but always lands 3–7 cm short will often outscore a device with a better average that scatters ±30 cm. Identify your sources of variance early and address them systematically.

Release inconsistency. The most common source of shot-to-shot variation. Any slop in the trigger mechanism — a rough latch, a ball that does not seat the same way every time, a pivot that has lateral play — produces unpredictable launch velocity. Sand, deburr, and tighten every moving part in the release train. Test the release with no ball loaded: the mechanism should feel identical every time.

Ball seating variation. The ball's position at the moment of release affects launch direction. Build a consistent backstop or cradle that positions the ball in the same orientation every shot. Inspect it before every launch at competition.

Surface interaction. If your projectile bounces or rolls after landing, the final rest position is not solely a function of your launch. A shot that hits carpet stops immediately; the same shot on tile might roll several feet. Know what surface you are shooting on, and if possible, run two to three warm-up shots on the actual competition surface before your scored attempts.

Temperature and tubing changes. Elastic components perform differently in a cold gymnasium than in your garage. If your competition is in a different environment from where you calibrated, expect a shift and plan for it. Arrive early, let your device reach the ambient temperature, and use any warm-up time to verify your table is still accurate.

Transportation damage. Travel flexes frames, loosens fasteners, and shifts alignment. Before every competition, go through a pre-flight checklist: check all pivot points, verify all fasteners are tight, confirm your angle reference marks are still accurate.

The data-logging and iteration process

A calibration table is not built in one session — it is refined over the season through repeated measurement. Structure your practice sessions so that data accumulates systematically rather than haphazardly.

For each session, record:

• Date and device configuration (any changes since last session)
• Setting used (draw length, angle, or whatever your primary parameter is)
• Target distance and actual landing distance for every shot
• Notes on anything unusual (different surface, cold room, tubing replaced)

After each session, update your calibration table and recalculate standard deviation for each setting. When standard deviation increases, something in your device changed — find it before competition.

Iterate on the device only when data tells you to. If your standard deviation is already 0.3 ft and your average is 0.2 ft from target, spending more time tweaking the mechanism is unlikely to help your score. Instead, spend that time practicing the competition routine: reveal the target, look up the setting, configure the device, launch two attempts, stay calm.

The Trajectory event page has current event-specific information and links to resources from SEALS Academy coaches.

Competition day execution

On competition day the target distance is revealed. You have a limited setup and launch window. The teams that score best are the ones who have rehearsed this routine until it is automatic.

Your sequence should be:

1. Record the announced target distance.
2. Look up the nearest data points in your calibration table.
3. Interpolate to find the correct setting and configure your device.
4. Verify ball seating and release mechanism before each attempt.
5. Launch your scored attempts with the same procedure every time.

Do not change your configuration between attempts based on a gut feeling about where the first shot landed. If your first shot was 10 cm short and you arbitrarily add 1 cm of draw, you are introducing a guess. Trust your table — unless you have clear evidence of a systematic offset (all shots are consistently short by the same amount), your calibration is more reliable than your in-the-moment instinct.

Practice and next steps

The core preparation tasks for Trajectory are straightforward, but they take time:

1. Build or acquire your launcher and verify it is mechanically consistent before doing any serious calibration work.
2. Define your primary adjustable parameter and build a preliminary calibration table across the full expected range.
3. Run 10 launches per setting, calculate means and standard deviations, and identify which settings have unacceptable variance.
4. Address variance sources — inspect the release mechanism, check ball seating, tighten fasteners.
5. Rebuild and verify your calibration table after any significant device change.
6. Practice the competition routine: timed target reveal, table lookup, configuration, launch.

For context on how Trajectory compares to other Science Olympiad events in terms of preparation time and strategy, see the guide on build events vs. study events. If you also compete in Mousetrap Vehicle, you will find the calibration methodology largely transfers — both events reward systematic data collection over inspired guessing.

Where to go from here

Trajectory is one of the more physics-grounded build events in Science Olympiad. Understanding the range equation, knowing when the 45-degree rule applies and when it does not, and building a dense calibration table puts you ahead of most competition. The students who score consistently well are not necessarily the ones with the most powerful launchers — they are the ones who have documented their device's behavior across the full competition range and practiced the competition-day routine until the target reveal produces no anxiety.

SEALS Academy coaches Trajectory and other SciOly build events. Sessions cover the physics behind the event, device design and testing methodology, and how to build a calibration process that holds up on competition day. See our SciOly coaching options.