This is one lesson document that runs as two class sessions, because the two families fail in different ways and each earns its own hour. Session A is curves: the curve drives the system width, and you run it first. Session B is elevation: what tips a carton once the belt, the load, and gravity all act at once. The single move that has to land in both sessions is the same one, run the static number, then ask what the package feels in motion. If a student leaves naming only the calculator output, the lesson didn't land.
| Segment | Min | What happens |
|---|---|---|
| The straight run ends here | 6 | Open on the hook. A straight run forgives; a curve doesn't. Set up that a correct static number can still fail on the floor. Don't resolve it yet. |
| Curves, width follows the curve | 18 | Teach the diagonal, not the width. Run the Curve Formula live from an inside radius and the largest carton. Establish the sequence: curve first, belt width second. Then work it backward (see the key teaching moment). |
| Skew, the companion geometry | 8 | Show skew as alignment sized from the same envelope. Keep it a survey; the locked skew length is Lesson 25. |
| The guardrail taper rule | 18 | Rigid versus non-rigid. Walk the taper design decision: when it saves money, and the poly-bag and padded-mailer case that wrecks it. Make them confirm the mix before they reach for it. |
| Short curve exercise | 8 | Hand a curve and a product. Run the requirement, then ask for the inside radius that would allow a narrower belt. |
| Close | 2 | The curve sets the width; you run it first. Bridge to Session B: same package, tilted floor. |
| Total | 60 | Session A baseline. |
| Segment | Min | What happens |
|---|---|---|
| Think like the package, past the static angle | 12 | Reprise the flagship device as the package's return to elevation. Teach the static tumble angle and name what it can't see. Render Think Like the Package prominently; it's the Part IV home for it. |
| Inertial energy and load shift | 12 | Incline start versus decline stop. Use the stack-of-books model for inertia. Drive the worst-case-load habit, not the average. |
| The thirds method, live | 12 | Draw the carton at the angle, mark the thirds, drop the center-of-mass line, then shift the load and watch it cross into the leading third. This is the key teaching moment. |
| Gravity pitch, spirals, lifts, mezzanines | 10 | Pitch at 2 to 8 inches per 10 feet, three-roller minimum, confirmed against the mix. Name spirals, lifts, and mezzanine integration as categories; selection is Lesson 17. |
| Riverside decline design | 12 | Hand them 16 ft AFF and about 40 ft of run. Let them find the Tall Case (see Riverside facilitation). |
| Forest, close, controls preview | 2 | Close on the pattern, then preview the VFD-ramp Controls Corner: the angle you designed and the ramp you need are two halves of one decision. |
| Total | 60 | Session B baseline. |
The thirds method is a five-minute CAD move that can prevent a five-day field fix. Show it live, don't describe it. Draw the carton at the incline angle, mark the thirds with two lines, drop the center-of-mass line, and confirm it sits in the middle third. Then shift the load toward the downhill end and watch the line cross into the leading third. The room sees the design fail in real time, which is exactly what a customer sees when you run it in front of them.
Pair it with the curve-formula-first discipline in Session A. Give the room a curve and a product and have them run the requirement. Then work the tool backward: ask what inside radius would let them use a narrower belt. A student who can run a calculator forward and backward understands it. One who can only push the button doesn't.
Hand the room the geometry and nothing else: the mezzanine deck is at 16 feet above finished floor, with about 40 feet of horizontal run before the main forklift aisle. Have them work out the available decline angle and check every product in the envelope against its tumble limit.
Do not tell them the Tall Case governs. Ask. Steer with questions until they find on their own that the 10 by 8 by 14 box, 14 inches tall on an 8-inch base, is the one that sets the ceiling on the angle. Then push them to run the thirds method on it with the load shifted forward and to name the decline stop as the dangerous moment.
If the Tall Case can't ride the available angle, they don't get to quietly include it or quietly drop it. Make them present it to Dana as an options-and-consequences conversation: what it costs to keep it, what changes if it's handled separately, and a recommendation without making her decision for her. Hold scope both ways: no final decline-belt or speed arithmetic here, that's Lesson 25, and no picking a specific decline conveyor against alternatives, that's the specialty elevation-equipment call in Lesson 17.
Q1, the taper decision. The taper is off the table for this mix, and the reason is the mix, not the geometry. The curve at a 32.5-inch inside radius with a 22 by 15 carton genuinely drives the run wider than the straight sections need, and run that requirement first regardless. But the taper back to a narrow run is only acceptable when every product is rigid, and the mix here includes non-rigid padded mailers that will bunch at the taper transition. So a defensible answer declines the taper and carries the wider belt, or handles the mailers on a separate path, or brings the customer a documented options conversation. An answer that tapers to hit the cost target without addressing the mailers has missed the rule. Grade the defense, not the verdict, but a student who tapers over a non-rigid mix is wrong.
Q2, the incline that passes the static check. The two factors are inertial energy and load shift. Inertial energy: when the belt starts or stops, the acceleration adds energy the static calc never included, so a package stable at steady speed can tip during the change. Load shift: contents that slide move the center of mass toward one end, so a package that passed with a centered load can tip with a shifted one. This is an incline, so the single most dangerous moment is startup, because inertia and any load shift both push toward the trailing edge and the box wants to tip backward. The design response is margin below the static limit plus a controlled VFD ramp rate for a gentler start, and always checking the worst-case load distribution. Full credit needs the incline-specific moment (startup, tipping backward), not a generic answer.
The mezzanine decline design and the thirds-method sketch are project-folder artifacts. They carry forward into validation, so reinforce the note-keeping habit here the same way you have since Lesson 1: have students file the decline angle, the per-product tumble check, the Tall Case thirds validation, and the pitch note in their Riverside project notes, dated. Never explain where the habit leads. The payoff is theirs to find later, and it lands hardest for the students who kept their notes without being told why.
Keep the two scope guards visible on your own board so you don't drift: the final decline-belt and speed arithmetic is Lesson 25, and the specialty elevation-equipment selection is Lesson 17. Students will want to solve both here. Name each for the category it belongs to and hand it forward.