Lesson 25: The Gap Check and Capacity Proof, Instructor Session Plan

Lesson 24 gave the perfect-world numbers their margin. This lesson runs the calc for real. The one outcome every student must leave with: the sequence order isn't optional, and the required rate drives every number on the sorter tab, so it gets confirmed in writing before the sorter tab is touched. A student who runs the calc once but never watches it break under a changing input doesn't yet know how to trust it. Don't lecture the sixteen steps off a slide. Run the sequence live on the Riverside numbers, then change the rate after the calc is done and make the room watch every sorter number go wrong while each one still passes its own check.

Run of Show (60-minute baseline)

Segment	Min	What happens
Now you prove it	6	Open on the hook and the stakes of a missed gap check. Michael's line: he's seen the transfer gap missed in proposals more than once, and every miss is a collision on every cycle in the field, found at commissioning. Final engineering is the same math as solutioning with the inputs confirmed and the tolerance tight. Set the stakes; don't teach the calc yet.
The sixteen-step sequence, grouped	10	Put the three bands on the board: package basics (1-7), sorter (8-13), transfer (14-16). Call out the rate-in-writing gate between package basics and the sorter. Make the dependency explicit: a bad input early produces a wrong answer that still passes its own check late. The guide's Section 5 is the authority; point them to it, don't reprint its table.
The sorter sequence and the gap check	18	Run CFPM, SGR, required sorter speed, both gap checks, and takeaway spur speed live on Riverside's numbers. Land the min carton as the binding SGR case and the max carton as the highest CFPM. Then the three levers when the gap fails. Key teaching moment, below, lives here.
The 90-degree transfer, live	10	Lateral distance, cycle time, minimum trunk-line gap, worked to the guide's 118 inches. Compare against the gap available. Drive home that every transfer gets its own gap check, and the four-inch margin is a floor, not a target.
Merge dead-time and the setpoints package	8	The merge is not free throughput; account for the dead time or the real rate comes in under the sum of the lane rates. Then assemble the setpoints package: belt speeds by section, VFD ramp rates, PLC delays, release modes. This is the bridge out of Part VI.
Riverside recalc and Forest close	8	Spring Ray's latency correction, half a second to one second. Make the room find what changes downstream of the scan point. Close on the driving question. Riverside facilitation, below.
Total	60	Baseline session. Expand with the stretch option below if you have 90 minutes.

Stretch option (for a 90-minute block):

A second column or a second transfer (add 30 min): hand the room a second sorter column, or a second transfer at a different trunk speed, and have each student find the binding case on their own. Running the sequence twice, on numbers that behave differently, is what turns the calc into a tool instead of a one-off. Make them defend which carton governs and which lever they'd pull if a check fails.

KEY TEACHING MOMENT | RUN IT, THEN BREAK IT

Move one: run the full sequence live. Work the Riverside numbers on the board, package basics to sorter to transfer, in order. Let the room see each output feed the next. When the sorter clears both gap checks at 55 inches produced against a 9-inch model minimum and a 9.5-inch geometric requirement, that's the calc passing honestly.

Move two: change the rate after the calc is done. Now tell the room the customer moved the required rate. Walk back through the sorter tab and show every number going wrong, CFPM, SGR, required sorter speed, the gap produced, and each one still passing its own internal check. That's the whole lesson in one move: the rate drives the sorter tab, so it gets confirmed in writing first. A student who has watched you run the sequence once but never run it under a changing input doesn't yet know how to trust it. Don't skip the break.

WATCH-FORS

The failure this lesson is built to prevent is a student who trusts a right-looking answer without checking the sequence behind it. Redirect each one back to the order and the gap check.

They run the sorter tab before confirming the rate. Stop them at the rate-in-writing gate. Every number below it's built on sand until the rate is confirmed.
They spec the takeaway spur at sorter speed. Always wrong. The carton leaves at an angle, so the spur runs faster to hold the carton's velocity in the direction of travel. Send them back to the cosine.
They skip the transfer gap check because the sorter passed. Different check, different collision point. The sorter passing tells you nothing about the trunk line.
They add up the lane rates as if the merge were free. Make them name the dead time. The merge is a throughput constraint, not just a directional transition.

RIVERSIDE FACILITATION | DO NOT TELL THEM, ASK

Have the room run the gap check on Riverside with the guide's numbers first, so they own a clean pass. Then spring Ray's correction: the WMS response he estimated at half a second in the room is confirmed at one second under peak load. Do not tell them what moves. Ask. Make them find, on their own, that the scan-to-divert distance was sized around the half second, that a carton travels farther in one second than in half of one, and that the fix of choice, changing the belt speed, feeds straight back into the gap produced and re-opens both gap checks.

Hold two lines all session. The sequence order is not optional. And the rate goes in writing before the sorter tab. The student who wants to shortcut either one is the student who writes a right-looking answer to the wrong check.

CHECKPOINT ANSWER KEY | NOT IN THE STUDENT FILE

The three levers. Rate, speed, or sorter model. A complete answer ties a downstream consequence to each. Speed: raising the sorter speed has to be checked against the takeaway spur speed and the conveyor's published maximum at the heaviest product, so you can't just turn it up. Rate: lowering the required rate changes what the system promises the customer's throughput will be. Model: selecting a lower gap requirement changes the line item and the price. The one you can't pull on your own is the rate, because it needs the customer's sign-off in writing. A strong answer also names the induction-gap move, adjusting upstream belt speeds to feed a bigger gap into the sorter. Don't accept a bare list of three words; look for the trade tied to each.
The transfer, then the latency recalc. Transfer options: reduce the trunk-line speed, increase the carton gap upstream, or specify a faster transfer to shorten the cycle time, each with its consequence (a slower trunk lowers throughput, a bigger upstream gap can pull the theoretical rate down, a faster transfer can change the line item). Then the recalc: everything downstream of the scan point is suspect. The scan-to-divert distance was sized around the old latency and now needs more distance, because the carton travels farther in the confirmed one second. If they close the gap by changing the belt speed instead, the speed feeds the gap produced, so the sorter gap checks re-run, and the theoretical rate and takeaway spur speed move with the speed. Look for them tracing the dependency chain from the changed number outward, not naming a single fix and stopping. A student who reaches for "make the WMS faster" as the only answer has missed that response time is physical.

INSTRUCTOR ONLY | DO NOT SHARE WITH STUDENTS

The two artifacts the students build today, the gap-check pass or fail record and the setpoints package, are the second piece of the validation package and project-folder deliverables the disciplined student carries straight into the capstone. Frame them as normal project work, not a graded exercise. The students who keep a real Riverside note now, with the worked gap checks and the setpoints table in it, are the ones who'll have a capacity proof ready when the capstone asks for one. Don't preview the payoff. Let the habit reward the ones who kept it.

One dry aside if it surfaces: the Riverside maintenance lead is also named Michael Collins, twenty years on site, a different person from the program's author. Handle it in one line and move on; don't belabor it.