Paper Bridge: When the Rubric Picks the Worst Design
A Year 7 team must design a paper bridge for a class competition. The bridge must span a 300 mm gap, support 500 g at the centre, and be built only from 20 sheets of A4 paper and 1 m of tape within 30 minutes. Scoring: 40 points for load (40 points at 1000 g or more, 30 at 750–999 g, 20 at 500–749 g, 10 below 500 g); 25 points for stiffness (25 if sag is under 10 mm, 15 if 10–20 mm, 5 if more); 20 points for material efficiency (20 if at most 12 sheets and 50 cm of tape, 10 if at most 16 sheets, 5 otherwise); 15 points for finishing with at least 5 minutes to spare (8 if less, 0 if unfinished). Load was added in 50 g steps at the centre until failure. Prototype 1: 4 sheets, 30 cm tape, failed at 220 g, sag 4 mm, finished in 9 min. Prototype 2: 15 sheets, 80 cm tape, held 640 g, sag 25 mm, finished in 14 min. Prototype 3: 20 sheets, 95 cm tape, held 900 g, sag 8 mm, finished in 26 min.
1. Calculate each prototype's score and judge whether the rubric selects the right design.
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Prototype 1: load 10 (below 500 g) + stiffness 25 (4 mm) + efficiency 20 (4 sheets, 30 cm) + time 15 (21 min spare) = 70. Prototype 2: load 20 (640 g) + stiffness 5 (25 mm) + efficiency 10 (15 sheets) + time 15 = 50. Prototype 3: load 30 (900 g) + stiffness 25 (8 mm) + efficiency 5 (20 sheets) + time 8 (4 min spare) = 68.
So the rubric selects Prototype 1 by two points. That is the wrong outcome: Prototype 1 fails the stated requirement of supporting 500 g, while Prototype 3 meets the load constraint with a wide margin, is four times stiffer, and is the only design that could be used in service.
The flaw is structural: the rubric treats the brief's mandatory requirement as just another scored category. A design that fails a pass/fail constraint should be disqualified, or at least capped well below any design that meets it. Efficiency and speed are then used to rank the designs that actually work. This is a good illustration of why designers separate constraints (must be met) from criteria (used to choose between compliant options).
2. Using the data, propose an improved design and predict how it would score.
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Prototype 3 already shows the right principle - a triangular truss made from rolled paper tubes - and its 8 mm sag and 900 g capacity confirm that depth plus triangulation carries load far better than a flat or corrugated sheet. Its weaknesses are cost (20 sheets) and time (26 min).
A hybrid aims at both: build the truss from about 12 sheets, using fewer, longer tubes for the top and bottom chords and short diagonal struts, rather than doubling every member. Twelve sheets keeps material efficiency at 20 points. Pre-roll tubes on the desk edge during the first five minutes and tape the joints in a fixed order to bring build time to about 20 minutes, earning the full 15 time points. Depth should be maintained at roughly 30–40 mm, since depth, not paper thickness, drove P3's stiffness.
Predicted score: load 30–40 (900 g is likely still achievable with a triangulated 12-sheet truss) + stiffness 25 + efficiency 20 + time 15 = 90–100, clearly ahead of all three prototypes and compliant with the 500 g requirement.
3. Critique the fairness of the testing procedure and describe how you would test the bridges.
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Several features make the comparison unfair. Load was added in 50 g steps, so scores jump at arbitrary thresholds - 640 g and 749 g score identically, and 900 g scores the same as 1000 g, which hides real differences. The prototypes were tested in order, so Prototype 3 was last: by then the desk edges may have shifted or sagged from the earlier failures, and tape residue on the supports could change how each bridge sat. Each bridge was tested once, with no repeat, so one weak glue joint decides the result. Sag was measured but the method and the load at which it was measured are not stated - sag at 200 g is not comparable with sag at 900 g.
A fairer protocol: fix the supports to a rigid frame and mark them so they cannot move; measure sag at a standard 500 g load with a ruler against a fixed datum; then load to failure in smaller 20 g steps; test every bridge three times or test three copies and average; and randomise the order of testing. Record the mode of failure (which member broke) so the result teaches something about the design.