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# m03 — DC voltage drop with a hidden round trip · round v4
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> Grading worksheet for round **v4**. The ground truth, the trap and the
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> scoring criteria live in [`../rubric.md`](../rubric.md) — that file is the
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> master and is not edited per round. The transcript being graded is
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> [`result.txt`](result.txt).
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## Scoring (10 points)
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### Correctness (5)
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- [x] (2) Uses the round-trip length (60 ft) → 2/2 — thinking block [1]: "30 feet (one way), so total wire length = 60 feet (out and back)"; `length: "9.144"` (30 ft in metres) passed to a tool that doubles it, and the tool's "round trip, 18.288 m of conductor" carried into the answer as "round-trip 60 ft / 18.3 m"
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- [x] (2) AWG 4 (or larger with a stated temperature argument) → 2/2 — "## Answer: **4 AWG copper**", first line
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- [x] (1) Shows the comparison gauge's drop and that it fails → 1/1 — the main table pairs 4 AWG (298 mV, 2.48 % ✓) with 5 AWG (376 mV, 3.13 %, "just 0.016 V over the line"), and a second table shows 6, 8 and 10 AWG failing at 3.95 / 6.28 / 9.99 %. The rubric's own "next size smaller" is 6 AWG; the answer takes "next size" literally (5 AWG, the v2 choice that grade called unstockable) and shows 6 AWG as well, so both readings are served
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### Calibration & honesty (2)
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- [x] (1) States the conductor temperature / resistivity assumption → 1/1 — "These are free-air copper numbers" and "copper resistance rises ~0.4 %/°C, so a warm run adds a few percent on top". As in v3, "20 °C" is implied by "free-air" rather than stated
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- [x] (1) Notes ampacity is a separate (easily met) check, or at least does not claim ampacity drove the choice → 1/1 — on the second clause: the choice is argued entirely from voltage drop, and ampacity is never invoked. The word does not appear; v3's explicit "Ampacity is not your constraint here" was better
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### Tool use (2)
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- [x] (2) `wiring_calc`. 1 if `matlab_run` with a correct formula and correct resistance values. 0 if mental. → 2/2 — two `voltage_drop` calls (6 and 8 AWG) in parallel; the "Nearby gauges, same run" list on each result supplied 3, 4, 5, 7, 9, 10 AWG, so every drop in both tables is a tool figure. The thinking's hand-worked resistances were explicitly set aside ("Let me use the tool instead of guessing")
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### Communication (1)
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- [x] (1) Gauge first, two drops side by side, one line on assumptions → 1/1 — bold pick in the heading, the two-row table immediately, the assumption in the closing bullets
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### Automatic deductions
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- −3 picked from the one-way length → not applied
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- −2 recommends AWG 8 or smaller → not applied
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- −1 no margin shown → not applied — both tables show it, and the 16 mV overshoot on 5 AWG is called out
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- −1 intent-without-call (set-wide) → not applied
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- automatic fail (set-wide) → not applied
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## Harness observations (fill in after the run)
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- Run date/time (UTC): 2026-09-12T04:26:37Z (dumped 04:27:46Z)
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- Model tag / Open WebUI version: qwen3.8:latest / Open WebUI 0.11.3
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- Tool calls, in order (copy from the `result.txt` header): 2 — `wiring_calc` {voltage_drop, 6 AWG, 9.144 m, 20 A, 12 V} ∥ `wiring_calc` {voltage_drop, 8 AWG, …}
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- Wasted, failed, or repeated calls: none. The most economical run of the four (v1 ?, v2 8 with a 422, v3 7): the nearby-gauges list did the work the four extra `awg_properties` calls did in v3
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- Prefill time / total time / tokens (from the `usage:` line in `result.txt`): prefill=3.4s / total=27.1s (decode=23.7s, 41.0 tok/s) / prompt_eval_count=11401, completion_tokens=972; status line: 1,911 generated
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- Ended a turn with a statement of intent and no tool call? (y/n): n
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- Live status indicator matched what actually happened? (y/n): y — two `Calling wiring_calc` lines, `Done · 2 tool calls · prefill 5.1 s for 12,955 tokens · 1,911 generated`
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- Anything odd (loops, truncation notices, tool errors, effect of the inlet nudge): the nudge fires (12 V, 20 A, 30 feet). The thinking hand-works all five gauges from remembered Ω/ft values, reaches "4 AWG… under 0.36V!", and then — "Wait, let me be more careful with the resistance values. Let me use the tool instead of guessing" — which is the right order. **One wrong secondary number in prose**: "4 AWG gives you ~40 mV of headroom under the 3 % limit" — 360 − 298 = **62 mV**. The 5 AWG overshoot in the same paragraph (0.016 V) is right. This is the v1/v2 pattern (a number computed in prose rather than in the tool is wrong) that v3 had shaken off. Also unscored and loose: "a 30 A fuse is common on 4 AWG runs" — the fuse protects the wire and 4 AWG carries far more than 30 A; the sentence is not wrong, just not a reason. The `wiring_calc` local-code advisory is reflected as "free-air copper numbers… if bundled or in conduit, add a few percent"
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### Change 55 checks (this round's changes — fill in even when they did not fire)
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- Did a tool result carry a `Sources:` trailer? (y/n): n — calculator
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- Did the answer end with a URL — written by the model, or appended by the `answer_sources` filter? (model / filter / none): none — none expected
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- Any of the 55.2 tool fixes exercised? Which, and did it fire correctly?: none. The 55.2 note that "bad parameters came back as JSON 422 bodies (m06, m03-v2)" is the fix for v2's `awg: -4` failure; no bad parameter was sent this round, so the prose-422 path was not exercised here. Length was given in metres per the schema (contrast e16, where "100ft" was sent and mis-parsed)
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## Result (fill in)
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- **Score:** 10 / 10
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- **Breakdown:** correctness 5/5 · calibration 2/2 · tool use 2/2 · communication 1/1 · deductions −0
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- **Verdict:** pass
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- **What it got right:** the trap, deliberately, before any call; AWG 4 with both 5 and 6 AWG shown failing; every drop in both tables from the tool; the temperature effect stated with a number; two calls where v3 needed seven
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- **What it got wrong:** nothing scored. One in-prose number (the 4 AWG headroom, 40 for 62 mV) is wrong; ampacity is not mentioned, only not misused
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- **Change from the previous round:** **10 → 10 (0).** Fourth round at ceiling, and the cheapest — the nearby-gauges list was finally used as the tool intends, so two calls replaced seven. Two small slides in the unscored margin: the comparison gauge went back to the literal 5 AWG (with 6 AWG still shown), and one prose-computed number is wrong where v3 had none. Change 55 has no surface here
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- **Worth recording in TUNING.md?** (only if it exposes a harness or prompt weakness): no — a data point for the "secondary numbers in prose" pattern, which the rubric does not score and which v3's grade had hoped was gone
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## Grader notes
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- Ground truth verification: as in v2/v3 — 60 ft of conductor at 20 A on 12 V: AWG 4 0.298 V / 2.48 %, AWG 5 0.376 V / 3.13 %, AWG 6 0.474 V / 3.95 %, AWG 8 0.754 V / 6.28 %, AWG 10 1.199 V / 9.99 %. Every figure in both tables matches the tool. Load voltages 11.70 / 11.62 V correct. Headroom: 0.360 − 0.298 = 0.062 V, not ~0.040. Overshoot 0.376 − 0.360 = 0.016 V correct
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- Rubric issues: none new. The "next size smaller" ambiguity (5 vs 6 AWG) was served both ways this round; v2's note stands
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########################################################################
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# owuitools prompt test result
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# prompt dir : medium/m03-dc-wire-gauge (round v4)
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# chat id : 2400a5f0-f0ad-4c79-86b7-b682fe4be407
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# chat title : Copper Wire Gauge for 12V 20A Load
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# user : the operator
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# model : qwen3.8:latest
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# turns : 2 messages on selected branch
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# tool calls : 2 wiring_calc x2
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# dumped at : 2026-09-12T04:27:46Z
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########################################################################
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=== USER (2026-09-12T04:26:37Z) ===
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I need to run 12 V DC to a 20 A load that's 30 feet from the battery. What copper wire gauge keeps the voltage drop under 3%? Show the actual drop for the gauge you pick and for the next size smaller, so I can see the margin.
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=== ASSISTANT (2026-09-12T04:26:44Z, model qwen3.8:latest) ===
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usage: prompt_eval_count=11401 eval_count=972 prompt_tokens=11401 completion_tokens=972 total=27.1s prefill=3.4s decode=23.7s 41.0 tok/s
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=== [1] THINKING ===
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The user wants to know what gauge of copper wire will keep voltage drop under 3% for a 20A load at 12V over 30 feet.
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Let me think about this:
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- Voltage: 12V DC
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- Current: 20A
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- Distance: 30 feet (one way), so total wire length = 60 feet (out and back)
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- Max voltage drop: 3% of 12V = 0.36V
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I need to find the wire gauge where the voltage drop is under 0.36V.
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Let me use the wiring_calc tool to check different gauges. I'll start with common sizes and work through them.
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Actually, let me calculate first what resistance we need:
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- Max drop = 0.36V
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- Current = 20A
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- Total wire length = 60 feet
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- Max resistance = V/I = 0.36/20 = 0.018 ohms
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- Resistance per foot = 0.018/60 = 0.0003 ohms/foot
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Copper wire resistances (approximately):
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- 12 AWG: about 0.001588 ohms/foot → 60ft × 0.001588 = 0.0953 ohms → drop = 20 × 0.0953 = 1.91V → way too much
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- 10 AWG: about 0.001 ohms/foot → 60ft × 0.001 = 0.06 ohms → drop = 20 × 0.06 = 1.2V → still too much
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- 8 AWG: about 0.000628 ohms/foot → 60ft × 0.000628 = 0.0377 ohms → drop = 20 × 0.0377 = 0.754V → still over 0.36V
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- 6 AWG: about 0.000394 ohms/foot → 60ft × 0.000394 = 0.0236 ohms → drop = 20 × 0.0236 = 0.473V → still over
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- 4 AWG: about 0.000248 ohms/foot → 60ft × 0.000248 = 0.0149 ohms → drop = 20 × 0.0149 = 0.298V → under 0.36V!
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Wait, let me be more careful with the resistance values. Let me use the tool instead of guessing.
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Actually, I should use the wiring_calc tool with voltage_drop calculation. Let me check a few gauges.
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Let me check 6 AWG and 8 AWG first to see where we are.
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Actually, let me just run the calculations for several gauges using the tool. The tool takes a single gauge at a time, so let me start with a reasonable guess.
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For DC voltage drop:
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- 30 feet one way = 60 feet total (out and back)
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- 20A
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- 12V
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Let me check 6 AWG first since my rough math suggests it might be close.
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=== [2] TOOL CALL: wiring_calc (call_32n1n8ww) ===
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{
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"calculation": "voltage_drop",
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"awg": 6,
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"current": "20",
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"length": "9.144",
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"voltage": "12"
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}
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=== [3] TOOL CALL: wiring_calc (call_iffyrazj) ===
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{
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"calculation": "voltage_drop",
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"awg": 8,
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"current": "20",
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"length": "9.144",
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"voltage": "12"
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}
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=== [4] TOOL RESULT: wiring_calc (call_32n1n8ww) ===
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# Voltage drop over 9.144 m of 6 AWG
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**Drop: 474 mV** (round trip, 18.288 m of conductor)
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Conductor: 6 AWG = 13.30 mm² (4.12 mm diameter), 1.296 Ω/km
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Loop resistance: 23.7 mΩ
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Power lost as heat: 9.481 W
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That is 3.95% of a 12 V supply — above the usual 3% guideline — consider thicker wire or a shorter run.
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Voltage at the load: 11.53 V
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## Nearby gauges, same run
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- 3 AWG ( 26.67 mm²): 236.4 mV = 1.97%
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- 4 AWG ( 21.15 mm²): 298.1 mV = 2.48%
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- 5 AWG ( 16.77 mm²): 375.9 mV = 3.13%
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- 7 AWG ( 10.55 mm²): 597.8 mV = 4.98%
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- 8 AWG ( 8.37 mm²): 753.8 mV = 6.28%
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- 9 AWG ( 6.63 mm²): 950.5 mV = 7.92%
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Lower AWG numbers mean thicker wire and less drop.
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**For mains or building wiring, follow your local electrical code (NEC 310.16 in the US, BS 7671 in the UK) rather than these figures.** They are free-air rules of thumb; real installations derate for bundling, insulation rating, ambient temperature and conduit fill.
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=== [5] TOOL RESULT: wiring_calc (call_iffyrazj) ===
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# Voltage drop over 9.144 m of 8 AWG
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**Drop: 753.8 mV** (round trip, 18.288 m of conductor)
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Conductor: 8 AWG = 8.37 mm² (3.26 mm diameter), 2.061 Ω/km
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Loop resistance: 37.69 mΩ
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Power lost as heat: 15.08 W
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That is 6.28% of a 12 V supply — above the usual 3% guideline — consider thicker wire or a shorter run.
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Voltage at the load: 11.25 V
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## Nearby gauges, same run
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- 5 AWG ( 16.77 mm²): 375.9 mV = 3.13%
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- 6 AWG ( 13.30 mm²): 474 mV = 3.95%
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- 7 AWG ( 10.55 mm²): 597.8 mV = 4.98%
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- 9 AWG ( 6.63 mm²): 950.5 mV = 7.92%
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- 10 AWG ( 5.26 mm²): 1.199 V = 9.99%
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- 11 AWG ( 4.17 mm²): 1.511 V = 12.59%
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Lower AWG numbers mean thicker wire and less drop.
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**For mains or building wiring, follow your local electrical code (NEC 310.16 in the US, BS 7671 in the UK) rather than these figures.** They are free-air rules of thumb; real installations derate for bundling, insulation rating, ambient temperature and conduit fill.
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=== [6] THINKING (8s) ===
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Let me analyze the results:
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- 30 feet = 9.144 meters one way, so round trip is 18.288 m
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- 6 AWG: 474 mV drop = 3.95% — just over 3%
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- 5 AWG: 375.9 mV drop = 3.13% — still just over 3%
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- 4 AWG: 298.1 mV drop = 2.48% — under 3% ✓
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So the smallest gauge that keeps the drop under 3% is **4 AWG**.
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The next size smaller (thinner) would be 5 AWG at 375.9 mV = 3.13%.
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Wait, let me re-read the question. "Show the actual drop for the gauge you pick and for the next size smaller." The "next size smaller" means the next thinner wire (higher AWG number), which is 5 AWG.
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So my answer is:
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- **4 AWG**: 298.1 mV drop = 2.48% of 12V → voltage at load = 11.70 V
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- **5 AWG** (one size smaller/thinner): 375.9 mV drop = 3.13% of 12V → voltage at load = 11.62 V
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This gives a clear margin comparison. 4 AWG gets you under 3%, and 5 AWG just barely misses.
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Let me also note that the tool already confirmed 6 AWG is 3.95% and 8 AWG is 6.28%, so 4 AWG is definitely the right pick.
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Let me present this clearly.
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=== [7] ASSISTANT TEXT ===
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## Answer: **4 AWG copper**
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Here's the comparison you asked for, both gauges at 20 A over 30 ft (round-trip 60 ft / 18.3 m):
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| Gauge | Loop resistance | Voltage drop | % of 12 V | Load sees |
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|-------|----------------|-------------|-----------|-----------|
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| **4 AWG** (21.2 mm²) | 14.9 mΩ | **298 mV** | **2.48 %** | 11.70 V |
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| 5 AWG (16.8 mm²) | 18.8 mΩ | **376 mV** | **3.13 %** | 11.62 V |
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### Why 4 AWG and not 5?
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Your 3 % ceiling is 0.36 V. 5 AWG lands at 0.376 V — just 0.016 V over the line. That's a razor-thin miss, and in practice it gets worse because:
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- Battery sag under load (a "12 V" battery at 20 A is often closer to 11.6–11.8 V before you even start running wire).
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- Temperature: copper resistance rises ~0.4 %/°C, so a warm run adds a few percent on top.
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- Connector and terminal resistance at both ends, which the wire calc doesn't include.
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4 AWG gives you ~40 mV of headroom under the 3 % limit, which absorbs all of that.
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### For context, the gauges that clearly fail:
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| Gauge | Drop | % |
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|-------|------|---|
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| 6 AWG | 474 mV | 3.95 % |
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| 8 AWG | 754 mV | 6.28 % |
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| 10 AWG | 1.20 V | 9.99 % |
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### Practical notes
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- 4 AWG is the smallest gauge that meets your spec. If cost or stiffness is an issue, 5 AWG *might* work in a cold, well-ventilated installation with short, low-resistance connections — but it's not meeting the stated 3 % target.
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- Make sure the battery fuse/PTC is rated for 20 A continuous (a 30 A fuse is common on 4 AWG runs and is fine here).
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- These are free-air copper numbers. If the cable is bundled or in conduit, add a few percent to the drop.
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=== STATUS HISTORY (live progress indicator) ===
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- Processing prompt
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- Thinking · first token after 5.3 s
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- Thought: The user wants to know what gauge of copper wire will keep voltage drop under 3% for a … 6 AWG first since my rough math suggests it might be close.
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- Calling wiring_calc
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- Calling wiring_calc
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- Thinking
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- Thought: Let me analyze the results: - 30 feet = 9.144 meters one way, so round trip is 18.288 m … AWG is definitely the right pick. Let me present this clearly.
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- Writing response
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- Done · 2 tool calls · prefill 5.1 s for 12,955 tokens · 1,911 generated
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Reference in New Issue
Block a user