[ { "id": "davinci", "title": "Water-raising machines", "file": "davinci-codex-atlanticus-machines.png", "code": "rho = 1000 kg/m^3 \"Illustrative water density\"\ng = 9.81 m/s^2\nflow = 0.002 m^3/s in 0.001..0.005 ± 10% \"Modern illustrative flow\"\nhead = 3 m \"Assumed lift height\"\nefficiency = 0.45 \"Assumed overall efficiency\"\npumpPower := rho*g*flow*head/efficiency [W]\ncheck drive: pumpPower <= 200 W\nsweep Flow: flow = 0.001, 0.002, 0.005 m^3/s", "output": "pumpPower", "vary": "flow", "question": "How much shaft power lifts a chosen water flow?", "expected": [ { "name": "pumpPower", "value": 130.79999999999998, "unit": "W" } ], "steps": [ { "title": "Preserve the source and the question", "prompt": "Create a Napkin study called “Water-raising machines — illustrative sizing”. Keep the attached historical drawing as a source reference. Pump topology and the water-lift intention; never infer dimensions from the folio. The engineering question is: How much shaft power lifts a chosen water flow? Do not invent historical dimensions or ratings.", "encoding": "napkin_capabilities → napkin_create → napkin_snapshot; optional napkin_edit set-drawing for source metadata." }, { "title": "Separate facts from assumptions", "prompt": "List what the source supports, what is uncertain, and what must be measured. For this first pass use clearly labeled modern illustrative values, never historical measurements. Model this chain: Flow, lift height, efficiency → shaft power → drive check.", "encoding": "Input quantities carry units, ranges, tolerances and assumption strings. Derived quantities retain equations." }, { "title": "Encode the compact sketch model", "prompt": "Use napkin_sketch to apply the following text to the study with the current expectedRevision and prefix \"davinci\". Explain pumpPower and open the study. These numbers are illustrative assumptions.", "encoding": "napkin_snapshot → napkin_sketch → napkin_explain → napkin_open; scalar code below." }, { "title": "Ask a decision question", "prompt": "Does required power exceed 200 W at 5 L/s? Which input dominates? Run the named scalar sweep in analytic mode and use napkin_analyze sensitivity for pumpPower versus flow. Report units, the check outcomes and assumptions; keep baseline inputs unchanged.", "encoding": "napkin_run for the sweep; napkin_analyze kind=sensitivity using returned quantity refs." }, { "title": "Compare against evidence and revise", "prompt": "Measure flow, lift and input torque/speed on a bench pump; compare power and losses. Attach test or external-analysis evidence as source references. Compare like-for-like conditions, explain any discrepancy, and revise only inputs justified by that evidence. Report what the model still cannot answer.", "encoding": "napkin_explain → evidence reference via napkin_edit → revision-checked input update → rerun; prior runs become stale." } ], "limitation": "A steady hydraulic power budget; no gear motion, cavitation or pump curve. Efficiency is assumed.", "capability": "Unit-aware scalar expressions, expression checks, analytic sweep and numerical sensitivity.", "takeaway": "Flow, lift height, efficiency → shaft power → drive check.", "assumptionNotice": "Every number is a modern illustrative assumption, not a historical reconstruction.", "validation": { "created": 8, "baselineStatus": "passed", "baselineChecks": { "davinci:check:drive": { "samples": [ { "time": 0, "value": { "value": 130.79999999999998, "unit": "W" } } ], "value": { "value": 130.79999999999998, "unit": "W" }, "passed": true } }, "runStatus": "failed", "sweep": { "id": "1b643f08-6619-471f-80ac-2c547de5055f", "revision": "1dfb7c12-c084-454d-8891-eef0e3c7b1b6", "scenario": { "id": "davinci:scenario:Flow", "kind": "scenario" }, "mode": "analytic", "backend": "napkin-analytic", "backendVersion": "0.1.0", "seed": 0, "status": "failed", "observations": { "davinci:check:drive": { "samples": [ { "time": 0, "value": { "value": 65.39999999999999, "unit": "W" } }, { "time": 1, "value": { "value": 130.79999999999998, "unit": "W" } }, { "time": 2, "value": { "value": 327, "unit": "W" } } ], "value": { "value": 327, "unit": "W" }, "failedSamples": [ 2 ], "passed": false } }, "resolvedValues": { "davinci:rho": { "value": 1000, "unit": "kg/m^3" }, "davinci:g": { "value": 9.81, "unit": "m/s^2" }, "davinci:flow": { "value": 0.005, "unit": "m^3/s" }, "davinci:head": { "value": 3, "unit": "m" }, "davinci:efficiency": { "value": 0.45, "unit": "" }, "davinci:pumpPower": { "value": 327, "unit": "W" } }, "assumptions": [ { "id": "davinci:rho", "text": "Illustrative water density" }, { "id": "davinci:flow", "text": "Modern illustrative flow" }, { "id": "davinci:head", "text": "Assumed lift height" }, { "id": "davinci:efficiency", "text": "Assumed overall efficiency" } ], "diagnostics": [] }, "sensitivity": { "kind": "sensitivity", "revision": "1dfb7c12-c084-454d-8891-eef0e3c7b1b6", "scenario": null, "method": "Central difference at ±1% of each input; elasticity = (dy/dx)·(x/y)", "limitations": [], "outputs": { "davinci:pumpPower": 130.79999999999998 }, "units": { "davinci:pumpPower": "W" }, "rows": [ { "input": { "id": "davinci:flow", "kind": "quantity" }, "name": "flow", "value": 0.002, "unit": "m^3/s", "derivative": { "davinci:pumpPower": 65400.00000000034 }, "elasticity": { "davinci:pumpPower": 1.0000000000000053 } } ], "evaluations": 3, "milliseconds": 0.49049999999999727 }, "validated": true } }, { "id": "watt", "title": "Separate-condenser engine", "file": "watt-steam-engine-condenser.png", "code": "pressure = 150 kPa in 100..200 ± 10% \"Assumed mean effective pressure\"\nswept = 0.01 m^3 \"Assumed swept volume per working stroke\"\nstrokes = 2 Hz \"Power strokes per second, not shaft rpm\"\nefficiency = 0.8 \"Assumed mechanical efficiency\"\nwork := pressure*swept [J]\nshaftPower := work*strokes*efficiency [W]\ncheck output: shaftPower >= 2000 W\nsweep Pressure: pressure = 100, 150, 200 kPa", "output": "shaftPower", "vary": "pressure", "question": "What shaft power follows from an assumed mean effective pressure?", "expected": [ { "name": "work", "value": 1500, "unit": "J" }, { "name": "shaftPower", "value": 2400, "unit": "W" } ], "steps": [ { "title": "Preserve the source and the question", "prompt": "Create a Napkin study called “Separate-condenser engine — illustrative sizing”. Keep the attached historical drawing as a source reference. Label the source as an 1878 published engraving of a 1784 design, and retain the condenser idea. The engineering question is: What shaft power follows from an assumed mean effective pressure? Do not invent historical dimensions or ratings.", "encoding": "napkin_capabilities → napkin_create → napkin_snapshot; optional napkin_edit set-drawing for source metadata." }, { "title": "Separate facts from assumptions", "prompt": "List what the source supports, what is uncertain, and what must be measured. For this first pass use clearly labeled modern illustrative values, never historical measurements. Model this chain: Mean effective pressure, displaced volume and stroke frequency → indicated work → shaft power.", "encoding": "Input quantities carry units, ranges, tolerances and assumption strings. Derived quantities retain equations." }, { "title": "Encode the compact sketch model", "prompt": "Use napkin_sketch to apply the following text to the study with the current expectedRevision and prefix \"watt\". Explain shaftPower and open the study. These numbers are illustrative assumptions.", "encoding": "napkin_snapshot → napkin_sketch → napkin_explain → napkin_open; scalar code below." }, { "title": "Ask a decision question", "prompt": "What mean effective pressure makes the 2 kW check pass? Run the named scalar sweep in analytic mode and use napkin_analyze sensitivity for shaftPower versus pressure. Report units, the check outcomes and assumptions; keep baseline inputs unchanged.", "encoding": "napkin_run for the sweep; napkin_analyze kind=sensitivity using returned quantity refs." }, { "title": "Compare against evidence and revise", "prompt": "Compare with a measured indicator diagram, actual displacement and brake power. Attach test or external-analysis evidence as source references. Compare like-for-like conditions, explain any discrepancy, and revise only inputs justified by that evidence. Report what the model still cannot answer.", "encoding": "napkin_explain → evidence reference via napkin_edit → revision-checked input update → rerun; prior runs become stale." } ], "limitation": "Not a steam cycle or condenser heat-transfer model. Mean effective pressure must come from evidence.", "capability": "Unit-aware scalar expressions, expression checks, analytic sweep and numerical sensitivity.", "takeaway": "Mean effective pressure, displaced volume and stroke frequency → indicated work → shaft power.", "assumptionNotice": "Every number is a modern illustrative assumption, not a historical reconstruction.", "validation": { "created": 8, "baselineStatus": "passed", "baselineChecks": { "watt:check:output": { "samples": [ { "time": 0, "value": { "value": 2400, "unit": "W" } } ], "value": { "value": 2400, "unit": "W" }, "passed": true } }, "runStatus": "failed", "sweep": { "id": "d72c2966-39cd-4e22-a02c-f341bbd28843", "revision": "bb9be4a2-4353-470b-96cb-41ed95aac02b", "scenario": { "id": "watt:scenario:Pressure", "kind": "scenario" }, "mode": "analytic", "backend": "napkin-analytic", "backendVersion": "0.1.0", "seed": 0, "status": "failed", "observations": { "watt:check:output": { "samples": [ { "time": 0, "value": { "value": 1600, "unit": "W" } }, { "time": 1, "value": { "value": 2400, "unit": "W" } }, { "time": 2, "value": { "value": 3200, "unit": "W" } } ], "value": { "value": 1600, "unit": "W" }, "failedSamples": [ 0 ], "passed": false } }, "resolvedValues": { "watt:pressure": { "value": 200, "unit": "kPa" }, "watt:swept": { "value": 0.01, "unit": "m^3" }, "watt:strokes": { "value": 2, "unit": "Hz" }, "watt:efficiency": { "value": 0.8, "unit": "" }, "watt:work": { "value": 2000, "unit": "J" }, "watt:shaftPower": { "value": 3200, "unit": "W" } }, "assumptions": [ { "id": "watt:pressure", "text": "Assumed mean effective pressure" }, { "id": "watt:swept", "text": "Assumed swept volume per working stroke" }, { "id": "watt:strokes", "text": "Power strokes per second, not shaft rpm" }, { "id": "watt:efficiency", "text": "Assumed mechanical efficiency" } ], "diagnostics": [] }, "sensitivity": { "kind": "sensitivity", "revision": "bb9be4a2-4353-470b-96cb-41ed95aac02b", "scenario": null, "method": "Central difference at ±1% of each input; elasticity = (dy/dx)·(x/y)", "limitations": [], "outputs": { "watt:shaftPower": 2400 }, "units": { "watt:shaftPower": "W" }, "rows": [ { "input": { "id": "watt:pressure", "kind": "quantity" }, "name": "pressure", "value": 150, "unit": "kPa", "derivative": { "watt:shaftPower": 16 }, "elasticity": { "watt:shaftPower": 1 } } ], "evaluations": 3, "milliseconds": 0.11654100000004064 }, "validated": true } }, { "id": "bell", "title": "Liquid transmitter", "file": "bell-telephone-notebook.png", "code": "voltage = 3 V \"Illustrative bench supply\"\nseriesResistance = 100 ohm\ntransmitterResistance = 200 ohm \"Illustrative nominal liquid-contact resistance\"\ndeltaResistance = 10 ohm in 1..30 \"Small imposed resistance change\"\nbaseline := voltage/(seriesResistance+transmitterResistance) [A]\nperturbed := voltage/(seriesResistance+transmitterResistance+deltaResistance) [A]\nsignalChange := abs(perturbed-baseline) [mA]\ncheck measurable: signalChange >= 0.2 mA\nsweep Contact: deltaResistance = 1, 10, 30 ohm", "output": "signalChange", "vary": "deltaResistance", "question": "How large is a static current change from a resistance perturbation?", "expected": [ { "name": "baseline", "value": 0.01, "unit": "A" }, { "name": "perturbed", "value": 0.00967741935483871, "unit": "A" }, { "name": "signalChange", "value": 0.3225806451612901, "unit": "mA" } ], "steps": [ { "title": "Preserve the source and the question", "prompt": "Create a Napkin study called “Liquid transmitter — illustrative sizing”. Keep the attached historical drawing as a source reference. Preserve the notebook entry and liquid-transmitter drawing; mark sound-to-resistance coupling as unresolved. The engineering question is: How large is a static current change from a resistance perturbation? Do not invent historical dimensions or ratings.", "encoding": "napkin_capabilities → napkin_create → napkin_snapshot; optional napkin_edit set-drawing for source metadata." }, { "title": "Separate facts from assumptions", "prompt": "List what the source supports, what is uncertain, and what must be measured. For this first pass use clearly labeled modern illustrative values, never historical measurements. Model this chain: Supply, series resistance, transmitter resistance and a perturbation → two DC operating points.", "encoding": "Input quantities carry units, ranges, tolerances and assumption strings. Derived quantities retain equations." }, { "title": "Encode the compact sketch model", "prompt": "Use napkin_sketch to apply the following text to the study with the current expectedRevision and prefix \"bell\". Explain signalChange and open the study. These numbers are illustrative assumptions.", "encoding": "napkin_snapshot → napkin_sketch → napkin_explain → napkin_open; scalar code below." }, { "title": "Ask a decision question", "prompt": "How large must the resistance change be to produce 0.2 mA? Run the named scalar sweep in analytic mode and use napkin_analyze sensitivity for signalChange versus deltaResistance. Report units, the check outcomes and assumptions; keep baseline inputs unchanged.", "encoding": "napkin_run for the sweep; napkin_analyze kind=sensitivity using returned quantity refs." }, { "title": "Compare against evidence and revise", "prompt": "Measure static resistance versus contact displacement and compare the predicted current difference. Attach test or external-analysis evidence as source references. Compare like-for-like conditions, explain any discrepancy, and revise only inputs justified by that evidence. Report what the model still cannot answer.", "encoding": "napkin_explain → evidence reference via napkin_edit → revision-checked input update → rerun; prior runs become stale." } ], "limitation": "A pair of DC points; no acoustics, diaphragm motion, waveform, intelligibility or transient circuit simulation.", "capability": "Unit-aware scalar expressions, expression checks, analytic sweep and numerical sensitivity.", "takeaway": "Supply, series resistance, transmitter resistance and a perturbation → two DC operating points.", "assumptionNotice": "Every number is a modern illustrative assumption, not a historical reconstruction.", "validation": { "created": 9, "baselineStatus": "passed", "baselineChecks": { "bell:check:measurable": { "samples": [ { "time": 0, "value": { "value": 0.3225806451612901, "unit": "mA" } } ], "value": { "value": 0.3225806451612901, "unit": "mA" }, "passed": true } }, "runStatus": "failed", "sweep": { "id": "7e1f6566-d01a-4874-a129-04b59fa70739", "revision": "184e723c-5268-4a74-817c-b20fba4be29d", "scenario": { "id": "bell:scenario:Contact", "kind": "scenario" }, "mode": "analytic", "backend": "napkin-analytic", "backendVersion": "0.1.0", "seed": 0, "status": "failed", "observations": { "bell:check:measurable": { "samples": [ { "time": 0, "value": { "value": 0.03322259136212709, "unit": "mA" } }, { "time": 1, "value": { "value": 0.3225806451612901, "unit": "mA" } }, { "time": 2, "value": { "value": 0.9090909090909097, "unit": "mA" } } ], "value": { "value": 0.03322259136212709, "unit": "mA" }, "failedSamples": [ 0 ], "passed": false } }, "resolvedValues": { "bell:voltage": { "value": 3, "unit": "V" }, "bell:seriesResistance": { "value": 100, "unit": "ohm" }, "bell:transmitterResistance": { "value": 200, "unit": "ohm" }, "bell:deltaResistance": { "value": 30, "unit": "ohm" }, "bell:baseline": { "value": 0.01, "unit": "A" }, "bell:perturbed": { "value": 0.00909090909090909, "unit": "A" }, "bell:signalChange": { "value": 0.9090909090909097, "unit": "mA" } }, "assumptions": [ { "id": "bell:voltage", "text": "Illustrative bench supply" }, { "id": "bell:transmitterResistance", "text": "Illustrative nominal liquid-contact resistance" }, { "id": "bell:deltaResistance", "text": "Small imposed resistance change" } ], "diagnostics": [] }, "sensitivity": { "kind": "sensitivity", "revision": "184e723c-5268-4a74-817c-b20fba4be29d", "scenario": null, "method": "Central difference at ±1% of each input; elasticity = (dy/dx)·(x/y)", "limitations": [], "outputs": { "bell:signalChange": 0.3225806451612901 }, "units": { "bell:signalChange": "mA" }, "rows": [ { "input": { "id": "bell:deltaResistance", "kind": "quantity" }, "name": "deltaResistance", "value": 10, "unit": "ohm", "derivative": { "bell:signalChange": 0.03121748503824906 }, "elasticity": { "bell:signalChange": 0.9677420361857215 } } ], "evaluations": 3, "milliseconds": 0.1742079999999646 }, "validated": true } }, { "id": "edison", "title": "Carbon-filament lamp", "file": "edison-electric-lamp-patent.png", "code": "voltage = 100 V \"Illustrative modern supply assumption\"\nresistance = 200 ohm in 100..400 ± 10% \"Assumed operating-temperature resistance\"\ncurrent := voltage/resistance [A]\npower := voltage*current [W]\ncheck powerBudget: power <= 60 W\ncheck currentBudget: current <= 0.6 A\nsweep Filament: resistance = 100, 200, 400 ohm", "output": "power", "vary": "resistance", "question": "What current and power does an assumed hot filament draw?", "expected": [ { "name": "current", "value": 0.5, "unit": "A" }, { "name": "power", "value": 50, "unit": "W" } ], "steps": [ { "title": "Preserve the source and the question", "prompt": "Create a Napkin study called “Carbon-filament lamp — illustrative sizing”. Keep the attached historical drawing as a source reference. Preserve the patent structure and filament-support intent; do not estimate temperature from the image. The engineering question is: What current and power does an assumed hot filament draw? Do not invent historical dimensions or ratings.", "encoding": "napkin_capabilities → napkin_create → napkin_snapshot; optional napkin_edit set-drawing for source metadata." }, { "title": "Separate facts from assumptions", "prompt": "List what the source supports, what is uncertain, and what must be measured. For this first pass use clearly labeled modern illustrative values, never historical measurements. Model this chain: Operating voltage and hot resistance → current and electrical power → supply checks.", "encoding": "Input quantities carry units, ranges, tolerances and assumption strings. Derived quantities retain equations." }, { "title": "Encode the compact sketch model", "prompt": "Use napkin_sketch to apply the following text to the study with the current expectedRevision and prefix \"edison\". Explain power and open the study. These numbers are illustrative assumptions.", "encoding": "napkin_snapshot → napkin_sketch → napkin_explain → napkin_open; scalar code below." }, { "title": "Ask a decision question", "prompt": "Which resistance values stay below both 60 W and 0.6 A? Run the named scalar sweep in analytic mode and use napkin_analyze sensitivity for power versus resistance. Report units, the check outcomes and assumptions; keep baseline inputs unchanged.", "encoding": "napkin_run for the sweep; napkin_analyze kind=sensitivity using returned quantity refs." }, { "title": "Compare against evidence and revise", "prompt": "Measure hot resistance and supply power; use optical and thermal measurements for brightness and lifetime. Attach test or external-analysis evidence as source references. Compare like-for-like conditions, explain any discrepancy, and revise only inputs justified by that evidence. Report what the model still cannot answer.", "encoding": "napkin_explain → evidence reference via napkin_edit → revision-checked input update → rerun; prior runs become stale." } ], "limitation": "DC electrical sizing only; no radiation, temperature-dependent resistance, vacuum physics, brightness or lifetime prediction.", "capability": "Unit-aware scalar expressions, expression checks, analytic sweep and numerical sensitivity.", "takeaway": "Operating voltage and hot resistance → current and electrical power → supply checks.", "assumptionNotice": "Every number is a modern illustrative assumption, not a historical reconstruction.", "validation": { "created": 7, "baselineStatus": "passed", "baselineChecks": { "edison:check:powerBudget": { "samples": [ { "time": 0, "value": { "value": 50, "unit": "W" } } ], "value": { "value": 50, "unit": "W" }, "passed": true }, "edison:check:currentBudget": { "samples": [ { "time": 0, "value": { "value": 0.5, "unit": "A" } } ], "value": { "value": 0.5, "unit": "A" }, "passed": true } }, "runStatus": "failed", "sweep": { "id": "e9896e98-84c5-41ce-a9eb-9515f0b4a57c", "revision": "948b7e73-c01b-4422-86ef-cb327df7d50d", "scenario": { "id": "edison:scenario:Filament", "kind": "scenario" }, "mode": "analytic", "backend": "napkin-analytic", "backendVersion": "0.1.0", "seed": 0, "status": "failed", "observations": { "edison:check:powerBudget": { "samples": [ { "time": 0, "value": { "value": 100, "unit": "W" } }, { "time": 1, "value": { "value": 50, "unit": "W" } }, { "time": 2, "value": { "value": 25, "unit": "W" } } ], "value": { "value": 100, "unit": "W" }, "failedSamples": [ 0 ], "passed": false }, "edison:check:currentBudget": { "samples": [ { "time": 0, "value": { "value": 1, "unit": "A" } }, { "time": 1, "value": { "value": 0.5, "unit": "A" } }, { "time": 2, "value": { "value": 0.25, "unit": "A" } } ], "value": { "value": 1, "unit": "A" }, "failedSamples": [ 0 ], "passed": false } }, "resolvedValues": { "edison:voltage": { "value": 100, "unit": "V" }, "edison:resistance": { "value": 400, "unit": "ohm" }, "edison:current": { "value": 0.25, "unit": "A" }, "edison:power": { "value": 25, "unit": "W" } }, "assumptions": [ { "id": "edison:voltage", "text": "Illustrative modern supply assumption" }, { "id": "edison:resistance", "text": "Assumed operating-temperature resistance" } ], "diagnostics": [] }, "sensitivity": { "kind": "sensitivity", "revision": "948b7e73-c01b-4422-86ef-cb327df7d50d", "scenario": null, "method": "Central difference at ±1% of each input; elasticity = (dy/dx)·(x/y)", "limitations": [], "outputs": { "edison:power": 50 }, "units": { "edison:power": "W" }, "rows": [ { "input": { "id": "edison:resistance", "kind": "quantity" }, "name": "resistance", "value": 200, "unit": "ohm", "derivative": { "edison:power": -0.2500250025002497 }, "elasticity": { "edison:power": -1.000100010000999 } } ], "evaluations": 3, "milliseconds": 0.0747079999999869 }, "validated": true } }, { "id": "tesla", "title": "Rotating-field motor", "file": "tesla-induction-motor-patent.png", "code": "frequency = 50 Hz \"Illustrative supply frequency\"\npoles = 4 \"Assumed total magnetic poles\"\nslip = 0.04 in 0.01..0.1 \"Assumed motoring slip\"\npower = 500 W \"Assumed mechanical shaft output\"\nsyncOmega := 4*pi*frequency/poles [rad/s]\nshaftOmega := syncOmega*(1-slip) [rad/s]\ntorque := power/shaftOmega [N*m]\ncheck torqueBudget: torque <= 4 N*m\nsweep Slip: slip = 0.01, 0.04, 0.1", "output": "torque", "vary": "slip", "question": "How do assumed slip and mechanical output set shaft speed and torque?", "expected": [ { "name": "syncOmega", "value": 157.07963267948966, "unit": "rad/s" }, { "name": "shaftOmega", "value": 150.79644737231007, "unit": "rad/s" }, { "name": "torque", "value": 3.315727981081153, "unit": "N*m" } ], "steps": [ { "title": "Preserve the source and the question", "prompt": "Create a Napkin study called “Rotating-field motor — illustrative sizing”. Keep the attached historical drawing as a source reference. Preserve the rotating-field winding idea; separate the conceptual motor from any later machine rating. The engineering question is: How do assumed slip and mechanical output set shaft speed and torque? Do not invent historical dimensions or ratings.", "encoding": "napkin_capabilities → napkin_create → napkin_snapshot; optional napkin_edit set-drawing for source metadata." }, { "title": "Separate facts from assumptions", "prompt": "List what the source supports, what is uncertain, and what must be measured. For this first pass use clearly labeled modern illustrative values, never historical measurements. Model this chain: Supply frequency and pole count → synchronous angular speed → slip-adjusted shaft speed → torque.", "encoding": "Input quantities carry units, ranges, tolerances and assumption strings. Derived quantities retain equations." }, { "title": "Encode the compact sketch model", "prompt": "Use napkin_sketch to apply the following text to the study with the current expectedRevision and prefix \"tesla\". Explain torque and open the study. These numbers are illustrative assumptions.", "encoding": "napkin_snapshot → napkin_sketch → napkin_explain → napkin_open; scalar code below." }, { "title": "Ask a decision question", "prompt": "How does increasing assumed slip alter the torque for a fixed 500 W shaft output? Run the named scalar sweep in analytic mode and use napkin_analyze sensitivity for torque versus slip. Report units, the check outcomes and assumptions; keep baseline inputs unchanged.", "encoding": "napkin_run for the sweep; napkin_analyze kind=sensitivity using returned quantity refs." }, { "title": "Compare against evidence and revise", "prompt": "Compare tachometer and dynamometer measurements and the motor datasheet. Attach test or external-analysis evidence as source references. Compare like-for-like conditions, explain any discrepancy, and revise only inputs justified by that evidence. Report what the model still cannot answer.", "encoding": "napkin_explain → evidence reference via napkin_edit → revision-checked input update → rerun; prior runs become stale." } ], "limitation": "Slip and output power are independent assumptions; no electromagnetic field solve, starting torque or torque-slip prediction.", "capability": "Unit-aware scalar expressions, expression checks, analytic sweep and numerical sensitivity.", "takeaway": "Supply frequency and pole count → synchronous angular speed → slip-adjusted shaft speed → torque.", "assumptionNotice": "Every number is a modern illustrative assumption, not a historical reconstruction.", "validation": { "created": 9, "baselineStatus": "passed", "baselineChecks": { "tesla:check:torqueBudget": { "samples": [ { "time": 0, "value": { "value": 3.315727981081153, "unit": "N*m" } } ], "value": { "value": 3.315727981081153, "unit": "N*m" }, "passed": true } }, "runStatus": "passed", "sweep": { "id": "19af94fe-4714-463a-b127-7d7f502fdb99", "revision": "d148472f-1666-4903-b57b-ca5c751a84dd", "scenario": { "id": "tesla:scenario:Slip", "kind": "scenario" }, "mode": "analytic", "backend": "napkin-analytic", "backendVersion": "0.1.0", "seed": 0, "status": "passed", "observations": { "tesla:check:torqueBudget": { "samples": [ { "time": 0, "value": { "value": 3.215251375593845, "unit": "N*m" } }, { "time": 1, "value": { "value": 3.315727981081153, "unit": "N*m" } }, { "time": 2, "value": { "value": 3.53677651315323, "unit": "N*m" } } ], "value": { "value": 3.53677651315323, "unit": "N*m" }, "failedSamples": [], "passed": true } }, "resolvedValues": { "tesla:frequency": { "value": 50, "unit": "Hz" }, "tesla:poles": { "value": 4, "unit": "" }, "tesla:slip": { "value": 0.1, "unit": "" }, "tesla:power": { "value": 500, "unit": "W" }, "tesla:syncOmega": { "value": 157.07963267948966, "unit": "rad/s" }, "tesla:shaftOmega": { "value": 141.3716694115407, "unit": "rad/s" }, "tesla:torque": { "value": 3.53677651315323, "unit": "N*m" } }, "assumptions": [ { "id": "tesla:frequency", "text": "Illustrative supply frequency" }, { "id": "tesla:poles", "text": "Assumed total magnetic poles" }, { "id": "tesla:slip", "text": "Assumed motoring slip" }, { "id": "tesla:power", "text": "Assumed mechanical shaft output" } ], "diagnostics": [] }, "sensitivity": { "kind": "sensitivity", "revision": "d148472f-1666-4903-b57b-ca5c751a84dd", "scenario": null, "method": "Central difference at ±1% of each input; elasticity = (dy/dx)·(x/y)", "limitations": [], "outputs": { "tesla:torque": 3.315727981081153 }, "units": { "tesla:torque": "N*m" }, "rows": [ { "input": { "id": "tesla:slip", "kind": "quantity" }, "name": "slip", "value": 0.04, "unit": "", "derivative": { "tesla:torque": 3.4538839132591814 }, "elasticity": { "tesla:torque": 0.04166667390046852 } } ], "evaluations": 3, "milliseconds": 0.10358300000001464 }, "validated": true } }, { "id": "wright", "title": "Wing-warping aircraft", "file": "wright-flyer-patent.png", "code": "rho = 1.225 kg/m^3 \"Illustrative air density\"\nspeed = 12 m/s in 8..18 ± 5% \"Illustrative flight speed\"\narea = 30 m^2 \"Assumed lifting area\"\nCL = 0.8 \"Assumed lift coefficient\"\nmass = 300 kg \"Assumed all-up mass\"\nweight := mass*9.81 m/s^2 [N]\nlift := 0.5*rho*speed^2*area*CL [N]\ncheck support: lift >= weight\nsweep Speed: speed = 8, 12, 18 m/s", "output": "lift", "vary": "speed", "question": "What airspeed gives enough idealized lift for an assumed mass?", "expected": [ { "name": "weight", "value": 2943, "unit": "N" }, { "name": "lift", "value": 2116.8, "unit": "N" } ], "steps": [ { "title": "Preserve the source and the question", "prompt": "Create a Napkin study called “Wing-warping aircraft — illustrative sizing”. Keep the attached historical drawing as a source reference. Preserve the wing-warping control concept and patent date; keep the drawing distinct from the 1903 flight. The engineering question is: What airspeed gives enough idealized lift for an assumed mass? Do not invent historical dimensions or ratings.", "encoding": "napkin_capabilities → napkin_create → napkin_snapshot; optional napkin_edit set-drawing for source metadata." }, { "title": "Separate facts from assumptions", "prompt": "List what the source supports, what is uncertain, and what must be measured. For this first pass use clearly labeled modern illustrative values, never historical measurements. Model this chain: Air density, speed, lifting area and assumed lift coefficient → lift compared with weight.", "encoding": "Input quantities carry units, ranges, tolerances and assumption strings. Derived quantities retain equations." }, { "title": "Encode the compact sketch model", "prompt": "Use napkin_sketch to apply the following text to the study with the current expectedRevision and prefix \"wright\". Explain lift and open the study. These numbers are illustrative assumptions.", "encoding": "napkin_snapshot → napkin_sketch → napkin_explain → napkin_open; scalar code below." }, { "title": "Ask a decision question", "prompt": "At what speed does this fixed-CL model first carry the assumed mass? Run the named scalar sweep in analytic mode and use napkin_analyze sensitivity for lift versus speed. Report units, the check outcomes and assumptions; keep baseline inputs unchanged.", "encoding": "napkin_run for the sweep; napkin_analyze kind=sensitivity using returned quantity refs." }, { "title": "Compare against evidence and revise", "prompt": "Replace CL with wind-tunnel or flight measurements; compare lift and inspect stall behavior. Attach test or external-analysis evidence as source references. Compare like-for-like conditions, explain any discrepancy, and revise only inputs justified by that evidence. Report what the model still cannot answer.", "encoding": "napkin_explain → evidence reference via napkin_edit → revision-checked input update → rerun; prior runs become stale." } ], "limitation": "Steady lift sizing only; no wing-warping control effectiveness, stall, stability, biplane interference or CFD.", "capability": "Unit-aware scalar expressions, expression checks, analytic sweep and numerical sensitivity.", "takeaway": "Air density, speed, lifting area and assumed lift coefficient → lift compared with weight.", "assumptionNotice": "Every number is a modern illustrative assumption, not a historical reconstruction.", "validation": { "created": 9, "baselineStatus": "failed", "baselineChecks": { "wright:check:support": { "samples": [ { "time": 0, "value": { "value": 2116.8, "unit": "N" } } ], "value": { "value": 2116.8, "unit": "N" }, "passed": false } }, "runStatus": "failed", "sweep": { "id": "d86b1885-032a-408e-995f-fc73598ea7bd", "revision": "6172485f-3820-406f-8113-cf9190153798", "scenario": { "id": "wright:scenario:Speed", "kind": "scenario" }, "mode": "analytic", "backend": "napkin-analytic", "backendVersion": "0.1.0", "seed": 0, "status": "failed", "observations": { "wright:check:support": { "samples": [ { "time": 0, "value": { "value": 940.8000000000001, "unit": "N" } }, { "time": 1, "value": { "value": 2116.8, "unit": "N" } }, { "time": 2, "value": { "value": 4762.800000000001, "unit": "N" } } ], "value": { "value": 940.8000000000001, "unit": "N" }, "failedSamples": [ 0, 1 ], "passed": false } }, "resolvedValues": { "wright:rho": { "value": 1.225, "unit": "kg/m^3" }, "wright:speed": { "value": 18, "unit": "m/s" }, "wright:area": { "value": 30, "unit": "m^2" }, "wright:CL": { "value": 0.8, "unit": "" }, "wright:mass": { "value": 300, "unit": "kg" }, "wright:weight": { "value": 2943, "unit": "N" }, "wright:lift": { "value": 4762.800000000001, "unit": "N" } }, "assumptions": [ { "id": "wright:rho", "text": "Illustrative air density" }, { "id": "wright:speed", "text": "Illustrative flight speed" }, { "id": "wright:area", "text": "Assumed lifting area" }, { "id": "wright:CL", "text": "Assumed lift coefficient" }, { "id": "wright:mass", "text": "Assumed all-up mass" } ], "diagnostics": [] }, "sensitivity": { "kind": "sensitivity", "revision": "6172485f-3820-406f-8113-cf9190153798", "scenario": null, "method": "Central difference at ±1% of each input; elasticity = (dy/dx)·(x/y)", "limitations": [], "outputs": { "wright:lift": 2116.8 }, "units": { "wright:lift": "N" }, "rows": [ { "input": { "id": "wright:speed", "kind": "quantity" }, "name": "speed", "value": 12, "unit": "m/s", "derivative": { "wright:lift": 352.79999999999825 }, "elasticity": { "wright:lift": 1.9999999999999898 } } ], "evaluations": 3, "milliseconds": 0.115916000000027 }, "validated": true } }, { "id": "goddard", "title": "Multistage rocket", "file": "goddard-rocket-patent.png", "code": "exhaustSpeed = 2000 m/s in 1500..2500 \"Illustrative effective exhaust speed\"\nratio1 = 3 \"Assumed wet-to-final mass ratio for stage one\"\nratio2 = 2 \"Assumed wet-to-final mass ratio for stage two\"\nstage1 := exhaustSpeed*log(ratio1) [m/s]\nstage2 := exhaustSpeed*log(ratio2) [m/s]\ntotalDeltaV := stage1+stage2 [m/s]\ncheck budget: totalDeltaV >= 3500 m/s\nsweep Exhaust: exhaustSpeed = 1500, 2000, 2500 m/s", "output": "totalDeltaV", "vary": "exhaustSpeed", "question": "What ideal velocity budget results from two assumed stage mass ratios?", "expected": [ { "name": "stage1", "value": 2197.224577336219, "unit": "m/s" }, { "name": "stage2", "value": 1386.2943611198905, "unit": "m/s" }, { "name": "totalDeltaV", "value": 3583.51893845611, "unit": "m/s" } ], "steps": [ { "title": "Preserve the source and the question", "prompt": "Create a Napkin study called “Multistage rocket — illustrative sizing”. Keep the attached historical drawing as a source reference. Preserve the 1914 staged apparatus; do not relabel it as the 1926 liquid-fuel rocket. The engineering question is: What ideal velocity budget results from two assumed stage mass ratios? Do not invent historical dimensions or ratings.", "encoding": "napkin_capabilities → napkin_create → napkin_snapshot; optional napkin_edit set-drawing for source metadata." }, { "title": "Separate facts from assumptions", "prompt": "List what the source supports, what is uncertain, and what must be measured. For this first pass use clearly labeled modern illustrative values, never historical measurements. Model this chain: Two dimensionless stage mass ratios and effective exhaust speed → summed ideal delta-v.", "encoding": "Input quantities carry units, ranges, tolerances and assumption strings. Derived quantities retain equations." }, { "title": "Encode the compact sketch model", "prompt": "Use napkin_sketch to apply the following text to the study with the current expectedRevision and prefix \"goddard\". Explain totalDeltaV and open the study. These numbers are illustrative assumptions.", "encoding": "napkin_snapshot → napkin_sketch → napkin_explain → napkin_open; scalar code below." }, { "title": "Ask a decision question", "prompt": "Does the ideal 3.5 km/s budget survive a lower assumed effective exhaust speed? Run the named scalar sweep in analytic mode and use napkin_analyze sensitivity for totalDeltaV versus exhaustSpeed. Report units, the check outcomes and assumptions; keep baseline inputs unchanged.", "encoding": "napkin_run for the sweep; napkin_analyze kind=sensitivity using returned quantity refs." }, { "title": "Compare against evidence and revise", "prompt": "Build a consistent stage mass budget, then compare engine-test effective exhaust speed and an external trajectory analysis. Attach test or external-analysis evidence as source references. Compare like-for-like conditions, explain any discrepancy, and revise only inputs justified by that evidence. Report what the model still cannot answer.", "encoding": "napkin_explain → evidence reference via napkin_edit → revision-checked input update → rerun; prior runs become stale." } ], "limitation": "Ideal rocket equation only; no gravity or drag losses, burn timing, structural staging feasibility or trajectory integration.", "capability": "Unit-aware scalar expressions, expression checks, analytic sweep and numerical sensitivity.", "takeaway": "Two dimensionless stage mass ratios and effective exhaust speed → summed ideal delta-v.", "assumptionNotice": "Every number is a modern illustrative assumption, not a historical reconstruction.", "validation": { "created": 8, "baselineStatus": "passed", "baselineChecks": { "goddard:check:budget": { "samples": [ { "time": 0, "value": { "value": 3583.51893845611, "unit": "m/s" } } ], "value": { "value": 3583.51893845611, "unit": "m/s" }, "passed": true } }, "runStatus": "failed", "sweep": { "id": "4b0fc982-0071-4c99-978d-0a3d6ecee842", "revision": "fd438224-05f9-4e01-8002-7cafcdd0b46d", "scenario": { "id": "goddard:scenario:Exhaust", "kind": "scenario" }, "mode": "analytic", "backend": "napkin-analytic", "backendVersion": "0.1.0", "seed": 0, "status": "failed", "observations": { "goddard:check:budget": { "samples": [ { "time": 0, "value": { "value": 2687.6392038420827, "unit": "m/s" } }, { "time": 1, "value": { "value": 3583.51893845611, "unit": "m/s" } }, { "time": 2, "value": { "value": 4479.398673070137, "unit": "m/s" } } ], "value": { "value": 2687.6392038420827, "unit": "m/s" }, "failedSamples": [ 0 ], "passed": false } }, "resolvedValues": { "goddard:exhaustSpeed": { "value": 2500, "unit": "m/s" }, "goddard:ratio1": { "value": 3, "unit": "" }, "goddard:ratio2": { "value": 2, "unit": "" }, "goddard:stage1": { "value": 2746.530721670274, "unit": "m/s" }, "goddard:stage2": { "value": 1732.8679513998632, "unit": "m/s" }, "goddard:totalDeltaV": { "value": 4479.398673070137, "unit": "m/s" } }, "assumptions": [ { "id": "goddard:exhaustSpeed", "text": "Illustrative effective exhaust speed" }, { "id": "goddard:ratio1", "text": "Assumed wet-to-final mass ratio for stage one" }, { "id": "goddard:ratio2", "text": "Assumed wet-to-final mass ratio for stage two" } ], "diagnostics": [] }, "sensitivity": { "kind": "sensitivity", "revision": "fd438224-05f9-4e01-8002-7cafcdd0b46d", "scenario": null, "method": "Central difference at ±1% of each input; elasticity = (dy/dx)·(x/y)", "limitations": [], "outputs": { "goddard:totalDeltaV": 3583.51893845611 }, "units": { "goddard:totalDeltaV": "m/s" }, "rows": [ { "input": { "id": "goddard:exhaustSpeed", "kind": "quantity" }, "name": "exhaustSpeed", "value": 2000, "unit": "m/s", "derivative": { "goddard:totalDeltaV": 1.7917594692280432 }, "elasticity": { "goddard:totalDeltaV": 0.9999999999999934 } } ], "evaluations": 3, "milliseconds": 0.0812090000000012 }, "validated": true } }, { "id": "whittle", "title": "Turbojet flow path", "file": "whittle-turbojet-patent.png", "code": "airflow = 10 kg/s \"Illustrative inlet air mass flow\"\nfuelFlow = 0.2 kg/s \"Illustrative fuel mass flow\"\nflightSpeed = 100 m/s\nexitSpeed = 450 m/s in 350..550 \"Assumed exhaust speed\"\npressureThrust = 0 N \"Assumed pressure-matched exhaust\"\nthrust := (airflow+fuelFlow)*exitSpeed-airflow*flightSpeed+pressureThrust [N]\ncheck thrustBudget: thrust >= 3500 N\nsweep Exhaust: exitSpeed = 350, 450, 550 m/s", "output": "thrust", "vary": "exitSpeed", "question": "What momentum thrust follows from assumed inlet and exit conditions?", "expected": [ { "name": "thrust", "value": 3590, "unit": "N" } ], "steps": [ { "title": "Preserve the source and the question", "prompt": "Create a Napkin study called “Turbojet flow path — illustrative sizing”. Keep the attached historical drawing as a source reference. Preserve the flow-path concept and identify the actual 1939 US patent sheet. The engineering question is: What momentum thrust follows from assumed inlet and exit conditions? Do not invent historical dimensions or ratings.", "encoding": "napkin_capabilities → napkin_create → napkin_snapshot; optional napkin_edit set-drawing for source metadata." }, { "title": "Separate facts from assumptions", "prompt": "List what the source supports, what is uncertain, and what must be measured. For this first pass use clearly labeled modern illustrative values, never historical measurements. Model this chain: Air and fuel mass flows, flight speed, exhaust speed and pressure thrust → net momentum thrust.", "encoding": "Input quantities carry units, ranges, tolerances and assumption strings. Derived quantities retain equations." }, { "title": "Encode the compact sketch model", "prompt": "Use napkin_sketch to apply the following text to the study with the current expectedRevision and prefix \"whittle\". Explain thrust and open the study. These numbers are illustrative assumptions.", "encoding": "napkin_snapshot → napkin_sketch → napkin_explain → napkin_open; scalar code below." }, { "title": "Ask a decision question", "prompt": "How much does the 3.5 kN check depend on assumed exit speed? Run the named scalar sweep in analytic mode and use napkin_analyze sensitivity for thrust versus exitSpeed. Report units, the check outcomes and assumptions; keep baseline inputs unchanged.", "encoding": "napkin_run for the sweep; napkin_analyze kind=sensitivity using returned quantity refs." }, { "title": "Compare against evidence and revise", "prompt": "Compare measured mass flow and net thrust; obtain exit conditions from an external cycle calculation or test. Attach test or external-analysis evidence as source references. Compare like-for-like conditions, explain any discrepancy, and revise only inputs justified by that evidence. Report what the model still cannot answer.", "encoding": "napkin_explain → evidence reference via napkin_edit → revision-checked input update → rerun; prior runs become stale." } ], "limitation": "An algebraic momentum balance; no compressor/turbine matching, combustion, thermal cycle or CFD.", "capability": "Unit-aware scalar expressions, expression checks, analytic sweep and numerical sensitivity.", "takeaway": "Air and fuel mass flows, flight speed, exhaust speed and pressure thrust → net momentum thrust.", "assumptionNotice": "Every number is a modern illustrative assumption, not a historical reconstruction.", "validation": { "created": 8, "baselineStatus": "passed", "baselineChecks": { "whittle:check:thrustBudget": { "samples": [ { "time": 0, "value": { "value": 3590, "unit": "N" } } ], "value": { "value": 3590, "unit": "N" }, "passed": true } }, "runStatus": "failed", "sweep": { "id": "dc11c457-f1e8-4ab1-895e-cfa80af6a7d6", "revision": "b06b70f1-bba1-4b60-9962-be2a756ab4fe", "scenario": { "id": "whittle:scenario:Exhaust", "kind": "scenario" }, "mode": "analytic", "backend": "napkin-analytic", "backendVersion": "0.1.0", "seed": 0, "status": "failed", "observations": { "whittle:check:thrustBudget": { "samples": [ { "time": 0, "value": { "value": 2569.9999999999995, "unit": "N" } }, { "time": 1, "value": { "value": 3590, "unit": "N" } }, { "time": 2, "value": { "value": 4610, "unit": "N" } } ], "value": { "value": 2569.9999999999995, "unit": "N" }, "failedSamples": [ 0 ], "passed": false } }, "resolvedValues": { "whittle:airflow": { "value": 10, "unit": "kg/s" }, "whittle:fuelFlow": { "value": 0.2, "unit": "kg/s" }, "whittle:flightSpeed": { "value": 100, "unit": "m/s" }, "whittle:exitSpeed": { "value": 550, "unit": "m/s" }, "whittle:pressureThrust": { "value": 0, "unit": "N" }, "whittle:thrust": { "value": 4610, "unit": "N" } }, "assumptions": [ { "id": "whittle:airflow", "text": "Illustrative inlet air mass flow" }, { "id": "whittle:fuelFlow", "text": "Illustrative fuel mass flow" }, { "id": "whittle:exitSpeed", "text": "Assumed exhaust speed" }, { "id": "whittle:pressureThrust", "text": "Assumed pressure-matched exhaust" } ], "diagnostics": [] }, "sensitivity": { "kind": "sensitivity", "revision": "b06b70f1-bba1-4b60-9962-be2a756ab4fe", "scenario": null, "method": "Central difference at ±1% of each input; elasticity = (dy/dx)·(x/y)", "limitations": [], "outputs": { "whittle:thrust": 3590 }, "units": { "whittle:thrust": "N" }, "rows": [ { "input": { "id": "whittle:exitSpeed", "kind": "quantity" }, "name": "exitSpeed", "value": 450, "unit": "m/s", "derivative": { "whittle:thrust": 10.20000000000002 }, "elasticity": { "whittle:thrust": 1.2785515320334286 } } ], "evaluations": 3, "milliseconds": 0.09329200000001947 }, "validated": true } }, { "id": "lamarr", "title": "Synchronized frequency hopping", "file": "lamarr-antheil-frequency-hopping-patent.png", "code": "dwell = 20 ms \"Illustrative dwell per channel\"\nsettling = 2 ms in 1..6 \"Assumed radio retuning time\"\nsyncError = 1 ms \"Assumed worst timing misalignment\"\nusableDwell := dwell-settling-2*syncError [ms]\ndutyFraction := usableDwell/dwell\ncheck usefulTime: usableDwell >= 10 ms\ncheck positiveBudget: dutyFraction >= 0\nsweep Retune: settling = 1, 2, 6 ms", "output": "usableDwell", "vary": "settling", "question": "How much time remains after retuning and synchronization allowances?", "expected": [ { "name": "usableDwell", "value": 16, "unit": "ms" }, { "name": "dutyFraction", "value": 0.8, "unit": "" } ], "steps": [ { "title": "Preserve the source and the question", "prompt": "Create a Napkin study called “Synchronized frequency hopping — illustrative sizing”. Keep the attached historical drawing as a source reference. Preserve coordinated transmitter/receiver switching; avoid claiming a modern digital protocol reconstruction. The engineering question is: How much time remains after retuning and synchronization allowances? Do not invent historical dimensions or ratings.", "encoding": "napkin_capabilities → napkin_create → napkin_snapshot; optional napkin_edit set-drawing for source metadata." }, { "title": "Separate facts from assumptions", "prompt": "List what the source supports, what is uncertain, and what must be measured. For this first pass use clearly labeled modern illustrative values, never historical measurements. Model this chain: Dwell, settling and synchronization-error allowance → usable time and duty fraction.", "encoding": "Input quantities carry units, ranges, tolerances and assumption strings. Derived quantities retain equations." }, { "title": "Encode the compact sketch model", "prompt": "Use napkin_sketch to apply the following text to the study with the current expectedRevision and prefix \"lamarr\". Explain usableDwell and open the study. These numbers are illustrative assumptions.", "encoding": "napkin_snapshot → napkin_sketch → napkin_explain → napkin_open; scalar code below." }, { "title": "Ask a decision question", "prompt": "What retuning delay leaves at least 10 ms of usable dwell? Run the named scalar sweep in analytic mode and use napkin_analyze sensitivity for usableDwell versus settling. Report units, the check outcomes and assumptions; keep baseline inputs unchanged.", "encoding": "napkin_run for the sweep; napkin_analyze kind=sensitivity using returned quantity refs." }, { "title": "Compare against evidence and revise", "prompt": "Measure tuning settle time and clock misalignment; inspect a radio trace with external tools. Attach test or external-analysis evidence as source references. Compare like-for-like conditions, explain any discrepancy, and revise only inputs justified by that evidence. Report what the model still cannot answer.", "encoding": "napkin_explain → evidence reference via napkin_edit → revision-checked input update → rerun; prior runs become stale." } ], "limitation": "Static timing budget only; no generated hop sequence, RF propagation, modulation, interference resilience or security claim.", "capability": "Unit-aware scalar expressions, expression checks, analytic sweep and numerical sensitivity.", "takeaway": "Dwell, settling and synchronization-error allowance → usable time and duty fraction.", "assumptionNotice": "Every number is a modern illustrative assumption, not a historical reconstruction.", "validation": { "created": 8, "baselineStatus": "passed", "baselineChecks": { "lamarr:check:usefulTime": { "samples": [ { "time": 0, "value": { "value": 16, "unit": "ms" } } ], "value": { "value": 16, "unit": "ms" }, "passed": true }, "lamarr:check:positiveBudget": { "samples": [ { "time": 0, "value": { "value": 0.8, "unit": "" } } ], "value": { "value": 0.8, "unit": "" }, "passed": true } }, "runStatus": "passed", "sweep": { "id": "c48c2c59-750f-4c4e-8c52-0180dc95f8b7", "revision": "9b24b473-ce1b-4ef7-a415-8b99b5122a98", "scenario": { "id": "lamarr:scenario:Retune", "kind": "scenario" }, "mode": "analytic", "backend": "napkin-analytic", "backendVersion": "0.1.0", "seed": 0, "status": "passed", "observations": { "lamarr:check:usefulTime": { "samples": [ { "time": 0, "value": { "value": 17, "unit": "ms" } }, { "time": 1, "value": { "value": 16, "unit": "ms" } }, { "time": 2, "value": { "value": 12, "unit": "ms" } } ], "value": { "value": 12, "unit": "ms" }, "failedSamples": [], "passed": true }, "lamarr:check:positiveBudget": { "samples": [ { "time": 0, "value": { "value": 0.8500000000000001, "unit": "" } }, { "time": 1, "value": { "value": 0.8, "unit": "" } }, { "time": 2, "value": { "value": 0.6, "unit": "" } } ], "value": { "value": 0.6, "unit": "" }, "failedSamples": [], "passed": true } }, "resolvedValues": { "lamarr:dwell": { "value": 20, "unit": "ms" }, "lamarr:settling": { "value": 6, "unit": "ms" }, "lamarr:syncError": { "value": 1, "unit": "ms" }, "lamarr:usableDwell": { "value": 12, "unit": "ms" }, "lamarr:dutyFraction": { "value": 0.6, "unit": "" } }, "assumptions": [ { "id": "lamarr:dwell", "text": "Illustrative dwell per channel" }, { "id": "lamarr:settling", "text": "Assumed radio retuning time" }, { "id": "lamarr:syncError", "text": "Assumed worst timing misalignment" } ], "diagnostics": [] }, "sensitivity": { "kind": "sensitivity", "revision": "9b24b473-ce1b-4ef7-a415-8b99b5122a98", "scenario": null, "method": "Central difference at ±1% of each input; elasticity = (dy/dx)·(x/y)", "limitations": [], "outputs": { "lamarr:usableDwell": 16 }, "units": { "lamarr:usableDwell": "ms" }, "rows": [ { "input": { "id": "lamarr:settling", "kind": "quantity" }, "name": "settling", "value": 2, "unit": "ms", "derivative": { "lamarr:usableDwell": -0.9999999999999787 }, "elasticity": { "lamarr:usableDwell": -0.12499999999999734 } } ], "evaluations": 3, "milliseconds": 0.18587499999995316 }, "validated": true } }, { "id": "fuller", "title": "Geodesic structure", "file": "fuller-geodesic-dome-patent.png", "code": "force = 2000 N in 1000..4000 \"Assumed axial force from external load analysis\"\narea = 100 mm^2 \"Assumed strut cross-sectional area\"\nallowable = 50 MPa \"Illustrative material stress allowance\"\nstress := force/area [MPa]\nmargin := allowable/stress\ncheck material: stress <= allowable\ncheck marginBudget: margin >= 1.5\nsweep Load: force = 1000, 2000, 4000 N", "output": "stress", "vary": "force", "question": "What axial stress follows for one idealized loaded strut?", "expected": [ { "name": "stress", "value": 20, "unit": "MPa" }, { "name": "margin", "value": 2.5, "unit": "" } ], "steps": [ { "title": "Preserve the source and the question", "prompt": "Create a Napkin study called “Geodesic structure — illustrative sizing”. Keep the attached historical drawing as a source reference. Preserve the triangulated dome topology; treat load-sharing as an unresolved structural question. The engineering question is: What axial stress follows for one idealized loaded strut? Do not invent historical dimensions or ratings.", "encoding": "napkin_capabilities → napkin_create → napkin_snapshot; optional napkin_edit set-drawing for source metadata." }, { "title": "Separate facts from assumptions", "prompt": "List what the source supports, what is uncertain, and what must be measured. For this first pass use clearly labeled modern illustrative values, never historical measurements. Model this chain: An externally supplied strut force, section area and allowable stress → axial stress and margin.", "encoding": "Input quantities carry units, ranges, tolerances and assumption strings. Derived quantities retain equations." }, { "title": "Encode the compact sketch model", "prompt": "Use napkin_sketch to apply the following text to the study with the current expectedRevision and prefix \"fuller\". Explain stress and open the study. These numbers are illustrative assumptions.", "encoding": "napkin_snapshot → napkin_sketch → napkin_explain → napkin_open; scalar code below." }, { "title": "Ask a decision question", "prompt": "Which supplied axial loads meet both stress and 1.5 margin checks? Run the named scalar sweep in analytic mode and use napkin_analyze sensitivity for stress versus force. Report units, the check outcomes and assumptions; keep baseline inputs unchanged.", "encoding": "napkin_run for the sweep; napkin_analyze kind=sensitivity using returned quantity refs." }, { "title": "Compare against evidence and revise", "prompt": "Use a structural analysis to obtain member forces; compare coupon, joint and buckling tests. Attach test or external-analysis evidence as source references. Compare like-for-like conditions, explain any discrepancy, and revise only inputs justified by that evidence. Report what the model still cannot answer.", "encoding": "napkin_explain → evidence reference via napkin_edit → revision-checked input update → rerun; prior runs become stale." } ], "limitation": "Single-member axial stress only; not a dome stiffness solve, FEA, buckling check or code-compliant building design.", "capability": "Unit-aware scalar expressions, expression checks, analytic sweep and numerical sensitivity.", "takeaway": "An externally supplied strut force, section area and allowable stress → axial stress and margin.", "assumptionNotice": "Every number is a modern illustrative assumption, not a historical reconstruction.", "validation": { "created": 8, "baselineStatus": "passed", "baselineChecks": { "fuller:check:material": { "samples": [ { "time": 0, "value": { "value": 20, "unit": "MPa" } } ], "value": { "value": 20, "unit": "MPa" }, "passed": true }, "fuller:check:marginBudget": { "samples": [ { "time": 0, "value": { "value": 2.5, "unit": "" } } ], "value": { "value": 2.5, "unit": "" }, "passed": true } }, "runStatus": "failed", "sweep": { "id": "59580292-d83a-4ad5-9270-606ab6cc8c37", "revision": "6ffea8b5-49cd-4f5c-889c-b58a0ace5a9b", "scenario": { "id": "fuller:scenario:Load", "kind": "scenario" }, "mode": "analytic", "backend": "napkin-analytic", "backendVersion": "0.1.0", "seed": 0, "status": "failed", "observations": { "fuller:check:material": { "samples": [ { "time": 0, "value": { "value": 10, "unit": "MPa" } }, { "time": 1, "value": { "value": 20, "unit": "MPa" } }, { "time": 2, "value": { "value": 40, "unit": "MPa" } } ], "value": { "value": 40, "unit": "MPa" }, "failedSamples": [], "passed": true }, "fuller:check:marginBudget": { "samples": [ { "time": 0, "value": { "value": 5, "unit": "" } }, { "time": 1, "value": { "value": 2.5, "unit": "" } }, { "time": 2, "value": { "value": 1.25, "unit": "" } } ], "value": { "value": 1.25, "unit": "" }, "failedSamples": [ 2 ], "passed": false } }, "resolvedValues": { "fuller:force": { "value": 4000, "unit": "N" }, "fuller:area": { "value": 100, "unit": "mm^2" }, "fuller:allowable": { "value": 50, "unit": "MPa" }, "fuller:stress": { "value": 40, "unit": "MPa" }, "fuller:margin": { "value": 1.25, "unit": "" } }, "assumptions": [ { "id": "fuller:force", "text": "Assumed axial force from external load analysis" }, { "id": "fuller:area", "text": "Assumed strut cross-sectional area" }, { "id": "fuller:allowable", "text": "Illustrative material stress allowance" } ], "diagnostics": [] }, "sensitivity": { "kind": "sensitivity", "revision": "6ffea8b5-49cd-4f5c-889c-b58a0ace5a9b", "scenario": null, "method": "Central difference at ±1% of each input; elasticity = (dy/dx)·(x/y)", "limitations": [], "outputs": { "fuller:stress": 20 }, "units": { "fuller:stress": "MPa" }, "rows": [ { "input": { "id": "fuller:force", "kind": "quantity" }, "name": "force", "value": 2000, "unit": "N", "derivative": { "fuller:stress": 0.009999999999999964 }, "elasticity": { "fuller:stress": 0.9999999999999964 } } ], "evaluations": 3, "milliseconds": 0.08875000000000455 }, "validated": true } }, { "id": "demestral", "title": "Hook-and-loop fastening", "file": "de-mestral-velcro-patent.png", "code": "area = 20 cm^2 in 5..40 \"Illustrative engaged area\"\nshearStrength = 5 N/cm^2 ± 20% \"Assumed tested shear capacity per area\"\nload = 50 N \"Illustrative application load\"\nsafety = 2 \"Assumed sizing factor\"\ncapacity := area*shearStrength [N]\nrequired := load*safety [N]\ncheck hold: capacity >= required\nsweep Engagement: area = 5, 20, 40 cm^2", "output": "capacity", "vary": "area", "question": "How large a bonded engagement area carries an assumed shear load?", "expected": [ { "name": "capacity", "value": 100, "unit": "N" }, { "name": "required", "value": 100, "unit": "N" } ], "steps": [ { "title": "Preserve the source and the question", "prompt": "Create a Napkin study called “Hook-and-loop fastening — illustrative sizing”. Keep the attached historical drawing as a source reference. Preserve hook/loop engagement intent and the 1955 patent; avoid implying trademark endorsement. The engineering question is: How large a bonded engagement area carries an assumed shear load? Do not invent historical dimensions or ratings.", "encoding": "napkin_capabilities → napkin_create → napkin_snapshot; optional napkin_edit set-drawing for source metadata." }, { "title": "Separate facts from assumptions", "prompt": "List what the source supports, what is uncertain, and what must be measured. For this first pass use clearly labeled modern illustrative values, never historical measurements. Model this chain: Engaged area, empirical shear strength, load and a sizing factor → shear capacity check.", "encoding": "Input quantities carry units, ranges, tolerances and assumption strings. Derived quantities retain equations." }, { "title": "Encode the compact sketch model", "prompt": "Use napkin_sketch to apply the following text to the study with the current expectedRevision and prefix \"demestral\". Explain capacity and open the study. These numbers are illustrative assumptions.", "encoding": "napkin_snapshot → napkin_sketch → napkin_explain → napkin_open; scalar code below." }, { "title": "Ask a decision question", "prompt": "What area passes, and how sensitive is the answer to measured shear strength? Run the named scalar sweep in analytic mode and use napkin_analyze sensitivity for capacity versus area. Report units, the check outcomes and assumptions; keep baseline inputs unchanged.", "encoding": "napkin_run for the sweep; napkin_analyze kind=sensitivity using returned quantity refs." }, { "title": "Compare against evidence and revise", "prompt": "Obtain product-specific shear and peel tests, aging and repeated-engagement data. Attach test or external-analysis evidence as source references. Compare like-for-like conditions, explain any discrepancy, and revise only inputs justified by that evidence. Report what the model still cannot answer.", "encoding": "napkin_explain → evidence reference via napkin_edit → revision-checked input update → rerun; prior runs become stale." } ], "limitation": "Uniform static shear with an empirical strength; no peel mechanics, individual hook contact, fatigue or textile modeling.", "capability": "Unit-aware scalar expressions, expression checks, analytic sweep and numerical sensitivity.", "takeaway": "Engaged area, empirical shear strength, load and a sizing factor → shear capacity check.", "assumptionNotice": "Every number is a modern illustrative assumption, not a historical reconstruction.", "validation": { "created": 8, "baselineStatus": "passed", "baselineChecks": { "demestral:check:hold": { "samples": [ { "time": 0, "value": { "value": 100, "unit": "N" } } ], "value": { "value": 100, "unit": "N" }, "passed": true } }, "runStatus": "failed", "sweep": { "id": "4fadd1bc-a3d2-4e83-9ae1-15dc1196b71d", "revision": "1897b376-812b-4a44-bf03-61c5bfed9c46", "scenario": { "id": "demestral:scenario:Engagement", "kind": "scenario" }, "mode": "analytic", "backend": "napkin-analytic", "backendVersion": "0.1.0", "seed": 0, "status": "failed", "observations": { "demestral:check:hold": { "samples": [ { "time": 0, "value": { "value": 25, "unit": "N" } }, { "time": 1, "value": { "value": 100, "unit": "N" } }, { "time": 2, "value": { "value": 200, "unit": "N" } } ], "value": { "value": 25, "unit": "N" }, "failedSamples": [ 0 ], "passed": false } }, "resolvedValues": { "demestral:area": { "value": 40, "unit": "cm^2" }, "demestral:shearStrength": { "value": 5, "unit": "N/cm^2" }, "demestral:load": { "value": 50, "unit": "N" }, "demestral:safety": { "value": 2, "unit": "" }, "demestral:capacity": { "value": 200, "unit": "N" }, "demestral:required": { "value": 100, "unit": "N" } }, "assumptions": [ { "id": "demestral:area", "text": "Illustrative engaged area" }, { "id": "demestral:shearStrength", "text": "Assumed tested shear capacity per area" }, { "id": "demestral:load", "text": "Illustrative application load" }, { "id": "demestral:safety", "text": "Assumed sizing factor" } ], "diagnostics": [] }, "sensitivity": { "kind": "sensitivity", "revision": "1897b376-812b-4a44-bf03-61c5bfed9c46", "scenario": null, "method": "Central difference at ±1% of each input; elasticity = (dy/dx)·(x/y)", "limitations": [], "outputs": { "demestral:capacity": 100 }, "units": { "demestral:capacity": "N" }, "rows": [ { "input": { "id": "demestral:area", "kind": "quantity" }, "name": "area", "value": 20, "unit": "cm^2", "derivative": { "demestral:capacity": 5 }, "elasticity": { "demestral:capacity": 1 } } ], "evaluations": 3, "milliseconds": 0.08583300000003646 }, "validated": true } }, { "id": "kilby", "title": "Miniaturized circuit", "file": "kilby-integrated-circuit-patent.png", "code": "resistance = 1000 ohm \"Illustrative circuit resistance\"\ncapacitance = 20 pF in 5..100 \"Assumed lumped capacitance\"\ntimeConstant := resistance*capacitance [ns]\nriseTime := 2.2*timeConstant [ns]\nfrequencyLimit := 1/(2*pi*timeConstant) [MHz]\ncheck edge: riseTime <= 100 ns\ncheck bandwidth: frequencyLimit >= 5 MHz\nsweep Parasitic: capacitance = 5, 20, 100 pF", "output": "timeConstant", "vary": "capacitance", "question": "How does assumed lumped parasitic capacitance limit a simple RC response?", "expected": [ { "name": "timeConstant", "value": 20, "unit": "ns" }, { "name": "riseTime", "value": 44, "unit": "ns" }, { "name": "frequencyLimit", "value": 7.957747154594767, "unit": "MHz" } ], "steps": [ { "title": "Preserve the source and the question", "prompt": "Create a Napkin study called “Miniaturized circuit — illustrative sizing”. Keep the attached historical drawing as a source reference. Preserve the actual 1964 patent sheet and flying-wire/equivalent circuit images; distinguish the 1958 demonstration. The engineering question is: How does assumed lumped parasitic capacitance limit a simple RC response? Do not invent historical dimensions or ratings.", "encoding": "napkin_capabilities → napkin_create → napkin_snapshot; optional napkin_edit set-drawing for source metadata." }, { "title": "Separate facts from assumptions", "prompt": "List what the source supports, what is uncertain, and what must be measured. For this first pass use clearly labeled modern illustrative values, never historical measurements. Model this chain: Assumed resistance and lumped capacitance → ideal one-pole time constant, rise-time estimate and cutoff.", "encoding": "Input quantities carry units, ranges, tolerances and assumption strings. Derived quantities retain equations." }, { "title": "Encode the compact sketch model", "prompt": "Use napkin_sketch to apply the following text to the study with the current expectedRevision and prefix \"kilby\". Explain timeConstant and open the study. These numbers are illustrative assumptions.", "encoding": "napkin_snapshot → napkin_sketch → napkin_explain → napkin_open; scalar code below." }, { "title": "Ask a decision question", "prompt": "Which capacitance values meet both a 100 ns rise-time budget and 5 MHz cutoff? Run the named scalar sweep in analytic mode and use napkin_analyze sensitivity for timeConstant versus capacitance. Report units, the check outcomes and assumptions; keep baseline inputs unchanged.", "encoding": "napkin_run for the sweep; napkin_analyze kind=sensitivity using returned quantity refs." }, { "title": "Compare against evidence and revise", "prompt": "Compare measured capacitance and oscilloscope response; validate the full circuit in an external circuit tool. Attach test or external-analysis evidence as source references. Compare like-for-like conditions, explain any discrepancy, and revise only inputs justified by that evidence. Report what the model still cannot answer.", "encoding": "napkin_explain → evidence reference via napkin_edit → revision-checked input update → rerun; prior runs become stale." } ], "limitation": "A generic one-pole proxy motivated by miniaturization, not the patent circuit reconstructed or simulated. No SPICE or transistor model.", "capability": "Unit-aware scalar expressions, expression checks, analytic sweep and numerical sensitivity.", "takeaway": "Assumed resistance and lumped capacitance → ideal one-pole time constant, rise-time estimate and cutoff.", "assumptionNotice": "Every number is a modern illustrative assumption, not a historical reconstruction.", "validation": { "created": 8, "baselineStatus": "passed", "baselineChecks": { "kilby:check:edge": { "samples": [ { "time": 0, "value": { "value": 44, "unit": "ns" } } ], "value": { "value": 44, "unit": "ns" }, "passed": true }, "kilby:check:bandwidth": { "samples": [ { "time": 0, "value": { "value": 7.957747154594767, "unit": "MHz" } } ], "value": { "value": 7.957747154594767, "unit": "MHz" }, "passed": true } }, "runStatus": "failed", "sweep": { "id": "c781b9be-6529-44fc-bae7-e11d679f7498", "revision": "aed824f7-1be6-4a60-be90-423e4b9d8a1c", "scenario": { "id": "kilby:scenario:Parasitic", "kind": "scenario" }, "mode": "analytic", "backend": "napkin-analytic", "backendVersion": "0.1.0", "seed": 0, "status": "failed", "observations": { "kilby:check:edge": { "samples": [ { "time": 0, "value": { "value": 11, "unit": "ns" } }, { "time": 1, "value": { "value": 44, "unit": "ns" } }, { "time": 2, "value": { "value": 220.00000000000003, "unit": "ns" } } ], "value": { "value": 220.00000000000003, "unit": "ns" }, "failedSamples": [ 2 ], "passed": false }, "kilby:check:bandwidth": { "samples": [ { "time": 0, "value": { "value": 31.830988618379067, "unit": "MHz" } }, { "time": 1, "value": { "value": 7.957747154594767, "unit": "MHz" } }, { "time": 2, "value": { "value": 1.5915494309189533, "unit": "MHz" } } ], "value": { "value": 1.5915494309189533, "unit": "MHz" }, "failedSamples": [ 2 ], "passed": false } }, "resolvedValues": { "kilby:resistance": { "value": 1000, "unit": "ohm" }, "kilby:capacitance": { "value": 100, "unit": "pF" }, "kilby:timeConstant": { "value": 100, "unit": "ns" }, "kilby:riseTime": { "value": 220.00000000000003, "unit": "ns" }, "kilby:frequencyLimit": { "value": 1.5915494309189533, "unit": "MHz" } }, "assumptions": [ { "id": "kilby:resistance", "text": "Illustrative circuit resistance" }, { "id": "kilby:capacitance", "text": "Assumed lumped capacitance" } ], "diagnostics": [] }, "sensitivity": { "kind": "sensitivity", "revision": "aed824f7-1be6-4a60-be90-423e4b9d8a1c", "scenario": null, "method": "Central difference at ±1% of each input; elasticity = (dy/dx)·(x/y)", "limitations": [], "outputs": { "kilby:timeConstant": 20 }, "units": { "kilby:timeConstant": "ns" }, "rows": [ { "input": { "id": "kilby:capacitance", "kind": "quantity" }, "name": "capacitance", "value": 20, "unit": "pF", "derivative": { "kilby:timeConstant": 1.0000000000000053 }, "elasticity": { "kilby:timeConstant": 1.0000000000000053 } } ], "evaluations": 3, "milliseconds": 0.06183299999997871 }, "validated": true } }, { "id": "engelbart", "title": "X–Y position indicator", "file": "engelbart-mouse-patent.png", "code": "wheelDiameter = 20 mm in 10..30 \"Illustrative rolling wheel diameter\"\ncounts = 100 \"Assumed counts per revolution\"\nstepSize := pi*wheelDiameter/counts [mm]\ncircumference := pi*wheelDiameter [mm]\ncheck resolution: stepSize <= 1 mm\nprobe resolutionValue: stepSize [mm]\nsweep Wheel: wheelDiameter = 10, 20, 30 mm", "output": "stepSize", "vary": "wheelDiameter", "question": "What surface displacement corresponds to one wheel-encoder count?", "expected": [ { "name": "stepSize", "value": 0.6283185307179587, "unit": "mm" }, { "name": "circumference", "value": 62.83185307179587, "unit": "mm" } ], "steps": [ { "title": "Preserve the source and the question", "prompt": "Create a Napkin study called “X–Y position indicator — illustrative sizing”. Keep the attached historical drawing as a source reference. Preserve the orthogonal-wheel X–Y measurement concept rather than substituting a later optical mouse. The engineering question is: What surface displacement corresponds to one wheel-encoder count? Do not invent historical dimensions or ratings.", "encoding": "napkin_capabilities → napkin_create → napkin_snapshot; optional napkin_edit set-drawing for source metadata." }, { "title": "Separate facts from assumptions", "prompt": "List what the source supports, what is uncertain, and what must be measured. For this first pass use clearly labeled modern illustrative values, never historical measurements. Model this chain: Wheel diameter and encoder counts → wheel circumference and displacement per count.", "encoding": "Input quantities carry units, ranges, tolerances and assumption strings. Derived quantities retain equations." }, { "title": "Encode the compact sketch model", "prompt": "Use napkin_sketch to apply the following text to the study with the current expectedRevision and prefix \"engelbart\". Explain stepSize and open the study. These numbers are illustrative assumptions.", "encoding": "napkin_snapshot → napkin_sketch → napkin_explain → napkin_open; scalar code below." }, { "title": "Ask a decision question", "prompt": "How does wheel diameter change spatial resolution at fixed encoder counts? Run the named scalar sweep in analytic mode and use napkin_analyze sensitivity for stepSize versus wheelDiameter. Report units, the check outcomes and assumptions; keep baseline inputs unchanged.", "encoding": "napkin_run for the sweep; napkin_analyze kind=sensitivity using returned quantity refs." }, { "title": "Compare against evidence and revise", "prompt": "Roll a measured distance; compare counts in both directions and assess slip. Attach test or external-analysis evidence as source references. Compare like-for-like conditions, explain any discrepancy, and revise only inputs justified by that evidence. Report what the model still cannot answer.", "encoding": "napkin_explain → evidence reference via napkin_edit → revision-checked input update → rerun; prior runs become stale." } ], "limitation": "Ideal no-slip wheel kinematics; no friction/contact solve, direction-decoding electronics or usability prediction.", "capability": "Unit-aware scalar expressions, expression checks, analytic sweep and numerical sensitivity.", "takeaway": "Wheel diameter and encoder counts → wheel circumference and displacement per count.", "assumptionNotice": "Every number is a modern illustrative assumption, not a historical reconstruction.", "validation": { "created": 7, "baselineStatus": "passed", "baselineChecks": { "engelbart:check:resolution": { "samples": [ { "time": 0, "value": { "value": 0.6283185307179587, "unit": "mm" } } ], "value": { "value": 0.6283185307179587, "unit": "mm" }, "passed": true }, "engelbart:probe:resolutionValue": { "samples": [ { "time": 0, "value": { "value": 0.6283185307179587, "unit": "mm" } } ], "value": { "value": 0.6283185307179587, "unit": "mm" } } }, "runStatus": "passed", "sweep": { "id": "81cf8ad9-53a9-4484-a559-66bcd991d15e", "revision": "95b6f9e8-0df8-4639-a4e3-19d27a988be4", "scenario": { "id": "engelbart:scenario:Wheel", "kind": "scenario" }, "mode": "analytic", "backend": "napkin-analytic", "backendVersion": "0.1.0", "seed": 0, "status": "passed", "observations": { "engelbart:check:resolution": { "samples": [ { "time": 0, "value": { "value": 0.31415926535897937, "unit": "mm" } }, { "time": 1, "value": { "value": 0.6283185307179587, "unit": "mm" } }, { "time": 2, "value": { "value": 0.9424777960769379, "unit": "mm" } } ], "value": { "value": 0.9424777960769379, "unit": "mm" }, "failedSamples": [], "passed": true }, "engelbart:probe:resolutionValue": { "samples": [ { "time": 0, "value": { "value": 0.31415926535897937, "unit": "mm" } }, { "time": 1, "value": { "value": 0.6283185307179587, "unit": "mm" } }, { "time": 2, "value": { "value": 0.9424777960769379, "unit": "mm" } } ], "value": { "value": 0.9424777960769379, "unit": "mm" } } }, "resolvedValues": { "engelbart:wheelDiameter": { "value": 30, "unit": "mm" }, "engelbart:counts": { "value": 100, "unit": "" }, "engelbart:stepSize": { "value": 0.9424777960769379, "unit": "mm" }, "engelbart:circumference": { "value": 94.24777960769379, "unit": "mm" } }, "assumptions": [ { "id": "engelbart:wheelDiameter", "text": "Illustrative rolling wheel diameter" }, { "id": "engelbart:counts", "text": "Assumed counts per revolution" } ], "diagnostics": [] }, "sensitivity": { "kind": "sensitivity", "revision": "95b6f9e8-0df8-4639-a4e3-19d27a988be4", "scenario": null, "method": "Central difference at ±1% of each input; elasticity = (dy/dx)·(x/y)", "limitations": [], "outputs": { "engelbart:stepSize": 0.6283185307179587 }, "units": { "engelbart:stepSize": "mm" }, "rows": [ { "input": { "id": "engelbart:wheelDiameter", "kind": "quantity" }, "name": "wheelDiameter", "value": 20, "unit": "mm", "derivative": { "engelbart:stepSize": 0.031415926535897365 }, "elasticity": { "engelbart:stepSize": 0.9999999999999818 } } ], "evaluations": 3, "milliseconds": 0.03750000000002274 }, "validated": true } }, { "id": "dyson", "title": "Cyclonic vacuum cleaner", "file": "dyson-cyclone-vacuum-patent.png", "code": "flow = 0.03 m^3/s in 0.01..0.05 \"Illustrative operating airflow\"\npressureDrop = 4000 Pa ± 20% \"Assumed measured total system loss\"\nefficiency = 0.5 \"Assumed fan efficiency at operating point\"\nshaftPower := flow*pressureDrop/efficiency [W]\ncheck motorBudget: shaftPower <= 300 W\nprobe fanPower: shaftPower [W]\nsweep Airflow: flow = 0.01, 0.03, 0.05 m^3/s", "output": "shaftPower", "vary": "flow", "question": "How much fan shaft power supports an assumed flow and pressure drop?", "expected": [ { "name": "shaftPower", "value": 240, "unit": "W" } ], "steps": [ { "title": "Preserve the source and the question", "prompt": "Create a Napkin study called “Cyclonic vacuum cleaner — illustrative sizing”. Keep the attached historical drawing as a source reference. Preserve the appliance layout and airflow path from the 1986 patent; avoid trademark endorsement. The engineering question is: How much fan shaft power supports an assumed flow and pressure drop? Do not invent historical dimensions or ratings.", "encoding": "napkin_capabilities → napkin_create → napkin_snapshot; optional napkin_edit set-drawing for source metadata." }, { "title": "Separate facts from assumptions", "prompt": "List what the source supports, what is uncertain, and what must be measured. For this first pass use clearly labeled modern illustrative values, never historical measurements. Model this chain: Flow, assumed measured system pressure drop and efficiency → required shaft power.", "encoding": "Input quantities carry units, ranges, tolerances and assumption strings. Derived quantities retain equations." }, { "title": "Encode the compact sketch model", "prompt": "Use napkin_sketch to apply the following text to the study with the current expectedRevision and prefix \"dyson\". Explain shaftPower and open the study. These numbers are illustrative assumptions.", "encoding": "napkin_snapshot → napkin_sketch → napkin_explain → napkin_open; scalar code below." }, { "title": "Ask a decision question", "prompt": "What airflow stays within 300 W if the assumed pressure drop holds? Run the named scalar sweep in analytic mode and use napkin_analyze sensitivity for shaftPower versus flow. Report units, the check outcomes and assumptions; keep baseline inputs unchanged.", "encoding": "napkin_run for the sweep; napkin_analyze kind=sensitivity using returned quantity refs." }, { "title": "Compare against evidence and revise", "prompt": "Measure pressure drop against flow, fan curve and dust-collection performance; replace constants with evidence. Attach test or external-analysis evidence as source references. Compare like-for-like conditions, explain any discrepancy, and revise only inputs justified by that evidence. Report what the model still cannot answer.", "encoding": "napkin_explain → evidence reference via napkin_edit → revision-checked input update → rerun; prior runs become stale." } ], "limitation": "Steady power budget; no cyclone separation efficiency, particle trajectories, fouling evolution or CFD. Pressure drop and efficiency may vary with flow.", "capability": "Unit-aware scalar expressions, expression checks, analytic sweep and numerical sensitivity.", "takeaway": "Flow, assumed measured system pressure drop and efficiency → required shaft power.", "assumptionNotice": "Every number is a modern illustrative assumption, not a historical reconstruction.", "validation": { "created": 7, "baselineStatus": "passed", "baselineChecks": { "dyson:check:motorBudget": { "samples": [ { "time": 0, "value": { "value": 240, "unit": "W" } } ], "value": { "value": 240, "unit": "W" }, "passed": true }, "dyson:probe:fanPower": { "samples": [ { "time": 0, "value": { "value": 240, "unit": "W" } } ], "value": { "value": 240, "unit": "W" } } }, "runStatus": "failed", "sweep": { "id": "9f667143-13c3-4cf0-be9b-4c0b998e5f72", "revision": "ee4edfe5-c621-44f2-a4a8-c6101d76e574", "scenario": { "id": "dyson:scenario:Airflow", "kind": "scenario" }, "mode": "analytic", "backend": "napkin-analytic", "backendVersion": "0.1.0", "seed": 0, "status": "failed", "observations": { "dyson:check:motorBudget": { "samples": [ { "time": 0, "value": { "value": 80, "unit": "W" } }, { "time": 1, "value": { "value": 240, "unit": "W" } }, { "time": 2, "value": { "value": 400, "unit": "W" } } ], "value": { "value": 400, "unit": "W" }, "failedSamples": [ 2 ], "passed": false }, "dyson:probe:fanPower": { "samples": [ { "time": 0, "value": { "value": 80, "unit": "W" } }, { "time": 1, "value": { "value": 240, "unit": "W" } }, { "time": 2, "value": { "value": 400, "unit": "W" } } ], "value": { "value": 400, "unit": "W" } } }, "resolvedValues": { "dyson:flow": { "value": 0.05, "unit": "m^3/s" }, "dyson:pressureDrop": { "value": 4000, "unit": "Pa" }, "dyson:efficiency": { "value": 0.5, "unit": "" }, "dyson:shaftPower": { "value": 400, "unit": "W" } }, "assumptions": [ { "id": "dyson:flow", "text": "Illustrative operating airflow" }, { "id": "dyson:pressureDrop", "text": "Assumed measured total system loss" }, { "id": "dyson:efficiency", "text": "Assumed fan efficiency at operating point" } ], "diagnostics": [] }, "sensitivity": { "kind": "sensitivity", "revision": "ee4edfe5-c621-44f2-a4a8-c6101d76e574", "scenario": null, "method": "Central difference at ±1% of each input; elasticity = (dy/dx)·(x/y)", "limitations": [], "outputs": { "dyson:shaftPower": 240 }, "units": { "dyson:shaftPower": "W" }, "rows": [ { "input": { "id": "dyson:flow", "kind": "quantity" }, "name": "flow", "value": 0.03, "unit": "m^3/s", "derivative": { "dyson:shaftPower": 8000.000000000067 }, "elasticity": { "dyson:shaftPower": 1.0000000000000084 } } ], "evaluations": 3, "milliseconds": 0.04920800000002146 }, "validated": true } } ]