Built to be checked, not blindly trusted
Engineers do not sign off on unverified AI output, and they should not. So ForgePilot recomputes its own results with plain deterministic arithmetic, independent of the AI, and shows you both. This page documents that verification layer against closed-form textbook solutions.
1 · Equations shown
Every report states the governing equation, the substitution, and the intermediate arithmetic. Nothing is a black box you have to take on faith.
2 · Machine-checked
For beam deflection, tolerance stack-ups, pressure vessels, and axial/torsion stress, your inputs are recomputed with pure deterministic arithmetic, no AI involved, and shown as an independent badge next to the AI report.
3 · Verify yourself
Every report ends with the hand spot-checks a senior engineer would run: the highest-leverage calculations, which inputs matter most, and what rests on assumptions vs given data.
Deterministic layer vs closed-form solutions
The cases below compare ForgePilot's machine-check layer against the exact closed-form solutions (Roark's Formulas, Shigley's, standard thin-wall and Lamé equations). These are the same computations that run live on your inputs in the workspace.
| Tool | Case | Inputs | Governing equation | Closed-form solution | ForgePilot machine-check |
|---|---|---|---|---|---|
| Beam Deflection | Cantilever, point load at free end | L = 500 mm, F = 1000 N, E = 68.9 GPa (Al 6061), I = 106,667 mm⁴ (20×40 rect) | δ = FL³/3EI, M = FL | δ = 5.669 mm, M = 500 N·m | δ = 5.669 mm, M = 500.0 N·m |
| Beam Deflection | Simply supported, central point load | L = 1000 mm, F = 500 N, E = 200 GPa (steel), I = 833,333 mm⁴ (50×100 rect) | δ = FL³/48EI, M = FL/4 | δ = 0.0625 mm, M = 125 N·m | δ = 0.063 mm, M = 125.0 N·m |
| Tolerance Stack-Up | 4-dimension chain | Tolerances ±0.05, ±0.03, ±0.02, ±0.01 mm | WC = Σ|tᵢ|, RSS = √(Σtᵢ²) | WC = ±0.1100 mm, RSS = ±0.0625 mm | WC = ±0.110 mm, RSS = ±0.062 mm |
| Pressure Vessel | Thin-wall cylinder | p = 1.5 MPa, rᵢ = 150 mm, t = 8 mm, Sy = 170 MPa (316L) | σ_hoop = pr/t, σ_long = pr/2t | σ_hoop = 28.13 MPa, σ_long = 14.06 MPa, FoS = 6.04 | σ_hoop = 28.13 MPa, σ_long = 14.06 MPa, FoS = 6.04 |
| Pressure Vessel | Marginal thin-wall (rᵢ/t = 6.25) | p = 1.5 MPa, rᵢ = 50 mm, t = 8 mm | Lamé: σ_hoop,inner = p(rₒ²+rᵢ²)/(rₒ²−rᵢ²) | σ_hoop,inner = 10.18 MPa (thin-wall would give 9.38) | Flags rᵢ/t < 10, reports Lamé 10.18 MPa alongside thin-wall |
| Stress Analysis | Axial, solid circular, with Kt | F = 5000 N, D = 50 mm, Kt = 2.0 | σ = Kt·F/A, A = πD²/4 | A = 1963.5 mm², σ = 5.09 MPa | A = 1963.5 mm², σ = 5.09 MPa |
| Stress Analysis | Torsion, solid circular shaft | T = 50,000 N·mm, D = 50 mm | τ = Tr/J, J = πD⁴/32 | τ = 2.04 MPa | τ = 2.04 MPa |
| Bolted Joint | M10 class 8.8, 75% preload, external load | At = 58.0 mm² (ISO 262), Sp = 600 MPa (ISO 898-1), K = 0.2, P = 6 kN, C = 0.25 | Fᵢ = 0.75·Sp·At, T = K·Fᵢ·d, σ = (Fᵢ + C·P)/At | Fᵢ = 26.1 kN, T = 52.2 N·m, σ = 476 MPa, SF = 1.26 | Fᵢ = 26.1 kN, T = 52 N·m, σ = 476 MPa, SF = 1.26 |
| Fatigue (steel) | Goodman criterion, machined 4340 | Sut = 1080 MPa, σa = 130, σm = 75 MPa, Kt = 2.0, ka = 0.8 (kb = kc = 1 stated) | Se = ka·0.5·Sut, n = 1/(Ktσa/Se + σm/Sut) | Se = 432 MPa, n = 1.49 | Se = 432 MPa, n = 1.49 |
| Thermal | Combined conduction + convection | Q = 80 W, L = 60 mm, A = 0.004 m², k = 160 W/m·K, h = 45 W/m²·K | ΔT = Q·(L/kA + 1/hA) | ΔT = 451.9 °C | ΔT = 451.9 °C, flags exceeded limit |
| Bearing Life | Ball bearing, ISO 281 | C = 32.5 kN (SKF 6208), P = 5.4 kN, N = 3000 RPM | L10 = (C/P)³, L10h = L10·10⁶/(60N) | L10 = 218.0 million rev, L10h = 1211 h | L10 = 218.0 million rev, L10h = 1211 h |
| Column Buckling | Pinned-pinned steel column | E = 200 GPa, I = 83,333 mm⁴, A = 600 mm², L = 1500 mm, Sy = 250 MPa | Le/r vs √(2π²E/Sy), Pcr = π²EI/Le² | Le/r = 127 > 126 (Euler), Pcr = 73.1 kN | Regime stated (Euler), Pcr = 73.1 kN; Johnson regime flagged instead when slenderness is below transition |
Verified July 2026 against hand calculations. The machine-check layer is deterministic: identical inputs always produce identical results.
A real case where the badge caught the AI, not the other way around
A fatigue safety-factor question came in through plain chat: steel part, Goodman criterion, a stated stress concentration factor. The AI reasoned through it in prose and wrote a safety factor of n = 3.38.
The deterministic machine-check layer recomputed the same inputs independently, with no visibility into the AI's reasoning path, and returned n = 2.53. The two disagreed.
Root cause, traced after the fact: the AI's prose answer had dropped the stress concentration factor (Kt) from the numerator on that pass, a dropped-term error, not a reasoning error. The kind of mistake a tired engineer makes by hand too, which is exactly why the badge exists next to the prose instead of replacing it.
AI prose answer
n = 3.38
Machine-check badge
n = 2.53 (correct)
This is the entire point of the deterministic layer: it doesn't trust the AI's arithmetic, it redoes it. Two more dated, real findings (not selected for flattery) are on the homepage.
Why this layer exists: honest scope
Language models can make arithmetic mistakes even when their engineering reasoning is sound, a dropped exponent, a unit slip. Industry surveys show most engineers redo AI math by hand for exactly this reason. Rather than pretend that risk away, ForgePilot puts a deterministic arithmetic layer next to the AI: where the two disagree, the badge tells you to trust the arithmetic.
The badge only appears where the computation is genuinely unambiguous. Standard beam configurations get badged; a propped cantilever does not. Axial and torsion stress get badged; bending without a defined moment arm does not. Steel Goodman fatigue gets badged with every assumption printed in the badge itself; aluminium fatigue never does, because no endurance limit exists to compute. A wrong badge would be worse than no badge.
And to be direct about what ForgePilot is not: it is not FEA. Meshed simulation of complex geometry is ANSYS-class work, and for final structural validation of complex parts, that remains the right tool. ForgePilot covers the classical analytical layer, concept and detail-stage reasoning, documentation, FMEA, standards compliance, and its hand calculations double as the sanity check on your FEA setup.
Run your own numbers through it
The fastest way to evaluate the verification layer is with a calculation you already know the answer to.
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