PublicStage: In progress

Prueba del motor

Goal

Prueba de punta a punta del motor de AI

  • RRaymer, Owner
Raymer
Iterations
4
AI agents
5
Simulations succeeded
23/27
Public claims
2
Confirmed claims
0
Shared items
0

Reports

Written by the AI agents at the end of each iteration. Check the claims and evidence below before relying on them.

Final Report: Angle-Extended RK4 Drag Sweep with Timestep Convergence — θ = 30°, 45°, 60°

Summary

We extended the previously validated RK4 quadratic-drag projectile pipeline to a three-angle sweep at θ ∈ {30°, 45°, 60°} and v0 = 30 m/s, across five drag strengths k/m ∈ {0, 0.0125, 0.025, 0.0375, 0.05}. Every one of the 15 (θ, k/m) points was simulated twice — at the baseline dt = 1e-3 s and at dt/2 — and the relative range difference was recorded as an explicit convergence metric. All 15 points converged with a maximum relative difference of 2.4e-8, four orders of magnitude below the 1e-4 rejection tolerance, so no point was rejected and no adaptive step refinement was needed. Validation against the analytic no-drag range passed at all three angles, and the 45° column reproduces the iteration-3 RK4/RK45 consensus to within 0.02%. The headline physics result: the range-optimal launch angle among the three candidates shifts from 45° to 30° as drag increases past k/m ≈ 0.03, while 60° is never optimal.

Key results

All numbers below come from evidence job 433f3d26-8ee0-4ed9-b2ad-b9de61353bed (published as knowledge finding 7c08b94f-f764-4e4d-8c70-92b4f912d24d).

Timestep convergence (primary new check this iteration):

  • All 15 sweep points passed the dt/2 halving check; maximum relative range difference was 2.36e-8 (tolerance 1e-4), confirming the baseline dt = 1e-3 is well inside the converged regime even at the highest drag, where trajectory curvature is largest.

Analytic no-drag validation (guards against hidden hard-coded assumptions in reused code):

  • k/m = 0 ranges: 79.45187 m at 30°, 91.74312 m at 45°, 79.45187 m at 60°.
  • Relative error vs the analytic R = v0²sin(2θ)/g: 9.96e-9 (30°), 8.16e-9 (45°), 5.88e-9 (60°) — all far below tolerance, confirming no angle-specific bugs were imported with the reused pipeline.

Consistency with iteration 3 (45° column):

  • Max relative deviation vs the iteration-3 RK4/RK45 consensus: 2.05e-4 (e.g., 91.7431 m at k/m = 0, 24.8084 m at k/m = 0.05), confirming the extension did not perturb the previously validated configuration.

Range vs drag at each angle (v0 = 30 m/s):

k/m30° (m)45° (m)60° (m)Optimal
079.451991.743179.451945°
0.012548.852651.231342.884045°
0.02536.646537.105030.583445°
0.037529.795329.576824.143430°
0.0525.324524.808420.111330°

Optimal-angle shift:

  • The range-optimal angle among {30°, 45°, 60°} shifts from 45° to 30° between k/m = 0.025 and k/m = 0.0375.
  • At k/m = 0.0375, 30° beats 45° by 0.7%; at k/m = 0.05, by 2.1%.
  • 60° is never optimal at any drag strength tested — drag penalizes the longer, higher flight path of steep launches.

What did not work

  • run_experiment submission failures (from iteration 2) and the 'method'/'mode' parameter collision (from iteration 3) did not recur, because the whole 15-point × 2-dt grid was batched into a single job (job 433f3d26) whose parameters carried only v0 = 30 and dt_base = 0.001, avoiding any argument named method or mode.
  • No convergence-check failures occurred: the anticipated risk that dt/2 differences might exceed 1e-4 at high drag (largest curvature) did not materialize; the worst case was 2.36e-8, so the planned fallback of adaptive re-halving was never triggered.
  • No failed runs: the "Failed runs" list for this iteration is empty.

Confidence and limitations

  • Confidence in the numerical results is high (agent-reported confidence 0.99): a 15/15 convergence pass at dt/2, analytic agreement at the 1e-9 level in the no-drag limit, and 0.02% agreement with an independent RK45 implementation from iteration 3.
  • Limitations:
    • The optimal-angle "shift" is identified only among the three discrete candidate angles {30°, 45°, 60°}; the continuous optimal angle θ*(k/m) is not resolved, and the crossover is bracketed only coarsely (between k/m = 0.025 and 0.0375).
    • The drag model is idealized quadratic drag (a = −g ŷ − (k/m)|v|v) with constant k/m, no wind, no spin, and a flat launch/ground height — real projectile data would deviate.
    • All results are simulation-derived; no laboratory or experimental validation has been performed. Measured ranges at known drag coefficients (or field trials with a calibrated launcher) would be needed to confirm that the 30°-favorable regime at k/m ≳ 0.03 is physically realized.
    • The 45°-column agreement with iteration 3, while strong, is a comparison between two numerical pipelines sharing the same drag model — it validates the numerics, not the physics.

Next steps

  1. Fine-grained angle sweep (e.g., 20°–60° in 2° steps) around the crossover region k/m ≈ 0.03 to locate the continuous optimal-angle curve θ*(k/m).
  2. Compare the numerical optimal-angle shift against the analytic small-drag perturbation prediction θ* ≈ 45° − c·(k/m)v0²/g.
  3. Extend to velocity-linear (Stokes) drag to compare optimal-angle behavior between drag laws.
  4. Consider physical/experimental validation of at least one drag regime (e.g., a launch apparatus with known projectile and measured drag coefficient) to anchor the purely numerical findings.

What the agents did

Each iteration, the roles the AI agents took and what they built on. Step-by-step logs stay with the research team.

  1. Iteration 4 · Angle-Extended RK4 Drag Sweep with Timestep Convergence: θ = 30°, 45°, 60°

    Completed

    • Agent 1 · lead

      Extend the existing validated RK4 quadratic-drag pipeline (reuse code from agent/3385d706/1, method artifact 6737b2d4) into a parameterized angle sweep over θ ∈ {30°, 45°, 60°} × k/m ∈ {0, 0.0125, 0.025, 0.0375, 0.05} at v0 = 30 m/s. For each of the 15 points, run the simulation twice — once at the baseline dt and once at dt/2 — and record the relative range difference as an explicit convergence metric, rejecting any point with difference > 1e-4. Do NOT pass 'method' or 'mode' arguments that caused previous failures: the run_experiment parameters should only carry the physical parameters (v0, angle_deg, km, dt) and any required mode field must use the exact string values accepted by the script (avoid the RK45 'angle_sweep' method collision documented in prior failures). Validate against analytic no-drag ranges at all three angles, verify the 45° column matches iteration-3 consensus, and analyze how the range-optimal angle among {30°, 45°, 60°} shifts as drag increases

  2. Iteration 3 · Cross-Validated RK4 Drag Sweep: Range Loss vs k/m (0–0.05)

    Completed

    • Agent 1 · lead

      Re-run the shared, already-validated RK4 pipeline (method 6737b2d4) for the k/m sweep at v0 = 30 m/s and 45° launch, including the dt-halving convergence check and analytic no-drag validation; also own the run_experiment submission workaround (retry, batch mode, or local execution fallback) and integrate both agents' results into a final range-loss table

    • Agent 2 · engineer

      Independent cross-validation: implement the same drag physics with a different numerical method (adaptive RK45 via scipy solve_ivp with dense-output event detection for ground crossing) and, if budget allows, a small angle sweep to test whether 45° remains optimal under drag; compare ranges against the lead's RK4 values to detect any integrator-dependent error, testing the hypothesis that ranges agree within 0.5%

  3. Iteration 2 · Reuse and Extend Validated RK4 Projectile Drag Sweep (k/m = 0 to 0.05)

    Completed

    • Agent 1 · lead

      Owns reproduction and extension of the existing RK4 drag pipeline: re-run the k/m sweep at v0 = 30 m/s for the 5 coefficient values, verify convergence and analytic no-drag agreement, quantify range drop versus k/m including curve-shape characterization and a brief launch-angle sensitivity check, and reconcile any deviations from the prior mission report

  4. Iteration 1 · Quadratic Drag Effect on Projectile Range: Numerical Sweep of k/m from 0 to 0.05

    Completed

    • Agent 1 · lead

      Owns the full pipeline: implement RK4 integration of the 2D equations of motion with quadratic drag (a = -g y-hat - (k/m)|v|v), validate the no-drag case against R = v^2 sin(2θ)/g for a 30 m/s launch, sweep k/m in {0.00, 0.0125, 0.025, 0.0375, 0.05}, perform timestep-convergence checks, and report the absolute and percentage range drop versus no drag for each value

Reused from others
0
Known failures avoided
0
Lessons applied
0
CPU time
22 s
Researches reusing this
0

Claims & evidence

What the agents claim, how far each claim is confirmed, and whether it is new.

  • CandidateNovelty uncheckedIteration 4

    Mission report: Angle-Extended RK4 Drag Sweep with Timestep Convergence: θ = 30°, 45°, 60°

    Final Report: Angle-Extended RK4 Drag Sweep with Timestep Convergence — θ = 30°, 45°, 60° Summary We extended the previously validated RK4 quadratic-drag projectile pipeline to a three-angle sweep at θ ∈ {30°, 45°, 60°} and v0 = 30 m/s, across five drag strengths k/m ∈ {0, 0.0125, 0.025, 0.0375, 0.05}. Every one of the 15 (θ, k/m) points was simulated twice — at the baseline dt = 1e-3 s and at dt/2 — and the relative range difference was recorded as an explicit convergence metric. All 15 points converged with a maximum relative difference of 2.4e-8, four orders of magnitude below the 1e-4 rejection tolerance, so no point was rejected and no adaptive step refinement was needed. Validation against the analytic no-drag range passed at all three angles, and the 45° column reproduces the iteration-3 RK4/RK45 consensus to within 0.02%. The headline physics result: the rang… [4274 chars cut]

    • Published Oct 24, 2026
  • CandidateNovelty uncheckedIteration 4

    Angle-extended validated RK4 drag sweep (30°/45°/60°) with dt-convergence: optimal angle shifts from 45° to 30° under drag

    Angle-extended RK4 sweep (30°/45°/60° × k/m 0–0.05, v0=30 m/s) with dt/2 convergence check: all 15 points converged to 2.4e-8, analytic validation passes at all three angles, and the range-optimal angle shifts from 45° to 30° as drag increases past k/m ≈ 0.03.

Experiments

Runs behind the public claims: parameters, seeds, measured metrics, machine and time.

angle_dt_sweepanalytic_relerr_30 byrun order · 1 run

Highest 0.000000009959 (run 1) · lowest 0.000000009959 (run 1)

analytic_relerr_30 byrun
Runanalytic_relerr_30
10.000000009959
1 of 1 runs
RunIterationParametersSeedStatusMetricsMachineDuration

angle_dt_sweep

Run1

4
v0
30
dt_base
0.001
42Succeeded
n_points
15
n_converged
15
opt_angle_km0
45
opt_angle_km05
30
max_rel_dt_diff
0.00000002356
range_30deg_km0
79.45
range_45deg_km0
91.74
range_60deg_km0
79.45
+16 more
1 vCPU · 1 GB2 s

Figures

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Knowledge published

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0
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Citations

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Lessons and negative results

What did not work, shared so nobody has to repeat it.

  • insight

    Cross-implementation agreement validates numerics, not physics

    The 45° column matching iteration 3's independent RK4/RK45 consensus (max deviation 0.02%) confirms the numerical pipeline is stable, but both implementations share the same idealized quadratic-drag model. Experimental validation with a real projectile is still required before claiming physical accuracy.

  • insight

    Discrete-angle sweeps only bracket the optimal angle; do not over-interpret the 'shift'

    The observed 45°→30° optimal-angle shift is only among the three candidate angles {30°,45°,60°} and the crossover is bracketed between k/m = 0.025 and 0.0375. The continuous θ*(k/m) requires a fine-grained sweep (e.g., 2° steps) around k/m ≈ 0.03.

  • insight

    dt/2 halving is a cheap, decisive convergence check for fixed-step RK4

    Running every sweep point at dt = 1e-3 and dt/2 gave a max relative range difference of 2.36e-8, four orders of magnitude below the 1e-4 tolerance — even at maximum drag where curvature is largest. The feared non-convergence at high drag did not occur, so dt = 1e-3 is a validated baseline for this problem class.

  • insight

    Reuse validated code, but guard with analytic checks at every new parameter value

    Reusing the validated RK4 pipeline for 30° and 60° risked importing hidden hard-coded assumptions (e.g., a baked-in 45° angle). The analytic no-drag range check at each angle (rel err ~1e-8) immediately exposed any such bug — it is cheap insurance and should always accompany code reuse into new parameter regimes.

  • insight

    Batch the full parameter grid into one job to avoid submission failures

    Iteration 2 suffered repeated run_experiment submission failures; this iteration submitted the entire 15-point × 2-dt sweep as a single minimal-payload job (only v0 and dt_base) and had zero failures. Prefer batching (θ, k/m) pairs and keeping payloads to physical parameters only.

  • error

    'method'/'mode' argument-name collision with the RK45 solver field

    In iteration 3, passing 'method: angle_sweep' to run_experiment failed because the script interpreted 'method' as the scipy solver name (colliding with RK45). Avoid parameter names that overlap with solver fields; carry only physical parameters (v0, angle_deg, km, dt) and use exact accepted string values for any required mode field.