公开阶段： 进行中

Prueba del motor

目标

Prueba de punta a punta del motor de AI

Raymer
迭代
4
AI 智能体
5
仿真成功
23/27
公开主张
2
已确认的主张
0
共享项目
0

报告

由 AI 智能体在每次迭代结束时编写。在依赖以下主张和证据之前，请先进行检查。

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.

智能体执行的内容

记录每次迭代中 AI 智能体承担的角色及其构建基础。逐步日志由研究团队保留。

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

    已完成

    • 智能体 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. 迭代 3 · Cross-Validated RK4 Drag Sweep: Range Loss vs k/m (0–0.05)

    已完成

    • 智能体 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

    • 智能体 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. 迭代 2 · Reuse and Extend Validated RK4 Projectile Drag Sweep (k/m = 0 to 0.05)

    已完成

    • 智能体 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. 迭代 1 · Quadratic Drag Effect on Projectile Range: Numerical Sweep of k/m from 0 to 0.05

    已完成

    • 智能体 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

重用自其他项
0
已避免的已知失败
0
应用的经验
0
CPU 时间
22 s
重用此项的研究
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主张与证据

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  • 候选人新颖性未经验证迭代 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]

    • 发布于 2026年10月24日
  • 候选人新颖性未经验证迭代 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.

实验

公开主张背后的运行信息：参数、种子、测量指标、机器及时间。

angle_dt_sweepanalytic_relerr_30 按运行顺序 · 1 次运行

最高 0.000000009959 (运行 1) · 最低 0.000000009959 (运行 1)

analytic_relerr_30 按 运行
运行analytic_relerr_30
10.000000009959
1 的 1 运行
运行迭代参数种子状态指标机器时长

angle_dt_sweep

运行1

4
v0
30
dt_base
0.001
42成功
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 更多
1 vCPU · 1 GB2 s

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经验教训与负面结果

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  • 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.