Research note / Cycle 006
The step between zero and one millimetre
A bidirectional software sweep tests what the proposed displacement channel would need to reveal before it could qualify a surrogate-strip bench.
The machine and the substitution
The proposed Space Elevator bench would pull an ordinary 100 mm strip while separately observing gauge extension, crosshead travel and grip motion. A frame display cannot supply all three observations. The earlier instrument-selection note retained P1 as a displacement requirement, with a conservative 22.5 micrometre planning sum against a 25 micrometre design allowance. It did not identify a purchasable sensor.
Voss and Reed now ask what could go wrong when a nominally similar channel is substituted. The software retains P1’s resolution, calibration, alignment, thermal, mounting and repeat allowances. Replacing its 2 micrometre resolution requirement with 10 micrometres increases the half-resolution contribution from 1 to 5; the total becomes 26.5 micrometres. Removing the mounting bound makes the total incomplete rather than smaller.
A range, not an endpoint
The new trace visits 0, 100, 200, 400 and 1000 micrometres in both directions. Those authored steps are comparison inputs, not movements of an installed instrument. An injected 30 micrometre bow at the 200 micrometre step leaves zero and 1000 unchanged. Two endpoint-only cases therefore supply identical readings despite different interior truth; both are held for missing range and return coverage.
Sampling the full grid exposes that bow. A separate return trace adds an 8 micrometre offset and exceeds the authored 6 micrometre calibration term. These are different failures: one is missed by the chosen observations, the other by omitting the return direction. A clean grid still says nothing about unsampled points unless an additional covering model is justified.
The reference can inherit the same error
In the false-separation case, the candidate readings and reference both inherit a 30 micrometre shift. Their residual is zero, and their supplied custody declaration says they are separate. The model gives the same favorable envelope decision as the clean control. It does not discover the hidden dependency.
The next equipment request must therefore ask for usable range, mounting evidence, calibration coverage and a reference with a demonstrably different origin. Reference custody remains unassigned, and the frame and channels remain unsecured. None of these software decisions authorizes a strip run, force measurement or strength claim.
Results at a glance
| Case | Conditional extension bound (um) | Maximum sampled residual (um) | Decision |
|---|---|---|---|
| complete_grid | 22.5 | 0 | conditional_model_envelope |
| coarse_resolution_swap | 26.5 | 0 | hold_in_model |
| missing_mount_bound | Incomplete | 0 | hold_in_model |
| endpoint_only_control | 22.5 | 0 | hold_in_model |
| endpoint_only_hidden_bow | 22.5 | 0 | hold_in_model |
| grid_exposes_bow | 22.5 | 30 | hold_in_model |
| return_hysteresis | 22.5 | 8 | hold_in_model |
| undeclared_shared_reference | 22.5 | 0 | conditional_model_envelope |