Value chain · CLM-0915
In plain terms
The leftover error does two different kinds of damage and they need separate budgets. A uniform tilt across the antenna does not weaken the beam, it moves it; everything else weakens it. Missing the receiver by 250 metres from geostationary orbit means pointing to about one and a half seconds of arc, and the steering system has to do somewhere between forty and a hundred and twenty times better than the structure can be pointed mechanically - depending on whether you take the whole structure or an individual sub-panel.
The claim as recorded
The residual phase error across a transmit aperture must be decomposed before a Ruze gain-loss relation is applied to it. Its PISTON component costs nothing, its TILT component mispoints the beam without reducing gain, and only the remainder costs peak gain and scatters power. Applying exp(-sigma^2) to the undecomposed residual double-counts the tilt. At 2.45 GHz from geostationary altitude, a 250 m ground miss corresponds to 1.4410 arcseconds of beam pointing, a phase gradient of 3.5872e-4 rad/m, or 6.986 mm of differential range across a 1 km aperture. Retrodirective control must therefore deliver pointing between 42 and 125 times better than the structure can be held to mechanically - between one and two orders of magnitude.
Evidence behind this: T0-derivation. The geometry is verified by reproducing a figure CLM-0160 already holds, at both ends of its range. CALC-107 carries the arithmetic.
Scope and limits
The decomposition is exact; the ARITHMETIC is specific to 2.45 GHz, a 1 km circular aperture with a 10 dB Gaussian taper, and geostationary range, and must be recomputed for any other geometry. Says nothing about whether any real system achieves the 42-to-125 improvement - only what is required of it. THE RANGE IS NOT IMPRECISION AND MUST NOT BE COLLAPSED TO A SINGLE FIGURE. CLM-0160 gives two mechanical tolerances - 1 arcminute for the spacetenna, 3 arcminutes for individual subarrays - and does not say which the comparison is against, so quoting one number would assert a choice the source does not make. Covers no pointing error from any source other than a linear phase tilt across the aperture.
What it assumes
Small angles. The conversion between a linear ramp's edge value and its rms depends on the aperture's shape AND illumination and is NOT the uniform-line factor - for the reference design's circular 1 km aperture with a 10 dB Gaussian edge taper it is 0.4020, against 0.5774 for a uniform line, and using the line factor overstates the rms by 43.6 per cent. See CALC-107.
Where it comes from
This is the project's own working, shown in full:
CALC-107. delta_theta = g/k for a phase gradient g. Cross-check on the geometry: 1 arcminute = 2.9089e-4 rad, times 35,786 km = 10.410 km, and 3 arcminutes gives 31.229 km, reproducing BOTH ends of the 10 to 30 km ground miss CLM-0160 records for 1 to 3 arcminutes of mechanical pointing tolerance. The 250 m and 10 degree RMS figures are both from CLM-0160 via NASA RP-1076. EVERY FIGURE RECOMPUTED INDEPENDENTLY ON REGISTRATION, 2026-09-14, from the stated relations rather than by re-running the author's working: 6.9860e-6 rad, 1.4410 arcsec, k = 51.3482 rad/m, g = 3.5872e-4 rad/m, 6.986 mm, 41.64 and 124.92 - the last two confirmed by the independent route through ground distance, 10.410/0.250 and 31.229/0.250.
Basis: arcseconds and arcminutes (pointing); metres (ground miss); mm (differential range)
Related records
- Answers question
- QST-013 not published in this release
Cite this
energyaperture.com/c/clm-0915
CLM-0915, Energy Aperture, as of 2026-09-13.
Connected records
Other published records linked to this one. A list, not a judgement.
- Also from SRC-107
- CLM-0033 (low confidence)Apart from a 1981 NASA review that found no evidence for the number and suggested a higher one, nobody was found to have revisited it, and...CLM-0060In 1981 a NASA review panel said the 230 watts per square metre figure rested on an obsolete theory with no experimental support, and made...CLM-0061The experiments were done. They found heating two or three times stronger than normal, not the tenfold effect predicted, no irregularities...CLM-0062By 1981 the theory was being revised to a steeper frequency dependence, which would raise the permitted power density.CLM-0063NASA suggested in 1981 that 550 to 600 watts per square metre might be reasonable, roughly two and a half times the figure still in use...CLM-0101The 1978 contract required the researchers to report fixes if ionospheric disturbance pushed the pilot-beam phase error past 2 to 3...CLM-0160A 1978-81 NASA design study calculated that simply pointing the satellite's structure accurately enough, without any electronic correction...CLM-0420NASA's 1981 report says the experiments found nothing supporting the 23 milliwatt limit, that the measured heating was two or three times...More on the source page.