Error-cone intercept modeling and altitude–wind-load synergy in large-aperture (8.6 m) parabolic-trough collectors

Abstract

The intercept factor of a parabolic-trough collector is routinely treated as a fixed constant, which obscures how it scales with aperture and with the deployment site. We promote the intercept factor to an analytical error-cone model — an explicit function of aperture, optical error budget, and absorber diameter — and couple it to site altitude through a wind-load-induced slope-error term in which reduced air density at altitude lowers the wind dynamic pressure on the mirror. Sweeping aperture to 8.6 m, the model's geometric intercept (≈0.99 for the EuroTrough geometry) is consistent with the peer-reviewed EuroTrough/LS-2 optical record and, after calibrating a single slope-error parameter, matches third-party element-level measurements of two 8.6 m molten-salt collectors (CGN, 80 mm, 0.966; Longteng, 90 mm, ≥0.98) to within 1%. The main result is a scaling law we call the altitude–wind synergy: the optical benefit of high-altitude siting grows monotonically with aperture, because a wide aperture both narrows the optical acceptance margin and amplifies wind-load deformation — exactly the term that altitude relieves — so large apertures gain disproportionately. The sign and aperture-scaling of the gain are robust across the full published range of the wind-deformation parameters; its magnitude (illustratively, the intercept gain from sea level to 2801 m rises from about +2×10⁻³ at 5.77 m to +24×10⁻³ at 8.6 m for a representative coefficient) is set by structural parameters not yet measured. Error-cone optics coupled with altitude–wind-load physics is therefore a necessary, analytically reproducible design tool for the large-aperture troughs now being deployed on high plateaus.