Heliostat Cosine-Efficiency & Flux Map (2D)

Sun Position

Elevation 45°

Azimuth 135°

Heliostat Field

Active heliostats 48

Aim-point spread σ 10°

Direct normal irradiance 850 W/m²

Wind speed 3 m/s

Receiver State

cool

hot

Peak flux density

— kW/m²

Peak panel temp

— °C

Total absorbed thermal power

— MW

Field-average cosine efficiency

— %

How it works

This is a top-down (bird's-eye) companion to the 3D receiver model. Instead of an illustrative mirror tilt, every heliostat's orientation here is derived from real solar geometry: given the sun's unit direction vector S (from elevation + azimuth) and the unit direction from the heliostat to the receiver aim point T̂, the law of reflection requires the mirror's normal to bisect them, N = (S+T̂)/|S+T̂|. The optical cosine efficiency — the dominant loss mechanism in real heliostat fields — follows directly:

cosθ = N·S = √((1 + S·T̂) / 2)     [half-angle form, γ = angle(S,T̂)]

A mirror facing the sun almost edge-on to its own reflected beam (large γ) loses most of its power to this geometric factor alone, even before any atmospheric loss — this is why real CSP fields de-rate heliostats far from the tower and on the side away from the sun. Reflected sunlight also loses intensity to clear-sky scattering over the slant path, modelled with the empirical Bird–Hulstrom transmittance:

τ(S_m) = 0.99321 − 1.176e−4·S_m + 1.97e−8·S_m²   (S_m ≤ 1000 m)
τ(S_m) = exp(−1.106e−4·S_m)                       (S_m > 1000 m)

Each heliostat's effective reflected power DNI·ρ·A·cosθ·τ is then spread as a Gaussian aim-point footprint of width σ across the receiver panels facing that heliostat's field azimuth — the same superposition idea as the 3D model, but now weighted by real optics instead of a flat per-mirror contribution. Panel temperature is the steady-state root of the same radiative + convective balance α·q = ε·σ_SB·(T⁴−T_amb⁴) + h·(T−T_amb), h ≈ 5.7+3.8·v_wind, solved every frame.

Sweep the sun's azimuth through a full day at low elevation and watch the field-average cosine efficiency swing — that swing, not the aim-spread alone, is what drives a real CSP plant's output curve over the course of a day.

Top-down field view · tower at centre

Heliostat (bright = high cosη) Sun bearing