SPF does not scale with filter loading — where is the knee?

It rises, then flattens, and past the knee it can fall. Do not size the loading from a linear calculation.

More filter means more shielding per unit area, so SPF climbs. Then the marginal return drops away: particles pack, dispersion degrades, the film stops being uniform, and efficiency falls back. Meanwhile the cost shows up as white cast, heavy feel and instability.

Particle size does not move it monotonically either — different sizes are efficient in different bands, so equal loadings at different sizes give clearly different SPF. Dispersion matters more than either: agglomerates cut the effective shielding area and land you well below theory.

Build a curve instead of a point: 5%, 10%, 15% at fixed everything else, measured in vitro, and read the knee off the graph. Keep film thickness and substrate consistent with real use, or the numbers will not transfer.

If the knee sits below the SPF you need with mineral filters alone, the honest options are a smaller particle size, a ZnO and TiO2 combination that covers UVA separately, or a small amount of organic filter — each with its own consequences for what you can claim.