Now lets look at an evening pic. The light in the evening is much less strong, allowing to better see the effect.
What we notice straight away is that the flame is obviously shooting off the white scale of the photo (the white balance clips the brightness of the flame to white), so it must be by far the brighest point in the scene.
The balloon and the sky share about the same amount of light. there's no strong key sunlight anymore so the main light source in this setting is behaving like an ambient low-intencity fill light.
Taking into account the low intencity fill light, and the high intensity flame, its clear that the illumination at the base of the balloon is fairly dim. The amount of light from the flame that's blocked out by the balloon is probably still pretty high! also the effect doesnt spread very far, so a strong fall-off on the flame's light source will be essential in bryce to simulate the same effect. Perhaps with a gradient ramp and range for extra controlability?
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