04 Protection
Skyshine (NCRP 151 approximation)
Ḣ ≈ 2.5×10⁻² (B_roof Ḋ_0 Ω^{1.3}) / d² (empirical, mSv/h, teaching form).
Listen
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Simulation
Skyshine (NCRP 151 approximation) — Change the numbers; the scene follows.
Where it works
Treatment vault
Primary barrier
In the bunker maze and barriers — time, distance, TVL, WUT, and weekly controlled-area dose.
Open this machineFormula
Variables
Results
Ḣ
Outdoor dose rate (approx.)
9.3973e-7mSv/h
Ḣ
Outdoor dose rate
0.001µSv/h
Explanation
What it means
Skyshine is photon (and neutron) radiation that goes through a thin roof, scatters in air, and comes down in the car park. It dominates when walls are thick and the roof is the cheap path. NCRP 151 / McGinley give empirical formulas in Ω (solid angle of the roof as seen from the source) and distance d from the isocentre to the outdoor point. This calculator uses a scaled teaching form: you supply a reference rate and it inverse-squares and scales Ω^{1.3}. This is a working relation in Radiation protection.
Where it is used
Clinically it sits on the Treatment vault — Primary barrier. In the bunker maze and barriers — time, distance, TVL, WUT, and weekly controlled-area dose. Protection equations are the wall, the occupancy factor, and the badge: time, distance, shielding, and WUT. They turn a room into a legal design.
Treatment vault · Open this machineHow to use it
Enter roof transmission B, isocentre dose rate (Gy/h), roof solid angle Ω (sr) and outdoor distance d (m). The constant 0.025 is a teaching scale matching order-of-magnitude McGinley numbers at 6 MV — verify against the NCRP 151 figure for a real design. Change one input and watch the curve and the simulation follow.
Symbols
- B_roofRoof transmission0.05
- Ḋ_0Isocentre dose rate6 Gy/h
- ΩSolid angle0.1 sr
- dOutdoor distance20 m
Worked example
A typical case from the default values: B_roof = 0.05 (Roof transmission); Ḋ_0 = 6 Gy/h (Isocentre dose rate); Ω = 0.1 sr (Solid angle); d = 20 m (Outdoor distance). Substituting into the relation gives Ḣ = 9.3973e-7 mSv/h; Ḣ = 0.001 µSv/h. These are teaching numbers — align them with your machine.
Typical values give
- Ḣ = 9.3973e-7mSv/h
- Ḣ = 0.001µSv/h
Where it comes from
The displayed formula is the working relation. Ḣ ≈ 2.5×10⁻² (B_roof Ḋ_0 Ω^{1.3}) / d² (empirical, mSv/h, teaching form). Usual reference: NCRP 151 / McGinley. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: NCRP 151 / McGinley
Assumptions & limits
Empirical, energy- and bunker-geometry specific. Neutrons have a separate skyshine (often worse, because they sail through a lead roof). A conservatively thick roof is usually cheaper than arguing about Ω^{1.3}.
Pitfalls
Tenth-value layers are for the broad beam in that material and that energy — not a photocopy from another bunker. Occupancy T is not a guess; it is a use pattern. Inverse-square fails against a large scatter source. Empirical, energy- and bunker-geometry specific. Neutrons have a separate skyshine (often worse, because they sail through a lead roof). A conservatively thick roof is usually cheaper than arguing about Ω^{1.3}.
Keep this
Time, distance, shielding — in that order — then calculate the wall. Empirical, energy- and bunker-geometry specific. Neutrons have a separate skyshine (often worse, because they sail through a lead roof). A conservatively thick roof is usually cheaper than arguing about Ω^{1.3}.
In this specialty