04 Protection
Thickness from HVL / TVL
x = TVL₁ + (n − 1) TVL_e with n = log₁₀(1/B). Broad-beam NCRP stacking.
Listen
Listen · English
Simulation
Thickness from HVL / TVL — 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
n
Number of TVLs
3
x
Thickness
108cm
Explanation
What it means
The first TVL is smaller than later ones because the beam hardens and scatter builds up; NCRP therefore publishes TVL₁ and an equilibrium TVL_e. After the first tenth-value, every extra decade of attenuation costs TVL_e. Concrete TVL_e at 6 MV is ~33–37 cm; lead is ~5.7 cm. Never mix narrow-beam μ with a broad-beam B. 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 B (or n_TVL), TVL₁ and TVL_e. If you only have one TVL, set both equal. B = 10^{−n}. Change one input and watch the curve and the simulation follow.
Symbols
- BTransmission0.001
- TVL_1First TVL34 cm
- TVL_eEquilibrium TVL37 cm
Worked example
A typical case from the default values: B = 0.001 (Transmission); TVL_1 = 34 cm (First TVL); TVL_e = 37 cm (Equilibrium TVL). Substituting into the relation gives n = 3; x = 108 cm. These are teaching numbers — align them with your machine.
Typical values give
- n = 3
- x = 108cm
Where it comes from
The displayed formula is the working relation. x = TVL₁ + (n − 1) TVL_e with n = log₁₀(1/B). Broad-beam NCRP stacking. Usual reference: NCRP 151. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: NCRP 151
Assumptions & limits
Photons. Neutrons need a separate TVL (concrete is good, lead is not). Doors, ducts and joints are leak paths not in this slab formula. Two-source (linac + PET) rooms superpose B requirements.
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. Photons. Neutrons need a separate TVL (concrete is good, lead is not). Doors, ducts and joints are leak paths not in this slab formula. Two-source (linac + PET) rooms superpose B requirements.
Keep this
Time, distance, shielding — in that order — then calculate the wall. Photons. Neutrons need a separate TVL (concrete is good, lead is not). Doors, ducts and joints are leak paths not in this slab formula. Two-source (linac + PET) rooms superpose B requirements.
In this specialty