Open Access
Table C.1
Description of symbols, with units expressed in length L, mass M, and time T.
| Sym. | Description | Units |
|---|---|---|
| a | Projectile acceleration | L T−2 |
| apeak | Peak acceleration | L T−2 |
| b | Viscous drag constant | M T−1 |
| b(z) | Viscous drag coefficient | M T−1 |
| d | Grain diameter | L |
| fo | Friction drag constant | M L T−2 |
 |
Friction drag constant for Fr model | M |
| f(z) | Friction drag coefficient | M L T−2 |
| g | Gravity | L T−2 |
| h | Inertial drag constant | M L−1 |
| h′ | Inertial drag constant for Fr model | M |
| h(z) | Inertial drag coefficient | M L−1 |
| m | Projectile mass | M |
| k | Friction drag constant | M T−2 |
| t | Time | T |
| tstop | Collision duration | T |
| v | Projectile velocity | L T−1 |
| vc | Collision velocity | L T−1 |
| v1 | Velocity when f(z) becomes constant | L T−1 |
| z | Projectile depth | L |
| zh | Depth when f(z) = h(z)v2 | L |
| zo | Depth when vc = 0 | L |
| z1 | Depth when v = v1 | L |
 |
Normalized depth when v = v1 | - |
| zstop | Final penetration depth | L |
| zstop,I | Regime I penetration depth | L |
 |
Regime I normalized penetration depth | - |
| zstop,II | Regime II penetration depth | L |
 |
Regime II normalized penetration depth | - |
| A | Projectile cross-sectional area | L2 |
| D | Projectile diameter | L |
| D′ | Effective projectile diameter | L |
| L | Length of the container | L |
| Fd | Total drag force | M L T−2 |
| Fr | Froude number | - |
| Frt | Transition Froude number | - |
| α | Constant related to scaling of f(z) | - |
| η | Constant related to scaling of h(z) | - |
| κ | Friction drag constant | M T−2 |
| λ | Characteristic length of the container | L |
| μ | Friction coefficient where μ = tan(ϕ) | - |
| ρg | Bulk density of granular bed | M L−3 |
| ρp | Projectile density | M L−3 |
| ϕ | Internal friction angle | ° |
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