"Particle velocity" has four distinct meanings — this tool calculates all four:
peak particle velocity (PPV) ground vibration from blasting (USBM formula),
settling velocity partikel menurut hukum Stokes,
terminal velocity general via drag-equilibrium iteration,
and wave particle velocity (v = 2πfA).
SI + imperial units. Everything is computed in your browser; nothing is uploaded.
⚠ Not a blast-design tool
Mode PPV memakai konstanta K dan β typical of the literature — real predictions require
site-specific calibration from seismograph data at your site.
The vibration-limit table below is general reference, not engineering advice.
Blast design and building-damage assessment must be performed by
a licensed geotechnical engineer / blasting expert in accordance with applicable regulations.
PPV = K·(D/√W)−β (USBM). W = charge per delay (rule of thumb: charges detonating within 8 ms count as one).
PPV = K · (D / √W)−β
Peak particle velocity
0mm/s
Peak particle velocity
0in/s
Scaled distance D/√W
0m/kg^½
Reference limit: 0 mm/s ·
max charge to stay below the limit: 0kg
Mode 2 — Settling velocity (Stokes)
v = g·d²·(ρp−ρf)/(18·μ) — valid only when Re < 1. The tool checks the regime automatically.
v = g·d²·(ρp−ρf) / (18·μ) · Re = ρf·v·d/μ
Settling velocity
0mm/s
Settling velocity
0m/s
Settling velocity
0m/hour
Bilangan Reynolds
0
Mode 3 — General terminal velocity
Sphere drag equilibrium, iterated from the Stokes guess with the Schiller–Naumann Cd. Valid for all Re.
v = √(4·g·d·(ρp−ρf) / (3·ρf·Cd))
Terminal velocity
0mm/s
Terminal velocity
0m/s
Koefisien drag Cd
0
Bilangan Reynolds
0
Mode 4 — Wave particle velocity
Pure harmonic oscillation: maximum medium particle velocity v = 2πfA.
vmaks = 2πfA · amaks = (2πf)²A
v maks
0mm/s
v maks
0m/s
a maks
0m/s²
a maks
0g
Worked example
Mode 1 — PPV: D=50 m, W=10 kg (K=1140, β=1.6)
SD = 50/√10 = 15.81 m/kg^½.
PPV = 1140 × 15.81−1.6 = 13.76 mm/s = 0.542 in/s.
DIN 4150-3 residential reference limit (<10 Hz): 5 mm/s → exceeds the reference limit
(general comparison, not a damage verdict).
Mode 2 — Stokes: 100 µm sand in water at 20 °C
v = 9.80665 × (10−4)² × (2650−998.2) / (18 × 1.002×10−3)
= 8.98 mm/s (= 32.33 m/hour).
Re = 998.2 × 0.00898 × 10−4 / 1.002×10−3 = 0.89 < 1
→ rezim Stokes valid (but near the limit).
Mode 3 — Terminal: 1 mm sand in water at 20 °C
Iterating from the Stokes guess of 898.13 mm/s → converges to
v = 155.19 mm/s, Cd = 0.898, Re = 154.6 (transitional regime).
Pure Stokes law would give 898.13 mm/s — wrong by almost 6×.
PPV = K·(D/√W)−β · v = g·d²(ρp−ρf)/18μ · v = √(4gd(ρp−ρf)/3ρfCd) · v = 2πfA
Mode 1 is the USBM empirical equation; K and β are site-specific and
the default values (K=1140, β=1.6) are merely typical literature values — calibration from seismograph
data is required for real predictions. K is defined for PPV in mm/s with D in meters and W in kg;
imperial inputs are converted to SI first.
Mode 2 assumes smooth spherical particles with ρp > ρf and laminar flow (Re < 1);
the tool rejects floating particles and warns when Re ≥ 1.
Mode 3 solves the force balance for spheres via fixed-point iteration using the
Schiller–Naumann drag correlation (Re ≤ 1000; Cd = 0.44 above that) — an honest simplification for
non-spherical particles.
Mode 4 assumes pure harmonic oscillation; this is the medium's particle velocity,
not the wave propagation speed.
Unit conversions use exact definitions: 1 in = 25.4 mm; 1 ft = 0.3048 m;
1 lb = 0.45359237 kg; g = 9.80665 m/s².
Vibration limit table (general reference)
DIN 4150-3 — guideline vibration-velocity values for short-term vibration,
measured at the foundation (linear interpolation between band points):
Tipe bangunan
< 10 Hz
10–50 Hz
50–100 Hz
Residential & similar buildings
5 mm/s
5–15 mm/s
15–20 mm/s
Komersial / industri
20 mm/s
20–40 mm/s
40–50 mm/s
Vibration-sensitive buildings
3 mm/s
3–8 mm/s
8–10 mm/s
SNI 7571:2010 (building-damage criteria for ground vibration):
buildings Class 2 → 3 mm/s, bangunan Class 3 (residential) → 5 mm/s (PVS).
All values above are general reference, not engineering advice —
not a substitute for a professional engineer's assessment.
Scope limits: what is calculated (and what is not)
Tool ini = EMPAT makna "particle velocity". Blast-vibration PPV,
Stokes settling, general terminal, and wave oscillation.
NOT projectile/bullet velocity. For muzzle velocity from energy or
a chronograph, use
muzzle-velocity (#1735).
NOT free-fall motion. For objects falling in air/vacuum (without a particle drag model),
use free-fall-velocity (#423).
NOT parabolic trajectory. For projectile motion (distance, time, impact angle), use
horizontal-projectile-motion (#1661).
NOT ballistic coefficient. For sectional density & BC of high-velocity projectiles,
use ballistic-coefficient (#1521).
This term has four distinct meanings depending on the field: (1) peak particle velocity (PPV) — maximum ground vibration velocity from blasting, in mm/s; (2) settling velocity — the velocity at which a particle falls/settles in a fluid according to Stokes' law; (3) terminal velocity — the final fall velocity when drag balances the particle's effective weight; (4) wave particle velocity — the oscillation velocity of medium particles as a mechanical wave passes, v = 2πfA. All four are calculated in this tool in four separate modes. Note: this is NOT projectile or bullet velocity — use the muzzle velocity calculator for that.
What is the peak particle velocity (PPV) formula?
The USBM empirical formula: PPV = K × (D/√W)^(−β). D is the distance from the blast point to the measurement point (meters), W is the explosive charge per delay (kg), while K and β are site-specific constants from field calibration. Example: D = 50 m, W = 10 kg, K = 1140, β = 1.6 → scaled distance SD = 50/√10 = 15.81 m/kg^½ → PPV = 1140 × 15.81^(−1.6) = 13.76 mm/s (= 0.542 in/s).
Apa itu scaled distance dan aturan 8 ms?
Scaled distance SD = D/√W combines distance and charge into a single parameter: two blasts with the same SD are predicted to produce the same PPV. W here is the maximum charge detonating in one delay — the industry rule of thumb: charges detonating within 8 ms count as a single charge. Example: D = 100 m, W = 25 kg → SD = 20 → PPV = 9.45 mm/s (with K = 1140, β = 1.6).
What are the safe ground-vibration limits for buildings?
As general reference (not engineering advice): DIN 4150-3 for short-term vibration at the foundation sets 5 mm/s for residential, 20 mm/s for commercial/industrial, and 3 mm/s for sensitive buildings at frequencies below 10 Hz — the values rise with frequency (e.g., 10 mm/s for residential at 30 Hz). SNI 7571:2010 sets a PVS limit of 3 mm/s for Class 2 and 5 mm/s for Class 3 (residential) buildings. Mode 1 of this tool compares your PPV result against your chosen limit. For real blast design, consult a licensed geotechnical engineer or blasting expert.
When does Stokes' law apply to settling velocity?
Stokes' law v = g·d²·(ρp−ρf)/(18·μ) is only valid when the particle Reynolds number Re = ρf·v·d/μ is less than 1 — meaning fully laminar flow around the particle. Example: a 100 µm sand grain (ρ = 2650 kg/m³) in water at 20 °C → v = 8.98 mm/s with Re = 0.89 — still valid but near the limit. 10 µm dust in water → v = 0.090 mm/s with Re = 0.0009 — very valid. If Re ≥ 1, use Mode 3 (general terminal velocity).
What is the difference between settling velocity and terminal velocity?
Settling velocity (Mode 2) uses Stokes' law, which is analytical but only valid for Re < 1 (small or very slow particles). Terminal velocity (Mode 3) is the general force-balance solution — particle effective weight = drag force — with the Schiller–Naumann drag coefficient iterated to convergence, so it applies at all Re. For large particles the two differ greatly: 1 mm sand in water gives 898.13 mm/s by Stokes (wrong, since Re ≫ 1) but 155.19 mm/s by the correct drag iteration.
How do you calculate the fall velocity of a particle too large for Stokes?
Use Mode 3: the tool iterates v = √(4·g·d·(ρp−ρf)/(3·ρf·Cd)) with Cd from the Schiller–Naumann correlation Cd = (24/Re)(1+0.15·Re^0.687), starting from the Stokes guess until the relative change is below 10^(−12). Example: 1 mm sand (ρ = 2650 kg/m³) in water at 20 °C → v = 155.19 mm/s, Cd = 0.898, Re = 154.6 (transitional regime). The iteration stops after a few steps because the corrections shrink rapidly.
What is the particle velocity formula for waves?
For pure harmonic oscillation, the maximum medium particle velocity is v_max = 2πfA, with f the frequency (Hz) and A the displacement amplitude (meters). The maximum acceleration is a_max = (2πf)²A. Example: f = 50 Hz, A = 1 mm → v_max = 314.16 mm/s and a_max = 98.7 m/s² (≈ 10.06 g). This is the velocity of the oscillating medium particles, not the wave propagation speed.
What units does this calculator use?
Mode 1 uses mm/s (the vibration industry standard) plus in/s, with 1 in/s = 25.4 mm/s. Distance input can be meters or feet and charge can be kg or lb — both are converted to SI automatically before constant K is applied, since K is defined for specific units. Modes 2–4 use SI (m/s, mm/s) with µm, mm, and inch input options for diameter/amplitude. All conversion factors use exact definitions (1 ft = 0.3048 m; 1 lb = 0.45359237 kg).
Does this calculator replace professional engineering analysis?
No. This is an educational tool. PPV predictions for real blasting require K and β constants from regressing seismograph data at that very site — K = 1140 and β = 1.6 are merely typical literature values and can be far off in different rock. The vibration limits in the table are general reference, not design criteria. Blast design, building-damage risk assessment, and regulatory compliance measurement must be performed by a licensed geotechnical engineer or blasting expert with calibrated seismographs.
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