This ideal lumped model treats the selected line as having equivalent horizontal drag D = ρCddLv²/2 opposed by selected submerged weight W. It then uses θ = atan(D/W), horizontal offset L sin θ and vertical shortfall L(1 − cos θ). This calculation is separate from the sampler sequence and does not predict bottom interaction or corrected survey depth.
Sampler Motion and Ideal Line Deflection
Explore an ideal straight-line deflection triangle from selected equivalent horizontal drag and submerged weight.
Equation Used
- Water density is fixed at 1025 kg/m³ and Cd at 1.2.
- The entered dL is treated as equivalent projected area.
- The line is straight, taut and in static equilibrium under one horizontal and one vertical force.
- Sampler drag, cable distribution, waves, vessel motion, stretch, calibration and seabed contact are excluded.
The cup animation illustrates a qualitative sampling sequence. The displayed geometric shortfall is not a corrected hydrographic depth.
Ideal force and geometry model
The entire selected line drag is collapsed into one horizontal force and the selected lead weight minus entered buoyancy into one vertical force. Their resultant defines a straight, taut line angle from vertical.
The calculator uses that ideal triangle. Separately, the animation shows the cups of a sounding sampler held open by a clip, closing when the bob touches bottom, and returning with a sample. This qualitative sequence does not model cable dynamics or seabed forces.
What the calculator determines
Select lead weight, buoyancy allowance, uniform current, line diameter and paid-out length. The calculator returns equivalent drag, ideal line angle, horizontal offset and the difference between line length and vertical projection.
The over-read is a geometric shortfall within this model, not a correction to a hydrographic sounding or proof of bottom contact.
Selected lumped identities
D = ρCddLv²/2 with fixed ρ = 1025 kg/m³ and selected-model Cd = 1.2. W = 4.44822Wlead,lbf − B. Then θ = atan(D/W), x = L sin θ and Δ = L − L cos θ.
The area dL and coefficient are assumptions. Real drag depends on line orientation, Reynolds number, roughness, sampler geometry and the current profile.
Selected-input example
At the defaults, the model uses a 14 lbf lead, 0.55 N buoyancy allowance, 1.5 kn uniform current, 12 mm line and 12 m length. The outputs are an idealized force-balance comparison, not a field correction.
Sampler operation and measurement limits
Hiscox illustrates the sampler in open and closed positions (items 841–842). During descent, a clip retains the cups. When the bob strikes bottom, the clip releases and the cups spring together. The animation shows these stages with simplified latch detail and illustrative proportions.
Accurate depth measurement requires calibrated equipment and corrections for the sounding system and operating conditions. The line-deflection calculation here does not account for distributed drag, vessel motion or bottom contact and is not a survey correction.
Questions
Is the line really straight?
Not generally. The straight taut line is an idealization.
Is drag distributed accurately?
No. The model uses dL as an assumed projected area and collapses drag to one horizontal force.
Is over-read a survey correction?
No. It is only L minus the vertical projection of the ideal straight line.
Does the model confirm bottom contact?
No. Contact, sampler drag, vessel motion, waves, stretch and calibration are excluded.
Technical references
Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances (1901), page 218, items 841–842: sampler sounding weight, cups open and closed.
- OpenStax University Physics, Drag Force — quadratic drag identity and coefficient/area dependence.
- NOAA Field Procedures Manual, manual depth measurement equipment — calibration and documentation requirements.
- NIST Special Publication 811 — SI units.
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