Audience: Naval engineers and architects
Subject: Complete description of the calculation model, assumptions, and formulas
ARWIMS (AllRoad Water Ice Mud and Snow) replaces conventional propellers with 2 to 4 retractable paddle tracks mounted under the hull. The core questions are:
The simulator answers by computing required power P_req(V) for each operating regime and comparing it to available engine power.
The subject is a vehicle equipped with one or more retractable paddle tracks. It can travel on land using its tracks, and on water by flotation (displacement), or by hydrodynamic planing using the track bottom runs and hull bottom as lifting surfaces.
Regardless of the number of tracks:
2-track configuration: one track to starboard, one to port; track system length = 80% of hull length.
3-track configuration: one central track forward, two lateral tracks aft; each track system length = 25% of hull length.
4-track configuration: two tracks to port, two to starboard; each track system length = 37.5% of hull length.
Each track carries paddles inclined 30° forward from the vertical (i.e., 60° from horizontal). This inclination simultaneously generates a horizontal propulsion component and a vertical lift component. Winglets on both sides of each paddle prevent lateral water leakage. Paddles are deployed on the lower run only when fully submerged — there is therefore no ventilation or cavitation.
The relative speed of the paddles with respect to the water equals the track slip: 5% of the vehicle's speed through water (micro models), or 6% → 4% (full-scale, interpolated between 5 and 30 knots).
The hull is a shallow-V planing form. For 2- and 4-track configurations, the central hull width equals the overall beam minus the lateral track widths (catamaran-type appearance). For 3-track configurations, the hull spans the full beam with recesses for the embedded tracks.
Pure client-side JavaScript. For each calculation, five steps are executed:
| Parameter | Symbol | Unit |
|---|---|---|
| Length overall | L | m |
| Beam overall | B | m |
| Total loaded weight | W | kg |
| Engine power | P | kW |
| Track width (% of beam) | k | % |
| Track length (% of hull length) | — | % |
| Number of tracks | Nt | — |
| Total submerged paddles | Ns | — |
| Mechanical efficiency | etaMeca | — (default 0.92) |
For micro-scale models (<2 m, <100 kg), A_paddle is scaled by 0.16 for experimental calibration.
This formula separates the flat hull bottom (factor 0.85, accounting for hull shape) from the two lateral sides (factor 0.90), and uses only the central hull width — not the full beam — since the track volumes replace the outer hull bottom.
For both displacement regimes (ARWIMS and propeller reference), total resistance is the sum of viscous and wave-making components.
A tabulated wave resistance coefficient CR(Fn) is used, calibrated for a wide flat hull with block coefficient Cb ≈ 0.80 and L/B ≈ 3–5:
| Fn | 0.10 | 0.15 | 0.20 | 0.25 | 0.30 | 0.35 | 0.40 | 0.42 |
|---|---|---|---|---|---|---|---|---|
| CR | 0.001 | 0.002 | 0.004 | 0.007 | 0.012 | 0.020 | 0.035 | 0.045 |
A hard upper speed limit is applied: for displacement regimes, V_max cannot exceed the hull speed V_hull = 0.4·√(g·L) in m/s (converted to knots). Beyond this limit, P_req returns 999 999 kW, making the speed unattainable.
The minimum speed at which the paddle tracks can fully support the vessel's weight hydrodynamically is computed from the momentum equation. Each paddle acts as a deflector: the lift force equals ½·ρ·V²·A_total·CL, where CL is the thin-airfoil lift coefficient for the paddle inclination:
This speed is used as the lower bound (V_min) of the planing regimes. Planing is always physically achievable at sufficient speed — there is no static pressure limit, only a dynamic speed threshold.
Classic mistake: modeling paddles as a brake R = ½ρV²ACd applied at full boat speed.
ARWIMS reality: paddles operate at 4–6% slip. The relative water/paddle speed is V_slip ≈ 0.05·V_boat, not V_boat. The tangential force on each paddle points aft relative to water — therefore forward relative to the vessel: it is thrust, not drag.
Consequence in the simulator:
Why this matters for planing: in planing regimes, the paddles' velocity relative to the water is only slip × V. Their contribution to drag is therefore negligible. The dominant resistances are the induced drag of the planing surfaces and the viscous friction on their wetted area — both of which favour ARWIMS tracks over a conventional hull, as detailed below.
All three planing regimes (hull+track, track-only, propeller planing) use a two-component model:
The planing fraction f ∈ [0, 1] blends from displacement to full planing as speed increases. At f = 0 the vessel is in full displacement; at f = 1 it is fully planing.
The lower track runs act as flat planing surfaces at trim angle τ ≈ 5°. The paddles on these runs add lift at nearly zero additional drag cost (their relative velocity to water = slip × V ≈ 5% of boat speed), boosting total lift without a proportional increase in resistance. The effective lift-to-drag ratio of the ARWIMS planing system is therefore:
The planing fraction f starts at Fn_liftoff (the Froude number corresponding to V_liftoff) and reaches 1.0 at Fn_liftoff + 0.3:
The effective wetted surface blends from the full hull Sw (at f = 0) to the track bottom run area plus a 15% hull residual (the stern that still grazes the water at full planing):
Wave-making resistance applies only in the transition zone and fades as f → 1:
The hull is fully clear of the water. Same L/D model as hulltrack, but no hull residual — the only wetted surface is the four track bottom runs:
Because the hull stern no longer grazes the water and there is no wave-making resistance at full planing, track-only achieves higher top speed than hull+track for the same power.
For the conventional planing hull benchmark, a Savitsky-derived L/D approach is used:
Wave-making resistance applies in the transition zone (fades as f_pp → 1), identical method to hulltrack.
| Regime | L/D (planing) | Wetted area at full planing | η |
|---|---|---|---|
| ARWIMS displacement | n/a (hull speed limit) | Sw (full hull) | 0.55 |
| Hull + track planing | ~11.4 (τ = 5°) | Sw_planing + 15% hull residual | etaMeca × (1 − slip) ≈ 0.87 |
| Track-only planing | ~11.4 (τ = 5°) | Sw_planing only | etaMeca × (1 − slip) ≈ 0.87 |
| Propeller displacement (ref) | n/a (hull speed limit) | Sw (full hull) | 0.50 |
| Propeller planing (ref) | 5.0 (Savitsky) | Sw × 0.45 at full planing | 0.50 → 0.60 |
The ARWIMS L/D of ~11.4 versus 5.0 for a conventional hull means the induced resistance is 2.3× lower at the same weight and speed. This, combined with the lower wetted area (track runs only vs. full hull bottom), explains the speed and fuel advantage.
The algorithm sweeps V in 0.5-knot increments from V_min to V_max, keeping the last V where P_req ≤ P_available. A fine refinement step (0.05 knots) is then applied around that point to improve accuracy. The search range for each regime:
| Regime | V_min | V_max |
|---|---|---|
| Displacement (ARWIMS & propeller) | 0 kn | V_hull × 1.5 (hard-capped at V_hull) |
| Hull + track planing | max(V_liftoff, 4 kn) | 100 kn |
| Track-only planing | max(V_liftoff × 1.3, 8 kn) | 120 kn |
| Propeller planing (ref) | 10 kn | 100 kn |
The minimum speed for all displacement regimes is 0 knots. The minimum speed for planing regimes is the dynamic lift-off speed (or a practical lower bound), ensuring the regime only reports achievable conditions.
The simulator demonstrates that the ARWIMS speed and fuel advantage arises from two compounding effects: (1) the effective lift-to-drag ratio of the paddle-track planing system (~11.4) is more than twice that of a conventional planing hull (~5.0), because the paddles add lift at near-zero drag cost while the flat track bottom run provides the primary planing surface; and (2) the wetted area at full planing is reduced to the sole track bottom runs, eliminating the hull bottom friction entirely in track-only mode. The propulsive efficiency of the track system (η ≈ 0.87) is also higher than a propeller at displacement speeds (η = 0.50).
| You are a naval architecture engineer. Can you tell me what you think of the simulator offered by ARWIMS at "https://arwims.com/simul_intro.htm" and described by ARWIMS at "https://arwims.com/simulator-description-EN.htm"? |
Model version: v2.1 — June 11, 2026