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 regime and comparing to available power.
The subject is a vehicle equipped with one or more
retractable paddle tracks.
This vehicle can travel on land using its tracks, and on
water by flotation, planing, or paddle-track propulsion.
Regardless of the number of tracks:
• A track is tensioned between a front roller and a rear roller
• It has an upper track run and a lower track run, both horizontal and
tangent to the rollers
• The front and rear rollers have the same diameter.
• The track system is embedded in the hull, and only the lower track run
protrudes slightly below the hull.
• One track to starboard, one to port, of equal length
• The track system length is 80% of the vehicle length
• The forward track system begins at 15% of hull length from the bow
• The aft track system ends at 5% of hull length before the transom
- 3-tracks configuration
• One central track forward, one port lateral track and one starboard lateral
track aft
• Each track system length is 25% of vehicle length
• The central track begins at 15% of hull length from the bow
• The lateral tracks end at 5% of hull length before the stern
• All tracks are located in the forward half of the vehicle
- 4-tracks configuration:
• Two tracks to port and two to starboard
• Each track system length is 37.5% of vehicle length
• The forward track system begins at 15% of hull length from the bow
• The aft track system ends at 5% of hull length before the transom
• The gap between the rear of the forward track system and the front of the
aft track system equals 5% of hull length
We divide the number of submerged blades by the number of
tracks to get the number of submerged blades per track.
This is also the number of blades per track run. The
number of blades per track is equal to twice the number of submerged blades to
account for the top track run, and we add 6 for the semicircles of the end
rollers. We round this number, which can only be a whole number.
The length of the track system is equal to the length of
twice the track run plus twice the radius of a roller.
Since wr know this track system
length, we can deduce the length of a track run. By dividing this length by the
number of blades per track section, we can calculate the length between two
rollers. Since this length between two rollers is equal to the radius of a
roller, we know the radius of the roller.
The length between two blades is equal to 100/90 of the
distance between two adjacent rollers on a track.
Therefore, we can calculate the length of a blade, and
since we know its width, we can calculate its area.
Each track has retractable paddles inclined 30° forward
from the vertical. These paddles simultaneously generate a horizontal
propulsion component and a vertical lift component.
Winglets are present on both sides of each paddle and
reduce water leakage to the extrados. Paddles on the upper track run and on the
curved portions around the front and rear rollers are always retracted. They
contribute neither to drag, nor propulsion, nor pitching. On the lower track
run, paddles are deployed only when the ground is not hard, and only when
fully submerged. There is therefore no ventilation or cavitation to
consider.
The relative speed of the paddles with respect to the
water equals the track slip, taken here as 5% of the vehicle's speed through
the water.
The radius of the front and rear rollers equals the
height of one paddle. The surface area of a paddle must be calculated from its
length, width, and inclined geometry.
The hull is of very shallow V type, designed for planing.
It begins with a straight stem with a more pronounced V entry. It includes a
fairing for the paddles extending lower than the lowest point of the central
hull, giving a catamaran like appearance. The fairing volume plays a secondary
or negligible role in buoyancy but contributes to water flow guidance.
For vehicles with 2 or 4 tracks:
• The width of the central hull equals the overall width minus the width of
the lateral tracks.
• The hull is of catamaran type.
• The lowest point of the central hull is higher than the bottom of the lower
track run by a distance equal to 20% of the spacing between the outermost tracks
For vehicles with 3 tracks:
• The width of the central hull equals the overall width
• Account for the recesses corresponding to the volume of the 3 embedded tracks
• The hull is light at the bow then flat, with recesses corresponding to the
upper part of the track systems
Pure client-side JavaScript, five steps:
• Read inputs
|
Parameter |
Symbol |
Unit |
|
Length overall |
L |
m |
|
Beam |
B |
m |
|
Displacement weight |
W |
kg |
|
Engine power |
P |
kW |
|
Track width (%B) |
k |
% |
|
Number of tracks |
Nt |
- |
|
Total submerged paddles |
Ns |
- |
submerged per track: n_s = Ns /
Nt
paddles per track: n_p = 2·n_s
+ 6
track system length: Ls = 0.8L (Nt=2),
0.25L (Nt=3), 0.375L (Nt=4)
track width: w_t = B·k/100
roller radius: r = Ls / (n_p·0.9)
projected paddle area (30°): A_p
= w_t · (0.9r) · cos30°
For models (<2 m, <100 kg), A_p
is scaled by 0.16 for experimental calibration.
Displaced volume: ∇ = W / ρ , ρ =
1025 kg/m³
Central hull width: Wc = B (Nt=3) else max(0.1, B - Nt·w_t)
Draft: T = ∇ / (L·Wc·0.8) ,
floor 0.15 m for full scale
Wetted surface: Sw = L·(2T + B)·0.7
Re = V·L / ν , ν = 1.19×10⁻⁶
m²/s
Cf = 0.075 / (log₁₀(Re) - 2)²
Rf = ½·ρ·V²·Sw_eff·Cf
Form drag = 0.2·Rf
Classic mistake: modeling paddles as a brake R = ½ρV²ACd.
ARWIMS reality: paddles operate at 4-6 % slip. Relative water/paddle speed is V_slip ≈ 0.05·V_boat, not V_boat.
The tangential force on the paddle points
aft relative to water, therefore forward relative to the vessel: it is thrust,
not drag.
Consequence in simulator (v1.8):
Why this is the main advantage:
Speed and fuel gains do not come from
higher propulsive efficiency, but from near-total
elimination of propulsive drag and wetted area reduction.
Before declaring a planing speed achievable, we verify that the tracks can actually carry the weight.
A regime is considered achievable only if the calculated lift is at least equal to the required lift, and at the same time the power needed is less than the available engine power.
|
Regime |
Sw_eff |
η |
Note |
|
Displacement |
Sw |
0.55 |
Fn < 0.4 |
|
Hull + track planing |
Sw·(1-0.60·f) |
0.92×(1-slip) |
f = (Fn-0.8)/0.4,
slip 0.05 (micro) or 0.06→0.04 |
|
Track-only planing |
Sw·(1-0.75·f) |
0.92×(1-slip) |
f = (Fn-1.4)/0.6, slip
0.05 (micro) or 0.06→0.04 |
|
Propeller planing |
Sw·(1-0.55·f) |
0.50+0.10f |
baseline, max 0.60 |
P_req(V) = (Rf + Rform) · V / η /
1000 [kW]
Algorithm steps V in 0.5-knot increments, keeps last V
where P_req ≤ P_available.
The simulator shows ARWIMS advantage comes from two
factors: (1) near-total elimination of propulsive drag (R_paddle=0)
with high mechanical efficiency η=0.92×(1-slip), and (2) wetted area reduction
by 40-75 % when planing on tracks. This combination explains the observed speed
increase and fuel reduction.
You can ask the AI of your choice what it thinks of our technology and simulator using the following prompt: You are a naval architecture engineer. Can you answer the following two questions?
You can easily download the simulator from https://arwims.com/arwims-sim.htm and modify the settings or refine it if you wish.
We will welcome your feedback.
Model version: v1.8 – May 14, 2026