Physics field notes / Voyager
Voyager builds an ocean from traveling wave components, then computes foil forces from the water flowing past each wing. These notes describe the equations, riding inputs, and gameplay assists used by the model.
01 / Ocean
The game adds directional components with their own amplitude, direction, phase, and frequency. The components can reinforce each other at one point and cancel a few meters away.
η(x, t) = Σ Ai cos(ki · x − ωit + φi)
How the model works
Frequency and wave number are linked with the deep-water gravity-wave relation. Wind swell follows a JONSWAP-shaped spectrum, spreading energy across frequencies around a peak. The game combines seeded wind swell with directional ground-swell components and retains the strongest components for the surface calculation.
02 / Foil
The force calculation subtracts local water velocity from the wing’s velocity. That relative flow sets speed and the incoming flow angle at the front wing and stabilizer.
Lift
Water density ρ, water-relative speed v, wing area S, and lift coefficient CL set the force.
Drag
The same square-law pressure drives drag. Doubling speed gives four times the force if the coefficients and immersion stay fixed.
Finite span
The model uses e = 0.9. Finite span reduces the ideal two-dimensional lift slope, while induced drag rises with the square of lift coefficient.
Operating limits
Before stall, lift coefficient grows with angle and stops at the foil’s configured maximum. Past the stall angle, the model decays lift. As a wingtip nears or crosses the surface, the immersion multiplier removes most of its support and adds a near-surface drag penalty.
03 / Ride decisions
Speed, trim, bank, and immersion change together. Where the next face is moving affects the input you need to make the connection.
Dynamic pressure rises with v², increasing lift and drag together.
The foil feels firmer as speed rises, while poor trim costs more drag.
A press adds an 800 N forward boost for at least two seconds, up to four while you hold it. A two-second, 40 N drag follows on flatter water, and a descending face waives that drag. Holding it on the flats for more than four seconds sinks the foil.
Use a short press to build speed, then release. The tradeoff changes when you are already driving down a useful face.
The required wing lift grows as 1/cos(bank). Lift-induced and spanwise turn drag can rise with the load.
A hard bank redirects support into the turn, with less margin left to hold height.
Tip immersion shrinks near the surface, reducing lift support and increasing the chance of a breach penalty.
The ride can feel free until a tip ventilates, then support drops abruptly.
04 / Wave energy
The learning logic estimates which nearby faces can help the ride. Physical wave energy describes the wave field and carries units. The rider’s on-screen energy percentage is a separate stamina budget for efforts such as pumping.
Learning cue / unitless
The game samples a reduced set of components, normalizes local height and slope, and clamps the result from 0 to 1. It uses that proxy to rank reachable faces and estimate support. The number is useful for guidance, but it is not joules.
Regular wave / J m−2
For a regular linear gravity wave with height H, mean total energy per horizontal area is one eighth of density times gravity times height squared. The engine also groups spectrum components into directional packets and computes an energy-like J/m² value before deriving flux from group velocity.
Coastal lab / teaching model
In finite depth, the dispersion relation becomes ω² = gk tanh(kh). The shallow side of a crest slows first. Over a simple shelf, crests become more parallel to shore as their travel direction turns toward it. NOAA’s refraction material shows how that bending can spread or concentrate wave energy along a coast.
The coastal lab uses this finite-depth idea for teaching. Voyager’s gameplay ocean does not sample bathymetry or refract swell. At Turtle Bay it does shelter the water behind the coast, which is a separate, simpler effect.
Sources and further study
NASA’s pages use airfoils in air, but the nondimensional lift and drag relationships also apply to a hydrofoil when density and velocity are taken from the water flow. MIT’s ocean engineering material covers the water-specific theory and its limits.
Voyager uses a simplified real-time force model with explicit gameplay assists. It is not a CFD solver, an engineering design tool, or a claim that every operating condition has been measured.