Four-player touch. Each quadrant belongs to its numbered pilot. Left stick steers, the throttle stays where you leave it, and Fire/Drop acts only for your vehicle. Pause stops the entire world. In face-to-face seating the far pair rotates 180°. One person at a time drives a vehicle; choose an unoccupied unit from the map.

Manual flight. The stick directly commands roll and pitch. Releasing roll gently corrects a moderate bank; pitch stays under pilot control. Keep enough throttle to stay above stall speed. This is simplified game handling.

Combat guidance. Cannon markers show a nominal reference-barrel estimate; combat rounds include random spread. This combat workshop is not yet an assessed calibration lab.

Planes. Along the flight path, m·a = T − k·v² − m·g·sin θ, where θ is the climb angle. Top speed comes when thrust equals drag, so v = √(T/k). Climbing trades speed for height. Banked turns follow v²/r = g·tan φ, and pulling up is limited to 6 g, so the turn rate is at most 6g/v. A slower plane turns tighter. Game rules: the wings keep your velocity pointed where the nose points, and below stall speed the nose drops.

Gyro-copter. The rotor pushes along its own axis. Net force = thrust + weight + drag. It hovers when thrust equals weight, which is the white mark on the throttle. Tilting sends part of the thrust sideways, so you move but need more throttle to stay up. Game rules: the chin gun tilts up and down toward targets by itself, and drag is −k·|v|·v.

Ships. Along the heading, m·a = T − k·v², so top speed is √(T/k). The rudder turns the ship at a rate of v/R, so a ship barely turns when it is stopped. Ships need water at least 3 m deep and stop when they run aground.

Cannon shells. Each shell leaves at the gun’s muzzle speed v₀ at the elevation you set, plus the ship’s own velocity. Only gravity acts after that. For a stationary launcher and equal launch and landing heights, R = v₀² sin 2θ / g, so 45° reaches farthest. A raised muzzle or moving vehicle changes that result. Hide the splash marker and pilots must work out the elevation from the target distance themselves.

Zeppelin. Net vertical force = buoyant force − weight. Up and down change the buoyant force by up to 8% (game rule: venting gas or dropping ballast). Bombs inherit the airship’s full velocity. For level flight, initial vᵧ = 0 and t = √(2h/g), where h is the release height above the landing surface. That is Certification A in the air.

Cars. Along the road, m·a = F − k·v² − C·m·g − m·g·sin θ: drive force minus drag, rolling resistance and the pull of gravity on a hill. Tyre forces share a grip limit of μ·m·g on level ground. Turning uses some of that grip, leaving less for acceleration. In a corner the tyres must supply v²/r of sideways acceleration, and they can give at most μ·g. Go faster than √(μ·g·r) and the car slides. The road has μ = 0.8 to 0.95 depending on the car; grass and sand have less. Wreck Coast is a 6.35 km circuit with two race laps: dockyard, open shipwreck, causeway, cliff switchbacks, a quarry fork and the harbor sweep. The gravel service lane is shorter and narrower; both routes stay open. Steering becomes gentler at speed. Brake overrides the gas and slows sideways motion too. Cars follow the ground; jumps are not modeled. In Race, the hovercraft has limited side-fan assistance; its Brake opposes drift.

Motorcycle. Light and quick, so its drive is limited by grip, not the engine: a bike accelerates at most μ·g. In a corner it leans so that tan φ = v²/(g·r), the same rule a banking plane follows. The screen shows the lean angle.

Hovercraft. It floats on a cushion of air, so there is almost no friction. Turning the hull does not turn your velocity: momentum keeps you sliding the old way until thrust changes it (Newton’s first and second laws). To corner, point the thrust along the change in velocity you want. It crosses land and water, but gravity pulls it down slopes and it cannot climb hills steeper than its thrust allows. Drift shows the angle between where you point and where you go.

Tanks. The same force balance as a car, with different mass and drive force. Tracks can turn the hull while standing still. Each side has a river, and tanks can cross only at its two shallow fords. The mortar fires only between 45° and 80°, so it uses the high-angle solution: with a stationary launcher and equal launch and landing heights, complementary angles have equal range (except the single 45° maximum).

Flagship battle. Each commander picks a Dreadnought, Sky carrier or Land fortress, then launches units from it. A catapult launches a plane at v = √(2Fd/m) adding the flagship’s velocity as a vector; with launch aligned to its motion, speeds add. A heavy bomber needs more force than a fighter. A hangar drop lets a plane fall until v² = 2gh reaches stall speed. Parachutes fall at about √(g/k) = 7 m/s while drag slows the forward drift. Torpedoes run at a steady 40 m/s, so they are aimed where the target will be: |P + V·t| = s·t. Miners and dredges get heavier as they fill (a = F/m). Couriers earn gold for every lap, more for laps under par (about 170 s). Units you drive yourself earn double. Small guns do only a fifth of their damage to a flagship’s armour.

Gun rounds. Plane and gyro-copter rounds leave at 300 m/s relative to the craft, plus the craft’s own velocity. Only gravity acts after that. Not modeled: wind, waves, fuel, real wing shapes.

Scoring. Downing or sinking an enemy scores a point for your team. Crashing into the ground or sea gives the other team a point.

Two laps through the dockyard, wreck passage, causeway, cliff switchbacks, quarry and harbor. Follow the numbered gates in order. The quarry service lane is shorter, narrower and gravel; the outer road stays open.

Brake before tight corners. Brake overrides Gas and slows sideways motion. Steering becomes gentler at high speed. Back to road returns you safely without advancing checkpoints. Cars remain on the ground; jumps are not modeled.

Each team delivers three supplies into its marked sea zone. The pilot holds course and altitude; the bombardier chooses release using the downward map, release height and ground speed. Crosses mark observed impacts.

Free pilots use Vehicles to explore aircraft, a gyro-copter, a ship, a tank or a buggy. The crew bomber stays reserved for its pair. This first mission tests the controls; the coordinated team rally comes later.

Swap roles exchanges the two crew stations. New approach returns the bomber to its starting course and removes its airborne supplies; delivered supplies and attempt counts remain. Lost vehicles return automatically. Rotate students while paused.

Keyboard: WASD / arrows steer the crew aircraft; E / slash release. Touch throttles stay set after release. Supplies are harmless. This practice does not certify written physics work.