Jet Roadster Ramp Hop (2D)

Side and rear views of a fictional jet-assisted roadster: ramp launch, mid-air thruster roll, cushioned landing and a hover-power calculator.

Switch to 3D

Presets

Playback

Scenario

Autopilot scripts, or press Restart after changing parameters.

Vehicle

Illustrative numbers, not any real product.

Run

Layers

Model checks

The science

What this is

A teaching model of a fictional jet-assisted electric roadster that drives up a ramp, leaves the ground, rolls once in the air using thruster torques and lands again. All numbers (1900 kg, 8 kN per nozzle, 100 kWh pack) are illustrative assumptions, not data for any real vehicle or manufacturer.

Rigid-body motion

The car is a 6-degree-of-freedom rigid body. Translation and rotation follow Newton and Euler:

m dv/dt = ΣF    I dω/dt + ω × Iω = Στ

Forces are gravity, four spring-damper wheels with friction, aerodynamic drag, ramp contact and the nozzle thrusts applied at their mounting points; their moment arms produce the torques that roll and pitch the car. The side view shows the (z, y) plane, the rear view the (x, y) plane, so the roll is visible there.

Jet thrust and hover power

An ideal ducted jet of disc area A that supports weight W = mg in hover accelerates air to twice the induced velocity vi (momentum theory):

vi = √(W / 2ρA)    Pideal = W3/2 / √(2ρA)    Pel = Pideal / η

The thrust per unit power falls as the exhaust gets faster, which is why hovering a car is extremely power hungry: about 2.5 MW for these numbers, so a 100 kWh pack lasts only about 144 s. Propellant is air; the energy bill is electrical.

Ballistic flight

Without thrust the centre of mass follows a parabola: apex height h = y0 + vy² / 2g and flight time t = (vy + √(vy² + 2g y0)) / g. Drag shortens the real range slightly.

Honest simplifications

  • Thrusters: first-order spool-up, no inlet losses, no heating.
  • Tyres: a simple friction model; no slip curves or load-dependent grip.
  • Drag is a single body drag area; no lift, no ground effect from the jets.
  • The autopilot is a tuned PD attitude controller, not a flight-certified design. Educational mechanics only.
What to try
  • Run The hop: the thrusters roll the car through 360 degrees in about 2 s and a short cushion burn softens the landing. Watch the rear view.
  • Run Ballistic jump and compare the range with the Check 1 formula.
  • Run Failed landing: the controller stops before the roll is finished and the car lands on its roof or side.
  • Run Hover attempt and lower the battery size: the hover time drops linearly with pack energy.
  • Increase the nozzle area: the hover power falls as 1/sqrt(A).
Altitude of the centre of mass (m)
Roll angle (deg) and roll rate (deg/s)
Total thrust (kN) and electrical power (MW)
Acceleration felt (g) and speed (m/s)