Tesla Roadster Flight Simulator

Nozzle flow and groups

The choked-flow relation follows NASA Glenn (https://www.grc.nasa.gov/WWW/k-12/airplane/mflchk.html). Each assumed identical jet has throat area $A_t$, regulated stagnation pressure $p_c$, and tank temperature $T$:

Ambient-matched expansion gives $v_e=\sqrt{2\eta_n c_pT[1-(p_a/p_c)^{(k-1)/k}]}$, $F_j=\dot m_jv_e$, and $I_{sp}=v_e/g_0$. Pressure thrust is zero only because exit pressure equals ambient. Group thrust and mass flow are the per-jet values times active count. Under fixed regulation, cooling raises flow and lowers exhaust speed equally, leaving thrust constant. An actual fixed nozzle need not behave this way off design.

One finite, cooling tank

The mass and rigid-tank first-law equations are derived here. Put $x=m_g/m_{g0}$, $n=k$ for adiabatic discharge or $n=1$ for isothermal discharge, and $q=(n+1)/2$. Then $T/T_0=x^{n-1}$, $p/p_0=x^n$ and

The hypothetical regulator ends flow at $p_{cut}=1.2p_c$. Retained mass sets usable inventory and maximum group on-time. Different groups draw from the same inventory, never independent tanks. A selected run starts fresh. Repeating the same fixed valve pulse without reheat gives $N=\lfloor t_{supply}/t_{burn}\rfloor$; this includes cooling between successive pulses through cumulative on-time, but no extra landing or return manoeuvre.

Variable-mass trajectories

Vehicle mass is empty-system mass plus remaining gas. Integrate upward acceleration $F_{lift}/m(t)-g_0$ twice using 201 samples, enforcing ground support before liftoff. After the pulse, use ballistic motion to return to launch level with no landing burn. Horizontal hop speed is constant. Set the overlap half-duration $d=(L_{obstacle}+L_{car})/(2v_x)$. For a proposed center time $c$, full-body clearance is governed by $\min[h(c-d),h(c+d)]$. The trajectory is unimodal, so the maximum of this minimum occurs when entry and exit heights balance. A 45-iteration bisection finds that center within the airborne interval; apex centering is also retained as a candidate against numerical roundoff. If the overlap lasts longer than the airborne event, achievable elevation is zero. The animation uses the optimized center, which can precede the apex.

For launch, inferred tire force is $F_w=m(0)v_{100}/t_{base}$. For braking it is $F_b=m(0)a_b$. Integrate $(F_{ground}+F_{jets})/m(t)$ for speed change, find target time by interpolation, and close the valves at the target or tank cutoff. Once jets stop, retain the constant tire force. A 401-point quadrature gives road travel. For the hop, horizontal position is exactly $x(t)=v_x t$, including after touchdown. Tire force is an assumed net value, not a tire or fan model.

Claim and obstacle screens

The conservative constant-loaded-mass estimate for 0–60 mph in 0.81 s is $F_{req}=\max[m(0)v_{60}/0.81-F_w,0]$. Its jet impulse is $J=0.81F_{req}$. Inverting the cooling discharge gives gas demand $m_{g0}\{1-[1-qJ/(m_{g0}v_{e0})]^{1/q}\}$ when the usable tank impulse suffices; otherwise the demand card shows a gap. Also compare required force with available rear thrust. A ratio below one for tank impulse alone does not prove adequate instantaneous thrust.

For the separate obstacle sizing screen, the ballistic apex estimate is $H_e=H_{obstacle}+H_{clear}+g_0t_{edge}^2/2$. The constant-loaded-mass impulsive approximations are $J_{approx}=m(0)\sqrt{2g_0H_e}$ and $m_{approx}=J_{approx}/v_{e0}$. These are not strict lower bounds for a vehicle losing propellant. NASA's ideal rocket equation (https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/ideal-rocket-equation/) gives $\Delta v=v_e\ln(M_0/M_f)$ for constant exhaust speed; its ideal impulsive gas demand is $M_0[1-\exp(-\Delta v/v_e)]$, which is smaller than $M_0\Delta v/v_e$.

For a positive pulse, the constant-mass lift screen is $F_{req}=m(0)g_0[1+\sqrt{1+8H_e/(g_0t_{cap}^2)}]/2$. Gas demand then uses the cooling-tank inversion above. This screen assumes overlap occurs in the ballistic segment. The optimized variable-mass trajectory takes precedence when the powered ascent contributes. For zero pulse duration the force, impulse and gas requirement cards are unavailable, and the obstacle comparison is omitted; no finite lift requirement is asserted. Actual zero-burn consumption remains zero.

Energy and independent examples

At initial gas temperature equal to ambient, reversible pneumatic exergy is $B_0=V[p_0\ln(p_0/p_a)-p_0+p_a]$. This is an ideal useful-work upper bound. Jet kinetic energy is integrated separately.

D. J. Dunn's attached Applied Thermodynamics PDF, pages 156 and 158, independently checks choked air flow and nozzle exit speed. The air constant is 287 J/(kg·K); nitrogen uses 296.8 J/(kg·K); both use $k=1.4$. These validate gas equations, not an actual Roadster.

Replay physics

The replay reads elapsed seconds and plays at 0.5× real-time speed. Physical position is transformed once as $x_s=x_{origin}+s x(t)$ and $y_s=y_{ground}+s h(t)$, using one fixed scale $s$ for both axes and the full event. The obstacle is placed at $v_x t_{place}$, with its real width and height. The dashed trajectory and ghost cars are precomputed independently of replay time. Hop horizontal speed persists through touchdown; only the vertical trajectory returns to zero. Braking and launch positions integrate their computed speed histories. A tire-only brake ghost uses $d=v_0^2/(2a_b)$. Cosmetic landing squat and dust do not change physical position.

Instantaneous plume length is proportional to active-group thrust and zero outside the actual pulse. This model deliberately retains constant regulated nozzle pressure. Tank pressure falls, but $\dot m\propto T^{-1/2}$ and $v_e\propto T^{1/2}$ cancel in thrust until the regulator cutoff; shortening the plumes merely with tank pressure would contradict that model. The map arrows show thrust; exhaust plumes point the opposite way.

Published prototype claims and hypothetical calculations are distinguished. The MotorTrend engineering visit, 16 October 2026 (https://www.motortrend.com/news/first-look-2028-tesla-roadster-performance-thrust-rocket), supplies the updated preset directions, propellant and volumes. Final production details remain unverified.

• Reported Rocket layout: four rear propulsion jets, four downward jets and two lateral jets at the nose. Exact map coordinates are schematic. A side view combines overlapping jets into axle pairs. Thrust uses four rear jets; Performance has no jets and is documented rather than offered as a thruster preset.
• The Front-jet alternative is deliberately hypothetical: four rear, two lift, two longitudinal braking and two side jets. It is required for front-jet braking and is not attributed to Tesla.
• Reported-trim mode uses 200 L for Thrust or 600 L for Rocket. Custom volume overrides those values. All vessels are represented by one equivalent shared tank.
• Nitrogen follows the engineering visit; dry air reflects the earlier reveal description and remains an alternative. The reported pressure of up to 10,000 psi does not establish the actual demonstration fill pressure or its gauge/absolute basis. The default 30 MPa absolute fill remains assumed; the allowed range extends to 100 MPa.
• Empty-system mass includes vehicle, occupants, vessels, piping and valves, with stored gas added separately. MotorTrend also quotes a 1,700 kg target without resolving this input's trim or loading basis; the default 2,000 kg is an independent scenario assumption. Per-jet nozzle size, losses and regulator settings remain assumed.
• Uniform ideal gas, rigid vessels and constant heat capacities. Isothermal discharge requires sufficient heat transfer. Fixed regulation, ambient-matched nozzles, efficiency and a 20% pressure reserve are assumptions. Flow delays, piping capacity and plume interaction are omitted.
• Lateral jets consume no gas in these translational manoeuvres. No yaw, roll or inverted-track dynamics is solved.
• Obstacle placement maximizes the minimum entry/exit elevation on the computed trajectory. Assumed car length is 4.6 m. Flight pitch remains zero; initial lowest-point height is conservatively zero. Braking nose dive, landing suspension compression and dust are illustrative, without adding forces or changing the computed trajectory.
• No landing pulse, attitude corrections, reheat or refill are included in repeat-pulse counts. Later pulses need not reproduce the first trajectory.
• Tire force may include hypothetical fan/aero assistance through the assumed baseline. No independent tire, fan or aerodynamic force model is provided.
• The replay input is physical time in seconds and runs at half real-time speed. Its end includes 0.6 s of hop rollout, 0.4 s of launch rolling or a 0.35 s stopped braking hold. The view uses a single constant scale for distance, height, car geometry and obstacle geometry throughout each event; there is no vertical exaggeration or time warping.

Use for short-event feasibility and sensitivity studies under the selected ideal-gas assumptions. No result independently verifies the unveiling claims. The reported jet/tire force ratio depends on the meaning and operating conditions of tire force; the default inferred ratio differs, and the model does not tune it to four or five.

At hundreds of bar, real-gas compressibility can substantially change inventory and available impulse. Very cold tank and nozzle states can cause condensation; the phase warning is only a rough screen. The full-supply plots and pulse count may extend into colder regimes than the first selected pulse. Nitrogen is the updated reported-prototype default; both gas choices remain idealizations.

Constant regulation and ideal expansion may overestimate useful thrust or understate consumption. Flow capacity, nozzle off-design shocks, thermal inertia, compressor recharge time and energy, humidity, drag, fan suction, active aero, ground effects, structural loads, occupant acceleration, attitude control and a controlled landing require separate models. The calculator is not a pressure-vessel, flight-control or vehicle-safety design tool.

The hop's displayed touchdown speed is the unbraked vertical return speed. The inverted half-pipe and axial roll are source context and are not animations of validated dynamics. Rocket's reported public-road restriction is a company statement, not a jurisdiction-specific legal assessment.

Claim gas and obstacle-estimate gas cards are blank if their impulse exceeds usable tank capacity. Obstacle requirement cards are also blank at zero pulse duration; the obstacle comparison is omitted rather than shown as a zero requirement. Constant-loaded-mass impulsive estimates are not strict lower bounds for a variable-mass vehicle. Check force and impulse separately. Pulse count is a tank valve-on-time budget, not a count of complete safe flights. Zero burn gives zero pulses by convention.

Metric/US display conversions keep physical quantities unchanged and preserve the explicitly selected 60 mph or 100 km/h target. Charts and drawing annotations retain their labeled SI engineering units; the drawing uses bar absolute, km/h, metres and physical seconds. Independent reference checks cite Dunn's original examples and exact attached-page quotes.