Calculating the Realistic Lift Numbers for a 2-Ton Hover Car
Magnetic Pressure Needed to Hold the Car
Levitation can be seen as magnetic pressure pushing up over the vehicle’s coupling area A. The upward force must equal the vehicle’s weight (F = m g).
- For m = 2000 kg and g = 9.81 m/s² → F ≈ 19,620 N
- If the coupler area A = 6 m² (e.g., 2 m × 3 m), required pressure is:
P = F / A ≈ 3,270 Pa (about 0.032 atm) - Magnetic pressure satisfies P = B² / (2 μ₀). Solving for B:
B ≈ 0.091 T (Tesla)
Reading: With a 6 m² coupler, a field of ~0.09 T is enough to counter gravity for a 2-ton car. Increasing area to 8–10 m² drops B to ~0.07–0.06 T; reducing to 4 m² raises it to ~0.11 T.
Field Energy You Must Sustain
Magnetic energy density equals magnetic pressure: u = B² / (2 μ₀) = P. For an interaction volume V = A × gap (take a gap of 0.2 m):
- u ≈ 3,270 J/m³
- V = 6 × 0.2 = 1.2 m³
- Stored field energy U ≈ 3,924 J (≈ 3.9 kJ)
This stored energy isn’t huge — the real challenge is replenishing losses to keep the field standing.
Power to Maintain the Field
For a resonant field, dissipated power is Ploss = ω U / Q, where ω = 2πf, f is frequency, and Q is the effective quality factor (including all losses in infrastructure and vehicle).
Using U ≈ 3.9 kJ:
- At f = 10 kHz:
- Q = 5,000 → ≈ 49 kW
- Q = 10,000 → ≈ 24.7 kW
- Q = 20,000 → ≈ 12.3 kW
- Q = 50,000 → ≈ 4.9 kW
- At f = 100 kHz: multiply all above values ×10 (e.g., Q = 10,000 → ≈ 246 kW)
Reading: To keep per-vehicle power in the single- to low-tens-of-kW range, you need low-ish frequencies (5–30 kHz) and/or very high Q (≥ 20,000). Superconductors or ultra-low-loss metamaterials help by increasing Q and reducing resistive losses.
What Changes the Answer Most
- Coupler area: Larger area halves required pressure and field B, and lowers stored energy for a given gap.
- Operating frequency: Ploss ∝ f. Higher frequencies ease beamforming but increase losses unless Q is exceptional.
- Effective Q: The biggest lever — increasing Q from 10k to 50k cuts losses ×5.
- Gap (standoff): Smaller gaps reduce interaction volume and stored energy, lowering losses.
Sanity Check
Rule of thumb: ~1 kW per 100–200 kg at high efficiency implies ~10–20 kW for a 2-ton car — consistent with the 10 kHz, Q ~20k–50k estimates above. This matches the power budget of modern EVs.
Bottom Line
- Minimum field: ~0.09 T for a 2-ton car with a 6 m² coupler
- Maintain power: ~5–25 kW per vehicle if operating at 5–30 kHz with Q = 20k–50k
- Higher frequencies sharply increase losses unless compensated by equally higher Q