Teaching model. A steady, axisymmetric vortex over flat-ish farmland with textbook-level equations and honest simplifications. It is not a forecast or engineering tool. Damage objects are inanimate, and nothing here shows people or animals.
Wind profiles. In the Rankine vortex (Rankine 1882) the air rotates as a solid body inside the core radius rc and as a free vortex outside:
v(r) = vmax r / rc (r ≤ rc), v(r) = vmax rc / r (r > rc)
The Burgers-Rott vortex (Burgers 1948; Rott 1958) is the smooth solution that balances radial inflow against viscous diffusion: v(r) = K (1 - exp(-r2/δ2)) / r. Its maximum sits at r = 1.1209 δ, so here δ = rc/1.1209 and K = vmax rc / 0.7153 put the peak exactly at rc for both models. Vertical structure (weaker at the ground and aloft), the inflow and the updraft are simple closed forms, not solutions of the Navier-Stokes equations.
Cyclostrophic balance and pressure. Where rotation is fast and the Coriolis force is negligible, the inward pressure force balances the centrifugal term:
dp/dr = ρ v2 / r ⇒ Δp(r) = ∫r∞ ρ v2/r' dr'
For Rankine this gives Δp = ρ vmax2 at the centre (half of it, ρv2/2, already at rc). For Burgers-Rott the integral is rho K2 ln2 / δ2 = 1.702 ρ vmax2. With ρ = 1.2 kg/m3 and 65 m/s, Δp is about 51 hPa (Rankine) or 86 hPa (Burgers-Rott). Radar-and-probe work on a violent tornado (Manchester, South Dakota, 2003; Lee et al. 2004) reported a drop of order 100 hPa, the same order of magnitude.
Enhanced Fujita scale. The EF scale (Texas Tech / US National Weather Service, in use since 2007; the original F scale is Fujita 1971) rates a tornado from its damage. The associated 3-second gust estimates are EF0 65-85 mph, EF1 86-110, EF2 111-135, EF3 136-165, EF4 166-200, EF5 over 200 mph (29-38, 38-50, 50-61, 61-74, 74-89, over 89 m/s). These are estimates attached to damage indicators, not measurements; the coloured bands here simply map wind speed to that table.
Translation speed. The ground-relative wind is the rotation plus the motion of the whole vortex. For an anticlockwise (Northern Hemisphere) vortex moving north, the right (east) side adds the translation speed to the rotation and the left side subtracts it, so the strongest winds and most damage tend to lie on the right of the track.
Swirl ratio (qualitative). Laboratory vortex chambers (Ward 1972; Church et al. 1979; Davies-Jones 1973) show that the swirl ratio S, the ratio of rotation to the updraft that feeds it, sets the structure: low S gives a narrow single-cell vortex, intermediate S a two-cell vortex with a downdraft down the axis (a wider, wedge-like core), and high S breaks the core into several small suction vortices orbiting the centre. Here S switches on an axial downdraft above about 0.4 and 2, 3 or 4 sub-vortices above about 0.8, 1.4 and 2.1. Those thresholds are illustrative; real storms do not follow a single number. Sub-vortices can raise the local peak gust well above the parent vortex maximum.
Condensation funnel. Air at the surface has temperature T and dew point Td. Lifted dry-adiabatically it cools 9.8 K/km while its dew point falls only about 1.8 K/km, so the spread closes at 8 K/km and cloud forms at about 125 m per kelvin of spread (cloud base here). Inside the vortex, the pressure drop Δp expands the air as well: ΔT = T [1 - (1 - Δp/p)0.2857], and 82 % of it counts toward closing the spread. The funnel therefore starts at height (spread - 0.816 ΔT)/0.008 K/m and reaches the ground when that is zero. Dry air (a large spread) can leave a violent tornado with only a dust whirl or a funnel that stops well above the ground: the funnel is the visible part, not the tornado. The model keeps the pressure drop constant with height below cloud base and ignores latent heating and mixing.
Debris. Each piece is a point mass with quadratic drag, m dv/dt = ½ ρ Cd A |u - v| (u - v) - m g, integrated implicitly so that the very light pieces stay stable. For a cube of side d and density ρd the terminal fall speed is vt = sqrt(2 ρd d g / (ρ Cd)) (Cd = 1.05). Pieces whose vt is below the local updraft are lofted, heavier ones lag the rotating air, drift outward (centrifuge effect) or stay near the ground. Real debris tumbles, has no fixed Cd and breaks up; no debris-wind feedback is modelled.
Damage thresholds. Illustrative: shed 38 m/s; trees 40-43; outbuilding roof 40, collapse 53, swept 75; house roof 46, collapse 62, swept 82; wooden pole 50; silo 58 m/s. Each object gets its own +-10 % scatter.
Simplifications. No terrain or obstacle effects on the wind, no tilt or occlusion of the vortex, no rain, no tornado life cycle (genesis, roping out). The funnel mesh, wall cloud and cloud deck are visual models driven by the equations above.