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The science
The wind field is the Burgers-Rott vortex, the classic analytic model of a tornado core: air spirals in toward the axis and rises, while angular momentum keeps it spinning.
v_theta(r) = [Gamma / (2 pi r)] (1 - exp(-r²/rc²)), u_r = -a r h'(z)/(1+s), w = 2 a h(z)/(1+s)², s = (r/R_in)²
The tangential wind peaks at r = 1.121 rc with v_max = 0.638 Gamma/(2 pi rc); the sliders set v_max and the radius of maximum wind and the model derives Gamma and rc. The radial inflow u_r and updraft w satisfy continuity exactly (div u = 0, checked numerically below); h(z) adds extra inflow in the lowest ~15 m where friction turns the flow inward.
Pressure. Outside friction layers the radial momentum balance is cyclostrophic, dp/dr = rho v²/r. Integrating inward gives a central deficit of rho (Gamma/2 pi rc)² ln 2 = 1.70 rho v_max²; an F3 core of 80 m/s is therefore about 130 hPa below ambient in this idealised model (measured deficits are smaller, a few tens of hPa up to about 100 hPa, because real cores are turbulent and not axisymmetric).
The funnel. A condensation funnel is air that has cooled below its dew point. Lifted air cools relative to its dew point by 6.2 K per km (dry adiabat 9.8 K/km minus dew-point fall 3.6 K/km), so cloud base sits at about 125 m per kelvin of dew-point spread; in addition, 1 hPa of pressure fall cools air by 0.0829 K (T = 290 K, p = 1000 hPa). The visible funnel is where those two coolings add up to the spread. With a small spread the funnel reaches the ground, with a large spread only a dust whirl shows at the surface and the funnel tip stays high.
Motion and the right-hand rule. Air around the tornado also moves with the storm, so ground-relative wind is the vortex wind plus the translation vector. On the right-hand side of the track the two add (strongest damage), on the left they subtract. The F rating shown uses vmax plus translation.
Debris. Each object has drag coefficient k = rho Cd A / (2 m); in air velocity u it relaxes toward u minus its sink speed, where k s sqrt(h²+s²) = g. Still-air terminal speed is sqrt(g/k): about 9 m/s for roofing sheet, 20 m/s for a 2x4 board and 76 m/s for a 400 kg round bale, so a bale needs F4 or stronger winds to be lifted, though it slides much earlier (static friction mu g against drag k v²).
Damage. Failure speeds are indicative values chosen to match the original Fujita damage descriptions (roof surface about 42 m/s, frame house destroyed about 68 m/s, tree uprooted about 34 to 52 m/s, silo about 62 to 88 m/s). Real damage depends on construction quality, duration and gusts. All structures are empty and inanimate.
Simplifications. Axisymmetric steady vortex (no multiple vortices, no changing swirl ratio), constant core with height, no rain-wrapped or rope stages, flat-ish terrain, point-mass debris with tumbling shown only visually. The scale used is the original Fujita scale (F0 to F5); the Enhanced Fujita scale (EF0 to EF5) assigns a similar class from damage indicators with revised wind estimates.