Drinking Bird Heat Engine

A heat engine running on room air

The bird is a closed glass system holding liquid dichloromethane (CH₂Cl₂, boils at 40 C) and its vapour. The wet felt on the head loses heat by evaporation, so the head is cooled towards the wet-bulb temperature, below the body temperature. Dichloromethane is volatile, so the cooler head has a lower vapour pressure than the body: ΔP = Pv(Tbody) - Pv(Thead). With the Antoine fit log10 P[bar] = 4.53691 - 1327.016/(T[K] - 20.474) every kelvin is worth about 2.2 kPa at room temperature.

Pressure lifts the liquid

The gap pushes liquid up the neck until it balances the weight of the column: h = ΔP / (ρ g cosθ) with ρ = 1325 kg/m³. The column follows with a 1.4 s lag. As liquid moves from the low bulb to the neck and head, the centre of mass rises. For a rigid pendulum about the hip, I θ'' = g (Mx cosθ + Mz sinθ) - c θ', with Mx = Σ m x and Mz = Σ m z over bulb, neck, head, hat and liquid. While M_z is negative the bird hangs stably (period 2π√(I/(g|Mz|))); once enough liquid has climbed, M_z becomes positive and there is no equilibrium, so the bird tips forward.

The dip resets the engine

When the bird has tipped about 78 degrees the lower end of the neck leaves the liquid in the bulb, a bubble of vapour passes up the tube, the two vapour spaces equalise and the column drains in about 0.3 s. The beak is in the water glass at this moment, so the felt is rewetted and warmed back towards room temperature. The bird swings upright and the cycle restarts. Without the water glass the felt dries (a few minutes in this model) and the head warms to room temperature, so the engine stops.

Head heat balance

C dTh/dt = hc A (Ta - Th) - L m'' A φ, where the evaporation flux is m'' = hm (ρvs(Th) - ρv,a) with hm = hc/(ρa cp) (Lewis analogy) and φ the wetness of the felt. Setting the left side to zero gives the wet-bulb limit, independent of h_c. Humid air has a small wet-bulb depression, so the bird slows or stalls: at 98 % relative humidity the model never nods. In this model the head is held well above the wet-bulb limit because every dip returns heat from the water.

Efficiency

The Carnot limit 1 - Thead/Tbody is tiny (a fraction of a percent for a kelvin of difference) and the bird does only a few millijoules of useful lifting work per nod: it is a demonstration engine, not a power source.

Honest simplifications

Lumped head and body temperatures, a single heat-transfer coefficient 6 + 9√v W/m²/K, no heat conduction through the vapour tube, a first-order column lag instead of two-phase flow, a rigid-body pendulum with linear air damping and a soft stop at 86 degrees, and an instantaneous bubble event. The charge, masses and distances are typical of a commercial bird but not measured from one specific model and the timings were tuned to a nodding period of tens of seconds. The wet-bulb check compares against an empirical psychrometer fit that assumes ventilated psychrometer conditions, so a difference of up to 0.8 K is allowed.