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Seahorse
Head size, spring and drag.
Suction and prey
Mouth, suction pulse and copepod behaviour.
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Layers
Model checks
The science
Rotation (pivot feeding). The head is a slender rod pivoting at the neck. A tendon behaves like a torsion spring that muscle loads slowly and a skeletal latch releases suddenly. After release the head obeys
I theta'' = -k theta - (rho Cd h L^4 / 8) w |w|, I = m L^2/3 + rho_w pi (h/2)^2 L^3 / 3The second term in I is the strip-theory added mass of the water that must be accelerated with the snout; the drag term is the quadratic torque on a rod swinging about its end. Without drag the motion is exactly harmonic: the release takes a quarter period and the stored energy 1/2 k theta0^2 becomes kinetic energy (both are checked above).
t_rot = (pi/2) sqrt(I/k)Power amplification. The energy is stored over t_load (tens to hundreds of ms) and released in t_rot (a few ms), so peak power is amplified by about t_load / t_rot. Direct muscle at about 300 W/kg (typical order of magnitude) would need the muscle mass listed in the readouts to match the release power.
Suction. After the rotation the mouth opens for a pulse of length t_suc. Outside the mouth the inflow speed is a power law of the distance r from the mouth:
u(r) = U0 (a/r)^n for r > aWith n = 2 this would be a steady point sink; experiments on pulsed suction in fishes report a faster decay (close to n = 3), which is why only prey within a few mouth radii are caught. Integrating dr/dt = -u(r) gives
r(t)^(n+1) = r0^(n+1) - (n+1) U0 a^n tso the capture time (r = a) is (r0^(n+1) - a^(n+1)) / ((n+1) U0 a^n). A copepod that starts swimming away at v_esc can only escape if it is outside
r_c = a (U0 / v_esc)^(1/n)when it reacts. Suction acts for a time tau before the reaction, so the largest gap that is still captured is
g* = ( r_c^(n+1) + (n+1) U0 a^n tau )^(1/(n+1))(valid when the suction window is long enough to finish the capture; a short pulse lowers the real limit).
Honest simplifications.
- Head = tapered rod with a fixed width-to-length ratio and a single drag coefficient; no tendon mass, joint friction, latch dynamics or body recoil.
- The flow field is a prescribed power law with a rectangular pulse, not a Navier-Stokes simulation; the real flow is unsteady, three-dimensional and depends on mouth shape. The bow wave that warns the prey is not modelled.
- The prey drifts until it reacts, then swims straight away at constant speed. It is drawn about 2x too large; the whole scene is slowed down by the chosen factor.
- Numbers (L = 30 mm, k, U0 = 2 m/s, copepod escape speed and latency, 300 W/kg muscle) are typical orders of magnitude chosen for teaching, not measured values for one species. Spot-check against Bergert and Wainwright (1997) and Van Wassenbergh et al. (2008) before quoting.
What to try
- Strike with the default settings: the head snaps up in about 3 ms and the copepod is drawn in before it reacts.
- Push the prey 4 mm further away (Prey a little too far away) and it escapes: suction falls as 1/r^3.
- Soften the spring: the slower snap gives the prey a head start.
- Set Cd to 0 and compare the rotation time with the quarter-period formula.
- Change the suction exponent n from 3 to 2 and see how much the reach grows.