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Running in the surf: hydrodynamics of the shore crab Grapsus tenuicrustatus

Marlene M. Martinez^*

Department of Integrative Biology, University of California at Berkeley, Berkeley CA 94720, USA

View larger version (24K): [in a new window]   Fig. 1. (A) Forces acting on the body of a crab locomoting through a fluid environment. The crab in the diagram is locomoting with its left side leading and is moving upstream against an ambient water current. The fluid motion relative to the crab is the vector sum of the flow due to the ambient current and the flow due to the motion of the crab. Buoyancy counteracts the crab’s weight. Lift, which acts perpendicular to the relative fluid motion, counteracts the weight (positive lift, acting away from the substratum) or augments the weight (negative lift, acting toward the substratum). Drag acts in the direction of relative fluid motion, resisting locomotion and tending to push the crab downstream. Acceleration reaction resists changes in velocity, augmenting drag as a crab accelerates relative to the fluid and counteracting drag as the crab decelerates. (B) A crab overturns, pivoting about its downstream leg, when the overturning moment about its center of mass exceeds the stabilizing moment. The overturning moment is the net horizontal force times the height of the center of mass. The stabilizing moment is the net vertical force times the distance from the center of mass to the trailing leg. (C) A crab that does not actively grasp the substratum washes away when the net horizontal force on its body exceeds the frictional force resisting dislodgment.

View larger version (12K): [in a new window]   Fig. 2. Speeds of five different crabs locomoting through still water over a flat substratum. Each data point represents one trial for an individual crab. Circles indicate slow punting and triangles indicate fast punting. A mean speed for each of these gaits was calculated for each crab; the overall mean for each gait was calculated as the mean (± S.D.) of the mean speeds of the five crabs.

View larger version (15K): [in a new window]   Fig. 3. The two postures of Grapsus tenuicrustatus (from Martinez et al., 1998) effected by changes in the coxa/basi-ischium joint, the basi-ischium/merus joint and the merus-carpus joint.

View larger version (23K): [in a new window]   Fig. 4. Water flow records from the lagoon, bay and wave-swept sites, measured at the approximate height of a crab (0.06m above the substratum). Mean and maximum velocities measured for the trials shown were 0.02ms-1, 0.04ms-1 (lagoon), 0.21ms-1, 0.40ms-1 (bay) and 0.30ms-1, 0.91ms-1 (wave-swept site).

View larger version (20K): [in a new window]   Fig. 5. Hydrodynamic forces on the body of a crab using the terrestrial (open circles) and aquatic (filled circles) postures at 0° angle of attack. Each data point represents the mean of five trials for an individual crab, and values are means ± 1 S.D. Reynolds numbers (based on maximum lateral width of a crab) range from 2.5x104 to 2.0x105. Drag force (A) was significantly different for the two postures at all velocities except 0.15ms-1. Lift force (B) was not significantly different for the two postures. Arrows indicate the mean slow and mean fast punting speeds.

View larger version (25K): [in a new window]   Fig. 6. Calculated contribution to drag on the crab due to drag on the swinging of one leg. Positive drag indicates drag acting in the opposite direction from the direction the whole crab is moving through the water (i.e. resisting forward movement). Negative drag indicates drag acting in the same direction as the crab is moving through the water (aiding forward movement). Filled circles indicate calculated drag on a crab model with legs not swinging. Open circles indicate the calculated drag on a crab model when adjusted for the contribution of one swinging leg. Grey triangles indicate the adjustment in drag due to one swinging leg. A, the time when a leg is not swinging relative to the body; B, the time when a leg is in the stance phase, generating thrust against the substratum and thus swinging with respect to the body; C, the time when a leg is in the swing phase and swinging with respect to the body.

View larger version (16K): [in a new window]   Fig. 7. Lift force on the body of a crab as a function of angle of attack. Values are means ± 1 S.D. of three replicate measurements at a velocity of 0.98ms-1 for one individual crab in the aquatic and the terrestrial posture. The actual values varied: the absolute value of the magnitude of the lift at angles of attack of +4° or -4° were greater for the aquatic posture than for the terrestrial posture, and lift acted upwards at angle of attack +4° but downwards at angle of attack -4°.

View larger version (21K): [in a new window]   Fig. 8. The means of the mean values for all crabs were used to estimate the forces acting on the body of a crab using different postures in various flow conditions. Fluid motion relative to the crab is right-to-left. Longer arrows represent larger forces. In air, crabs are shown only in the terrestrial posture. Wapp, apparent weight (= weight-buoyancy); A, acceleration reaction; D, drag; L, lift. (A) Crab is locomoting through still fluid (water or air). Fastest punting speed in water=0.67ms-1. Fastest recorded run on land=1.4ms-1. Crab is locomoting at +4° angle of attack. Body acceleration=1.13ms-1. (B) Crab is standing in moving fluid (water or air). Fastest water flow measured in the field at wave-swept site=1.6ms-1, acceleration=1.71ms-2. Air speed in hurricane 45ms-1. Crab is standing with 0° angle of attack relative to oncoming flow. Acceleration reaction force was not calculated in the terrestrial hurricane condition because acceleration data appropriate to the size scale of a crab was not available. Note that a crab locomoting in water at its fastest punting speed generates positive lift greater than its effective weight if the crab uses a +4° angle of attack.

View larger version (13K): [in a new window]   Fig. 9. (A) Effect of body acceleration on the critical punting speed to overturn a crab in still water. Means of mean measurements for five crabs were used to calculate critical punting speed. Filled symbols and solid lines represent a crab in the aquatic posture. Open symbols and dashed lines represent a crab in the terrestrial posture. Angles of attack were –4° (circles), 0° (squares) and +4° (triangles), respectively. (B) Effect of water acceleration on the critical ambient water velocity necessary to wash away a crab standing with an angle of attack of 0°. Calculations assumed that crabs grasped the substratum with maximum horizontal tenacity (13N). Means of mean measurements for five crabs were used to calculate critical water velocities. Filled symbols indicate a crab using the aquatic posture. Open symbols represent a crab using the terrestrial posture in water.

View larger version (11K): [in a new window]   Fig. 10. Drag CD (A, planform; B, projected) and lift CL (C) coefficients as a function of Reynolds number for various animals. Black and grey diamonds indicate data for Grapsus tenuicrustatus in the aquatic and terrestrial postures, respectively. Diamonds represent data measured on animals near a substratum. Circles represent data measured on animals far from a substratum. Symbols are labelled as follows: A–C, crabs (Blake, 1985); D, crab (Plotnik, 1985); E,F, crayfish (Maude and Williams, 1983); G, lobster (Bill and Herrnkind, 1976); H, lobster in tail-flip posture (Jacklyn and Ritz, 1986); I,J, isopods (Alexander, 1990); K, euphausid (Torres, 1984); L, eurypterid (Plotnik, 1985); M,N, cockroaches (Full and Koehl, 1993); O, barnacle, (P, snail, Q,R, limpets (Denny et al., 1985); S, scallop (Hayami, 1991); T, sea urchin (Denny and Gaylord, 1996); U, inclined sand dollar (Nakamura, 1994); V, sea anemone (Koehl, 1977). Lift coefficients were measured at positive angles of attack: G. tenuicrustatus +4°; A–C, +5°; S, +25°.