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. 2023 Jul 18;120(30):e2219972120. doi: 10.1073/pnas.2219972120

Table 1.

Explanations of the symbols used in the model and present in the main text. Full list of all symbols with descriptions is presented in SI Appendix, Table S11

Explanations of the symbols appearing in the main text
L=Δll/lc Downward stroke: dimensionless maximal reach of the average of two midlegs [scaled by the capillary length, lc (originally used in ref. 19)]
Ω=ωlc/g1/2 Dimensionless angular velocity of the average four legs’ rotation of a jump (originally used in ref. 19)
M=m/(ρlc2Clw) Dimensionless index of insect body mass with respect to the leg; body mass with respect to maximal water mass can be displaced by the average of four legs (originally used in ref. 19)
Lm=Δll/lc Midleg downward stroke; dimensionless maximal reach of the midleg (modified L for midleg only)
Ωm=ωelc/g1/2 Dimensionless angular velocity of midleg rotation of a jump (modified Ω for midleg only)
Mm=m/(ρlc2Cm0lm) Dimensionless index of insect body mass with respect to the midleg; body mass with respect to maximal water mass can be displaced by the midleg (modified M for midleg only)
ω Angular velocity of midleg rotation of a jump
ωe Derived angular velocity of midleg rotation of the empirical jump

ωt

Hypothetical angular velocity of midleg rotation of the hypothetical jumps (i.e., surface tension jumps of Gigantometra gigas and Ptilomera tigrina; drag-involving jump of Aquarius paludum)

ωc

Critical angular velocity of leg rotation; For a given midleg length and body mass, descending midleg can produce a dimple of the critical dimple depth, hc , with ωc

Db Duration of dimple breaking
lc=[σ/(ρg)]1/2 Capillary length
Δll=ll-yi Maximal downward reach of the midleg
lw Wetted length of the leg
ll Entire length of the midleg consisting of femur, tibia, and tarsus
lm Constant wetted length of midleg (the length of tibia plus tarsus of the midleg)
yi Initial height of the body center from the undisturbed free surface
σ Surface tension coefficient of water
ρ Density of water
g Gravitational acceleration
m Mass of the water strider
C Flexibility factor; function of wetted length of a leg, lw , and its bending rigidity, B
Cm0

Midleg flexibility factor; function of wetted length of a midleg,

lm , and its bending rigidity, B (bending rigidity is explained in SI Appendix, Table S11).

E Young’s modulus of insect cuticle
r Radius of the wetted midleg as a cylinder
rb Radius of the wetted midleg as a cylinder surrounded by air bubble