Table 1. Notations used in the article.

Symbol	Definition and units	Other explanation
r	Radial coordinate	Variable in ARSLIP and SLIP models
θ	Angular coordinate	Variable in ARSLIP and SLIP models
R	(AR)SLIP spring natural length	Optimized for each fly. Set to be within 10% of the measured mesothoracic leg
Rtri	Tripod spring natural length	Optimized for each fly
ks	Radial spring constant	Variable in ARSLIP and SLIP models
ka	Angular spring constant	Variable in ARSLIP and SLIP models
k	Spring constant for individual legs	Variable in springy tripod
rm	Mid-stance height	Experimentally determined for each step (see Figure 7A)
v	Speed or horizontal velocity
V	ARSLIP potential energy
$\stackrel{-}{r}$ ≡ r/ R	Nondimensional radial coordinate
γs	Nondimensional radial spring constant	${\gamma }_s=\frac{k_{s}R}{mg}$
γa	Nondimensional angular spring constant	${\gamma }_a=\frac{k_a}{mgR}$
${\stackrel{-}{r}}_m$	Nondimensional mid-stance height	rm / R
Ω	Nondimensional mid-stance angular speed
Fr	Froude number – nondimensionalized speed	v 2/(g*leg length)
L	Tripod spread	Experimentally determined for each step (see Figure 7A)
Vtri	Tripod potential energy
g	Gravitational constant
m	Mass of the fly	Mass was kept fixed; average mass of flies of a particular sex and genotype was measured
ARSLIP	Angular and radial spring-loaded inverted pendulum