SME
Biomechanics
Gait analysis
Use this for “A person takes 0.7 m steps at 110 steps a minute with 0.9 m legs. How fast are they walking, and when would they break into a run?”
Diagram
Stride
=
2
×
step
=
2
×
0.7
m
=
1.40
m.
v
=
step
×
cadence
60
=
0.7
×
110
60
=
1.28
m/s.
Fr
=
v
2
gL
=
1.28
2
9.81 × 0.9
=
0.187:
a
walk.
Runs
above
√
0.5gL
=
2.10
m/s.
This is an example. Type your own values to start a new problem.
v (m/s)
=
step (m)
×
cadence (steps/min)
60
stride
Stride length
calculated · m
L
Leg length
example · m
Fr
Froude number
calculated
vᵣᵤₙ
Walk–run speed
calculated · m/s
Formulas
v
=
step
×
cadence
60
1.2833
=
0.7
×
110
60
stride = 2 × step
1.4 = 2 × 0.7
Fr
=
v
2
9.81 ×
L
0.1865
=
1.2833
2
9.81 × 0.9
vᵣᵤₙ
=
√
0.5 × 9.81 ×
L
2.1011
=
√
0.5 × 9.81 × 0.9
Assumptions
•
Steady walking on level ground; a step is heel to heel of opposite feet, a stride heel to heel of the same foot, so two steps.
•
The Froude number compares the speed with the leg’s pendulum: people switch to a run near Fr = 0.5.
•
g = 9.81 m/s².
Step-by-step
WE KNOW
step = 0.7 m, cadence = 110 steps/min, L = 0.9 m
FIND
walking speed (v), stride length (stride), Froude number (Fr), walk–run speed (vᵣᵤₙ)
Step 1 · Find walking speed (v)
Use v = step × cadence ÷ 60
Each step moves the body one step length; cadence counts the steps a minute, and a minute is 60 s.
v
=
0.7
×
110
60
v
=
77
60
v
=
1.2833
m/s
Step 2 · Find stride length (stride)
Use stride = 2 × step
A stride is two steps: left then right.
stride = 2 × 0.7
stride = 1.4 m
Step 3 · Find Froude number (Fr)
Use Fr = v² ÷ (9.81 × L)
The speed squared over g times the leg length: how fast the walk is for the leg.
Fr
=
1.2833
2
9.81 × 0.9
Fr
=
1.2833
2
8.829
Fr
=
1.647
8.829
Fr = 0.1865
Step 4 · Find walk–run speed (vᵣᵤₙ)
Use vᵣᵤₙ = √(0.5 × 9.81 × L)
The
speed
where
Fr
reaches
0.5:
v
2
=
0.5gL,
so
v
is
its
square
root.
vᵣᵤₙ
=
√
0.5 × 9.81 × 0.9
vᵣᵤₙ
=
√
4.905 × 0.9
vᵣᵤₙ
=
√
4.4145
vᵣᵤₙ = 2.1011 m/s
Check
Put the numbers back in. Both sides should match.
1.2833
=
0.7
×
110
60
✓
1.4 = 2 × 0.7 ✓
0.1865
=
1.2833
2
9.81 × 0.9
✓
2.1011
=
√
0.5 × 9.81 × 0.9
✓
Topic check
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