## Normalisation formulae for reporting gait analysis data

To convert to dimensionless units, divide quantity by ...

Mass: m
Length, distance: l
Time: (l/g)^1/2
Velocity: (g.l)^1/2
Acceleration: g
Force: m.g
Moment: m.g.l
Work: m.g.l
Power: m.(g)^3/2.(l)^1/2
Angular Velocity: (g/l)^1/2
Angular Acceleration: g/l
Moment of Inertia: m.l^2

where m = body mass, l = lower-limb length (hip-joint to floor) and g = gravitational constant (9.81 ms^2)

```    To those interested in the normalization issue, I can advertize
here my Letter to the Editor in Gait and Posture: "Scaling Gait Data
to Body Size", vol. 4 : 222 - 223. I received it just the other day.
It is preceded by a paper by Zijlstra, Prokop and Berger (4: 212 -
221) and an editorial by D.Sutherland(4: 209 - 211), all related to
the normalization subject.

Your quest for normalized data for joint moments, work etc is
certainly very relevant. I have some scattered data on this point,
all expressed in dimensionless quantities s' = s/l , W' =
W/mgl etcetera.

>From Hof, Geelen and Van den Berg, " Calf muscle moment, work and
efficiency in level walking" J Biomech 16: 523 - 537 (1983):

Preferred steplength s' at an imposed speed v'
s' = 1.1 v'^1/2 +- 0.2
negative work at ankle, Winter's A1
W-' = (2.91 +- 0.52 ) * 0.01  (independent of speed or steplength)

>From Hof et al. "Calf muscle work and segment energy changes in humen
treadmill walking", J. Electromyogr. Kinesiol. 2: 203 - 216 (1993):

positive work at ankle, Winter's A2
W+' = 0.046 s'^2   (dependent on steplength only).
kinetic+potential energy of swing leg
E' = 0.23 v'^2

Data that relate joint moments, work, etc to speed are very relevant
indeed as a reference in  patient research, because these people
usually walk at speeds far below "normal". Gait labs with those nice
VICONs or ELITEs and undergraduate students should have no problem to
gather these data from normal subjects!
We - that is our  Laboratory of Human Movement Analysis- are in
the process of preparing EMG data obtained at walking speeds between
0.5 and 2 m/s. If there is interest we can post them when ready.```
```    To show the power of this normalization follows here a table with
data from Table 2.3 in Rose et al. Human Walking (2nd ed. of Inman).
It gives preferred speed and cadence as a function of age. Leg length
is from the original source, the book of Sutherland.

leg                      NORMALIZED
(yr)   (st/min)     (m)   (m/s)      S/L

1.00     176     0.32     0.63      1.36     0.53     0.36
1.50     171     0.36     0.71      1.39     0.54     0.38
2.00     156     0.39     0.71      1.41     0.52     0.37
2.50     156     0.41     0.80      1.49     0.53     0.40
3.00     154     0.44     0.86      1.51     0.55     0.41
3.50     160     0.47     0.99      1.59     0.58     0.46
4.00     152     0.49     0.99      1.58     0.57     0.45
5.00     154     0.53     1.08      1.58     0.60     0.47
6.00     146     0.57     1.09      1.57     0.59     0.46
7.00     143     0.62     1.15      1.57     0.60     0.47
adult    111     1.00     1.45      1.57     0.59     0.46

It is clearly seen that the normalized quantities are essentially
unchanged above age 3 1/2.

Greetings from NL,At Hof
Department of Medical Physiology
University of Groningen
Bloemsingel 10
NL-9712 KZ GRONINGEN
The Netherlands
Phone: (31) 50 3632645
Fax:   (31) 50 3632751

(14 June 1996)```