View Full Version : Summary of responses to normalisation of joint torques

Susan K M Wilson
02-14-2007, 08:52 PM
Dear all,

Many thanks to all of you who responded to my query regarding normalisation
of forces and moments to bodyweight/mass and height.

>From your responses it has become clear that normalisation means
representing the data as a unitless value which enables a more acuarte
comparison between large groups of subjects who may vary widely in their
stature. So, a Force (in Newtons) would be normalised to Body weight (also
in Newtons) and that a joint torque/ Moment (in Newton-metres) would be
normalised to bodyweight (Newtons) * height (metres). Height could represent
the overall height of the subject or as some of you have recommended, the
limb length of each subject.

Armed with this new information I re-read some of the journal articles and
found that a few authors have written bodymass in the text but have actually
normalised to body weight- hence my original confusion!! I hope other
people find the information below as useful as I did. I have posted my
original query followed by a summary of responses.

Thanks again,

Susan Wilson

Original query:

My research has involved investigating the effect of chair biomechanics on
the ability of older adults to stand up with and without the use of their
arms. I am mainly focusing on the peak moments created at the upper and
lower limb joints. My query is with regard to the normalisation of joint
torques for comparison between subjects. I have reviewed a number of papers
that have normalised their data to Body mass and have thus been able to
compare between groups and test conditions. I have however read a few
papers that normalise their data to body height as well as body mass.

I am keen to get a better understanding of why you would normalise your data
to body height (and body mass) as surely the height of the subject/ body
segment has already been taken into account during initial calculations.


Usually normalization procedures involve converting the absolute units of
measurement into a percentage of some standard value with the same units
that makes sense. For example, investigators commonly convert ground
reaction forces to a percentage of body weight since the units of
measurement are the same and ground reaction forces are directly related to
each person's body weight.

A common method for normalizing joint torques is to normalize them to the
product of body weight (not body mass) times body height. This gives the
same units of N*m to both the absolute measurements of torque (moment) and
the noramlizing value of weight in Newtons times height in meters. This
also makes sense since body weight is generally correlated with the ability
to generate muscle force and body height is generally correlated with the
moment arms for internal muscle forces (taller people have larger skeletal
frame sizes and therefore have larger moment arms for their internal muscle
forces than shorter individuals. Please note that the normalizing value is
body weight in Newtons times height in meters, not mass times height. The
unit for mass is the kg.

Hope this helps, Mike Gross


Michael T. Gross, PT, PhD


Program in Human Movement Science

Division of Physical Therapy

University of North Carolina at Chapel Hill 919-843-8680 Voice

919-966-3678 FAX

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I think the idea behind normalizing the joint moments by height is that
taller people are assumed to have longer moment arms. For lower extremity
joints, you might try normalizing the moments by (body weight x leg
length); that has worked well for me in the past.

Hope this helps,



Ross Miller

Doctoral student, Dept. of Kinesiology

6 Totman Building

University of Massachusetts Amherst

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First I am assuming you are using a rigid linked system. Thus from a
persons body height, you can determine a the length of a persons torso from
published anthropometric tables. A moment is F*d. Thus if you normalize,
you are finding the relative torque per unit length of the subject's torso.

Normalizing relative to body mass is done via F=ma. You can find a persons
torso mass from published anthropometric tables as well and apply the same
logic for relative body mass. It should be noted however that there are a
lot of assumptions when using rigid linked systems to determine torque,
especially in the torso. I recommend you read up on some literature on the
Topic. Adams and McGill would be a good start in understanding lumbar

Hope this helps,

Cyril J. Donnelly

MSc Candidate 2007

UW Biomechanics

Waterloo, Ontario, Canada


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The whole objective to normalizing data is for the comparison of variables
across samples of different anthropometrics (height, weight, somatotypes,
etc). Technically, a parameter is normalized to output a DIMENSIONLESS
quantity used for between subject analysis. This ratio allows for the
comparison of variables without the effects of covariates (ie, time,
different body types). Thus, joint torques are typically normalized by
height and weight since they are calculated with force and length
dimensions. The height and weight are used in the initial torque
calculations to estimate the inertial parameters (COM location, segmental
mass) but the torque magnitudes are outputted in absolute units (ie, N-m).

With between subject comparison, normalization is done to output them as %

Hope this helps.

Arnel Aguinaldo MA ATC

Director, Center for Human Performance

3020 Childrens Way 5054

San Diego, CA 92123

858.966.5424 - office

619.250.0184 - mobile

858.966.7494 - fax

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Moment should be normalized to standing height x body weight, not body mass.
Moment is moment arm times force. Force is correlated to body weight while
moment arm is correlated to standing height.

Bing Yu, PhD

Associate Professor, Director

Center for Human Movement Science

The University of North Carolina at Chapel Hill

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In my opinion, the reason to normalize joint moments is to insure that the
data from larger subjects isn't more "important" than the data from smaller
subjects when comparing different mechanics. For example, suppose you are
comparing the knee moments when rising from a chair, with and without the
use of your arms. Perhaps most of your subjects generate about 10% less
knee torque when using their arms but you have one subject who generates 30%
more torque when using his/her arms. Furthermore, suppose that the outlier
subject is the heaviest and tallest subject in your test. If you scale
torques by mass and height, the outlier won't have exceptional influence in
your data; on the other hand, if you don't scale the torques, the difference
in the outlier's torques between with/without arms will be a bigger
influence (more Newton-meters difference).

That is the reason to normalize. When normalizing a torque, I feel that you
should divide by a mass and a length to get a unitless value. In my early
research, I used to normalize by body height and mass. However the trick is
what mass and length (height? leg length? etc.). In my opinion, it is
extremely difficult to specify a mass and length that is the right choice
for comparing data across subjects. Therefore in my more recent research, I
tend to not normalize, and just compile and analyze calculated forces
(Newtons) and torques (Newton-meters).

- Glenn S. Fleisig, Ph.D.


Glenn S. Fleisig, Ph.D., Smith & Nephew Chair of Research American Sports
Medicine Institute

833 St. Vincent's Drive, Suite 100

Birmingham, AL 35205

(email) glennf@asmi.org

(tel) 205-918-2139

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The best type of moment of forces normalization depends on many factors, in
particular the studied population. I provided explanation how it should be
done in children at: Lebiedowska MK. Growth Normalization of Biomechanical
Factors in children 6-18 years old . In: Karwowski W, editor. International
Encyclopedia of Ergonomics and Human Factors. New York: Francis and Taylor;
2006 (second edition), 360-364

I have no experience with eledery population data, but I would suggest you
follow the following algoritm:

1. Find the best exponential fit between body mass and body height in your
subjects. (From mathematical point of view it is equivalent the slope of
llinear approximation between the log of body mass- and log -body height ).
I guess it should be close to 3.

2. Normalize the moment of forces by diviiding them by the body height to
the power equal to the slope.

This is the best normalization - check the variability and age indpendency.

3. Calculate the normalzed moment of forces using : body mass (alone) and
body mass* body height.

4. Compare the variability of the best normalzation with the other
normalization :

5. Select the normalization with lowest variability, and check if normalized
moment of forces are age independent.

6. If they still depenent on the age of your subjects, you can contact me
and I will provide you further suggestions how to introduce the age
Good luck


Maria K. Lebiedowska

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The different views you receive would be very interesting to read, and I
would appreciate if you could share them with me.

For my contribution, there are a few articles that discuss the different
normalisation procedures - {Moisio, 2003 #311} and {Pierrynowski, 2001 #308}
are the two main articles that I refer to, but there are also others
referenced in these.

Jodie McClelland

PhD Candidate

Musculoskeletal Research Centre

School of Physiotherapy

La Trobe University

Bundoora, Victoria 3086, Australia


(03) 9479 5715

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Physically it is better no normalize moments by dividing by body weight (not
mass)x stature or leg length. First, because then you get a non-dimensonal
quantity, second because a moment is the product of a force, which can be
expected to be proportional to weight, with a moment arm, which can be
expected to be proportional to leg length or stature. A problem is that in
practice moment arms are badly correlated with limb length..(Maganaris 200?)
There is a paper of mine on this subject: Hof (1996) Gait & Posture 4:
222-223 I enclose a copy.

At Hof

Quote "I am keen to get a better understanding of why you would normalise
your data to body height (and body mass) as surely the height of the
subject/ body segment has already been taken into account during initial

That's a good question, these are my thoughts:

Normalisation is not normal. What I mean by that is that usually publishers
only semi normalise data into a rate or ratio IE Nm/kg or watts/kg. This may
be because it is more intuitive to read and understand that information than
if the data were fully normalised into a dimensionless figure, which has no
meaning on its own. This may be overcome if everybody fully normalised data.

However it is probably beyond the ken of some to do this and it is not
always useful. How one normalises data (or not) may depends on what it is
you need to conclude from the results.

IE it is pointless normalising pressure data for the plantar foot pressure
if you are interested in peak pressure or pressure /time curves. Heavier or
taller people are not likely to require higher pressures to cause tissue
pathology as in diabetes for instance.

In your case however I would think that normalising moments to height and
weight may be advantageous ie Nm/ (kg x H). H = height or limb length (I
like limb length better). If you required to look at the powers for the
subjects then normalising power would look something like this
(Watts/kg*(g*h)^1/2). g = gravity h = height.

So if your subjects had a very wide range of hieght it is also likely that
they also would have a wide range of limb length from shortest to longest.

If you apply 100N to a 1000mm arm length then you have 100Nm external moment
about the shoulder and a reciprocal internal moment produced by the muscle
of 100Nm. But the same force on a short arm of 500mm has only 50Nm internal
moment to produce the same effect. In this case there is static equilibrium
and so no work or power is taking place in terms of physics. If you
normalise to weight it might be likely that the smaller person is lighter
but not necessarily proportionally. What if the short person is very fat and
the tall person very lean and skinny and weights are the same eg 80kg.

Normalised by weight the tall person achieves 100/80 = 1.25Nm/kg and the
small person 50/80 = 0.625Nm/kg. Normalised by weight and height though, the
tall person achieves (I'll use arm length here) 100/(80* 1) =1.25 and the
small person achieves 50/(80*0.5) = 1.25. Are any of these values useful in
terms of characterising how easily, or if, the subject is able to rise from
the chair?

So if we look at the torque produced by the elbow extensors about the elbow
our 80kg subjects must produce min (40 * (9.81+acc of CoM)) Newtons of
vertical force at the hand per arm to start to raise the bodyweight. Lets
say this force is 420N i.e.10.5m/s/s*40kg => 420N * external Moment arm
(forearm = 500mm and 250mm) = 210Nm and 105Nm external moments respectively.

So therefore the extensors produce the equal and opposite torque or Internal
Moments to balance for equilibrium. Are the muscles producing more force in
the tall subject, perhaps not since the extensor lever arm is twice the
length of the short arm. Let's say 50mm and 25mm so the muscles produce

210/0.05 and 105/0.025 = 4200N. So the lifting force is equal and the muscle
forces are equal but the moments are double for the tall man. (Four times if
the small subject were half the tall subject's weight) So if you produce a
table or graph that only shows values normalised to Nm/kg it might be
intuitive to think that the tall subject could more easily raise his body
weight than the short subject. You can see from the above however, that they
both have the same acceleration of CoM. By normalising with weight and
height or limb length the values are equal and it would be more intuitive to
think that they have equal ability to raise their body weight.

If the small subject were half the weight of the tall subject then half the
force to raise the body would be required so therefore 20kg*10.5m/s/s = 210N

* 0.25m = Ext moment of 52.5Nm. 52.5Nm/(40*0.25)= 5.25 and the same equation
for the tall subject of 80kg = Ext moment 210Nm - 210Nm/(80*0.5)= 5.25.

If the small subject is the same weight as the tall subject then the
normalised value = 105Nm/80 = 1.31Nm/kg fully normalised value =

105Nm/(80*0.25) = 5.25.

Notice that Torque = 210Nm V's 105Nm V's 52.5Nm

Semi normalised Torque = 2.625Nm/kg V's 1.31Nm/kg V's 1.31Nm/kg (notice the
limb length variation make a differenc to the outcome)

Normalised by weight and limb length = 5.25 V's 5.25 V's 5.25 (weight or
limb length do not alter the outcome value but on its own what does 5.25


So that it is likely that if the limb length is proportional to the height
within a population then the fully normalised value will be the same for the
same rate of CoM acceleration regardless of weight of the subject. Just to
check that, suppose the tall man weighs in at 120kg.

120*10.5 /2=630N/0.5=315N/(120*0.5) = 5.25

Does that make sense Susan? I hope so. All the best Dave Smith