View Full Version : Free Moment Normalization Parameters Summary

07-29-2009, 12:15 AM
I recently posted about free moment normalization parameters and received a wide variety of responses. Although some feel that free moment should be normalized to a measure of length (height, leg length, or foot length), others felt free moment did not need to be normalized and yet others suggested it would be best to present both normalized and non-normalized data. Several researchers pointed out that non-normalized data (or data normalized non-traditionally) may be useful, yet they also stated it is important to include parameters that enable other researchers to normalize your data for comparisons with literature values, future studies, and different species. Below is my original post followed by the ten responses.

Becky Fellin, M.S.
American Society of Biomechanics Student Representative
Research Assistant
Biomechanics and Movement Science
University of Delaware
Newark, DE 19716

Original Post:
Free moment, or the torsional loading between the foot and the ground, has been studied on a limited basis for gait analyses. Cavanagh and Holden proposed normalizing free moment to bodyweight (BW) and height in their 1991 paper about free moment. For joint moments, it is generally accepted that they need to be normalized to account for differences in height, through overall height or length of a particular segment. However, as free moment is in essence a moment without a reference segment, perhaps it would be better to only normalize it to BW.

A cited reference search on Web of Science turned up 16 citations of Cavanagh and Holden, 1991. Of those, 12 papers calculated free moment for activities ranging from standing to running and jumping. Six normalized to BW and height as Cavanagh and Holden did. Two normalized to BW and leg length, two did not normalize, and two did not state their normalization technique.

I am curious what thoughts the biomechanics community has about appropriate normalization parameters for free moment. I will post a summary of replies.


How about body weight and foot length? If a free moment is the torsional load between the foot and the ground, it seems that, all else being equal, a larger foot would generate a larger moment.

- Jesse

Jesse W. Young, Ph.D.
Postdoctoral Research Fellow
Department of Anthropology
University of Texas at Austin
1 University Station C3200
Austin, TX 78712
Phone: (512) 232-6380

Email: jesse.young@mail.utexas.edu
Web page: www.jessewyoung.com

Although free moment is a torque cause by a couple of forces with same magnitude in opposite direction, it is still a moment whose magnitude is determined by magnitude of force and moment arm which are likely affected by body weight and height. Therefore, free moment should be normalized to body weight and height as Cavanagh and Holden recommended.

Bing Yu, PhD
Associate Professor
Center for Human Movement Science
University of North Carolina at Chapel Hill

Hi Rebecca,

I was one of the 12 citing that paper, although my study compared arm-swinging apes to human runners (Chang et al. AJPA 2001). In order to make comparisons across large size ranges and very different gaits, I felt that normalization was necessary. In general, you should normalize if you need to make such comparisons to test your hypothesis. If your subject pool is pretty homogenous, then it will probably not make much difference to your own study conclusions. But, in the future others may want to compare their work to yours, in which case you should at least provide some subject parameters to allow that (e.g., mean BW, leg length, height).

In general, I would tend to not recommend normalizing with only BW. You end up with funny units of length to describe a moment, which leaves you discussing an abstract metric of moment arms instead of the free moment in which you are interested. I would go with BW and leg length personally, but probably any characteristic segment length would do. Humans scale pretty regularly within the species, so you likely would not be adding much variability to your data if you used any segment length within the leg. If you were comparing humans to say, flamingos, then you would have to think more carefully about it since relative dimensions of segments would be very different between the two species.

With that said, what determines a 'characteristic' length for free moment is an interesting question. Leg length is status quo and is somewhat standardized in the literature, but I could see reasons for foot length to be appropriate, since foot length might have a direct effect on how the free moment is generated--it is also easy to measure. Likely the largest "free moment generators" are going to be muscles crossing the hip that cause internal/external rotation, so you could use a measure of femoral thickness or some measure of moment arm of these internal/external rotators--but that would be hard to measure. Again, you probably would end up with the same results (comparing within your subject pool) whether you used leg length, height, foot length or femoral thickness, so I would opt for something easy to measure and easily comparable across other studies. Hope this helps.


Young-Hui Chang


Interesting question. I think you could justify it either way. I don't think that one could be determined to be "better" or "worse," it depends on the question one is attempting to answer.

I look forward to the responses.



Timothy E. Hewett, PhD, FACSM
Director, Professor
The Sports Medicine Biodynamics Center
The Human Performance Laboratory
Cincinnati Children's Hospital Medical Center
University of Cincinnati College of Medicine
Departments of Pediatrics, Orthopaedic Surgery, Biomedical Engineering and Rehabilitation Sciences
3333 Burnet Avenue
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Free moment (I presume you mean free vertical moment) can describe the
torsional loading between the foot and the ground. Thus one could perhaps normalise by BW and foot length! However, as with other force-platform measures the free vertical moment determined for gait and posture activities is affected by movement of all body segments (higher up the kinetic chain)about the vertical axis, which I presume is why previous authors have normalised to BW and height. Personally I don't see any reason why you could not normalise to just BW, other than the units (Nm/N BW) might look a bit strange? It will be interesting to see what others think.

John Buckley
Vision & Mobility Research Team, and
RCUK Research Fellow in Medical and Healthcare Technology
School of Engineering, Design and Technology
University of Bradford, UK

Dear Rebecca,

in my opinion the normalization of the free moment depends on the purpose of your analysis, that is the reason why the normalization is necessary. If it is necessary for comparing the dynamics of or collecting data from different subjects, then the solution of using both Weight and Height should be adopted, like in Benedetti MG, 1997 doi: 10.1016/S0268-0033(97)00041-7

Again, if the purpose is to compare your results with some reference graphs provided by other authors, their technique of normalization must be adopted to perform the visual comparison.

I want to underline that the problem you submitted still exists for another aspect related to dynamics: what about the normalization of joint powers? Apparently it is far to be consistent among the researchers.


Pietro Garofalo M. Eng.
Ph.D. Candidate
INAIL Prosthesis Centre - Research Area
Via Rabuina 14
40054 Vigorso di Budrio, Italy
Ph: +39 0516936602
Mobile: +39 3934144631
Mobile in Holland: +31 0621294335


Might it not depend on for what purpose is the free moment of interest to your study.

Dave Smith
Applied Biomechanics MSc

Hi Becky,
I’ve been thinking about this since we talked at ACSM. I agree with Pietro that the purpose of normalization is to reduce/ remove the influence of differing body sizes across subjects on inter-subject variation in free moment measures. Thus, if you are comparing between two groups of people, or making repeated measures within a group which is not homogeneous in height and weight, normalizing to both parameters is appropriate – to reduce the influence of height and weight as covariates.
Clare E Milner PhD FACSM
Assistant Professor, Biomechanics
Dept of Exercise, Sport, & Leisure Studies
University of Tennessee
1914 Andy Holt Avenue, 341 HPER
TN 37996-2700

Phone: 865-974-7667
Fax: 865-974-8981

Dear Rebecca,

I've just submitted proofs on a paper in which we argue that the basis for arm swinging is a reduction in free vertical moment. In this study we used MgL to normalize (and nondimensionalize) free moments, where M is body mass, g is gravity, and L is leg length.

It generally seems most appropriate to use normalization factors with the same units as the outcome being normalized. In the case of free moments, we would expect moments to increase not only with body mass, but also with body size. The free moments seem to arise primarily from the swinging of the legs and arms. As these move further from the body centerline, free moments should increase. We usually use leg length to quantify body size (because it relates most directly to the sagittal dynamics in locomotion) and so for convenience we also used leg length as part of our free moment normalization. Other measures, like stature or hip width, might also be used to good effect.

Hope that helps!

Best regards,
Steve Collins
Postdoc, T.U. Delft

Ray Browning and I have faced normalization issues with regard to forces and moments with regard to obesity.
Reasonable people can disagree on these matters and opinions change over the years.
So, I suggest that you publish your data in several formats (i.e. raw N-m, and non-dimensionalized) so that your data can be compared to literature values in the past and future.
Also, once you have your data, see if normalization affects your conclusion. If it does, then, that is yet another reason for why you should publish both.

Sometimes, non-dimensionilizing data hides the main message. e.g. if we compare a 200kg obese person vs.a lean 50 kg person of the same height walking, the GRF's per kg body mass is almost the same. But, that neglects that the knee joint surface areas are probably the same also , so the contact pressures may be 4x greater in the obese person.
Rodger Kram, Ph.D.
Associate Professor
Integrative Physiology Dept.
Univ. of Colorado
Boulder, CO 80309-0354