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.

Responses:

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

Professor

Program in Human Movement Science

Division of Physical Therapy

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

919-966-3678 FAX

================================================== =========================

================================================== =========================

=

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

-----------------------------------

Ross Miller

Doctoral student, Dept. of Kinesiology

6 Totman Building

University of Massachusetts Amherst

================================================== =========================

================================================== =========================

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

biomechanics.

Hope this helps,

Cyril J. Donnelly

MSc Candidate 2007

UW Biomechanics

Waterloo, Ontario, Canada

jondonnelly32@hotmail.com

================================================== =========================

================================================== =========================

=

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 %

BW-H.

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

================================================== =========================

================================================== =========================

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

================================================== =========================

================================================== =======================

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

================================================== =========================

================================================== ======================

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

corrections.

Good luck

Sincerely

Maria K. Lebiedowska

================================================== =========================

================================================== ========

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

j.mcclelland@latrobe.edu.au

(03) 9479 5715

================================================== =========================

================================================== ========================

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

calculations."

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

represent?)

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

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.

Responses:

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

Professor

Program in Human Movement Science

Division of Physical Therapy

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

919-966-3678 FAX

================================================== =========================

================================================== =========================

=

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

-----------------------------------

Ross Miller

Doctoral student, Dept. of Kinesiology

6 Totman Building

University of Massachusetts Amherst

================================================== =========================

================================================== =========================

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

biomechanics.

Hope this helps,

Cyril J. Donnelly

MSc Candidate 2007

UW Biomechanics

Waterloo, Ontario, Canada

jondonnelly32@hotmail.com

================================================== =========================

================================================== =========================

=

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 %

BW-H.

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

================================================== =========================

================================================== =========================

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

================================================== =========================

================================================== =======================

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

================================================== =========================

================================================== ======================

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

corrections.

Good luck

Sincerely

Maria K. Lebiedowska

================================================== =========================

================================================== ========

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

j.mcclelland@latrobe.edu.au

(03) 9479 5715

================================================== =========================

================================================== ========================

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

calculations."

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

represent?)

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