In constant pace running it seems plausible that air resistance plus braking forces at landing will of course balance with propulsive forces.

The question at hand though is the torques rather than the linear forces.

Wind resistance is a force that reacts to movement rather than a constant force like gravity. I agree that wind resistance will diminish the effect of forward acting torques and enhance the effects of rearward torques whilst on stance.

Data from a runner accelerating on a treadmill, or a runner at low speed (low wind resistance) would show whether wind resistance creates a substantial counter torque. I think the data here http://w4.ub.uni-konstanz.de/cpa/article/viewFile/3291/3092 shows that at modest speeds (4m/s or 8mph), there is a very large discrepancy between foot forward of support compared to foot behind support. This discussion is continuing here https://canute1.wordpress.com/2009/12/31/creating-optimum-stride-length-and-cadence/#comments so I will make my comments there.

]]>It is similarly plausible that the head-back angular impulse due to air resistance together with the head-back angular impulse due to GT in early stance will match the head-forward angular impulse due to GT in late stance.

Without a precise estimate of air-resistance it is not possible to make an absolutely definitive statement, but I see no reason to suggest that air-resistance is inadequate to account for the discrepancy. ]]>

Thanks for running the calculations and sharing the results. I’ not sure if your calculations were for hGRF only or both hGRF and vGRF? It would be nice to have the complete picture.

From a look at the hGRF graph, I’d say around a 1/3 difference between head back and head forward torque would sound about right. The graph looks almost like a squashed sine wave with but with the noticeable asymmetry in the first half of the gait where the hGRF does not peak but instead drops and then rises again to form to small peaks.

With regard to your point about head-wind, these trials were carried out outdoors rather than on a treadmill so there will be wind resistance and as the runners were at 6 minute mile pace it will not be negligible. However, I wouldn’t expect it to account for all the difference either between head forwards and head back torque via hGRF.

With regard to your point about the first half of stance being the most significant in balancing the torques, I’ll wait until it is clear if you considered both vertical and horizontal GRF in your calculation before commenting.

Regarding your last point about the pivot point of the torques, this is an area that needs careful consideration.

I think the hGRF that acts in early stance will produce a head forward torque pivoting around the foot. At the same time there will be a vGRF induced head backward torque also around the foot.

In the second half of stance the vGRF will produce a head forwards torque around the foot. The hGRF is not so clear cut as it depends on how it is created. If its source is gravity, it will act around the foot. If its source is a muscular driver from the hip then it will have a strong component around the hip. However, if it is muscular involving extension it will act at the foot and if it is muscular involving leg swing it will again act around the foot. On balance, the majority pivot point is likely to be the foot I think.

Thanks for sending the force plate data. I will present the details of the computation in the calculations page (side panel of this blog) as soon as I can find time to lay it out in an adequately annotated form. Meanwhile, here are the results

The quantities of interest are the angular impulses (product of torque due to the various forces of interest x time, averaged over the time periods of interest.

Because the weight of the runners is unknown, I express values of angular impulse in the units of body-weight.metre.sec (instead of the conventional newton.metre.sec). We could assume a typical weight of say 65 Kg and convert all units to newton.metre.sec but this would not affect the relative values of the angular impulse due to the various different forces. I have assumed that the distance from centre of mass to ground is 1 metre, and that this remains approximately constant throughout the time on stance (though for most runners, the COM does fall in early stance and rise in late stance. However I think that errors due to mis-estimate of height of the COM are likely to be smaller than errors due to uncertain estimates of the GRF.

Due to the approximations involved in the calculation,. I would estimate that the computed angular impulses have an uncertainty of 0.01 units.

The results are:

Head-forward angular impulse due to gravitational torque after mid-stance: 0.022 units

Head-back angular impulse due to gravitational torque before mid-stance: 0.016 units.

Head-forward angular impulse due to braking before mid-stance: 0.018 units

Head-back angular impulse due to forward GRF after mid-stance: 0.027 units

Head-back angular impulse due to vertical GRF before mid-stance: 0.026 units

Head-forward angular impulse due to vertical GRF after mid-stance 0.024 units

The conclusion from these computations is that the gravitational torque prior to mid-stance provides about 2/3 of the compensation for the head forwards angular impulse due to gravitational torque acting after mid-stance, while the backward push (that evokes the forward GRF) provides about 1/3 of the compensation.

However, because of the uncertainty due to the approximations in the calculation and the approximations in the estimate of GRF, it is plausible that the backward push might account for anything from zero to just over half of the compensation for the head forwards angular impulse due to gravitational torque. So the computation does not provide an unequivocal answer to our debate but tends to support the hypothesis that the largest part of the compensation is provided by head-back gravitational torque acting before mid-stance, with a minor part possibly accounted for by the backward push.

There is one additional point to note about these calculations. GRF produces rotation about the centre of mass, while gravity produces rotation about the point of contact between foot and ground. I am not sure that it makes any sense to claim that the rotation about the centre of mass can compensate for rotation about the point of contact between foot and ground. I need to think about this a little more, but I am inclined to think that these two angular rotations have to be compensated separately. If so, the small difference between the computed rotational impulse due to gravity before mid-stance and that after mid-stance is likely to be a measurement error – or maybe due to wind resistance. Where the force plate data collected on a treadmill?

]]>Just sent through the data to your e-mail. ]]>

Hopefully get something to you tomorrow. ]]>

That is great. I think the most helpful format would be an excel spreadsheet with time in one column and horizontal GRF in the adjacent column. You could send the document, as an attachment to canutewp@gmail.com ]]>

Canute, I’ve got some data together from the force plate graph – before I type it up, what format do you want it in?

]]>Thanks for the physics lesson!!

]]>The linear example is good as it is easier to show what is happening there.

If you lean forward slowly in your chair it produces a reactive force that pushes back on the chair. Because you are leaning forward slowly, the friction of the chair against the ground is enough to stop the chair moving.

Now if you lean backwards very quickly, the reactive force at the chair is sharp enough to overcome friction and the chair moves forwards and will continue to roll along forwards a little. So in that way, you can use the external force of friction to impart net momentum into the system.

It’s the same if you are on a bike or a skateboard – you can lean forwards slowly and then lean backwards quickly to produce asymmetric impulses that result in net propulsion. The key to this mechanism is the external force of friction though. If you are in an environment with no external forces, say floating in deep space, you can not change your net momentum by moving your body. So the basic principle of the necessity of an external force to change a body’s net momentum holds true I think. The effect of that in running is that the movements of your limbs when airborne have little or no effect on your momentum so will not cause you to rotate forwards or backwards in flight.

The effect of moving the limbs and especially swinging the leg forwards whilst on stance may well have interesting effects on angular movement and that is as far as Canute and I have got in the discussion.The next step is to do some calculations see how likely these effects are.

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