Sorry to contribute almost 2 years after question was asked, but I can't help it the Google brings me to this discussion, right now ! ... ;-)
The question is strange or weird, in the way that asker start presuming something about "The magnitude of acceleration", as if with the moving legs, one must make abstraction of the whole body ?
Accelleration & speed ?
- While walking, as we look ONLY at horizontal movement.. (see end of contribution), there is only an accelleration at start, then at constant walking speed, horizontal accelleration of the total mass = zero. We all know that, so, why starting with the confusion ?
- Yes, legs "(speudo) swing" involve constant accellerations (+X to zero in absolute coordinates, from +X/2 to -X/2 relative to the total body mass gravity point). It is clear that if these legs had a futile mass of their own (like with birds legs, or insects..) the lost momentum capacity to get the energy delivered by the muscle to move the total body forward (as a non efficient fraction of total enery used), would be much lower. However, there we've got nothing more, nothing less then a personal muscular strenght level, interferring with the motion. If longer + heavier legs provide more power at the same time, the loss to total speed must be compensated... equally, OR partially, OR in excess ... we can't say much on the individual muscularity of a person !!
Skeleton ! You cannot change that.
At the other hand, it's completely logic that walking speed is determined "most" by the lenght of the legs, and the proportion between upper & lower legs.
- Total leg lenght is offering the classic lever based speed increase at a constant power supply. (given : air resistance is futile at low speeds) (That's why we also drive a bike, to go much faster with the same leg power available)
- If a classic range of proportions between lower and upper leg is about 5 (lower: floor to knee) to 3.4 à 4,0 ... (upper: knee to hip joint), then it is clear that not just the total leg lenght plays it's role, but also this often disregarded proportion, allowing for better or worse mechanics to get the momentum in a "double coordinated rolling motion" be transformed in linear motion. In other words : some people are better build then others, purely mechanically, for walking or running, and nothing you can change about that.)
- Now, even more spectacular can be the actual joint sizes and angles, specifically at the hip. A 0.5 inch, 1 inch, 1.5 inch... more sidewards placement of leg bone axis, related to the joint movement center, can make a fenomenal difference in the way the muscular contractions are transformed in momentum. You could fail to use optimum power, practically, just because the momentum hits the (strain & pain) limit. Again, lever forces, but here in a rather negative way, to many of us. Reason why actually MOST people are slow walkers and runners, EVEN when having the same lenght of legs or same amount of muscle.
- Same spot : the actual attachment/movement angle at the joint, differs a lot by individual, and contributes to the former effect (better or worse transformation in momentum)
- The global flexibility at this hip joint, also determines the pace length we COULD do, even making abstraction from the leg length. It's clear, that a person which skeleton offers a larger "comfortable" moving angle, will be favoured.
Pendulum ?? ... complex muscular machine.
- The link given above ( http://silver.neep.wisc.edu/~lakes/BME315ScalingWalk.html ) with the conclusion "the walking speed is proportional to the square root of leg length" is very interesting indeed, from (however) the mechanics within a "dead machine" model. Legs only profit little from the pendulum mechnics, and are driven with the power from within, not from outside the so called pendulum system.
- We all know what happens with a constant swinging pendulum : stop the energy supply, and it's swing speed will "die out" only very, very slowly, on the little friction there is.
The comparison with legs misses the point there completely, because : in walking, apart from moving forward at a mostly constant speed + a friction, we are CONSTANTLY lifting ourselves up, at every step ! Lifting, falling, lifting, falling. Both the whole body, and the legs individually. We forget about it because it's visually not a great deal (unless you start filming it !!) Most of our energy is lost in "climbing" a never ending sinus. 4 legged animals make less vertical sinus. 6 legged again less ... A bike is the ideal ! ...
- So where the pendulum mechanics model got lost completely, thus, is that legs do NOT swing free, they are lifted in double semi circular motion, placed on the ground, then LIFTING the whole body weight on one leg while letting it continue "falling forwards", etc etc
I think that mr. Rod Lakes , from the linked article/research , should review his complete model... het just started with a false comparison.
I think, it must be clear that walking speed has so MANY parameters, and that the 4-fold dimentional approach of the skeleton mechanics is determining the baseline !!
Speed then, could be augmented in training (muscle and metabolics) but will never be able to drive away much from what the mechnical provision basically offered. A shortlegged person, with bad upper/lower proportion, and negative influencing hip joint axis extention + angle, will never walk "fast" even if he is bulking with muscle ...