Kevin in MD wrote:

If external power as represented by force plates is the gold standard, then running on force plates into a headwind at speed of x will give a different force

__and therefore acceleration profile__ particularly for horizontal forces.

However, the underlined part of the statement is not strictly true. Force plates fixed to the ground will measure the force applied to the ground by the runner's foot (F_ground) which would be equal to the sum of forces required to move the runner's center of mass (COM) forward. When running at a constant speed in a fluid like air the sum of forces would be:

0 = F_runner + F_drag + F_ground ---> -F_ground = m*a + 1/2 * rho * v^2 * C_d * A

Where F's are forces, m is the runner's mass, a runner's acceleration, rho is the air density, v is the runner's velocity relative to the fluid, C_d is the runner's coefficient of drag, and A is the runner's frontal surface area. Obviously drag is a pretty complicated topic and has components of form drag, skin drag, parasitic drag, etc. but I think this simplification will work to a reasonable approximation.

So, my point is that a force plate will measure the sum of forces from which power can be calculated. Conversely the Stryd (I believe) only measures the acceleration of the COM of the runner (a in the equation above). Thus variations in the other variables of the equation like a runner's mass or the velocity of the wind relative to the runner will go unaccounted.

However, what I failed to consider earlier is that during the time period in which the running is not contacting the ground and is effectively floating, The F_ground drops out of the equation and any acceleration (or more accurately deceleration) would be due to the fluid. Therefore measuring larger magnitude decelerations during this phase of the gait, and subsequent accelerations during the toe-off or other speed producing phases of the gait, may be an effective way to account for wind speeds.

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