Is ground reaction force reduced when squatting with heels?

[spacediver]

If you're squatting in heels, your feet are on an incline. Wouldn't the ground reaction force be reduced by a factor of the cosine of the angle of inclination? And if so, how can this be a good thing?

[spacediver]

How can reaction force follow along? The target direction of your force is upwards, normal to the (horizontal) ground, and in the opposite direction of the gravity vector. You achieve this by pushing against the ground, and the ground pushes back up. If you're pushing directly downwards on an incline (the ground in this case is the incline of the sole of the shoe), the ground reaction force in the vertical direction is going to be reduced by a factor of the cosine of the angle of inclination.

Think about doing a standing vertical jump on an incline. You're not going to be able to jump as high. The ankle can't compensate so that the reaction force follows along.

Or so my thinking goes.

[spacediver]

Just did a fast calculation.

Suppose shoe is 9 inches long, with a 0.5 inch heel raise.

arctan(0.5/9) = 3.18 degrees.

cos (3.18 degrees) = 0.998

So you only lose about a fifth of a percent of ground force reaction, which may be a small enough cost for the biomechanical benefits of a raised heel (which themselves may lead to greater force production).

[MBasic]

If you're squatting in heels, your feet are on an incline. Wouldn't the ground reaction force be reduced by a factor of the cosine of the angle of inclination?

no.

[Savs]

How can reaction force follow along? [...]

The ground reaction force acts against the sole of the shoe and is normal to the ground. That force is transmitted through the shoe and acts on your foot; however, the force acting on the foot is composed of two components: a force normal to the incline and a frictional force parallel to the incline. The vector sum of those two is equal to the ground reaction force.

[Sean Herbison]

I was going to respond, but Savs already did, so the thread is effectively finished now.

[Savs]

Also, since most of these shoes are laced/strapped/etc. I was thinking that the shoe/foot system was more of the same entity so even friction wasn't even that big of a deal.

Sean, I guess we're not finished. See what happens here? We can't leave it alone.

I thought to myself, yeah, somebody is going to say something about the one force I called a "frictional force". I thought of going back and editing the post to put frictional between quotation marks, but too much time had passed and that would show up as an edit and then people would think, wow, that guy is really fucked up if he needs to fix that minor detail. And here we are.

The top of the shoe and straps work primarily by friction, but in any event let's lump all forces parallel to the inclined plane together and call them frictional forces. We can decompose the force into two orthogonal forces (along basis vectors spanning the space). One we'll call the normal force, and the other the frictional force. Kthxbai.

[Savs]

I wasn't meaning to bust chops

I know. But in case you were just a little, I busted yours for busting mine. :-) I also got to make my minor correction, so I got it out of my head and now can get some other things done today.

When I read these words, I got the "flashback" effect. Buzzers went off. "IMT!" "IMT!" "IMT!"

I included them just for you!

[Sean Herbison]

I thought of going back and editing the post to put frictional between quotation marks, but too much time had passed and that would show up as an edit

I've avoided making posts better for just that reason. I don't like having "edited" under my posts.

(Want to know a secret? I just edited this post.) (Twice.)

[Karl Schudt]

If you're squatting in heels, your feet are on an incline. Wouldn't the ground reaction force be reduced by a factor of the cosine of the angle of inclination? And if so, how can this be a good thing?

The reaction force will be exactly the same if you are lifting the same mass with the same acceleration.

F=ma