Optimal Width of a rotating wheel

[lehnim]

Given this setup

note: i just created arbitrary values if it helps, if not working with variables to find a general solution works fine too
I am trying to find what the optimal width(would look like depth in the photo) of the wheel would be to generate the most power. I am stumped on how to begin the problem and am looking for ideas.

Thanks in advance

 

[berkeman]

Given this setup

note: i just created arbitrary values if it helps, if not working with variables to find a general solution works fine too
I am trying to find what the optimal width(would look like depth in the photo) of the wheel would be to generate the most power. I am stumped on how to begin the problem and am looking for ideas.

Thanks in advance

Welcome to the PF.

It's not very clear what you are asking. I don't see a wheel, and which way is wide? Do you want a wheele that will be able to go down into that depression and come back out again? What makes one wheel size better than another?

 

[lehnim]

Welcome to the PF.

It's not very clear what you are asking. I don't see a wheel, and which way is wide? Do you want a wheele that will be able to go down into that depression and come back out again? What makes one wheel size better than another?

Sorry for not being clear. The "wheel" is the cross, that is a side view. It rotates about its center point clockwise due to the wind. The width I am referring to would be into the page (what would be the z axis)

 

[berkeman]

Sorry for not being clear. The "wheel" is the cross, that is a side view. It rotates about its center point clockwise due to the wind. The width I am referring to would be into the page (what would be the z axis)

Hmm, that's not a very efficient way to generate power from the wind -- is that your intent? And for the most power generation given that side view, you would use an infinitely deep paddlewheel...

 

[lehnim]

Hmm, that's not a very efficient way to generate power from the wind -- is that your intent? And for the most power generation given that side view, you would use an infinitely deep paddlewheel...

I understand both points, but in non ideal circumstances there becomes a point where the friction from the weight of the wheel is so large that making it wider has diminishing returns, it is that width that i am trying to find.

 

[berkeman]

So since this is for schoolwork, how do you think you should factor in axle friction in order to set up an equation that you can optimize?

 

[lehnim]

So since this is for schoolwork, how do you think you should factor in axle friction in order to set up an equation that you can optimize?

So i understand how to find friction because as width increases, so does weight, which means force of gravity goes up and thus kinetic friction. Would the other side of the equation be the force of drag which increases as width increases because surface area does?