Leverage

[bumpyride]

Any of you Engineer types have an idea on how to figure how much greater leverage it takes to get a board up on edge as it gets wider?

Here's the criteria:

Board width in 1/2 cm increments, starting at 19cm.

Binding length fixed at 22.5 cm. (this would be the longest distance from where the binding makes contact at the front of the toe and the back of the heel), and the width of the contact point at toe and heel would be 3.175cm. Don't try to figure out how boot sizes would come into play, let's just say 27.5 for argument's sake. Save this for later.

Binding angles fixed at 60 degrees, and at 45 degrees. At 60 degrees the closest contact point on toe and heel is 3.175 cm from the edge(first picture and 3rd picture--the yellow pad), and at 45 degrees it is 1.588cm from edge (second picture).

I'm obviously not an engineer, and my solution would be simply try to put a digital torque wrench on a plate in the binding and then change the widths of the boards. There's a couple of variables in there that would have to be well thought out. I figured that someone out here might be able to do it with a little bit of engineering.

For fun a guy could try and figure how much the leverage is increased for every 3 degree boot angle difference, and then how much advantage a guy with a larger foot has.

[kjl]

I think you got a whole bunch of different questions going on in that can of worms you asked about. But I love nerding out, so:

The amount of torque required to keep a board up on edge with respect to board width should be pretty easy: torque is linear with respect to the length of the lever arm, so a 20cm wide board will require ~5% more torque to keep up on edge than a 19cm board. A 25cm wide board will require ~31% more torque up on edge than a 19cm board, which is probably why when I put hardboots at 60 degrees on a powder board I can carve it but I end up with bruises on my legs from the boot cuffs.

The whole boot angle, foot size, thing as it relates to the amount of torque you're applying to the board is a big mess of stuff. Yeah, at 0 degrees it's all toe/heel pressure, so the amount of torque is a combination of how hard you are pushing down or pulling up with your toes and how hard you are pushing forwards on the tongue or backwards on the back cuff of your boots. At 90 degrees the toe/heel pressure contributes nothing to the torque around the edge and it's all about how hard you are pushing on the cuffs of the boots. (The amount that your "pushing down or pulling up with your toes" matters is cos(binding angle)).

As to foot/boot size, at the first naive look, yeah, a guy with a 15% larger foot will create 15% more torque if he applies the same # of lbs of pressure on the balls of his feet, but consider that the lever arm from his ankle to the balls of his feet are also 15% longer, so he is generating 15% less lbs of pressure on the balls of his feet if his calves are exactly as strong as the other guy, so it's actually a wash. The real measurement to take would be the distance from the ankle fulcrum to where the calf muscle hooks up to the heel, which would be 15% larger, so he might be generating 15% more torque. But then consider the same size people generally don't have 15% larger feet than each other; he's probably 15% taller, which means the cross section of his calf is 115%^2 or ~32% bigger, which means he's generating ~32% more force with his calf, which means 115%*132% = ~52% more torque, but on the other hand, his mass is roughly 115%^3 = ~52% more weight to support.

Which basically boils down to: He is generating ~52% more torque but requires ~52% more torque to keep his edge up, so it's a complete wash, except that the bigger guy probably has way worse shin bang and bruises all over his calves.

At least, that's what I think, but take into consideration that it probably took me 15 minutes of "right before sleepy time" time to write this, of which maybe 1 minute was thinking about that one engineering class I took 15 years ago.

[bumpyride]

Ken,

I admire your bravery. It's like the first guy that has to go out into the middle of the gym floor with his date that's wearing a refurbished bridesmaid dress on prom night and slow dance to Chicago's Color my World.

[pebu]

I almost did the same thing last night but then I got frustrated after writing a paragraph then erasing a couple times it after thinking that wasn't quite right after each one. So I ended up ignoring it. Sorry.

[Jack M]

CT = CCT

clockwise torque = counter clockwise torque.

torque = force x lever length

play around with this and you'll notice that Burton cap straps actually decrease your leverage in softboots.

[kjl]

play around with this and you'll notice that Burton cap straps actually decrease your leverage in softboots.

That can't be right - the location of the strap should be irrelevant to the transfer of torque from your boot to the board, right?

[pebu]

The board wants to lay flat. So do you... Fortunately there are bindings and boots to hold you to (roughly) 90 degrees to the plane of your board. This causes stresses between you and your board.

Also KJL, I just thought of something... You can't really say that a 20cm board needs 20% more torque than a 19cm board because the lever is actually a line between your center of gravity (probably somewhere in the torso area) and the edge, not between the center of the board and the edge of the board. I think the moment on the edge of the board will be roughly 20% less on a 19cm board than a 20cm board.

(trying to visualize stress/strain/moment/shear curves as I type.)

Hey, I have an idea... Lets get some poor sap mechanical engineering student to do this for a senior project...