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Forces on a twintip

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rynhardt
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Forces on a twintip

Postby rynhardt » Fri Jan 12, 2018 11:14 pm

I expect there are going to be several different opinions on this, so it probably deserves its own topic.

Looking at the forces that a twintip experiences, there is never going to be just one answer as the loads are dynamic in nature.

However, I'm going to be looking at two specific scenarios and try and explain my thought processes.

An important assumption is that the board can be treated as an ideal beam. Given that there is a fair amount of precedence for treating ideal beam analysis as a fair representation of real world beam behaviour, I do believe this assumption is valid. We can of course debate what are suitable values for moment of inertia and elastic modulus, but certainly the qualitative results will remain the same.

The first scenario I want to analyse is where the rider's weight is entirely supported by the water load (pressure), with no velocity relative to the water. This is of course an idealised scenario, and the closest real-life instance might be where you land flat on the water coming down from a tiny little jump, at zero forward velocity.
Anyway, the reason this is useful is because then we can approximate the load on the board as a simply supported beam with double overhangs, experiencing uniform load. Of course, in our case the diagram is turned upside down, and the reactive forces are the rider's feet.

So what the red deflection line tells us is that the tips as well as the centre of the board experiences an upward deflection, and the bits under the rider's feet experience a downward deflection.

Also, in this state, the board is the most evenly loaded and all parts of the board contribute towards supporting the reactive forces (the rider's feet).
Any other scenario where the loading is not uniform anymore will mean that some parts of the board will need to work harder to support the load. We can look at that next.
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621-elastic-curve.jpg
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Last edited by rynhardt on Fri Jan 12, 2018 11:25 pm, edited 1 time in total.

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Re: Forces on a twintip

Postby rynhardt » Fri Jan 12, 2018 11:23 pm

Enter Savitsky et al.

When the board is in motion at fixed velocity, the water load (pressure) distribution becomes non-uniform.
The bulk of the water load (pressure) is now centred around the stagnation line, which in most cases will be between the rider's feet.
The forward foot may in fact be supported only by the board, with no help from the water.

In this case the centre of the board will experience an even more extreme upwards deflection than the previous uniform loading scenario.
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vlcsnap-2018-01-12-21h56m58s413 (2).png
Savitsky.jpg
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Sun
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Re: Forces on a twintip

Postby Sun » Fri Jan 12, 2018 11:37 pm

In regards to post #1:

Your approach is correct, you can resolve the long axis of the board into a beam bending case. Naturally the short axis of the board is different, but I agree that this is an appropriate first step for sizing, as the long axis should experience the greatest load.

However, you should review the shear and bending moment diagram for that load case before you make the statement "the board is the most evenly loaded and all parts of the board contribute towards supporting the load"

For the load case you presented, the general shape of the shear and moment diagrams would look something like the attached rough sketch:
Shear Moment Diagram.jpg
Shear Moment Diagram.jpg (30.93 KiB) Viewed 1340 times
Without knowing the relative magnitudes of the applied loads, I cannot exactly tell you where you will experience the highest bending moment, but it is likely to be the middle of the board. The foot pads may experience the highest load, and will be more likely to as the tips get longer relative to the distance between the footpads. However, there are clearly local maxima around the middle of the board and the footpads. The point which experiences the maximum bending moment experiences the maximum stress. This is usually why beams (or boards) supported in this fashion are thickest in the middle.

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Re: Forces on a twintip

Postby downunder » Sat Jan 13, 2018 4:48 pm

Have a play in here:
https://webstructural.com/beam-designer.html

Instead of steel, we might use a carbon modulos on top/ bottom of wood beam:)

Let us know :)
D.

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Re: Forces on a twintip

Postby rynhardt » Sun Jan 14, 2018 10:39 am

Sun wrote:
Fri Jan 12, 2018 11:37 pm
In regards to post #1:

Your approach is correct, you can resolve the long axis of the board into a beam bending case. Naturally the short axis of the board is different, but I agree that this is an appropriate first step for sizing, as the long axis should experience the greatest load.

However, you should review the shear and bending moment diagram for that load case before you make the statement "the board is the most evenly loaded and all parts of the board contribute towards supporting the load"

For the load case you presented, the general shape of the shear and moment diagrams would look something like the attached rough sketch:
Shear Moment Diagram.jpg

Without knowing the relative magnitudes of the applied loads, I cannot exactly tell you where you will experience the highest bending moment, but it is likely to be the middle of the board. The foot pads may experience the highest load, and will be more likely to as the tips get longer relative to the distance between the footpads. However, there are clearly local maxima around the middle of the board and the footpads. The point which experiences the maximum bending moment experiences the maximum stress. This is usually why beams (or boards) supported in this fashion are thickest in the middle.
Thanks for the shear and moment diagrams! :thumb:
Let me rephrase then: The load (water pressure) is the most evenly distributed, and the reactive forces are mostly symmetrical around the centre, which implies that the forward half of the board doesn't work any harder than the back half.

Unless someone wants to volunteer to do a plate analysis I'm going to assume the short axis can be treated as uniform across the entire board.

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Re: Forces on a twintip

Postby rynhardt » Sun Jan 14, 2018 10:39 am

downunder wrote:
Sat Jan 13, 2018 4:48 pm
Have a play in here:
https://webstructural.com/beam-designer.html

Instead of steel, we might use a carbon modulos on top/ bottom of wood beam:)

Let us know :)
D.
Thanks. I might just do that for the hell of it :-)

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Re: Forces on a twintip

Postby downunder » Sun Jan 14, 2018 2:08 pm

rynhardt wrote:
Sun Jan 14, 2018 10:39 am
Sun wrote:
Fri Jan 12, 2018 11:37 pm
Thanks for the shear and moment diagrams! :thumb:
Let me rephrase then: The load (water pressure) is the most evenly distributed, and the reactive forces are mostly symmetrical around the centre, which implies that the forward half of the board doesn't work any harder than the back half. is

Unless someone wants to volunteer to do a plate analysis I'm going to assume the short axis can be treated as uniform across the entire board.
First diagram:

The water pressure is not evenly distributed and no, they are not symmetrical around the middle. The pressure is linear because the board is under an angle in the water, length wise.
Edging harder, bigger linear water forces.

Look at the perspex. The left side is above water, where is the water pressure on that part? I would argue that on this pic, the water line is in the middle, no? So the forces are linear from the middle to the tip, with the biggest on tip.

Water pressure is linear from depth to water surface where is zero, not uniform.

The problem is, as I mentioned, the support is not fixed, but free. Ok, for the sake of discussion, one support can be fixed, but than, the other one is free (left side on this pic). Free as left foot :) So the red line on the diagram does not represent the board when riding. Plus, non uniform i-beam, etc.

Second diagram, Savitsky:

This is a plain board ride against the water, not edging. Not sure what is this proving when we just do not ride a TT that way 99% of time.

Thoughts?

D.

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Re: Forces on a twintip

Postby rynhardt » Mon Jan 15, 2018 8:08 pm

Dusted off some of my FEA skills and modeled a 1400x400 board with slightly tapered tips, flat (no rocker). I used a uniform load of 1500N/m2 on the board.

First pic is the top view with colour coded deformation scale.

I did 3 scenarios for feet placed:
400 apart: camber (negative rocker) is almost non-existent
600 apart: camber is somewhat noticeable
800 apart: camber is more noticeable

Deformation is scaled up by a factor of 3 to make the differences more apparent.

What was a bit of a surprise to me is how the length of the tips vs the bit between the feet influence the results. Thinking about it I realised that the stress that the tips experience also has to affect the rest of board.
This is similar to a guitar string tensioned across the bridge and nut - the more stress in the string as a whole, the less it deflects under a load.

As expected, the biggest stress is at the boundary of the feet. (colour coding)

For my next trick I'm going to see if I can do a non-uniform load or two..
Attachments
140_top.PNG
140_40.PNG
140_60.PNG
140_80.PNG
Top view
Last edited by rynhardt on Mon Jan 15, 2018 8:14 pm, edited 2 times in total.

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rynhardt
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Re: Forces on a twintip

Postby rynhardt » Mon Jan 15, 2018 8:11 pm

downunder wrote:
Sun Jan 14, 2018 2:08 pm

This is a plain board ride against the water, not edging. Not sure what is this proving when we just do not ride a TT that way 99% of time.

Thoughts?

D.
Well sure. But I have to start somewhere. It's easier for me to understand one scenario at a time, and I simply picked the easiest one to start with :D

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rynhardt
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Re: Forces on a twintip

Postby rynhardt » Mon Jan 15, 2018 10:17 pm

I decided to do a step-wise approximation for the non-uniform (savitsky) load case.

Did a quick graph in Excel to get the approximate shape, then applied the loads in 10cm bands down the length of the board.
End result is as expected, with a fairly large downwards deformation at the stagnation (hinge) point. (deformation scale is 3x)

Keep in mind the analysis is qualitative in nature and only intended to show what riding forces would do to a board if it wasn't built to withstand these forces.
In this case the board model has a uniform thickness throughout whereas a normal board would be much thicker in the middle.

I've included the results with force indicators and without.
Left foot is fixed (no translation - green arrows).
Water pressure is red arrows (size of arrows do not indicate anything, look at left property pane for pressure gradient)
Right foot has 400N (approx 41kg, or half my weight) going downwards.
Attachments
Savitsky.jpg
Savitsky.jpg (16.39 KiB) Viewed 1086 times
savitsky loads.PNG
140_nonuniform_length.PNG
140_nonuniform_length_hiddenforces.PNG


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