Calculating Relative Stick Flex.

[puckpilot 312]

I was poking around the web trying to find out how companies measure flex and I came across these resources.

http://www.acs.psu.edu/drussell/publications/russell-hunt-tpt-formatted.pdf
http://twu.tennis-warehouse.com/learning_center/hockeyflex.php

Apparently there's a formula for it. 

Flex = [48EI/L^3]*D

where, EI = the flextural rigidity of the material being measured, L = the length, and D = the distance of deflection.

Any way before everyone's eyes glaze over. There's a practical application. After I messed around with the formula given the information in the two resources I derived a simple formula for relative flex. It doesn't take into account things like variation on stiffness along the shaft, kick points, manufacturer bias and stuff like that, but I think it can be a helpful guide, if I'm correct that is. I haven't done serious math in a long time, so I could be completely out to lunch on this. Any way here's the formula.

Flex Relative = (Absolute Flex)/L^3

L needs to be in meters for the formula to work.

But I think it's right given this the statement below that was in one of the resources.

The force needed to bend a stick by one inch depends on the bending length. To measure the flex, the shaft is usually supported at two points a distance L apart, then the force is applied half way between the two supports. The standard test distance is L = 1.0 m.

However, if L is shortened to say 0.5 m then the force to bend the stick by one inch will increase by a factor of 8. If it takes 85 lb to bend a one meter section of the stick by one inch, it will take 680 lbs to bend a 0.5 m section of the same stick by one inch.

If we plug the information from the red text into my formula it seems to work.

We get Flex Relative = 85/(.5)^3 = 85/.125 = 680

Also the formula does roughly follow the rule of thumb that a 1 inch change in length will change the flex around 2-5 flex. It just with the formula, you can be more exacting, because that change isn't uniform. Taking 1 inch off a 100 flex 60" stick does not change the flex the same amount as taking 1 inch off a 70 flex 60 inch stick.

So how does this help someone looking for a stick?

I'll use myself as an example. I found a 55-flex stick that was 58" long felt just right for me in terms of flex. But it was too long. But once I cut it down to my preferred length it was too stiff. After playing around with a bunch of sticks, I figured that maybe at 53" the right stick would be around 45 flex for me.

So if I calculate the Relative Flex of that 58" inch stick. 58" = 1.47 meters

Relative Flex = 55/(1.47)^3 = 55/3.18 = 17.3 lbs/inch

So my ideal stick would have a Relative Flex of 17.3 lbs/inch

With that information, I can calculate what Absolute Flex I would need for a 53" stick to fit my needs. I can do this by just rearranging my formula, and using 53" (1.35 meters) as the length.

Absolute Flex = (Relative Flex)*L^3 = 17.3 * (1.35)^3 = 17.3*2.46 = 42.6 lbs / inch.

The answer seems to fit in line of what my experimenting has told me. But like I said, this is just a guideline because there are lots of other things that factor into stick preference, etc. But for those still following, what do you think? Does my math seem right? Is this useful? 

[Ps12 11]

On 7/6/2017 at 6:09 PM, puckpilot said:

I was poking around the web trying to find out how companies measure flex and I came across these resources.

http://www.acs.psu.edu/drussell/publications/russell-hunt-tpt-formatted.pdf
http://twu.tennis-warehouse.com/learning_center/hockeyflex.php

Apparently there's a formula for it. 

Flex = [48EI/L^3]*D

where, EI = the flextural rigidity of the material being measured, L = the length, and D = the distance of deflection.

Any way before everyone's eyes glaze over. There's a practical application. After I messed around with the formula given the information in the two resources I derived a simple formula for relative flex. It doesn't take into account things like variation on stiffness along the shaft, kick points, manufacturer bias and stuff like that, but I think it can be a helpful guide, if I'm correct that is. I haven't done serious math in a long time, so I could be completely out to lunch on this. Any way here's the formula.

Flex Relative = (Absolute Flex)/L^3

L needs to be in meters for the formula to work.

But I think it's right given this the statement below that was in one of the resources.

 

 

If we plug the information from the red text into my formula it seems to work.

We get Flex Relative = 85/(.5)^3 = 85/.125 = 680

Also the formula does roughly follow the rule of thumb that a 1 inch change in length will change the flex around 2-5 flex. It just with the formula, you can be more exacting, because that change isn't uniform. Taking 1 inch off a 100 flex 60" stick does not change the flex the same amount as taking 1 inch off a 70 flex 60 inch stick.

So how does this help someone looking for a stick?

I'll use myself as an example. I found a 55-flex stick that was 58" long felt just right for me in terms of flex. But it was too long. But once I cut it down to my preferred length it was too stiff. After playing around with a bunch of sticks, I figured that maybe at 53" the right stick would be around 45 flex for me.

So if I calculate the Relative Flex of that 58" inch stick. 58" = 1.47 meters

Relative Flex = 55/(1.47)^3 = 55/3.18 = 17.3 lbs/inch

So my ideal stick would have a Relative Flex of 17.3 lbs/inch

With that information, I can calculate what Absolute Flex I would need for a 53" stick to fit my needs. I can do this by just rearranging my formula, and using 53" (1.35 meters) as the length.

Absolute Flex = (Relative Flex)*L^3 = 17.3 * (1.35)^3 = 17.3*2.46 = 42.6 lbs / inch.

The answer seems to fit in line of what my experimenting has told me. But like I said, this is just a guideline because there are lots of other things that factor into stick preference, etc. But for those still following, what do you think? Does my math seem right? Is this useful? 

Are you saying absolute flex is what you need to start at before you cut it down to your preferred size. The math is confusing me. 

And I want to add I've been following your posts on this topic as I am 5'4" and have bounced between junior and intermediates sticks. 52 or a bit short tee seems to be the right length but I can't quite get the snap I want. 

 

[puckpilot 312]

3 hours ago, Ps12 said:

Are you saying absolute flex is what you need to start at before you cut it down to your preferred size. The math is confusing me. 

And I want to add I've been following your posts on this topic as I am 5'4" and have bounced between junior and intermediates sticks. 52 or a bit short tee seems to be the right length but I can't quite get the snap I want. 

 

 

Here's another example. Maybe it will make things clearer. Let's say Bob is using a 75 flex stick. The stick was originally 63" but they cut it down to 60 inches. They find that the stick flexes just perfectly for them at that length. One day, during a hockey skills course the instructor gets them to try a shorter stick, and they realise that they can handle the puck way better with 56 " stick. But when they cut their 75 flex stick down to 56", it's way too stiff for them to shoot properly with.

The rule of thumb says that taking 1" off a stick increase the flex by 2-5. So at 60" the 75 flex stick was supposedly playing at 81-90 flex, and taking it down another four inches supposedly turned it into a 89-110 flex.

Now Bob decides goes to his local hockey shop. He looks at a 70 flex stick intermediate stick. Off the rack that stick is 58" so he thinks taking two inches off will bring it's flex up to around 74-80, which might be too soft for him. It seems Bob is kind of stuck. Noway he's going to get the perfect balance of length and flex, right? 

Well let's use the formula and see what we come up with.

The absolute flex of Bobs perfect flexing stick is 75 flex at a length of 60" or 1.525 meters

If we calculate its relative flex we get  75/(1.524^3) = 75/3.54 = 21.18

So theoretically Bob wants is a 56" or 1.42 meter long stick with a relative flex of 21.18.

To get that stick, he needs to find the right absolute flex stick to cut down. To find out what flex that stick is, you just need to rearrange the formula.

Absolute flex = Relative flex * Length^3 = 21.18*(1.42)^3 = 21.18*2.86 = 60.57

So according to the formula, a 60 flex stick cut down to 56" will give him approximately the same flex feel as his old 75 flex stick at 60" 

 

Does that help clarify things? If not I can explain further.

The formula is:

relative flex = absolute flex / Length^3

Relative flex changes with the length of the stick. This is the real stiffness of the stick relative to it's length.

Absolute flex is the flex rating given by the manufacture.

Length^3 is the length of the stick given in meters then cubed.

 

Knowing these things should allow someone to change the length of their stick and know which flex stick to buy to maintain their preferred flexiness of their shaft. The only thing one needs is the flex rating to stick that they feel flexes perfectly for their own tastes and the length of that stick. 

Now this doesn't account for difference in feel of different kick points or quirks of individual manufactures. For example, warrior sticks play less stiff than Bauer and CCM. True sticks to me play somewhere in between. So things aren't quite exacting, but they should get people into the right ball park.

 

Does everything make sense now? Just tell me what you don't understand and I can explain further.

 

[Giraffe14 23]

13 hours ago, puckpilot said:

Now this doesn't account for difference in feel of different kick points or quirks of individual manufactures. For example, warrior sticks play less stiff than Bauer and CCM. True sticks to me play somewhere in between. So things aren't quite exacting, but they should get people into the right ball park.

 

I think this ^ is the biggest issue with the formula. Cutting/extending mid kick sticks seems to have a greater impact on flex than on low kick sticks. 

I thought the tennis warehouse flex study was interesting, and I wish something similar could be done on each new generation of sticks from all the manufacturers. 

[puckpilot 312]

1 hour ago, Giraffe14 said:

I think this ^ is the biggest issue with the formula. Cutting/extending mid kick sticks seems to have a greater impact on flex than on low kick sticks. 

I thought the tennis warehouse flex study was interesting, and I wish something similar could be done on each new generation of sticks from all the manufacturers. 

For me, I find that individual manufacturer quirks have bigger impact than flex profile. I got a Bauer 1N that feels stiff even after I added two inches to it. Where as my Warrior QRL feels perfect in flex even when it's two inches shorter. ¯\_(ツ)_/¯

Im totally with you there in the tennis warehouse thing.