Thread: Front suspension: displacement vs stress. Engineers, to me!

1. Front suspension: displacement vs stress. Engineers, to me!

I know this must have been discussed to death over the years, but most of what Google turns up are somewhat unrelated discussions.

This discussion is about hardtails only. FS adds too many other factors in.

I ride a SS 29er hardtail, my style is mostly stand-and-mash. As I was mashing up a hill the other day, I observed the fork compressing under my weight.

I started thinking about the conventional wisdom - the force that causes fork compression is ultimately force that doesn't turn the crank. Therefore, when you use suspension, all else being equal, you're not pedaling as efficiently as you could be if you were riding rigid.

However, I imagined a free-body diagram (you'll have to imagine it too as I'm not going to draw it out!): truncated 2D bike frame with frame, fork, handlebar, crank arm. The crank arms are parallel to the ground, all external forces act in the negative y-direction, the hubs provide the two points where reaction force will be applied in the positive y-direction.

Between the rider's weight and leg force generated, there are external forces acting on the handlebar and end of crank arm. Let's say there is a resultant force of 10N acting straight down on the crank arm. Due to bike/rider geometry, the reaction forces are 7N on the front hub and 3N on the rear.

Those 7N on the front hub, those are going to act along that line whether there's a suspension fork or rigid. The force will displace a suspension fork, but if applied to a rigid fork, all it would do is increase the internal stress of the rigid. None of it would be magically shuttled to the crank just because there's a different kind of fork up front.

That's a static analysis of course. I also considered what would change at each moment of the revolution of the crank arm - how the distribution of force between the X and Y directions would be a function of the angle of the crank arm as it went from 90* to 180*. With this visualization, I saw how angular crank displacement may be affected by a suspension fork.

As the crank moves past the 90* position, force in the y-direction begins to be generated. Given the assumption that a distribution of force over the suspension fork displaces it, the whole front end of the bike starts to dip down. This change in geometry means that there may be moments when the tip of the crank isn't turning much relative to the movement of the front end. Rather, both are moving downward at different rates (and different angles). Now, whether this actually affects how much force is transferred to the rear wheel, I do not know.

Bottom line question: does a suspension fork actually "rob energy" from the crank? Or is it simply that a rigid fork makes everything feel tighter to the rider and it's only a perceived difference?

Bottom line answer: I don't know. I think this would require some modeling and experimentation.

Does it matter? Not really. Suspension forks these days are super light and awesome, and you can lock them out to get the best of both worlds. For instance, the Manitou Tower Pro I run is lighter than the boat-anchor steel fork that came with my bike. Plus I ride faster with front squish.

But this is an interesting question to me from a theoretical standpoint. I'd like to hear the opinion/analysis of other engineers and people who have taken a few physics classes. Time to freak out with your inner geek out.

2. Originally Posted by HOV
does a suspension fork actually "rob energy" from the crank?
If it was just a perfectly efficient spring, probably not, but the damper converts a large amount of the energy put into the fork into heat.
(Note: Not an engineer.)

3. also not an engineer, but know enough science to know that all the number crunching and computer models in the world don't mean squat for this situation without a way to apply it to the real, irregular, imperfect trails we ride.

and what I know is that squish (through suspension, tires, and riding technique) helps smooth a rough trail and lets you ride faster. and of course local conditions matter.

4. Originally Posted by NateHawk
also not an engineer, but know enough science to know that all the number crunching and computer models in the world don't mean squat for this situation without a way to apply it to the real, irregular, imperfect trails we ride.

and what I know is that squish (through suspension, tires, and riding technique) helps smooth a rough trail and lets you ride faster. and of course local conditions matter.
Yup, hence:

Originally Posted by HOV
Does it matter? Not really. Suspension forks these days are super light and awesome, and you can lock them out to get the best of both worlds. For instance, the Manitou Tower Pro I run is lighter than the boat-anchor steel fork that came with my bike. Plus I ride faster with front squish.

But this is an interesting question to me from a theoretical standpoint. I'd like to hear the opinion/analysis of other engineers and people who have taken a few physics classes. Time to freak out with your inner geek out.
But there actually is a benefit to answer this question with analysis: it may very well be that what feels good to us while riding has no real benefit at all. Hence, we could just save the effort of reaching down to lockout our forks, or we don't have to worry about bar-mounted lockouts, or we don't have to worry about buying forks with them.

5. I've owned a fork with a lockout for 10 years. I can count the number of times I've used it on one hand, and they were all within the first week or two of owning it. I hate the way my locked out fork feels. more rigid than the steel rigid fork on my commuter.

having a lockout probably matters more the more travel you have, but for my bike, the lockouts are worthless

6. There is no question that a suspension fork dissipates energy. That's its very purpose. If you are climbing and the fork bobs then it also dissipating energy and since you are the only source of energy, it is dissipating energy generated by you the rider. Whether that feels good or ends up making you a faster rider depends on many factors.

7. Originally Posted by borabora
There is no question that a suspension fork dissipates energy. That's its very purpose. If you are climbing and the fork bobs then it also dissipating energy and since you are the only source of energy, it is dissipating energy generated by you the rider.
True... but is just as much energy wasted by cyclically pressurizing a rigid fork? I'm starting to get unit confusion thinking about this.

For instance, you correctly said that a suspension fork dissipates energy, and the only energy available is from the rider. Some energy is dissipated as joules of heat from friction of moving mechanical parts. Some energy is dissipated by means of cyclical changes to the working fluid of the shock by means of pressure and volume changes. Or by the displacement of a spring times the spring constant. Some energy returns the fork to its original position but nothing returns the energy to the rider.

The flip side is the isometric effort required to press on an unyielding rigid fork. It does take some energy in the form of the conversion of chemical potential energy to move muscles that push on something. But when pushing on a rigid fork nothing moves, there is only internal stress within the fork. Stress has units of N/m^2, same as pressure, which is not the same as energy. However, it does take energy to perform isometric movements - holding yourself in a static pullup position you'll know that with a certain intensity inside of 30 seconds. It does take energy to stand and mash in this scenario.

I suppose it's accurate to say that there's no mechanical work applied to the system in the case of a rigid fork, but within the rider's body there is definitely energy being used, also dissipated in the form of heat.

8. Originally Posted by HOV
True... but is just as much energy wasted by cyclically pressurizing a rigid fork? I'm starting to get unit confusion thinking about this.

For instance, you correctly said that a suspension fork dissipates energy, and the only energy available is from the rider. Some energy is dissipated as joules of heat from friction of moving mechanical parts. Some energy is dissipated by means of cyclical changes to the working fluid of the shock by means of pressure and volume changes. Or by the displacement of a spring times the spring constant. Some energy returns the fork to its original position but nothing returns the energy to the rider.

The flip side is the isometric effort required to press on an unyielding rigid fork. It does take some energy in the form of the conversion of chemical potential energy to move muscles that push on something. But when pushing on a rigid fork nothing moves, there is only internal stress within the fork. Stress has units of N/m^2, same as pressure, which is not the same as energy. However, it does take energy to perform isometric movements - holding yourself in a static pullup position you'll know that with a certain intensity inside of 30 seconds. It does take energy to stand and mash in this scenario.

I suppose it's accurate to say that there's no mechanical work applied to the system in the case of a rigid fork, but within the rider's body there is definitely energy being used, also dissipated in the form of heat.
I don't think that an answer exists to your question because not only are trail conditions variable but different bikers' behaviors vary too. I could try to climb efficiently while using a suspension fork while using tons of body English to minimize jarring my head when using a rigid fork. Who is to say what the biker should do in one case or another?

I happen to mostly ride rigid and believe that, in general, a rigid bike climbs better than a HT or FS. But there are technical climbs where a suspension can reduce effort because besides climbing I expend effort threading, lifting my wheel, and absorbing shocks with my body. On a HT those efforts would be less.

9. Focus on your mechanics not your equipment. Concentrating on smoothing your pedal stroke out will eliminate most bob. if you are standing and mashing you should want most of you weight on the rear wheel for max power transfer to the mechanism that is driving your bike forward. Take some weight off your hands and smooth out your pedal stroke.

10. Originally Posted by borabora
I don't think that an answer exists to your question because not only are trail conditions variable but different bikers' behaviors vary too. I could try to climb efficiently while using a suspension fork while using tons of body English to minimize jarring my head when using a rigid fork. Who is to say what the biker should do in one case or another?

I happen to mostly ride rigid and believe that, in general, a rigid bike climbs better than a HT or FS. But there are technical climbs where a suspension can reduce effort because besides climbing I expend effort threading, lifting my wheel, and absorbing shocks with my body. On a HT those efforts would be less.
The only thing I disagree wth is the statement that there is no answer to the question. This isn't a question about real-world riding on various trails, it's about the comparison of two idealized structures - one has an energy dissipation mechanism and the other doesn't.

The system I described originally didn't even have a rider, it only had forces that represent what a rider would exert on the structure in an idealized situation. But your comment about the fork being an energy dissipation mechanism was correct, and it forced an expansion of the boundaries of the system under consideration. The rider would need to be considered in terms of rate of work input to the system (in terms of Watts generated by crank rotation), and rate of work output (in terms of Watts generated by wheel rotation).

Without consideration of the rider's rate of work input, then the answer is overly simple: a HT will cause energy loss and a rigid won't. That's definitely not the whole story, even for a simplified, idealized analysis.

11. Originally Posted by LaXCarp
Focus on your mechanics not your equipment. Concentrating on smoothing your pedal stroke out will eliminate most bob. if you are standing and mashing you should want most of you weight on the rear wheel for max power transfer to the mechanism that is driving your bike forward. Take some weight off your hands and smooth out your pedal stroke.
No thanks, stand-and-mash is my style; it works for me and my blinglespeed. But your advice and good intentions are appreciated.

Your comment gets to the heart of the question - you mentioned that rider weight should be rear-biased if doing stand-and-mash because it would transfer power better to the rear wheel. How do you know? You just completed the analysis with an assumption; I'd like to know how you got there.

A tiny bit off topic: I experimented with rear weight bias to see if it would reduce fork compression while out of the saddle. I didn't measure carefully, but it seemed as though it did not reduce fork displacement much at all. Which makes sense - unless you're climbing in a wheelie there's going to be weight on the front hub every time your body comes down. The fork will compress every stroke.

12. Well I'm neither an engineer or very smart apparently.

Last week after cleaning my bike I must have left the fork in lockout on my full squish. I rode about three miles on a moderate trail, and couldn't figure out why the bike was acting differently.
I did notice I was using my arms a lot more to absorb bumps. When I finally stopped and tried to compress front fork it dawned on me it was locked. Man did I feel stupid!
But also glad I have a front fork!

13. Originally Posted by LaXCarp
Focus on your mechanics not your equipment. Concentrating on smoothing your pedal stroke out will eliminate most bob. if you are standing and mashing you should want most of you weight on the rear wheel for max power transfer to the mechanism that is driving your bike forward. Take some weight off your hands and smooth out your pedal stroke.
^^^I think this is closer to answering the OP's question.
Better form creates a more efficient use of power.

Last season I swapped a 4" fork for my rigid fork, just to see how I'd like it (I soon switched back). I noticed that when I do a standing climb, I not only pull up with the hand on the side that is on the downstroke, I also push down with the opposite hand. This is my habit, learned over many years of rigid riding, of assuring that the front tire is tracking on the ground despite not having suspension ("damping", if you will). With a rigid fork, all the forces balance nicely, and that front tire stays planted. With a suspension fork, it is bobbing like crazy - plus it is redundant for me to push down on the grip while climbing. I adjusted my hand forces to mostly pull up. This reduces bobbing (approaching a theoretically "rigid" scenario of zero displacement), and increases traction on the rear tire. It noticeably increased my speed on short, steep climbs where just a few punchy pedal stabs in a higher gear are as good as smooth circles in a slightly lower gear.

So I am concluding, anecdotally, that the fork does eat up a small amount of power, and benefits greatly from better form.

The 4" fork does, however, return the favor when the energy input to the system comes in excess both from gravity as well as high-frequency vertical displacements of the entire system (aka "bumps" ).

-F

14. Originally Posted by Fleas
^^^I think this is closer to answering the OP's question.
Better form creates a more efficient use of power.
Not really... my original question was about a comparison of two systems where one is dampened and one is not. It has nothing to do with riders or riding form; his response was well intentioned but off topic.

Originally Posted by Fleas
With a suspension fork, it is bobbing like crazy - plus it is redundant for me to push down on the grip while climbing. I adjusted my hand forces to mostly pull up. This reduces bobbing (approaching a theoretically "rigid" scenario of zero displacement), and increases traction on the rear tire. It noticeably increased my speed on short, steep climbs where just a few punchy pedal stabs in a higher gear are as good as smooth circles in a slightly lower gear.
I completely agree with your technique and evaluation of the benefit of punchy pedal stabs, especially applied to hardtail SS riding as I do. There's just no such thing as smooth circles when you have one gear, so pulling like a mother****er on the bars and mashing is the only way up. That is my monster mash uphill bliss and the #1 reason I ride SS. Total body strength applied to power up the hill for me > spinny hip flexor burn in a low gear that I don't have anyway.

However, I disagree that pulling up on the bars reduces fork bob. What it does is allow your legs to push with a force greater than that of your own bodyweight by bracing your body against the handlebars. But your body weight is still acting cyclically downward. The only ways to reduce cyclical weight loading over the front hub are to (1) bias your weight to the rear until you're doing a wheelie, or (2) put a foot down.

Biasing weight way to the rear may reduce the load over the front hub, but the increase in awkward factor is probably not worth the negligible reduction in fork bob unless traction is the main concern.

Anyway, all of this is fun to discuss but still OT. The original question was very narrow in scope: the free body diagrams of two 2D structures compared in terms of how efficient they are given identical loading.

15. Idealy you shouldn't be putting any force on the handlebars when you pedal, you should lightly hold them to control the wheel. The suspension bob is then from the force on your pedals (since the force isn't directly over the rear hub). Since your style is "stand-and-mash", you are relying alot on your own weight to put force on your pedals, then your legs will push your weight back up. A fork will lose energy from friction and simply because it's dampened. So since some of your pedal force is going into compressing the springs (air or coil), and if all other variables are equal, a rigid fork will waste less energy.

For a suspension fork, lockout will help, also putting more weight over the rear wheel and having smoother pedaling will also help.

16. Originally Posted by tim_from_PA
So since some of your pedal force is going into compressing the springs (air or coil), and if all other variables are equal, a rigid fork will waste less energy.
How about the energy required to put stress on a rigid fork?

All things equal, a rigid fork still wants to bob but it can't. So it just gets stressed cyclically.

We may not see it, but even a rigid fork will have some strain. A little tiny bit within the elastic region of the metal.

17. Yes I agree, but the amount you loose with a suspension fork will be orders of magnitude larger than what you loose from a rigid fork.

18. Tim- is that true though?

Imagine a pushing a heavy wooden box. You use 5 calories of food energy to move your legs and displace the box a meter. Your energy is dissipated via displacing the box and friction.

Now imagine trying to push a concrete box that's too heavy for your puny 5-calorie effort to move. You push against it until you've used all your calories but nothing has been displaced.

In both situations, 5 cal of enery have been used by the box pusher. One box is displaced, the other has just been stressed but no work was applied to the system.

Perhaps the key here is rate of work (power). Static pushing will eventually use those calories but it will take a lot longer to burn through them. So it takes less power.

19. I’ll take a stab at it from a very simply energy model, by comparing only a suspension fork vs a rigid fork. Take the classic definitions that Energy = ability to do Work, and Work = Force * Distance.

In our simple, ideal model, I’ll make the following very generalized assumptions. What that we desire as a rider is to have as much Energy transferred through the bike and into the ground. What we want to minimize is anything that would hinder this Energy on its path to the ground.

If the Energy we’re applying into the bike is by the Work we’re doing, then by association, we want as much of or Work making it to the ground as well. That Work comes from the Force we exert on the bike. Most of the Force goes into the cranks, but a smaller component is from our torso bobbing up and down over the handlebars. This Force from our torso is transferred to the fork.

On a suspension fork, this smaller torso Force moves the suspension over a Distance, so we can assume we’d get a tangible Value. On a rigid fork, it is negligible. That Value from the suspension is work we end up putting into the machine, ie being absorbed by the machine, ie not being transferred to the ground like we want. That work is turned into heat, and you can consider it as being lost.

Therefore, a rigid fork, under completely ideal conditions, robs less input energy than a suspension fork.

Not sure if my thought process is logical, but that’s a quickly hashed out thought experiment.

20. Thinking further about this, I remembered the concept of "strain energy". Here's a .pdf that describes it pretty well.

http://homepages.engineering.aucklan...ain_Energy.pdf

I think that is the best answer possible short of crunching numbers. Displacement of a suspension fork will store some and dissipate some energy, but putting stress and therefore strain on a rigid fork will dissipate energy in the form of strain energy.

As to which is greater, that would require some actual numbers. I was taught to never do math in public...

21. Originally Posted by Zuarte
On a suspension fork, this smaller torso Force moves the suspension over a Distance, so we can assume we’d get a tangible Value. On a rigid fork, it is negligible. That Value from the suspension is work we end up putting into the machine, ie being absorbed by the machine, ie not being transferred to the ground like we want. That work is turned into heat, and you can consider it as being lost.

Therefore, a rigid fork, under completely ideal conditions, robs less input energy than a suspension fork.

Not sure if my thought process is logical, but that’s a quickly hashed out thought experiment.
Thanks for taking a stab at it.

I think you're close, but the bolded part is an assumption about which my entire question is posed. By making the assumption that putting stress on a rigid fork requires negligible energy, you've already answered the question.

I'm pretty sure strain energy is the factor that is the key to the answer- see post #20 above.

22. Back to the OT part I go...
I'm not so much trying to answer your question as much as I'd like to hear your conclusion considering what info has been posted in this thread.

In the real world scenario, fork bob can come from weight shifts (pedaling) or from acceleration that actually lightens the front end. On the rigid fork you can lighten the front end without lifting it off the ground. With a suspension fork, if you lighten the load, it extends - which will exacerbate the bob on the following pedal stroke. This is why I think technique - even the stand and mash technique - plays a big part in pedal energy loss.

Also, the reaction to the standing pedal downstroke is pulling up on the bars with the same side hand. If you tried this on ice (which I have), you get an immediate sense of which forces are dominant and which forces balance the others.

So I am still going with rigid is more efficient by a little bit.

If you want to analyze power lost in suspension travel or rigid fork deflection, just consider the frequency at which the rigid fork rebounds (or the time it takes) compared to that at which the suspension fork rebounds. You are applying force over a greater distance and time to displace the suspension fork. If all the forces are equal b/suspension and rigid, then you are doing more work on the suspension fork. The rigid fork, even a carbon one, also has much lower damping (= more efficient energy return from strain).

-F

23. After reading the strain section in that pdf, I still maintain my original conclusion that the energy is negligible compared to a suspension fork. Strain is simply deformation of a material divided by the original unloaded length of that material. As long as we’re dealing with elastic loading conditions, the deltaD of a rigid fork is magnitudes smaller than a suspension fork that can bob many millimeters while pedaling.

To me, there is no hidden energies to recover from a rigid fork as it gets cycled through loads, if that’s what you’re getting at.

Now, if you start comparing different rigid fork materials (steel, carbon fiber, titanium, ect), where their deltaD’s are all along the same magnitude, then I believe you can start quantifying differences. But compared to a suspension fork, the rigids deflect on a micro scale compared to a suspension’s macro scale.

I can’t help but think I’m still missing some crux of the point you’re trying to make, per a hidden recoverable energy. Great discussion though!

24. ...and as for the elastic strain energy U, that is a function of the force P and the deltaD. Again, the deltaD's are so drastically different between suspension and rigid that for any U we can calculate from a rigid fork, the the suspension U* will be super large by comparison.

* This is sort of a faux pas by pretending a suspension fork is a single rigid material and it's travel is the deltaD.

25. Originally Posted by fleas
Also, the reaction to the standing pedal downstroke is pulling up on the bars with the same side hand. If you tried this on ice (which I have), you get an immediate sense of which forces are dominant and which forces balance the others.
That sounds compelling, I'd really like to try it.

Originally Posted by fleas
If you want to analyze power lost in suspension travel or rigid fork deflection, just consider the frequency at which the rigid fork rebounds (or the time it takes) compared to that at which the suspension fork rebounds. You are applying force over a greater distance and time to displace the suspension fork. If all the forces are equal b/suspension and rigid, then you are doing more work on the suspension fork. The rigid fork, even a carbon one, also has much lower damping (= more efficient energy return from strain).

-F
Ok, that's fair.

26. Originally Posted by Zuarte
After reading the strain section in that pdf, I still maintain my original conclusion that the energy is negligible compared to a suspension fork. Strain is simply deformation of a material divided by the original unloaded length of that material. As long as we’re dealing with elastic loading conditions, the deltaD of a rigid fork is magnitudes smaller than a suspension fork that can bob many millimeters while pedaling.

To me, there is no hidden energies to recover from a rigid fork as it gets cycled through loads, if that’s what you’re getting at.

Now, if you start comparing different rigid fork materials (steel, carbon fiber, titanium, ect), where their deltaD’s are all along the same magnitude, then I believe you can start quantifying differences. But compared to a suspension fork, the rigids deflect on a micro scale compared to a suspension’s macro scale.

I can’t help but think I’m still missing some crux of the point you’re trying to make, per a hidden recoverable energy. Great discussion though!
My take on the OP's point is that s/he wonders if the energy wasted by a suspension fork might be matched by the bio-mechnical energy wasted within a rider using a rigid fork due to the harshness of the rigid fork. I think that the OP is aware that the suspension fork "does more work" and therefore itself wastes more energy than a rigid fork. But the rider then wastes internally what the rigid fork saves. It's sort of a zero sum game theory.
Personally, I don't think so.

27. Originally Posted by Zuarte
After reading the strain section in that pdf, I still maintain my original conclusion that the energy is negligible compared to a suspension fork. Strain is simply deformation of a material divided by the original unloaded length of that material. As long as we’re dealing with elastic loading conditions, the deltaD of a rigid fork is magnitudes smaller than a suspension fork that can bob many millimeters while pedaling.

To me, there is no hidden energies to recover from a rigid fork as it gets cycled through loads, if that’s what you’re getting at.

Now, if you start comparing different rigid fork materials (steel, carbon fiber, titanium, ect), where their deltaD’s are all along the same magnitude, then I believe you can start quantifying differences. But compared to a suspension fork, the rigids deflect on a micro scale compared to a suspension’s macro scale.

I can’t help but think I’m still missing some crux of the point you’re trying to make, per a hidden recoverable energy. Great discussion though!
No, you got it. Now that strain energy has been quantified I'm good with rough estimations of magnitude. Since the formula for strain energy under axial load is

U = Integral from 0 to L of (P^2/2EA) dx

A force of 10N is going to produce super tiny U due to the enormous size of Young's Modulus.

The energy required to compress a spring or working fluid is going to be orders of magnitude higher, so yes I agree with you.

28. Originally Posted by borabora
My take on the OP's point is that s/he wonders if the energy wasted by a suspension fork might be matched by the bio-mechnical energy wasted within a rider using a rigid fork due to the harshness of the rigid fork. I think that the OP is aware that the suspension fork "does more work" and therefore itself wastes more energy than a rigid fork. But the rider then wastes internally what the rigid fork saves. It's sort of a zero sum game theory.
Personally, I don't think so.
Precisely. Now, I don't think so either.

29. Every engineering model is flawed, but some are useful. Having said that, I think your simplifying assumptions go too far & make your model unusable for the stated purpose. I'm going to take a stab at a different set of simple assumptions to try to explain why a suspension fork is more efficient in rough conditions.

Let's say you are pedaling on a level smooth surface with a rigid-fork bike. You are contributing a certain amount of energy via the pedals just to overcome friction in order to maintain constant forward momentum. Now assume you encounter an unmovable obstacle, say a 10" diameter log. The angle of incedence between the tire & the log is fairly high since the log is fairly small compared to the tire. The force acting against the tire has mostly an upward component to force the tire up, but also a smaller horizontal component in opposition to your forward momentum. Hence your forward momentum is impeded & you must either pedal harder or suffer a slow-down.

Now assume a suspension fork in the same situation. Because the tire yields more in the vertical direction, the impact between the tire & the log is not as brief as in the rigid-fork case, & as the tire rolls over the obstacle much more of the incident force that would have been acting against your forward momentum is deflected upward & dissipated into the shock dampening mechanism.

A few more comparisons:

The tire strikes the log in the same location in both cases & the initial angle of incedence is the same. In the case of the rigid fork the strike is brief & the force is transferred very quickly. In the case of the suspension fork, becaue the wheel displaces vertically it stays in contact with the log much longer. As it passes over the log, much more of the force is now acting vertically rather than horizontally because the angle of incidence is much closer to vertical.

In the rigid bike case, the entire bike frame tilts up & most of the vertical energy dissipation must be done by the rider (flexing knees, back, arms, etc.). So the rider must overcome the negative forward momentum & dissapate the vertical force at the same time. In the suspension case, most of the vertical force is dissapated in the shock & there is less negative forward momentum.

On a level smooth surface with no obstacles, the rigid fork is obviously more efficient. The act of pedalling & maneuvering will dissapate more forward momentum energy in a suspension bike than in a rigid bike.

If one has good bunny-hop skills, you can probably clear individual obstacles more efficiently on a rigid bike than a suspension bike. But do you always encounter obstacles individually? In the early days of suspension forks, some old-timers were saying they were just a crutch for riders without skills. But it soon became apparent that trail features that were unridable on a rigid bike could be ridden by a suspension bike.

30. Burtronix, I agree with your model and scenario. When the terrain starts getting bad enough, suspension definitely makes a difference. And I don't see any conflict between your model and mine (at least in my mind). I was simplifying things down to the point where external forces on the bike were minimized as much as possible. This was the best way I could think of to control the conditions where a single variable factor - the fork - could be compared. For me this meant the hypothetical case of two bikes are on a smooth, inclined slope.

The additional forces caused by terrain can certainly be a game changer.

31. OT, but I agree with the terrain comments as well.

HT these days is great; forks are so light and lock out anyway. It's nice to have the flexibility (pun intended).

But riders seeking Zen simplicity, troglodytes, technophobes, hard core weight weenies, fat bikers, smooth trail racers, and adventure seekers have valid reasons to go rigid too. I have one of each because bicycle.

32. Didn't really read through the whole thread but the OP seems to forget that the fork is not the only form of suspension on a hardtail. The air in the tires provide considerable damping too, so even a full rigid bike has some degree of suspension. Now, if you rode your bike without tyres, then probably all the rattling would tend to kill some moving parts sooner than normal.

33. true but this variable is assumed to be the same in the model with a suspension fork.

I think that if you treat this problem as a static analysis, you aren't going to show much of a difference, but when treated as a dynamic analysis, you will find (my intuition tells me) that a rigid fork is more efficient. I don't think I can even do a dynamic analysis like that by hand, certainly not while I'm at work...

34. Originally Posted by justwan naride
Didn't really read through the whole thread but the OP seems to forget that the fork is not the only form of suspension on a hardtail.
Tim already addressed this one, but just to be repetitive: if you read the description of the original free body diagram, it ends at the hub. Tires weren't a consideration because (1) they're constant between both fork variations, and (2) the less variables to consider, the better. The hub is the (idealized) rigid point on both bikes at which reaction force is generated to either compress a suspension for or stress a rigid one.

Originally Posted by tim_from_PA
true but this variable is assumed to be the same in the model with a suspension fork.

I think that if you treat this problem as a static analysis, you aren't going to show much of a difference, but when treated as a dynamic analysis, you will find (my intuition tells me) that a rigid fork is more efficient. I don't think I can even do a dynamic analysis like that by hand, certainly not while I'm at work...
I agree, I came to the same conclusion around post #9. Forces balance well from a static sense. But things are either displacing or straining. So the Hamiltonian method is the way to go here: consider energy in and energy out.

Energy in = caloric expenditure from rider

Energy out (suspended) = (rotational) kinetic energy of crank, change in pressure/volume of fork working fluid and/or compression of spring, heat out due to friction of moving parts within the fork

Energy out (rigid) = (rotational) kinetic energy of crank, strain energy

Even though some of that energy out on the suspension fork is "recovered" when the fork returns to its original position, it's not a reversible process because no energy is returned to the rider.

35. Unfortunately I kind of flipped again on this one last night. So I submitted it to Mythbusters. The writeup:

There's a myth related to bicycles: that a suspension fork will ultimately take away energy from the crank, therefore a rigid fork is more efficient.

Assumptions: hardtail bike (full suspension adds too many variables), straight and level pedalling, smooth surface.

From the perspective of energy analysis, the myth seems to be true. Since all mechanical work is supplied by the rider, a suspension fork will convert that work input to presure/volume changes within the fork's working fluid, or to compressing a spring, and some joules will be converted to heat. The rest goes to turning the crank.

A rigid fork, however, will convert that work to strain energy within the fork, and the rest goes to turning the crank. Strain energy for an axial load is represented by the square of the force applied divided by 2 times the modulus of elasticiy times the area of the material. Since, in this case, force is fairly low, the huge modulus of elasticity in the denominator makes strain energy very small compared to the work that a suspension fork dissipates.

However, when the analysis shifts to more of a statics/dynamics point of reference, given same riding position between both structures, a certain amount of weight is going to act cyclically over the fork. That shifting/cycling weight will never be available to turn the pedal because it's a function of rider and bike geometry only. That cyclical weight over the fork is really what drives the compression of the suspension fork. So yes, there is rider-sourced energy dissipated within the fork, but it was never usable for turning pedals anyway... for either structure.

Followng that, if we analyze the losses associated with compressing or stressing either fork, the suspension fork loses more because compressing stuff takes more energy than straining a rigid bar. So where does that extra energy go on the rigid side? Reaction force transferred to the rider? The answer isn't as clear. We need Mythbusters to put this to the test!

Imagine how many bicycling accidents you can help prevent by keeping peoples' hands from reaching to their fork lockout switches!

36. Here is another body mechanics based solution similar to my smoothing out the pedal stroke idea. What about riders who blow off this input of energy by moving the bike slightly side to side when aggressively pedaling? This could eliminate all force put into a suspension fork.

Similarily, since all force is transferred to the front wheel/tire of a rigid fork, is this energy not transferred as increased friction to the ground, and because the rear wheel is the driving force of a bicycle does this act as a brake therefore negating the "loss" of energy caused by a suspension fork?

I'm no engineer, just a logical thinker.

37. Originally Posted by HOV
- you mentioned that rider weight should be rear-biased if doing stand-and-mash because it would transfer power better to the rear wheel. How do you know?

The fork will compress every strok.
because the chain is attached to the rear wheel

Pedal circles not squares, I run 150mm fork that I can pedal with no measurably pedal induced compression while standing.

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