Rear suspension and rear hub question.

[cal3thousand]

So am I understanding it right that 'technique' now has an effect on physics?

I must be misunderstanding it, but my belief is that 'technique' and 'suspension' are not mutually exclusive.

Technique can affect not only effective spring rate, suspension travel, and damping rate, but also effective bump length. Really.

Yes, you change spring rate of the whole machine using your legs. But suspension does not negate my legs. In fact, it increases my range of spring rate that I can change.

 

[Chalo]

Yes, you change spring rate of the whole machine using your legs. But suspension does not negate my legs. In fact, it increases my range of spring rate that I can change.

That does not reflect the approach of my many suspension bike owning customers over the years. They use suspension as a substitute for acquiring technique.

A lot of them don't even leave the confines of streets and multi-use paths. They use suspension as a substitute for standing up when they run into something.

 

[TiagoSantos]

There's a local co-op bike shop setup by some bike anarchists. Awesome idea, really cheap parts and you can go in there and use their tools, or pay a token fee to have someone more experienced help you out.

Everyone I've talked to raves about this place and they love it. Except my buddy from work who went in there with his nice work clothes and wearing a pair of expensive looking sunglasses (it was sunny as hell, and we work in the dark all day). He got treated like shit, too much of a yuppie, I guess?

The whole point of a bike revolution, or e-bike revolution in our forum's case, is to make things more accessible to the general public. Wouldn't it be much better to have e-bikes generally accepted as the incredible alternative to cars that they are? A 'holier-than-thou' attitude about bike 'technique' or making people thing they're inferior because they could care less about learning the finer points of riding a bike like it was a jazz piano will do just about zero to convince anyone to ride a bike.

 

[hjns]

It looks to me that there are now two discussions ongoing. One about the actual differences between hardtail and FS, and the other about the (lack of) technique of the users. Maybe it is good to separate these when discussing the impact on a rear hub?

 

[Chalo]

Wouldn't it be much better to have e-bikes generally accepted as the incredible alternative to cars that they are? A 'holier-than-thou' attitude about bike 'technique' or making people thing they're inferior because they could care less about learning the finer points of riding a bike like it was a jazz piano will do just about zero to convince anyone to ride a bike.

There are bikes built especially for folks like that, too. The Dutch ride them. They don't have gimmicky mechanical suspension or high price tags; they just go when you push the pedals.

This is more or less what bikes look like when they are a real, broadly accepted alternative to motor vehicles. You can see bikes like this in Amsterdam, Mumbai, Shanghai, Cairo, and Jakarta. What you won't see in any of those places is a lot of marketing-driven (exxtreeme!!!) double-boingers.

 

[mvly]

All things constant, the force experienced by the bearing on the hub motor can be modeled as an impulse (Dirac delta) if the bike is a hard-tail. Fat/thick tires will lower the magnitude of the impulse and spread the energy between the few ms, essentially a fatter shorter delta.

However on a full-suspension bike, the wheel is allowed to move, thus, the force on the bearings is DEFINITELY lowered in magnitude, though it's still a impulse at the instantaneous contact assuming same bike tires. Moreover, the energy is spread more evenly during this transaction. Think of it as (((impulse, then constant magnitude, then low))) for Full Suspension VS (((impulse, low, then another impulse, low))), etc for the hardtail as it bounces after the impact.

I don't know where Chalo took physics or math, but it's definitely not more for full suspension. I think he is confused about the acceleration of the whole swing arm. But if you think about it, the acceleration is same or less in the full suspension as there is give in the swing-arm vs a hardtail frame.

 

[Chalo]

Here in this discussion I see a conflation of structural loads (tire/rim/spoke/hub body/axle) and shock/vibe loads, which are a product of sudden acceleration.

If the hub displaces farther, faster, with more reversals, because it is mounted on a swingarm, then the acceleration (shock & vibration) of the non-structural components (magnets, wires, sensors, circuit boards) will be higher. That's what I'm saying. The cush of a tire attenuates the vertical acceleration of the hub, but the movement of a swingarm exaggerates it. So a system where the tire works more deeply and the frame deflects less will reduce the magnitude of accelerations on the motor, even if it's harder on a sitting person's butt, and even if it causes bigger stress excursions on the spokes.

The seat is not the hub! Swingarm suspension is designed to diminish displacements at the seat, with a side effect of larger displacements at the hub.

The structural parts of the system are designed for dynamic loads; the electrics-- maybe, maybe not. It looks like they are mostly designed to be cheap.

 

[cal3thousand]

All things constant, the force experienced by the bearing on the hub motor can be modeled as an impulse (Dirac delta) if the bike is a hard-tail. Fat/thick tires will lower the magnitude of the impulse and spread the energy between the few ms, essentially a fatter shorter delta.

However on a full-suspension bike, the wheel is allowed to move, thus, the force on the bearings is DEFINITELY lowered in magnitude, though it's still a impulse at the instantaneous contact assuming same bike tires. Moreover, the energy is spread more evenly during this transaction. Think of it as (((impulse, then constant magnitude, then low))) for Full Suspension VS (((impulse, low, then another impulse, low))), etc for the hardtail as it bounces after the impact.

I don't know where Chalo took physics or math, but it's definitely not more for full suspension. I think he is confused about the acceleration of the whole swing arm. But if you think about it, the acceleration is same or less in the full suspension as there is give in the swing-arm vs a hardtail frame.

I think he has to understand that there is less peak force in a suspended bike. He, himself, advocates the use of your legs as dampers. " ...suspension as a substitute for standing up when they run into something"

But he's a minimalist in regards to bikes, so he would rather do without the suspension and use his legs.

Those of us that are not purists in regards to biking, but more enthused by e-bikes, understand that the heavy hubs benefit from damping that the human legs cannot fully supply at these weights.

 

[cal3thousand]

Here in this discussion I see a conflation of structural loads (tire/rim/spoke/hub body/axle) and shock/vibe loads, which are a product of sudden acceleration.

If the hub displaces farther, faster, with more reversals, because it is mounted on a swingarm, then the acceleration (shock & vibration) of the non-structural components (magnets, wires, sensors, circuit boards) will be higher. That's what I'm saying. The cush of a tire attenuates the vertical acceleration of the hub, but the movement of a swingarm exaggerates it. So a system where the tire works more deeply and the frame deflects less will reduce the magnitude of accelerations on the motor, even if it's harder on a sitting person's butt, and even if it causes bigger stress excursions on the spokes.

The seat is not the hub! Swingarm suspension is designed to diminish displacements at the seat, with a side effect of larger displacements at the hub.

The structural parts of the system are designed for dynamic loads; the electrics-- maybe, maybe not. It looks like they are mostly designed to be cheap.

further does not go with faster. It's one or the other. Long wavelength, short frequency OR high frequency, short wavelength. ceterus paribus.

The machine that has less time to decelerate will feel a greater peak force. What's more abrupt and forceful? The pitchers hand as he throws the ball (long acceleration) or the catcher's hand as he catches the ball (short deceleration).

I think we can agree purely on the audible evidence that the glove feels a higher force of impact.

 

[Chalo]

The machine that has less time to decelerate will feel a greater peak force. What's more abrupt and forceful? The pitchers hand as he throws the ball (long acceleration) or the catcher's hand as he catches the ball (short deceleration).

I think we can agree purely on the audible evidence that the glove feels a higher force of impact.

Can we agree that upon hitting a given step-up at say 20mph, assuming no bunny hops or the like, that the duration of the upward acceleration is the same whether the bike is suspended or not, being a function of speed, step height, and wheel diameter only?

And can we agree that if suspension is present in that case, that the hub will displace farther-- within the same duration-- than it would if the bike had no mechanical suspension and relied solely on its tires?

Do you see yet what I'm saying here?

Furthermore, can we agree that on encountering a step-down at the same speed, the downward acceleration of the hub of the unsuspended bike is most likely to be that of gravity, whereas that of the suspended bike is determined by the spring rate pushing it down, and the damping rate opposing the spring? That the downward acceleration of the sus bike's wheel is therefore the rate of gravitational acceleration plus the acceleration of the extending suspension link? And that therefore, upon hitting the immovable ground, the sus bike's wheel can really only be descending faster than the rigid bike's when it is stopped?

Stepping up farther in the same duration equals higher acceleration. Being pushed down more quickly from the same height equals higher acceleration. Being slowed to a stop from a higher speed equals higher acceleration.

Your backside doesn't notice this stuff, but your wheel goes through it.

 

[cal3thousand]

The machine that has less time to decelerate will feel a greater peak force. What's more abrupt and forceful? The pitchers hand as he throws the ball (long acceleration) or the catcher's hand as he catches the ball (short deceleration).

I think we can agree purely on the audible evidence that the glove feels a higher force of impact.

Can we agree that upon hitting a given step-up at say 20mph, assuming no bunny hops or the like, that the duration of the upward acceleration is the same whether the bike is suspended or not, being a function of speed, step height, and wheel diameter only?

And can we agree that if suspension is present in that case, that the hub will displace farther-- within the same duration-- than it would if the bike had no mechanical suspension and relied solely on its tires?

Do you see yet what I'm saying here?

Why would the duration be the same? The suspension compresses, spreading the time that the force acts upon the bike. Otherwise, why would you suggest using your legs in the other example?

 

[shock]

I fail to see how acceleration has anything to do with wear and tear on a wheel hub. Unless you are doing a sticky tire, smokey burnout; "acceleration" from suspension travel is negligible.

If a suspended bike is like a dragster in terms of "acceleration wear" then a hardtail is like the same dragster hitting the wall at 200mph decelerating to 0 mph in a second. Which one does more damage?

 

[Chalo]

And can we agree that if suspension is present in that case, that the hub will displace farther-- within the same duration-- than it would if the bike had no mechanical suspension and relied solely on its tires?

Do you see yet what I'm saying here?

Why would the duration be the same? The suspension compresses, spreading the time that the force acts upon the bike. Otherwise, why would you suggest using your legs in the other example?

Your legs are proactive-- they can begin raising the bike before you hit the step, and continue to gradually apply load afterwards. Anyway, I stipulated that wasn't happening in this case.

The tire/suspension/your butt can only react to a bump during the time it's applied, see? That's predicated by the bump size, wheel diameter, and road speed, as I said. Suspension can slow the rebound, but has no effect on how fast a bump is encountered. At the same speed, the duration of onset is the same. But since the sus bike's hub moves farther in the same time, its acceleration force is higher.

 

[Chalo]

I fail to see how acceleration has anything to do with wear and tear on a wheel hub. Unless you are doing a sticky tire, smokey burnout; "acceleration" from suspension travel is negligible.

I'm talking vertical accelerations, e.g. shock and vibration. Not the movement parallel to the ground.

 

[mvly]

The machine that has less time to decelerate will feel a greater peak force. What's more abrupt and forceful? The pitchers hand as he throws the ball (long acceleration) or the catcher's hand as he catches the ball (short deceleration).

I think we can agree purely on the audible evidence that the glove feels a higher force of impact.

Can we agree that upon hitting a given step-up at say 20mph, assuming no bunny hops or the like, that the duration of the upward acceleration is the same whether the bike is suspended or not, being a function of speed, step height, and wheel diameter only?

And can we agree that if suspension is present in that case, that the hub will displace farther-- within the same duration-- than it would if the bike had no mechanical suspension and relied solely on its tires?

Do you see yet what I'm saying here?

Furthermore, can we agree that on encountering a step-down at the same speed, the downward acceleration of the hub of the unsuspended bike is most likely to be that of gravity, whereas that of the suspended bike is determined by the spring rate pushing it down, and the damping rate opposing the spring? That the downward acceleration of the sus bike's wheel is therefore the rate of gravitational acceleration plus the acceleration of the extending suspension link? And that therefore, upon hitting the immovable ground, the sus bike's wheel can really only be descending faster than the rigid bike's when it is stopped?

Stepping up farther in the same duration equals higher acceleration. Being pushed down more quickly from the same height equals higher acceleration. Being slowed to a stop from a higher speed equals higher acceleration.

Your backside doesn't notice this stuff, but your wheel goes through it.

OK I am trying to think like you to find where the flaw is in your thinking is. So answer these few questions to help guide you:

Lets get the easy stuff out of the way. Chalo, you are saying on the step down there is more force on the bearing simply because you have gravity plus the spring shock force, i.e. when the bike jumps off the curb, the acceleration is the gravity + the spring/air shock which is greater when the wheel actually touch the ground. Yes! I totally agree with you! Indeed the wheel will see both the force of the gravity + the shock. BUT... only in certain situation. Lets compare...

1) If you have full suspension and jump a curb @ 20mph+. Now envision a hard-tail jumping a curb at the same 20mph+ speed. Which bike's rear wheel will hit the ground first? Then tell me at the point and time of contact of the first bike to the ground, what is the force on the wheel? Keep in mind, most of the bike is still suspended in midair.

2) Now some time has passed so that on the hard-tail the rear wheel FIRST make contact with the ground. Tell me the force on the two bike's rear wheel. Keep in mind the full-suspension wheel is already on the ground.

3) Note that as the bikes are flying off the curb, the rider is suspended in mid air for a few ms. When the wheel hits the ground for either bike, the weight of the bike + the rider's weight are not full pushing down on the rear wheel yet because it is FIRST contact. Now say a few ms later, the rider's weight hits the seat sending the force to the rear wheel for the hard-tail and the suspension + rear wheel for the full-suspension bike. Just looking at the force on the rear wheel itself, which bike will have greater force on the wheel?

4) Now say the 2 bikes are traveling at 2mph off the curb. Which bike's rear wheel will hit the ground first? Answer the same for 2) and 3) for this scenario.

Now lets compare the step up case (unit step function):

1) If you have full suspension and hit a crub on the rear wheel @ 20mph+. Now envision a hard-tail doing the same at the same 20mph+ speed. What is the force on the rear wheel at the point and time of FIRST contact for the full suspension. How about the hard-tail?

2) Assuming 1) where can these force be distributed in the full-suspension case and the hard-tail case.

3) Keeping in mind Every force has equal and opposite force is the object is rigid, Tell me the equal and opposite force on the rear wheel at the moment of FIRST contact for both cases.

4) Assuming the rider does NOT use their legs to cushion in either case, i.e. they are just sitting flat on the seat post. What is the normal force to the rider at the moment of FIRST contact for each of the bikes? What is the force on the rear suspension? What is the opposite force on the the rear suspension? Note the rear suspension's displacement. Now tell me the same for the hard-tail keeping in mind there is NO displacement on the hard-tail.

5) Now let some time pass, i.e. for the full suspension bike, the shock compresses but the bike's seat height stays the same. For the hard-tail, the seat is displaced higher as expected. However tell me the displacement of the two wheels? Now tell me what is the force at this moment for either bike at the bike seat.

Hopefully after you answer these questions you will start to realize how having a full-suspension bike reduces stress on the bearings.

 

[Chalo]

You're still conflating structural forces and accelerations.

Structural forces only matter to the structural elements of the bike, for instance the bearings as you point out. But the structural parts of the bike are designed to tolerate those forces. Transient peak forces on the structural parts of the bike could be higher for either bike, depending on many factors of the surface and the suspension's characteristics.

In many cases, the structural peak forces on a rigid bike will be higher than that of a sus bike. And the structural force peaks will almost always be longer in duration (rider "landing" on bike vs. wheel extending and briefly smacking on the ground). There is more work (F * D) in the high stress level regime of those unsuspended hits, even if the transient peaks are just as high for the sus bike. So if you want to bend a bike, use a rigid one. But that's not what I'm talking about.

The magnets in the motor are not structural. They're not in the force path. Same with wires, halls, plugs, pass-throughs, printed circuits and other critical bits that are not part of the bike's structure. The forces that will cause a magnet to unstick, a wire to fatigue and break, or an electrolytic capacitor to bust one of its leads, are strictly due to acceleration (not in the vehicular sense, but in the physics sense). The hub of a sus bike sees higher and more frequent acceleration forces because it moves around more. There's more shock and vibration in the unsuspended parts of a suspended vehicle than in any part of an unsuspended vehicle on the same course. And the hub is not suspended.

As an illustration of the forces I'm talking about, consider this. When I build or repair a spoked wheel, I get the spokes good and tight-- always at least 100kgf of tension on the spokes of the tighter side, but sometimes more. Friction in the spoke nipples and rim holes leads to a residual twist in each spoke that I can only partly remove by backing up a little when I tighten them. Each time of the spokes unwinds, there is a little "tick" or "ping" sound as it releases. And you can only get it to release by applying a big enough load to the rim that the spoke's tension drops low enough for it to unwind. If I go out and test ride the bike, a few of the spokes will relax, but not all of them. I weigh about 325 pounds! If I sling it around turns or really mash the pedals from a standing position, I can get a few more to unwind. But if I continue down that path, I'll hurt the wheels I just repaired.

You know what does allow the spokes to unwind? Me bouncing the wheel and tire on the ground like a basketball. The acceleration of the relatively low mass wheel and tire hitting the ground produces a force spike, very short but intense enough to unload the spokes and let them unwind. The amount of physical work involved when I roll up against a curb is huge compared to just bouncing the wheel, but the transient force of bouncing the wheel is actually higher, and the spokes let me know that with a distinctive sound.

That is why the hub of a sus bike sees harder accelerations than the one on a rigid bike. It moves farther, faster, and it starts & stops more abruptly. The structural forces transmitted through the hub are less, but the inertial loads on the hub are more. Structural parts of the hub (flanges, shell, sidecovers, bearings, axle) have to withstand both transmitted and inertial loads, but nonstructural parts only see the inertial loads.

Chalo

 

[TiagoSantos]

I think others have made better arguments as why you are wrong than I can. Still, you keep saying a suspended wheel travels further - hmm. If the wheel hits a bump, it will travel just enough to clear the bump, not more. If you hit it hard enough to bounce off the bump, I fail to see how hitting it on a hard tail would be any smoother, or less of a bounce - rider technique notwithstanding. We're not comparing good riders in hard tails vs idiots in Walmart FS bikes.

Sorry, but I think your clear bias against full suspension bikes is clouding your judgement.

OT, but your example of dutch people riding hardtails has nothing to do with my argument or the thread. Obviously hardtails are cheaper, easier to maintain. Those bikes you pointed to are also not riding around at +30mph. I understand gimmicks and marketing, but some things have a clear purpose - otherwise we'd all be riding fixies.

 

[Chalo]

I think others have made better arguments as why you are wrong than I can. Still, you keep saying a suspended wheel travels further - hmm. If the wheel hits a bump, it will travel just enough to clear the bump, not more.

The ratio between what's taken up by the tire and what's taken up by the suspension is different. If the suspension is softer than the tire (and it always is), then the suspension moves more. If the tire is softer than a rigid frame (and it always is), then it moves more.

Whatever compliance occurs in the tire subtracts both depth and onset rate from the hub motor's reaction to a bump. But in order to get the tire working deeply, something has to be pressing hard against it. Suspension is designed to do the opposite.

The question wasn't "which is better?", but rather which is rougher on a hub motor. I've made my case to anyone who's willing to think with his brain instead of what his suspended butt tells him. His butt is getting a very different story than the hub at the other end of the swingarm.

 

[mvly]

You're still conflating structural forces and accelerations.

Force = Mass*Acceleration

Structural forces only matter to the structural elements of the bike, for instance the bearings as you point out. But the structural parts of the bike are designed to tolerate those forces. Transient peak forces on the structural parts of the bike could be higher for either bike, depending on many factors of the surface and the suspension's characteristics.

"Transient peak forces on the structural parts of the bike could be higher for either bike" ---> Now you are talking. Particularly the hard-tail.

In many cases, the structural peak forces on a rigid bike will be higher than that of a sus bike.

Yup that is what everyone here is telling you.

And the structural force peaks will almost always be longer in duration (rider "landing" on bike vs. wheel extending and briefly smacking on the ground).

For which bike? I would say the full suspension. But keep in mind what you said before.

There is more work (F * D) in the high stress level regime of those unsuspended hits, even if the transient peaks are just as high for the sus bike.

I am not convince. Work = energy. And law of conservation of energy say in both cases, the energy dissipated from the transaction is equal. I am not convince the transient peaks are just as high for sus bike. You said yourself before "the structural peak forces on a rigid bike will be higher than that of a sus bike."

So if you want to bend a bike, use a rigid one. But that's not what I'm talking about.

Not sure what you mean here. I would much rather bend a sus bike. It's much easier. LOL.

The magnets in the motor are not structural. They're not in the force path. Same with wires, halls, plugs, pass-throughs, printed circuits and other critical bits that are not part of the bike's structure. The forces that will cause a magnet to unstick, a wire to fatigue and break, or an electrolytic capacitor to bust one of its leads, are strictly due to acceleration (not in the vehicular sense, but in the physics sense).

I think you mean vibration which are impulses with opposite signs in rapid succession.

The hub of a sus bike sees higher and more frequent acceleration forces because it moves around more. There's more shock and vibration in the unsuspended parts of a suspended vehicle than in any part of an unsuspended vehicle on the same course.

Right... But compare for me the forces of between those. I mean which would you prefer? I whack you with a inflatable toy hammer a hundred times. Or I use a real hammer and whack you only ONCE. I would go with the former easily!

And the hub is not suspended.

So you are saying if the hub was suspended it would be better? hummm this seems so much similar to having a sus bike. Instead of have the hub suspended, we just have the thing holding the hub suspend.

As an illustration of the forces I'm talking about, consider this. When I build or repair a spoked wheel, I get the spokes good and tight-- always at least 100kgf of tension on the spokes of the tighter side, but sometimes more. Friction in the spoke nipples and rim holes leads to a residual twist in each spoke that I can only partly remove by backing up a little when I tighten them. Each time of the spokes unwinds, there is a little "tick" or "ping" sound as it releases.

Sounds to me you are using inertial to your advantage. Once you can't tight anymore and try to apply torque on the spoke, it will not give. However if you loosen a bit and then twist again, the momentum, in some cases, is enough to push you pass the initial stop position.

And you can only get it to release by applying a big enough load to the rim that the spoke's tension drops low enough for it to unwind. If I go out and test ride the bike, a few of the spokes will relax, but not all of them. I weigh about 325 pounds! If I sling it around turns or really mash the pedals from a standing position, I can get a few more to unwind. But if I continue down that path, I'll hurt the wheels I just repaired.

Not sure how this relates.

You know what does allow the spokes to unwind? Me bouncing the wheel and tire on the ground like a basketball. The acceleration of the relatively low mass wheel and tire hitting the ground produces a force spike, very short but intense enough to unload the spokes and let them unwind.

Yup you just prove our point. The impulse are deforming the threads to a point to allow you to loosen them. Think of the toy hammer vs the real hammer example. Do you think soft bounces will get the spokes to unwind?

The amount of physical work involved when I roll up against a curb is huge compared to just bouncing the wheel, but the transient force of bouncing the wheel is actually higher, and the spokes let me know that with a distinctive sound.

Yup work and power are totally different beast. There is definitely more work done when you roll up against the curb than bouncing the wheel. And yes the transient force is much higher on the bouncing the wheel. Hurray! you just proved our point.

That is why the hub of a sus bike sees harder accelerations than the one on a rigid bike.

Nope. Everything you said before supports the opposite.

It moves farther, faster, and it starts & stops more abruptly.

which part? Now tell me about the hard-tail and how it moves.

The structural forces transmitted through the hub are less, but the inertial loads on the hub are more.

I think this was the point of the thread. The guy was asking if it's better for the hub to be on sus vs hard-tail. You said here the force through the hub is less! Ummm. If you think about it a bit, the inertial load on the hard-tail is actually more. You have more mass to move.

Structural parts of the hub (flanges, shell, sidecovers, bearings, axle) have to withstand both transmitted and inertial loads, but nonstructural parts only see the inertial loads.

Yup again this is the point of the thread. The bearings has to withstand the transmitted forces and it is less as you said for the sus bike. I don't think it needs to withstand inertial loads. Because inertial loads has nothing to do with how long the bearings will last. Its a property of the object. It it does not have to withstand itself. More mass more inertial loads.

Chalo, sounds like you are agreeing with us without explicitly saying it. In my books, this is good enough for me.

 

[Chalo]

You're being dense.

The suspension bike allows the seat to move up and down less because the hub moves up and down MORE. If you can't grasp the other implications of that, you're just out of your depth in this discussion.

The question was about the hub, not the parts of the bike above the suspension components.

 

[shock]

Yes. And the hub moving more is a GOOD thing. When compressed, the hub is moving a swingarm & damper, as opposed to moving the entire bike+rider+batteries. Just because one likes hardtail bikes better, does not disqualify them from the laws of physics. Suspension becomes more and more relevant as weight and speed increases in any vehicle, not only in part wear but in handling characteristics. Can you imagine if cars had no suspension? They would literally rattle apart, and wheel hub bearing replacement would be required every oil change. To pun Romney; You're entitled to your own motorized hardtail, but you're not entitled to your own facts.

 

[TiagoSantos]

The hub moves more because in a rigid bike the tire deflects? Hmm.. I'd hazard a guess that the very small difference in travel over a big enough bump for this conversation to matter, might be offset by the shock's dampening. If acceleration is the relationship between a change in velocity in a certain measure of time, a decent shock will ensure the time delta is big enough to compensate for any minuscule difference in tire deflection. By the way, what do you think the spring rate of a normal bike tire is? And do you really think the tire will only deflect on a full suspension bike once the shock bottoms out?

Some anecdotal evidence for you - I rode bmx bikes for over a decade. We're pretty good at absorbing impacts with our bodies. I can't tell you how many taco'd wheels and broken hubs I've seen on bmx bikes that would have been fine on a suspended bike. Yeah, yeah, that's a structural load, versus an acceleration. You hold on to that thought if it makes you happy