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  1. #1
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    Trade-offs in anti-squat suspension theory

    Please critique this perception of full suspension anti-squat if you find this interesting.

    I guess I may have been using the term "squat" incorrectly. I've always considered that when a full suspension frame pitch rotated rearward from a compressing rear suspension, whether or not the front end extended, this was “squat”. I guess this action is technically called "wallow". Squat is when the CM compresses overall when the front suspension doesn’t extend enough to compensate for the rear suspension’s compression. The attached picture below describes how the anti-squat line is determined. (Thanks to Strong-Like-Bull for the graphic.)

    For example if the CM is half way between the wheels there is no squat when the rear suspension compresses 1 inch it the front suspension extends 1 inch and the CM remains at the same height. However, due to the practice of putting the seat quite rearward of wheel-base center, if the rear suspension compressed 1 inch and the front extended the same, then the CM would wallow rearward and compress (squat) significantly.

    It's amazing to me that no one could point this definition of squat clearly in all these years of discussion I was involved in before. Maybe it should have been obvious.

    Springs alone when coasting prevent squat unless there is a rolling surface (road or trail) induced compression of the CM when not pedaling or braking.

    The Instant Center of Forces (ICF, also called the Pole of Moments) is where the drive-line such as a chain-line crosses the swingarm-line. A line drawn from the rear tire patch though the ICF is the net geometric acceleration reaction direction of any vehicle.

    When the ICF is aligned with the anti-squat line, then the front suspension extends while the rear suspension squats, rotating the frame around a CM that remains at the same height (no matter where the CM was located horizontally). There is still acceleration wallow unless the CM is directly above the front wheel when ICF is aligned with the anti-squat line.

    So only when an ICF is out of alignment with that anti-squat line will the rider input produce extension or squat to the CM.

    I think this is a very non-intuitive definition of squat.

    It is my experience that more than just a little wallow destabilizes confidence inspiring handling, traction consistency, and braking power.

    Some varying amount of extension consistent with driving torque can counteract frame wallow for crisper acceleration while pedaling (like a runner leans low and forward at the start blocks and rises in height at a regressive rate while accelerating until obtaining full speed running height). On a bike that accelerating CM extension counters wallow without anti-wallow help from damping, but at the sacrifice of some bump compliance while accelerating that is translated into increased suspension kickback to the frame and/or pedals.

    Furthermore, if the suspended CM (mostly rider weight) was able to spin the pedals in perfect circles to accelerate, I think that a line from the rear wheel ground patch, inline with the CM, produces reaction where the CM plus rear and front suspension all extend the same amount (“perfectly” stable extension while accelerating, with no wallowing.). If the rider, who is 80 – 90 % of the suspended mass, is leaned forward pressing mostly downward on the pedals in line with the ICF line, in a commonly normal pedal cadence, then there can be nearly 80- 90 % counter-extension bio-pace, so there would be nearly no extend bob either.

    However, 100% stable anti-bob (no squat or wallow), in other words 100% bio-pace, would have rigid ride characteristics. So for bump compliance travel compression, some stable frame tolerant amount of squat is necessary to avoid noticeable reverse pedal cadence kickback (to avoid greater than 100% bio-pace). Actually some digressive rate of bio-pace as travel is compressed is more stable at the frame and more pedal spin compliant than hardtail like 100% bio-pace. Therein lies the elegance of fine-tuning the travel path sensitive dynamics to balance and hide the trade-offs in stability verses pedaling efficiencies into a bike’s suspension so that it simply rides great in a wide range of conditions.

    “Stable Platform shocks”, digressive rate compression damped shocks aid the range of pedaling stability for more softly sprung longer travel suspension, and hide the awkwardness of less than elegantly tuned geometry in more firmly sprung shorter travel suspension.

    Thanks for any critiques of this perception.

    - ray
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  2. #2
    The Ancient One
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    A critique in blue

    I will critique the first half of this. The second half gives me a headache.
    Quote Originally Posted by derby
    Please critique this perception of full suspension anti-squat if you find this interesting.

    I guess I may have been using the term "squat" incorrectly. I've always considered that when a full suspension frame pitch rotated rearward from a compressing rear suspension, whether or not the front end extended, this was “squat”. I guess this action is technically called "wallow". Squat is when the CM compresses overall when the front suspension doesn’t extend enough to compensate for the rear suspension’s compression. The attached picture below describes how the anti-squat line is determined. (Thanks to Strong-Like-Bull for the graphic.)

    No, you were using the term "squat" correctly. It means that the rear suspension compresses from acceleration or chain torque. It doesn't matter what happens at the front. "Wallow", as I use it at least, means overreaction of the suspension to a bump or dip.

    The graphic shown depicts a 100% anti-squat line for steady state acceleration. You're not going to get steady state acceleration from pedaling, but if you could, the bike shown would not compress at the rear and would rise in the front, thereby raising the CM.


    For example if the CM is half way between the wheels there is no squat when the rear suspension compresses 1 inch it the front suspension extends 1 inch and the CM remains at the same height. However, due to the practice of putting the seat quite rearward of wheel-base center, if the rear suspension compressed 1 inch and the front extended the same, then the CM would wallow rearward and compress (squat) significantly.

    The situation you describe where the CM remains at the same height requires that the rear squat and the front lift the same amount when the CM is in the middle of the wheel base. This is the most energy-efficient way to set up a vehicle. If the CM is exactly in the middle, and if the spring rate and damping rate at front and rear are the same, then no vertical movement of the CM occurs when you have zero anti-squat. People who sell 4-bar linkage kits for drag racing your muscle car will tell you to move the linkage from ~100% anti-squat for racing to 0% for regular driving by making the linkage parallel and level. On a chain drive, zero anti-squat means the line from contact patch through pole of moments or instant centre of forces coincides with the ground line.

    If the CM is more to the rear of the wheelbase, then some anti-squat would be required. For example if the weight distribution is 62.5% to the rear and 37.5% to the front then 25% anti-squat would be required for no vertical movement of the CM. The slanting line in your graphic would have to intersect the vertical line through the front hub 25% of the way up.


    It's amazing to me that no one could point this definition of squat clearly in all these years of discussion I was involved in before. Maybe it should have been obvious.

    No one pointed it out because no one uses that definition. I have pointed out several times that the most energy efficient setup is one that lets the rear end squat just enough to compensate for the rise at the front so that the CM remains level.

    Springs alone when coasting prevent squat unless there is a rolling surface (road or trail) induced compression of the CM when not pedaling or braking.

    The Instant Center of Forces (ICF, also called the Pole of Moments) is where the drive-line such as a chain-line crosses the swingarm-line. A line drawn from the rear tire patch though the ICF is the net geometric acceleration reaction direction of any vehicle.

    It has to be a chain line, or possibly a belt line; the concept is not used for drive shafts. The line through the ICF creates what is called the chain pull angle. The greater the angle--the more it deviates from the ground line--the more torque on the suspension. The torque can be pro-squat if the angle is below the ground line.

    When the ICF is aligned with the anti-squat line, then the front suspension extends while the rear suspension squats, rotating the frame around a CM that remains at the same height (no matter where the CM was located horizontally). There is still acceleration wallow unless the CM is directly above the front wheel when ICF is aligned with the anti-squat line

    This is all wrong. I explained this above. For steady state acceleration (like on a motorcycle with the throttle held in one position) the situation shown in Strong Like Bull's graphic would result in no squatting at the rear and rising in the front.

    So only when an ICF is out of alignment with that anti-squat line will the rider input produce extension or squat to the CM.

    I think this is a very non-intuitive definition of squat.

    It is my experience that more than just a little wallow destabilizes confidence inspiring handling, traction consistency, and braking power.

    Some varying amount of extension consistent with driving torque can counteract frame wallow for crisper acceleration while pedaling (like a runner leans low and forward at the start blocks and rises in height at a regressive rate while accelerating until obtaining full speed running height). On a bike that accelerating CM extension counters wallow without anti-wallow help from damping, but at the sacrifice of some bump compliance while accelerating that is translated into increased suspension kickback to the frame and/or pedals.

    Furthermore, if the suspended CM (mostly rider weight) was able to spin the pedals in perfect circles to accelerate, I think that a line from the rear wheel ground patch, inline with the CM, produces reaction where the CM plus rear and front suspension all extend the same amount (“perfectly” stable extension while accelerating, with no wallowing.). If the rider, who is 80 – 90 % of the suspended mass, is leaned forward pressing mostly downward on the pedals in line with the ICF line, in a commonly normal pedal cadence, then there can be nearly 80- 90 % counter-extension bio-pace, so there would be nearly no extend bob either.

    However, 100% stable anti-bob (no squat or wallow), in other words 100% bio-pace, would have rigid ride characteristics. So for bump compliance travel compression, some stable frame tolerant amount of squat is necessary to avoid noticeable reverse pedal cadence kickback (to avoid greater than 100% bio-pace). Actually some digressive rate of bio-pace as travel is compressed is more stable at the frame and more pedal spin compliant than hardtail like 100% bio-pace. Therein lies the elegance of fine-tuning the travel path sensitive dynamics to balance and hide the trade-offs in stability verses pedaling efficiencies into a bike’s suspension so that it simply rides great in a wide range of conditions.

    “Stable Platform shocks”, digressive rate compression damped shocks aid the range of pedaling stability for more softly sprung longer travel suspension, and hide the awkwardness of less than elegantly tuned geometry in more firmly sprung shorter travel suspension.

    Thanks for any critiques of this perception.

    - ray
    More on steady state acceleration and pedaling: Everything I've said so far comes straight out of various text books. The Milliken book on vehicle dynamics makes a point that the 100% anti-squat formulas only apply during steady state acceleration when the whole vehicle can be considered as acting like a rigid body as far as its reaction to the acceleration is concerned. This means that the CM is considered to be reacting horizontally backwards to the same force acting forward at the ground. The Milliken book makes it clear that the formula does not apply to the transition periods between deceleration or no acceleration and the steady state. But they don't give any formulas that do apply.

    So I've had to make up my own. The problem to be dealt with is suspension wind-up. This is where some of the rider's pedal force goes into compressing or extending the rear suspension instead of horizontally accelerating the CM. This is in my opinion the main source of pedaling inefficiency in FS bikes. Since most of the observed bobbing is caused not by pedal force transferred through the chain but by up and down weight shift in the act of pedaling, maximum pedaling efficiency as I define it does not mean no bobbing. It just means no bobbing caused by torque during the force transfer from ground to CM.

    The neutral force transfer situation occurs when the chain line passes through the IC and everything is aligned as in the diagram below. You can achieve neutrality with a chain line not through the IC, but the calculation is more complicated.
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  3. #3
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    Have you visited my site recently?

    For about the last year I've had a worked example up of a bike analysed both ways. The first showing the height the COM needs to be to provide no squat (no compression of the rear suspension) under acceleration. The second example shows where the COM needs to be to provide no change in height during acceleration.

  4. #4
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    Thanks

    Thanks Steve for taking all the time to comment so thoroughly. Does your drawing imply chainline is through IC too? Or does the formula apply to any gear set?

    I have a motorcycle too. I don’t understand what you mean by “steady state” acceleration. When the throttle is held in on place there is no acceleration, there is only cruising, the same as if the bike was coasting with no wind and any other friction resistance. If throttle was help in an open position just following an increase in throttle to the steady throttle position from a more closed position previously, the acceleration would become noticeably digressive-rate while the speed accelerated up to match the more open throttle position. Even without wind and friction that would be the case.

    I would consider steady state acceleration to have a constant rate of increase in speed, which would normally require a progressing-rate of power input. This seems similar to the increasing power section of the bicycle crank cycle of normal reciprocating pedaling power application when accelerating or climbing.

    The ICF includes both the extension or compression produced from accelerating the suspension from the ground traction point with swingarm pivot center extending when above parallel, or compressing below, parallel with the ground line, plus the extension or compression produced by drive-line torque between the frame and compression when behind the wheel or extending when drive line is in front of the wheel. “Chain-pull” is one type of drive line, there is no reason I can think of that the ICF cannot be used for any suspension plus any drive-line analysis.

    It makes clear sense to me now that the anti-squat line in the graphic is the line that when aligned with the ICF will produce acceleration which lifts the front suspension enough to offset the compression of the rear suspension, where the sagged CM between the wheels only rotates (wallows), but doesn’t rise or fall vertically (doesn’t extend or squat).

    When the CM rotates only without vertical change on a smooth service is neutrally balanced on the springs to comply evenly to bump compression and dip extension. All seems simple enough there.

    The problem with steady height CM rotation is the whole suspended-mass rotates with the CM, including the frame. The seat rotates rearward and the cranks rotate forward with the rider wallowing aboard when seated. When the seated rider rotates rearward the vertical alignment of the rider’s shoulder above the knees above the pedals is altered. The wallowing of the rider’s power alignment reduces maximum power to only the fleeting moments when the rider is balanced over the pedals. So a seated rider compensates by bobbing his upper body forward in rhythm with each power downstroke to the pedals.

    A well-balanced and efficient pedaling full suspension bike with little wallow and little squat has a rider aboard who does very little vertical lunging while seated climbing, and very little handlebar pulling except on the very steepest slopes, the rider only moves side to side balancing over each pedal.

    The standing while pedaling rider introduces another consideration of balance tradeoffs that few designs handle as well as when the rider is seated.

    When the ICF is below the anti-squat line there is not only CM rotation (wallow), the CM also dips (squats) during acceleration.

    Steve’s drawing logically shows a bike that while the chain-line passes through the IC, so that the ICF is at the IC (and well in front of the anti-squat with free wallow line), produces some significant amount of CM wallow and squat if used without platform damping reducing the severity. A very low granny gear would likely move the ICF back behind the anti-squat line to eliminate squat and wallow when accelerating. If this picture is an example of ITC, it is exactly the effect I experienced when test riding. ICT designs produce significant squat and wallow without taming by platform shocks in my experience. ICT efficency requires the low CM of a light rider pulling on bar ends. (Pulling on the bar ends makes the pedal stroke a little more horizontal and bio-paces the CM more forward while pulling.)

    I've added a modified copy of Steve's graphic showing where the ICF would be for no squat of the frame and CM. It looks like that could occur on this suspension example in some lower granny gear set.

    The last four or five paragraphs of my original post explains need for counter wallow alignment of the ICF behind the anti-squat line to produce an efficient pedaling bike without adding on significantly firm platform damping.

    The more elegant designs I've ridden have nearly all acceleration gears with an ICF aligned behind the anti-squat line when travel is near sag, but as travel compresses below sag the ICF point migrates forward and/or downward to locations below the anti-squat line to counteract the bump induced activation of kickback. This will also produce a more steady pedal spin through bumpy conditions.

    - ray
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    Last edited by derby; 02-15-2004 at 11:06 AM.

  5. #5
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    Can you explain?

    I agree with your conclusion on the left. The Instant Center of Forces (ICF) of the drive-line force and suspension force resistance to acceleration from the ground, is right on the anti-squat line. The CM will only wallow a little, but not squat when pedaling.

    But the CM on the right will squat and wallow quite a lot, without taming from platform shocks. The ICF is well below the line of anti-squat (with free CM wallow). Which means there is much less than 100% anti-squat.

    I don't understand what the perpendicular blue lines from the red ICF line from ground are refering to in the second picture.

    I've copied your web page graphic in. And in a second copy I added the coordinates for the "anti-squat" line in light blue and the ICF is circled in red (which happens to be at the suspension IC at the moment pictured).

    - ray
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    Last edited by derby; 02-15-2004 at 09:29 AM.

  6. #6
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    I'm not sure if there's something wrong with your post but it appears that the right side has been chopped off.

    Your comment about the diagram on the right needing a stable platform shock is interesting. That diagram is actually a diagram of the bighit I rode for three years. Far from needing a stable platform shock to prevent wallow and squat, it was one of the best pedalling bikes I've ridden. Acceleration wise on par with my 5-spot and on paper similar to an ellesworth ID.

    I've yet to find a bike which complies with the diagram on the left, that is having a suspension geometry with enough antisquat to satisfy the zero squat criteria. With a 24" wheel (and revised suspension geoemetry) on my bighit I was close but the loss in handling from the steeper angles made the bike less satisfying to ride and too twitchy.

    I think the perpendicular blue lines are showing the fore/aft position of the COM, but right now I can't get to the pics to check.

  7. #7
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    I guess I was a little quick in my assessment of the second pic from your site, the one with the CM up at a more normal height. The gear set used is a huge factor in how a suspension reacts to pedaling. In the lower granny gears the chainline should cross the swingarm line just behind or very nearly on the CM inertia’s anti-squat diagonal light blue line I added, to produce only some mild frame/CM wallow movement when pedaling that good damping should keep tame, but no squat. In the middle ring there would be some mild wallow and squat, but mild due to the lesser pedaling acceleration toque in higher gears, and in the big ring higher gear pictured the pedaling torque would be rather mild and damping should keep bob to a low level. Platform shocks would nearly eliminate the mild squat and bob in the bigger two rings.

    The picture on the left with the very low impossible height CM, would jack up terribly with each pedal stroke in the granny gears but ride with no squat (or jack) in the high gear pictured.

    I thought the Big Hit would have the common Horst link snappier pedaling stability rather than the bob and wallowing of an Id. ICT is virtually a medium-low monopivot smooth pedaling design, but rather unstable in action without significant compression platform damping help. Following a friend on his Id with a fast damped normal Vanilla-R it pedal bobbed half its travel in the middle ring, and bobbed over an inch pedaling up steep climbs. The rider, who is very fast and a strong climber, preferred the much smoother ride of a non-platform shock and was used to the roller-coaster ride during pedaling. He has since replaced it with a 5-Spot and raves at the much improved handling using a very similar fast damped Vanilla shock (probably mostly due to the proper height BB and slacker fork angle). You are about 40 pounds lighter than me too, so you don't swing as much weight around so high up as me when riding a less stable pedaling bike.

    - ray

  8. #8
    Old Fart at Play
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    So which bike should I get,...

    ... the one with the blue fork, or the one with the cool swing link fork (kind of reminds me of my old Girvin)? I don't know squat about wallow.

  9. #9
    The Ancient One
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    Quote Originally Posted by derby
    Thanks Steve for taking all the time to comment so thoroughly. Does your drawing imply chainline is through IC too? Or does the formula apply to any gear set?

    The drawing, as I said, assumes the chain line is through the IC. You can achieve the same balanced effect with another chain line but the calculation is more complicated. (As I also said.) At the bottom I am going to show diagrams of the Truth and Tracer that will indicate that they are virtually identical when my formula is applied at the 25 mm sag point. But the chain line on the Tracer passes over the IC, so a vector correction is necessary to get the force acting around and through the IC. That is indicated in the diagram. You can't use the pole of moments as a rotation center. I use the IC. Don't argue against it any more. I'm not going to change, so live with it. Believe what you will but accept that this is my analysis.

    I have a motorcycle too. I don’t understand what you mean by “steady state” acceleration. When the throttle is held in on place there is no acceleration, there is only cruising, the same as if the bike was coasting with no wind and any other friction resistance. If throttle was help in an open position just following an increase in throttle to the steady throttle position from a more closed position previously, the acceleration would become noticeably digressive-rate while the speed accelerated up to match the more open throttle position. Even without wind and friction that would be the case.

    Steady state means a constant rate of force at the ground. The acceleration rate will decrease with increased drag from wind until a constant speed is reached. Without wind or or any other kind of drag the speed would increase indefinitely until the speed of light was reached, by which time the mass would be infinite. Below I'm going to show a graph from a drag racing software site. It shows force at the ground contact point in terms of time. You'll notice a sharp ramping up for the first tenth of a second or so and more or less level force after that. That sharp ramping represents the transition or non-steady state phase. Drag racers with 100% anti-squat will show a brief jacking of the rear during that transition phase. It enhances traction but wastes energy. They don't care about wasted energy. Bicyclists do. That's why my formula calls for less than 100% anti-squat for maximum pedal efficiency.


    I would consider steady state acceleration to have a constant rate of increase in speed, which would normally require a progressing-rate of power input. This seems similar to the increasing power section of the bicycle crank cycle of normal reciprocating pedaling power application when accelerating or climbing.

    The ICF includes both the extension or compression produced from accelerating the suspension from the ground traction point with swingarm pivot center extending when above parallel, or compressing below, parallel with the ground line, plus the extension or compression produced by drive-line torque between the frame and compression when behind the wheel or extending when drive line is in front of the wheel. “Chain-pull” is one type of drive line, there is no reason I can think of that the ICF cannot be used for any suspension plus any drive-line analysis.

    You clearly don't understand the pole of moments theory. Below I will include a diagram explaining it. It only applies to chains because it involves the pulling together of axle and frame that only occurs with chains. It also assumes that the suspension is affected by the thrusting force at the ground, not at the axle. In effect the axle is not a pivot as far as the reaction force at the ground is concerned.

    It makes clear sense to me now that the anti-squat line in the graphic is the line that when aligned with the ICF will produce acceleration which lifts the front suspension enough to offset the compression of the rear suspension, where the sagged CM between the wheels only rotates (wallows), but doesn’t rise or fall vertically (doesn’t extend or squat).

    When the ICF or pole of moments lies on the 100% anti-squat line then the rear end will neither squat nor jack during steady state acceleration. Lose the concept of wallow. It just means the rear end squats and you don't like it.

    When the CM rotates only without vertical change on a smooth service is neutrally balanced on the springs to comply evenly to bump compression and dip extension. All seems simple enough there.

    The problem with steady height CM rotation is the whole suspended-mass rotates with the CM, including the frame. The seat rotates rearward and the cranks rotate forward with the rider wallowing aboard when seated. When the seated rider rotates rearward the vertical alignment of the rider’s shoulder above the knees above the pedals is altered. The wallowing of the rider’s power alignment reduces maximum power to only the fleeting moments when the rider is balanced over the pedals. So a seated rider compensates by bobbing his upper body forward in rhythm with each power downstroke to the pedals.

    A well-balanced and efficient pedaling full suspension bike with little wallow and little squat has a rider aboard who does very little vertical lunging while seated climbing, and very little handlebar pulling except on the very steepest slopes, the rider only moves side to side balancing over each pedal.

    The standing while pedaling rider introduces another consideration of balance tradeoffs that few designs handle as well as when the rider is seated.

    When the ICF is below the anti-squat line there is not only CM rotation (wallow), the CM also dips (squats) during acceleration.

    Steve’s drawing logically shows a bike that while the chain-line passes through the IC, so that the ICF is at the IC (and well in front of the anti-squat with free wallow line), produces some significant amount of CM wallow and squat if used without platform damping reducing the severity. A very low granny gear would likely move the ICF back behind the anti-squat line to eliminate squat and wallow when accelerating. If this picture is an example of ITC, it is exactly the effect I experienced when test riding. ICT designs produce significant squat and wallow without taming by platform shocks in my experience. ICT efficency requires the low CM of a light rider pulling on bar ends. (Pulling on the bar ends makes the pedal stroke a little more horizontal and bio-paces the CM more forward while pulling.)

    I've added a modified copy of Steve's graphic showing where the ICF would be for no squat of the frame and CM. It looks like that could occur on this suspension example in some lower granny gear set.

    I've added slanted lines to the two diagrams of Truth and Tracer below to show the line through ICF in a 22/34 gear. They are the uppermost lines. You get about 100% anti-squat (for steady state acceleration, which doesn't occur on bicycles) in both cases. The difference between the designs at sag is miniscule. As you move farther into travel, the Tracer squats more or extends less for any given gear.

    The last four or five paragraphs of my original post explains need for counter wallow alignment of the ICF behind the anti-squat line to produce an efficient pedaling bike without adding on significantly firm platform damping.

    The more elegant designs I've ridden have nearly all acceleration gears with an ICF aligned behind the anti-squat line when travel is near sag, but as travel compresses below sag the ICF point migrates forward and/or downward to locations below the anti-squat line to counteract the bump induced activation of kickback. This will also produce a more steady pedal spin through bumpy conditions.

    - ray
    Good luck.
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  10. #10
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    Forgive me for not understanding your conclusions.

    I’ve never thought of the ICF (or Pole of Moments) as a rotation center. Nothing rotates around the ICF.

    The ICF is an alignment point to compare in angle with the rear wheel ground contact point and the gound line. Your drawing at the bottom of the ICF (PM) is how I see it when using a chain-drive line. The ICF line from the ground is the net force direction of rear chain-drive and suspension from the ground (when ICF is in front of the driven wheel).

    The ICF angle is handy to compare in alignment with the suspended CM anti-squat force line.

    The anti-squat force (ASF) angle is the direction of acceleration force to maintain the FULLY suspended CM at its height, so the CM doesn’t squat lower or extend higher.

    The fleeting moment when the ICF angle = ASF angle, then there is no CM squat or extension when accelerating, steady state or not. Squat rotates around the combination of both wheel’s ground contact points modified of course by the suspension paths.

    Wallow rotates around the suspended CM. The pitch change of wallow depends on the amount of increase or decrease in acceleration. Once a steady state rate of acceleration was achieved, then the oscillation of wallow ceases and a constant amount of slackened pitch from static sag would be maintained. When acceleration rate is decreased the pitch will settle (wallow) forward until coasting when pitch becomes the same as static sag. I think you would agree since you were only considering steady state (which doesn’t ever happen on a bicycle, but may be possible with mechanical or computer controlled acceleration with specially prepared motor vehicles.).

    And now I hear you are saying that less than 100% anti-squat is more efficient. Since you don’t qualify or explain this conclusion I assume you are referring to pedaling in very bumpy terrain.

    There is no optimum best efficiency trade-off between anti-squat and bump compliance, it depends on the rider’s interest and terrain. Greater than 100% anti-squat is most efficient on smooth terrain such as pavement. Less than 100% anti-squat, sometimes much less, is more efficient on very bumpy terrain. So it depends on what you want to optimize. And all designs change in percent of squat during travel. The trick is to optimize the amount of squat (or extension) most desirable during each area of the travel use.

    Pedaling wallow is just as inefficient, if not more inefficient, than bob (squat). When pedaling combines both squat and wallow the pedaling becomes very inefficient, rocking and bouncing the rider around so there is irregular and reduced pedaling power. The use of slower damping than required for coasting really helps reduce such noticeable pedaling inefficiencies.

    Any particular design may be more efficient than another in a limited range of terrain. Most experts have found that the classic Horst link has best-optimized pedaling extension and squat trade-offs and actively reduces wallow in the widest variety of terrain, without the aid of more damping than required for stable coasting.

    - ray

  11. #11
    The Ancient One
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    Quote Originally Posted by derby
    Forgive me for not understanding your conclusions.

    I’ve never thought of the ICF (or Pole of Moments) as a rotation center. Nothing rotates around the ICF.

    Actually at any given instant the axle can be said to be rotating around the ICF, or any other point along the swing arm line, for that matter.

    The ICF is an alignment point to compare in angle with the rear wheel ground contact point and the gound line. Your drawing at the bottom of the ICF (PM) is how I see it when using a chain-drive line. The ICF line from the ground is the net force direction of rear chain-drive and suspension from the ground (when ICF is in front of the driven wheel).

    I don't understand this at all.

    The ICF angle is handy to compare in alignment with the suspended CM anti-squat force line.

    The anti-squat force (ASF) angle is the direction of acceleration force to maintain the FULLY suspended CM at its height, so the CM doesn’t squat lower or extend higher.

    Absolutely wrong. In classical orthodox motorsports suspension theory, 100% anti-squat during steady state acceleration means that the rear shock absorber does not compress from the load shift to the rear caused by the acceleration. The front end could actually rise in the air, and in drag racing it frequently does, and the rear shock still does not compress. The CM of course then must rise, changing the calculation, but the pivot point and ICF also rise. One thing that never happens with 100% anti-squat is for the rear shock to compress. And the rear shock would have to compress for the CM to stay at the same height, because the front end must rise.

    The fleeting moment when the ICF angle = ASF angle, then there is no CM squat or extension when accelerating, steady state or not. Squat rotates around the combination of both wheel’s ground contact points modified of course by the suspension paths.

    I feel a headache. . .

    Wallow rotates around the suspended CM. The pitch change of wallow depends on the amount of increase or decrease in acceleration. Once a steady state rate of acceleration was achieved, then the oscillation of wallow ceases and a constant amount of slackened pitch from static sag would be maintained. When acceleration rate is decreased the pitch will settle (wallow) forward until coasting when pitch becomes the same as static sag. I think you would agree since you were only considering steady state (which doesn’t ever happen on a bicycle, but may be possible with mechanical or computer controlled acceleration with specially prepared motor vehicles.).

    coming on.

    And now I hear you are saying that less than 100% anti-squat is more efficient. Since you don’t qualify or explain this conclusion I assume you are referring to pedaling in very bumpy terrain.

    Orthodox suspension theory says that the most efficient suspension setup is where the CM stays level. If the CM is right in the middle of the wheel base, and if the travel and shock rates at front and rear are the same, then the most efficient setup under steady state acceleration is 0% anti-squat. My pole of moments diagram gave one example of 0% anti-squat. A more likely scenario would be if chain line, swing arm line and ground line are all parallel. What I was talking about is my own theory of suspension windup during transition from deceleration to acceleration. Keep in mind that the pedal force begins to increase while the bike is still decelerating, under the influence of drag, from the last pedal stroke. So initially acceleration is not even yet occurring. But the increasing force at the wheel can move the suspension instead of pushing the CM forward. That's what wastes rider energy and that's what the a'/b' = a/b formula is referring to.

    There is no optimum best efficiency trade-off between anti-squat and bump compliance, it depends on the rider’s interest and terrain. Greater than 100% anti-squat is most efficient on smooth terrain such as pavement. Less than 100% anti-squat, sometimes much less, is more efficient on very bumpy terrain. So it depends on what you want to optimize. And all designs change in percent of squat during travel. The trick is to optimize the amount of squat (or extension) most desirable during each area of the travel use.

    Pedaling wallow is just as inefficient, if not more inefficient, than bob (squat). When pedaling combines both squat and wallow the pedaling becomes very inefficient, rocking and bouncing the rider around so there is irregular and reduced pedaling power. The use of slower damping than required for coasting really helps reduce such noticeable pedaling inefficiencies.

    The amount of pitch change cause by actual acceleration on a bicycle is so small that the rider could scarcely perceive it. The acceleration levels are simply too low. It's all a question of small amounts of energy loss with each stroke adding up over time.

    Any particular design may be more efficient than another in a limited range of terrain. Most experts have found that the classic Horst link has best-optimized pedaling extension and squat trade-offs and actively reduces wallow in the widest variety of terrain, without the aid of more damping than required for stable coasting.

    Who are these experts? I thought we were the experts.

    - ray
    So follow me, follow
    Down to the hollow,
    And there let us wallow
    In glorious mud.

  12. #12
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    Sometimes the truth hurts.

    Your PofM (ICF) illustration or any PofM that intersects the ground line, all the way to parallel swingarm and drive-line with the ground line intersecting at the ground horizon, would require a CM at the horizon for 100% anti-squat. And that is the only scenario, ICF (pofM) at ground line with CM at horizon, that could maintain constant 100% anti-squat during perfectly steady state acceleration. However that is clearly impractical.

    I'll explain further below why 100% anti-squat suspension is fleeting.

    It's likely that when rear drive-line plus suspension extension direction from the ground is the same as fully suspended CM squat inertia, there is no acceleration squat, e.g. When ICF angle of extension force = ASF compression (squat) force, then there is 100% anti-squat.

    Seems simple on the surface. However the CM is FULLY suspended. At 100% anti-squat the rear suspension plus drive-line is lifting the frame (frame rotating around the CM) along the ICF angle from the ground and aligned with the ASF line. The ICF angle of force from the ground is at an angle that is forward of the CM itself (unless CM is on the ASF line). CM on the ASF line is impractical with full suspension unless perhaps the rider is hanging on some very high rise bars climbing a really steep incline. So, other than when the CM is hanging off the bars, when the bike is accelerated with ICF angle inline with ASF the front suspension rises and the frame wallows (whether or not the rear suspension compresses).

    If the rear of the frame doesn't wallow in compression around the CM, as the front suspension extends from acceleration, then the CM rises (extends, which is the inverse of squat) with the front suspension, it wasn't 100% anti-squat. It was greater than 100% since the CM extended when accelerated, eh?.

    If the CM doesn't rise there must be wallow (if we are talking about FULL suspension). With wallow the ICF then changes (moves forward) with rear suspension compression and looses alignment with ASF. This should show that 100% anti-squat is fleeting with FULL suspension. Anti-squat is always in a transitory state.

    The trick is to balance the bio-pace of the oscillating anti-squat forces with the trade-offs required for efficient acceleration and bump compliance. So far Horst has produced the most versatile and relatively stable application of full suspension. Some riders like to bias more squat for easier pedaling bump compliance at the cost of more wallow to be slower damped, at the sacrifice of some amount of coasting bump compliance. Some riders like a bias having less squat or even some rear suspension extension for maximum rapid acceleration and climbing on smoother surfaces with fast damping for maximum bump compliance when coasting, at the cost of bump compliance and more bump kickback when pedaling.

    Test riding is the true proof of what bike works best for each individual rider.

    This seems simple enough.

    - ray

  13. #13
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    Your PofM (ICF) illustration or any PofM that intersects the ground line, all the way to parallel swingarm and drive-line with the ground line intersecting at the ground horizon, would require a CM at the horizon for 100% anti-squat. And that is the only scenario, ICF (pofM) at ground line with CM at horizon, that could maintain constant 100% anti-squat during perfectly steady state acceleration.
    My illustration was of 0% anti-squat. If you put the CM on the ground line (anywhere on it, it doesn't have to be at the horizon) then you would also have 0 squat under steady state acceleration. If you want to say that 0 is 100% of 0 you can; but really it's mathematically meaningless. If the CM is anywhere above the ground line, then there is some squat from acceleration and nothing is 0% of something, so you have 0% anti-squat.

    You're arguing stuff that is standard, orthodox suspension theory in motorsports, is generally accepted, and has been experimentally verified probably hundreds of thousands of times. And you're getting it wrong.

    Below is a picture from Cocco's motorcycle book illustrating a typical set-up for a street bike. The angle represented by the Greek letter tau is slightly smaller than the angle represented by the Greek letter sigma. Sigma is the chain pull angle. Tau is the load transfer angle. The text accompanying the picture says:

    It represents a streetbike whose chain pull angle [sigma] is slightly wider than angle [tau], so under acceleration the rear suspension will tend to rebound and lift the rear end of the motorcycle.
    100% anti-squat is when the two angles are the same. This applies to a bike in a state of accelerational equilibrium where nothing is changing as far as the forces acting on the bike are concerned (wind resistance is ignored) and the bike can be considered as a rigid body as far as the load transfer is concerned.
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    Last edited by Steve from JH; 02-19-2004 at 08:50 AM.

  14. #14
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    Just as I suspected

    You verified what I said in my previous post on the CM at ground height producing constantly 100% anti-squat when the PofM (ICF) is also anywhere on the ground line. Hey we agree on something!

    And I agree that when the PofM angle from the ground equals the CM anti-squat line there is no CM squat, and "100% anti-squat". Another agreement, or did I mis-understand what you said?

    The picture of the motorcycle is also consistent with my perspective. It is clearly greater than 100% anti-squat to avoid acceleration wallow. Slight acceleration rear suspension extension to better match the front extension is much less noticeable on the street than power modulation wallow and the resulting difficulties with already highly sensitive street handling.

    It would be interesting to see how motocross bikes are balanced with the CM. I've noticed when they are rider weight sagged about 4 inches or so, motocross bikes have a near horizontal swingarm. I suspect motocross bikes have a much lower PofM angle, probably less than 100% anti-squat for better bump compliance and more consistent traction in dirt. They have powerful smooth motors and long and rather slow damped travel to control wallow for smooth pitch changes.

    On bicycles we must be much more efficient with our designs or simply cover up acceleration and handling inefficiencies with slower damping.

    - ray

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    Omg!

    With the length and detail of this thread how do you guys find time to ride ? I'm just glad there's people like you that understand this stuff so that people like me can take advantage of it when we ride.

  16. #16
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    You verified what I said in my previous post on the CM at ground height producing constantly 100% anti-squat when the PofM (ICF) is also anywhere on the ground line. Hey we agree on something!

    No, I said that zero divided by zero is mathematically meaningless. What you would have is no squat or jack on the suspension from chain torque and no squat from acceleration. You ain't got nothin.

    The picture of the motorcycle is also consistent with my perspective. It is clearly greater than 100% anti-squat to avoid acceleration wallow. Slight acceleration rear suspension extension to better match the front extension is much less noticeable on the street than power modulation wallow and the resulting difficulties with already highly sensitive street handling.

    You need to avoid this concept of "wallow". It's used to mean what happens when you hit a bump or dip and you have either too soft a spring, too little compression damping, or both. What happens with 100% anti-squat and an accelerating motorcycle is that the whole bike rotates backward around the ground contact point, extending the front suspension and lifting the CM some. Do you ever notice any significant extension of the front while pedaling? I don't. I don't think these steady state acceleration formulas apply very well to pedaling a bike. The acceleration is just too low.

    Road racing motorcycles generally have quite a lot of lift or jack in the back--more than in the one pictured--so as to keep the pitch of the frame at the same level as the front rises. That keeps the steering angles the same. Formula racing cars, on the other hand, only have about 30% or so of anti-squat, I have heard.

    Dirt bikes definitely use extending rear suspensions to aid in jumping and landing jumps. But what extends a suspension with the wheel spinning freely involves a different calculation. Basically the bigger the angle between chain line and swingarm line the more extension. The ground doesn't figure into it.

    As I have said before, I don't think these anti-squat concepts apply very well to pedaling a bike, but the principles that lie behind them do. I think the critical concern is energy efficiency because the rider is so weak compared to an engine. And I think the best energy efficiency will occur with my a'/b' = a/b formula. It deals with the transition from deceleration to acceleration that occurs with each pedal stroke (particularly when climbing) and the idea is to avoid diverting pedal energy into suspension movement instead of acceleration during the force transfer that causes the transition. The motorsports anti-squat concepts are dealing with how to counter and how much to counter the load shift to the rear that results from an already established acceleration.

  17. #17
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    You are probably right about the motocross bikes needing something greater than 100% anti-squat to be able to jump without doing a reverse flip. (Although reverse flips are becoming the latest standard in X-Game extreme jumping. Nuts! Those x-riders are setting their bikes up very differently than racers).

    Wallow would be obvious in fork extension when pedaling if not for stiction and rebound damping being tuned for deeper travel compressed spring rebound control. I notice that the acceleration wallow induced fork extension bob is about the same as the rear compression when I climb steeper smoother terrain on my bike.

    a'/b' = a/b using multi-pivots or monopivot is fleeting and a comfortable average or middle gear set amount of squat and wallow when using slow damping for recreational riding. And in the lowest granny gears becomes far away from a'/b' = a/b (rather close to b'/a' = a/b) to become very close to 100% anti-squat, when most other designs become greater than 100% anti-squat in the lower granny gears producing sharper bump induced travel pedal kickback.

    When the angle between chainline to swingarm line is larger there would be greater oscillation of applied torque and resulting wallow and squat due to the impossibility of anything near steady-state acceleration power input when pedaling. But if steady-state acceleration was achieved, the pitch of the frame would attain just as steady and stable an attitude as a different combination of chain and swingarm angle having the same PofM angle from the ground on the same bike (CM height the same too). A different rate of steady-state acceleration between the two would produce a different steady state of wallow pitch angle and different amount of squat.

    I have a hunch that, if this could be made light and stiff enough, a short travel rear suspension bike with greater than 100% anti-squat would out perform rigid race bicycles in street time trials, climbing stages, and finish line sprints. Perhaps some kind of vertically flexible stays, such as the Ibis Bow-ti design or Cannondale Scalpel, without the need for a heavy damper, perhaps using some type of friction compression-biased damper, optimized to extend slightly when pedaling.

    Well this has been a good discussion I feel like I've discovered and realized more of the dynamics. Thanks a lot for your interest. I think I understand that you don’t believe there is suspended CM acceleration induced wallow at 100% anti-squat. And you may even believe that the formula, a'/b' = a/b, is 100% anti-squat. I believe that the PofM (ICF) does directly relate to ground reaction through the chain-drive and wheel, modified by the independently rotating path's swingarm line. And when PofM is on the “anti-squat line” there is 100% anti-squat (no height change, no compression or extension) of the CM, but there is some amount of suspended CM wallow until the fleeting steady state rate of acceleration is achieved.

    - ray
    Last edited by derby; 02-21-2004 at 11:34 AM.

  18. #18
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    It's a crazed obsession of overly curious minds. Got to think about something to block out the pain of climbing.

    I doubt if any one really understands this stuff completely. Bob Grivin's Proflex monopivot designs copied and modified later by Santa Cruz, Haro, Cannondale, Ellsworth, and Super-Go, and Horst Leitner's multi-link designs later modified by Specialized, Giant, Mongoose, Turner, Titus, Intense, and Ellsworth were the two significant breakthroughs in active suspension designs. All other designs are evolutions (and usually de-evolutions) of those two real pioneers in fine tuning bicycle full suspension. The short multi-link type designs such as VPP could prove to be a significant direction of suspension path design, but there are some significant refinements needed.

    - ray

  19. #19
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    To me, anti-squat means pooping before the ride, rather than in the woods during the reide.

    Quote Originally Posted by derby
    Please critique this perception of full suspension anti-squat if you find this interesting.

    I guess I may have been using the term "squat" incorrectly. I've always considered that when a full suspension frame pitch rotated rearward from a compressing rear suspension, whether or not the front end extended, this was “squat”. I guess this action is technically called "wallow". Squat is when the CM compresses overall when the front suspension doesn’t extend enough to compensate for the rear suspension’s compression. The attached picture below describes how the anti-squat line is determined. (Thanks to Strong-Like-Bull for the graphic.)

    For example if the CM is half way between the wheels there is no squat when the rear suspension compresses 1 inch it the front suspension extends 1 inch and the CM remains at the same height. However, due to the practice of putting the seat quite rearward of wheel-base center, if the rear suspension compressed 1 inch and the front extended the same, then the CM would wallow rearward and compress (squat) significantly.

    It's amazing to me that no one could point this definition of squat clearly in all these years of discussion I was involved in before. Maybe it should have been obvious.

    Springs alone when coasting prevent squat unless there is a rolling surface (road or trail) induced compression of the CM when not pedaling or braking.

    The Instant Center of Forces (ICF, also called the Pole of Moments) is where the drive-line such as a chain-line crosses the swingarm-line. A line drawn from the rear tire patch though the ICF is the net geometric acceleration reaction direction of any vehicle.

    When the ICF is aligned with the anti-squat line, then the front suspension extends while the rear suspension squats, rotating the frame around a CM that remains at the same height (no matter where the CM was located horizontally). There is still acceleration wallow unless the CM is directly above the front wheel when ICF is aligned with the anti-squat line.

    So only when an ICF is out of alignment with that anti-squat line will the rider input produce extension or squat to the CM.

    I think this is a very non-intuitive definition of squat.

    It is my experience that more than just a little wallow destabilizes confidence inspiring handling, traction consistency, and braking power.

    Some varying amount of extension consistent with driving torque can counteract frame wallow for crisper acceleration while pedaling (like a runner leans low and forward at the start blocks and rises in height at a regressive rate while accelerating until obtaining full speed running height). On a bike that accelerating CM extension counters wallow without anti-wallow help from damping, but at the sacrifice of some bump compliance while accelerating that is translated into increased suspension kickback to the frame and/or pedals.

    Furthermore, if the suspended CM (mostly rider weight) was able to spin the pedals in perfect circles to accelerate, I think that a line from the rear wheel ground patch, inline with the CM, produces reaction where the CM plus rear and front suspension all extend the same amount (“perfectly” stable extension while accelerating, with no wallowing.). If the rider, who is 80 – 90 % of the suspended mass, is leaned forward pressing mostly downward on the pedals in line with the ICF line, in a commonly normal pedal cadence, then there can be nearly 80- 90 % counter-extension bio-pace, so there would be nearly no extend bob either.

    However, 100% stable anti-bob (no squat or wallow), in other words 100% bio-pace, would have rigid ride characteristics. So for bump compliance travel compression, some stable frame tolerant amount of squat is necessary to avoid noticeable reverse pedal cadence kickback (to avoid greater than 100% bio-pace). Actually some digressive rate of bio-pace as travel is compressed is more stable at the frame and more pedal spin compliant than hardtail like 100% bio-pace. Therein lies the elegance of fine-tuning the travel path sensitive dynamics to balance and hide the trade-offs in stability verses pedaling efficiencies into a bike’s suspension so that it simply rides great in a wide range of conditions.

    “Stable Platform shocks”, digressive rate compression damped shocks aid the range of pedaling stability for more softly sprung longer travel suspension, and hide the awkwardness of less than elegantly tuned geometry in more firmly sprung shorter travel suspension.

    Thanks for any critiques of this perception.

    - ray

  20. #20
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    Bump.
    I love this kind of discussion.

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