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The Physics of Chainstay Length?

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The Physics of Chainstay Length?

Old 08-24-15, 02:30 PM
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The Physics of Chainstay Length?

There are a zillion-or-so articles out there that purport to explain chainstay length. The conventional wisdom seems to be that:
  • Long Chainstays == Comfort and Stability

    Short Chainstays == Racing-type Acceleration


It is clearly obvious that this is a vast oversimplification. It may also be the case that this is just one of the old-wives-tales of cycling. It is also clear that this sidesteps constraints on frame design caused by things like chainring clearance, wide rim and tire clearance, etc. It also make the assumption that racing means one-and-only-one style of riding -- riding where rapid acceleration and quick handling are keys to success.

I would like to know something about the actual physics that comes into play regarding chainstay length, not dwelling on generic advice like, "for touring you want ...; for criteriums you want...; etc." Can anyone help explain this aspect of frame design in an engineering rather than a sales manner? Thanks.

[1] Like these:

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Old 08-25-15, 12:30 AM
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Take two tubes of the same material, equal diameter, and equal wall thickness. The only difference between them is the length. Anchor one end of the tube and apply a fixed force to the free floating end. The longer tube will flex more. This is due to the interplay between the elasticity of the material and leverage (force lines and cross sections).

This is a great book to read that can help you understand engineering principles, and how they work when applied to structures/assemblies.

https://www.amazon.ca/Structures-Thin.../dp/0140219617
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Old 08-25-15, 06:58 AM
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Here is my engineering perspective: long chainstays help keep your foot from hitting your panniers. People I trust that make mountain bikes say that they like the handling of bikes with short chain stays. Otherwise, I'm pretty sure it's all fashion. It's not even clear that people really like the feel of stiff chainstays. Sure, if they are too wimpy then it affects shifting. But longer chainstays provide a better chain line.
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Old 08-25-15, 07:02 AM
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Originally Posted by justinzane
There are a zillion-or-so articles out there that purport to explain chainstay length. The conventional wisdom seems to be that:
  • Long Chainstays == Comfort and Stability

    Short Chainstays == Racing-type Acceleration


It is clearly obvious that this is a vast oversimplification. It may also be the case that this is just one of the old-wives-tales of cycling.
I tend to agree with old wive's tale.

Bikes with long chain stays are almost always built with more relaxed steering.
Bikes with short chain stays are almost built with quick steering.

I think the chain stay length has less to do with it and it's mostly head tube angle and fork choices.
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Old 08-25-15, 07:20 AM
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Much of the reason that short chainstayed bikes are "quick" handling is that they often have short wheel bases, reactive steering geometry and a weight distribution which places more weight on the front wheel. Just like the early claims of Columbus frames being faster then 531 ones BITD. Well the Col. tubed frames were more often a racing geometry and the 531 ones more often a "club' or touring geometry. There's a lot of old wives tales out there.

To add to Eric's suggestion I'll say that longer stays make for smoother chain runs, are more tolerant of cross chain angles. leave more room for fenders and wide tires. Lastly many will say that weight distribution can be played with by using stay length without effecting the rider's fit or toe clip overlap (front center). Andy.
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Old 08-25-15, 12:24 PM
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My experience has been that short chainstays don't allow the rear wheel to stay planted. When you stand to sprint or climb, the wheel breaks loose and scrubbs side to side. This works in opposition to your desire to get down the road or up the hill faster. Longer chainstays seem to keep the rear wheel in place. I'm guessing that the effect of the longer lever with long chainstays overrides the effect of putting more weight on the rear wheel when the chainstays are short. I think that short chainstays are nothing but marketing. In other words, short chainstays sell, long ones don't.
As far as handling is concerned, unless you go to extremes, chainstay length/wheelbase has no detectable effect on how "quick" a bike handles. "Quickness" is determined by front end geometry, primarily from trail.
Bottom line, short chainstays are the exact opposite of what the marketers claim they are.
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Old 08-26-15, 10:02 AM
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Originally Posted by taras0000
Take two tubes of the same material, equal diameter, and equal wall thickness. The only difference between them is the length. Anchor one end of the tube and apply a fixed force to the free floating end. The longer tube will flex more. This is due to the interplay between the elasticity of the material and leverage (force lines and cross sections).

This is a great book to read that can help you understand engineering principles, and how they work when applied to structures/assemblies.

https://www.amazon.ca/Structures-Thin.../dp/0140219617


Yeah, but on the vast majority of bikes the rear end is triangulater. What you say describes the canti structure of forks, though they are pretty vertical and function a lot like posts. The rear of the bike is a truss, and the lengthening of the elements, even if as you say they remained constant section, is probably the same as you describe, but it is a massive section, the truss, not the tubes, so the effect is that in both cases it might as well be solid. Lateral effects are different, but bending effects in the vertical axis as described are pretty masssively braced.
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Old 08-26-15, 12:42 PM
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Originally Posted by taras0000
Take two tubes of the same material, equal diameter, and equal wall thickness. The only difference between them is the length. Anchor one end of the tube and apply a fixed force to the free floating end. The longer tube will flex more.
Well explained. And, in the days of yore, when designers and builders had a very limited selection of tubes to work with, that seems to be significant, though how it is relevant to anything but mitigating rough roads does not make sense to me currently.

With modern material, it should be rather manageable to create 415mm stays that have the same stiffness/strength as 390mm stays. Even without changing to composites, by doing calibrated tempering/shot peening/etc. the same metal stock can have a reasonable range of properties. So, the question then becomes how does length alone change the ability of a bike to accelerate (in the forward direction, with force/torque provided by the rider)? And how, again assuming comparable levels of compliance, impact stability
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Old 08-26-15, 01:35 PM
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I have a few questions for the framebuilders regarding this subject.

Does the longer wheelbase act the same way as a shopping cart coaster - the wheel further behind the turning point makes it more stable in forward motion? Same concept as behind rake and trail, as I imagine it anyway.

Moving the wheel back means more weighted front wheel. Is that enough to materially affect handling?

The longer leverage will keep the front from coming up as easily when you put a lot of torque to the pedals. That seems like a win for the longer chainstay in any scenario, right?

Longer wheelbase increasing the turning radius, but is that really enough difference that you'd notice in a blind test?

Has anyone looked at how the bike's self-stability is affected by this small difference in wheel-base length? With otherwise the same frame for example.
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Old 08-26-15, 02:51 PM
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Originally Posted by unterhausen
Here is my engineering perspective: long chainstays help keep your foot from hitting your panniers.
Definitely, though that does not directly influence comfort, stability or acceleration. More in the "utility" category I'd say.
Originally Posted by unterhausen
People I trust that make mountain bikes say that they like the handling of bikes with short chain stays. Otherwise, I'm pretty sure it's all fashion. It's not even clear that people really like the feel of stiff chainstays. Sure, if they are too wimpy then it affects shifting.
Fashion, old-habits-dying-hard, etc.... That is exactly why I'm trying to figure out the physical, mechanical, force vectors, kinda explanation. And, just like thoroughly unstable airplanes -- F16 -- work well for some expert users in some situations -- dogfighting; some pretty darn unstable and uncomfortable bikes may be the ideal ride for skilled riders in certain situations. I'm trying to avoid anecdote and focus on physics in this post because I'm simply overwhelmed with anecdotal explanations on both sides of the chainstay length discussion. (Not a criticism of your post, BTW, just frustrtion. )
Originally Posted by unterhausen
But longer chainstays provide a better chain line.
Simple geometry so dictates. And, I would naively assume that less friction on the sides of the chain would minimally improve efficiency and shifting ease. I'm betting, though, that that is an almost irrelevantly small improvement.
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Old 08-26-15, 03:43 PM
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Originally Posted by justinzane
And, just like thoroughly unstable airplanes -- F16 -- work well for some expert users in some situations -- dogfighting; some pretty darn unstable and uncomfortable bikes may be the ideal ride for skilled riders in certain situations. I'm trying to avoid anecdote and focus on physics in this post because I'm simply overwhelmed with anecdotal explanations on both sides of the chainstay length discussion. (Not a criticism of your post, BTW, just frustrtion. )
actually, to the pilot, an F16 is very stable. They do have a negative stability limit. Unstable planes without compensation have a bad history of crashing. Bikes with short chainstays aren't necessarily unstable either. There was a time when people built some really weird bikes with very steep front ends, and they had relatively low trail for such a bike. Which might not have been the best idea. You can build a higher trail version of the same bike with short chainstays, and it probably will handle fine. My problem with short chainstays is doing wheelies on 19 percent climbs. The short chainstays on current mountain bikes are coupled with fairly high trail.

As far as physics goes, the structural stuff is something you could do with a computer, if you wanted. It really depends on specific tubing, dropouts, and wheels though. Handling is not something that is as well codified. Apparently the motorcycle people are a lot better at this than cyclists, but I haven't really looked at it at all. There are no metrics that I know about, so computing something would be difficult

And my explanation for this lack of physics models for bikes is that we don't really need them. Sure, if you are designing a carbon frame, you need something. Geometry is controlled by external factors, like rider fit and the bike's purpose, tire size selection, etc. For road bikes, the trend is towards bigger tires. Same for mountain bikes. So that is the biggest concern for me

Last edited by unterhausen; 08-26-15 at 03:47 PM.
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Old 08-26-15, 04:52 PM
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Originally Posted by MassiveD
Yeah, but on the vast majority of bikes the rear end is triangulated. What you say describes the canti structure of forks, though they are pretty vertical and function a lot like posts. The rear of the bike is a truss, and the lengthening of the elements, even if as you say they remained constant section, is probably the same as you describe, but it is a massive section, the truss, not the tubes, so the effect is that in both cases it might as well be solid. Lateral effects are different, but bending effects in the vertical axis as described are pretty masssively braced.
Yes. What you say is true about the forks being cantilevered and the rear being a truss. It was the reason I suggested the link to the engineering book in my reply to the OP. It goes into a lot of detail about that stuff in quite a simple way. Really good read for anyone interested in how things work/stay together/not fall apart.

Going back to the truss rear end of a bicycle. When pedalling forces are put on the bike, the tendency for the bike is to twist around the axis of the seat tube (visible with standard diameter steel tubes). So although the truss is stable in vertical compression (and why the double diamond design of the bicycle has proven so effective), it is still subject to the lateral forces imposed by the twist through the frame (the direction in which the truss is weak). Larger diameter tubes, or shorter sections will help to stiffen this up in this respect.

There is so much that goes into designing a bike, and how it handles, that general rules don't really apply here. You can make a bike that accelerates like a rocket and handles like a fighter jet, and still have long chainstays and a long wheelbase. Is it going to handle identically to a bike with short CS and short WB? No. Certain aspects of frame designs carry certain attributes (with certain weights) to the overall feel of a bike. These aspects and attributes can be massaged over certain ranges to dial in the feel of a bike.
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Old 08-26-15, 05:05 PM
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Originally Posted by unterhausen
And my explanation for this lack of physics models for bikes is that we don't really need them. Sure, if you are designing a carbon frame, you need something. Geometry is controlled by external factors, like rider fit and the bike's purpose, tire size selection, etc. For road bikes, the trend is towards bigger tires. Same for mountain bikes. So that is the biggest concern for me
Note that this example could refer to a Downhill bike, a loaded tourer, a criterium bike, etc.

Even if one is designing a steel frame for a particular rider for a particular use there is a choice about how to size the chainstays. Say we are spec'ing a TT bike for Mr. Eaton M. Dust. We know he should have a reach=440, stack=550, 77 deg seat, ... 622x25 on 23mm wide rims, etc. That info gives is some clear minimums. It also means that we do not have to deal with some concerns like heel-pannier clearance and so on.

Suppose we know that we cannot go shorter than 382mm and further suppose that neither Mr. Dust or ourselves are at all interested in complying with conventional wisdom, but only make design decisions based on demonstrable functionality. Do we spec 382mm? 390? 400?

Acknowledging that a less rattled, more comfortable rider is usually faster; but knowing that Mr. Dust will sacrifice small amounts of comfort for speed, which length gets picked and why?
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Old 08-26-15, 05:14 PM
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Originally Posted by taras0000
You can make a bike that accelerates like a rocket and handles like a fighter jet, and still have long chainstays and a long wheelbase. Is it going to handle identically to a bike with short CS and short WB? No. Certain aspects of frame designs carry certain attributes (with certain weights) to the overall feel of a bike. These aspects and attributes can be massaged over certain ranges to dial in the feel of a bike.
So, perhaps an example... Take an old rather generic frame, say a 1982 Motobecane Super Mirage 57cm. Having borrowed Harry Potter's wand, I can add 15mm or remove 15mm from the chainstays without changing stay stiffness or weight. What goes in this table?

[table="width: 500"]
[tr]
[td]Variant[/td]
[td]Acceleration[/td]
[td]Stability[/td]
[td]Conmfort[/td]
[/tr]
[tr]
[td]Long +15[/td]
[td][/td]
[td][/td]
[td][/td]
[/tr]
[tr]
[td]Original +0[/td]
[td][/td]
[td][/td]
[td][/td]
[/tr]
[tr]
[td]Short -15[/td]
[td][/td]
[td][/td]
[td][/td]
[/tr]
[/table]
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Old 08-26-15, 08:53 PM
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The physics will dictate that your table will look like this:

Variant Acceleration Stability Comfort
Long +15 -1 +1 +1
Original +0 0 0 0
Short -15 +1 -1 -1

Now, in reality, those numbers would read more like +0.1, -0.1...or even 0.01 if all you were going to factor in was chainstay length. Stability and comfort are also influenced by head tube angle, fork rake, seat tube angle and tubing choice. Handling will be influenced by Head Tube angle, Fork rake, wheelbase, and stiffness. With so much overlap, making changes to one aspect of a frame to achieve a desired effect will have affects on other attributes of the ride. This applies more to frames made of a homogenous material, like steel, titanium, or aluminum. Composites will allow you to manipulate the aspects a little more individually, without having as much of an effect elsewhere in the frame, but the interplay is still there. A good frame builder will know how much of an effect a change will have and how to achieve a balance to best satisfy the rider.

All of this info is opinion/knowledge based on what I've come across in 15 years of riding and racing bicycles (mostly on the track) and racing motorcycles as well. Most of my experience in testing out frame geometry took place on velodromes where small differences in geometry have a more apparent/measurable (by the seat of your pants) effect. It's much easier to feel these things out in that controlled environment. I've probably ridden/tested 50-60 track bikes, and probably 20-30 road bikes. Mountain bikes are another thing and I haven't ridden many of these over the years. There are people out there like engineers and frame builders that have built more bikes and ridden more than me and know this interplay better than I do.

If you're curious to find out how I would classify what effects the ride of a bike the most I would say it goes like this:

1) Knowledge/Engineering.
- the proper use of materials as well as geometry will have the greatest effect in determining the frames handling.

2) Geometry (when considered singularly)
- Front end (HTa, fork rake)>wheelbase>Chainstay length>STa

3) Material (when considering stiffness)
- Stiffness affects handling as well as acceleration. Fewer losses in efficiency mean you move faster. The right amount of stiffness will lead to a bike that feels solid when cornering, tracks well, yet is flexible enough to absorb some bumps when heeled over in a turn. Too much or too little stiffness upsets this feeling.

4) Wheels
- Light wheels, heavy wheels, larger tires, wider rims, differing tire pressures. Lots going on here as well. Probably for another thread.
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Old 08-26-15, 11:56 PM
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Much of the physics is less complicated than it seems at first, even if nothing is definitive.

Generalizations mostly originated with steel bikes, which are more prone to lateral flex. The ultralight tube sets used in high performance steel bikes could flex quite a bit in the front triangle, so by a simple application of leverage ratios, you tend to want short chainstays to make the most of the more substantial rear end. With carbon fiber and today's ultra stiff construction, it makes much less difference. The frames will be laterally stiff regardless of chainstay length. Still, to make the most of the material you do use, it can be considered an optimization.

Handling is affected by both the weight distribution and affect of pedaling in proportion to the BB position within the wheelbase. Pedals near the rear wheel makes the front end lighter, and reduces pedaling induced steering. Closer to the front wheel and you tend to get a more planted front wheel with less road buzz, and less direct impact translation from the rear. The most comfortable seat on a bus is in the middle.

When you have more weight on the front wheel, you tend to want less trail so rider movements affect the steering less. More weight on the rear and you want more trail to increase the self stability and body English effects. Forward weight balances easily because the front wheel does the correction, but turning tightly takes more steering input with a longer wheelbase.

So when you look at it this way, it makes sense that a MTB with short chainstays would have desireable handling characteristics, and why racers like it due to quicker handling. Because bikes are all about balancing variables, it can turn into black magic quickly.
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Old 08-27-15, 09:26 AM
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Originally Posted by taras0000
Stability and comfort are also influenced by head tube angle, fork rake, seat tube angle and tubing choice. Handling will be influenced by Head Tube angle, Fork rake, wheelbase, and stiffness. With so much overlap, making changes to one aspect of a frame to achieve a desired effect will have affects on other attributes of the ride. This applies more to frames made of a homogenous material, like steel, titanium, or aluminum. Composites will allow you to manipulate the aspects a little more individually, without having as much of an effect elsewhere in the frame, but the interplay is still there.
I know that you are speaking from a position of far more knowledge and experience than I have. I also know that there are many ways to change the ride characteristics of a bike. But I am trying really hard to limit this discussion to only chainstay length.

Originally Posted by taras0000
A good frame builder will know how much of an effect a change will have and how to achieve a balance to best satisfy the rider.
How do they know? Experience and gut feeling? Experimental testing and analysis? This is the core of the question.

Let me try another example... Given this BikeCAD model (realizing that it should have a 73 deg. head angle, not 72),



What difference would there be to the rider going from 395mm stays to 400 or 405mm stays?
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Old 08-27-15, 09:29 AM
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Originally Posted by taras0000
All of this info is opinion/knowledge based on what I've come across in 15 years of riding and racing bicycles (mostly on the track).... It's much easier to feel these things out in that controlled environment. I've probably ridden/tested 50-60 track bikes, and probably 20-30 road bikes.
I am most jealous of that experience. I hope, someday, to live close enough to a velodrome to be able to try.
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Old 08-27-15, 10:17 AM
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Originally Posted by catgita
Generalizations mostly originated with steel bikes, which are more prone to lateral flex. The ultralight tube sets used in high performance steel bikes could flex quite a bit in the front triangle, so by a simple application of leverage ratios, you tend to want short chainstays to make the most of the more substantial rear end. With carbon fiber and today's ultra stiff construction, it makes much less difference. The frames will be laterally stiff regardless of chainstay length. Still, to make the most of the material you do use, it can be considered an optimization.
Thanks. That help clarify where the conventional wisdom started.

Originally Posted by catgita
Handling is affected by both the weight distribution and affect of pedaling in proportion to the BB position within the wheelbase. Pedals near the rear wheel makes the front end lighter, and reduces pedaling induced steering. Closer to the front wheel and you tend to get a more planted front wheel with less road buzz, and less direct impact translation from the rear. The most comfortable seat on a bus is in the middle.
I'm assuming that this really only applies to positions where the rider's center of gravity is horizontally close to the BB. Riding flat, as one does on aero bars or really in the drops, the rider's CoG tends to be far in front of the BB and the rider's weight is more evenly distributed between elbows, pubic bone and feet.

My formula for proper bus seating is:
Code:
max(average(distance(potential_seat, child_seat))) for all child_seats


Originally Posted by catgita
When you have more weight on the front wheel, you tend to want less trail so rider movements affect the steering less. More weight on the rear and you want more trail to increase the self stability and body English effects. Forward weight balances easily because the front wheel does the correction, but turning tightly takes more steering input with a longer wheelbase.
I think I understand, but I'm unsure how this relates to chainstay length. Are you saying that the handling is proportional to:
Code:
(cos(chainstay_angle_orig) * chainstay_length_orig) - cos(chainstay_angle_new) * chainstay_length_new) 
/ 
(cos(chainstay_angle_orig) * chainstay_length_orig) + front_center_distance)
?
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Old 08-27-15, 10:53 AM
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Physics,? yardstick like a tuning fork vibrates at a higher frequency as you shorten the vibrating length.. try it .


A Bicycle? the C of G relative to the rider's Butt mass relative to the wheel .. of for example :

the old long chainstay MTB..vs NORBA MTB race designs .

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Old 08-27-15, 11:09 AM
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Had a Klein Quantum(Aluminum) & a Pinarello Montello(Steel). Pretty similar in geometry but, even with the longer chain stays on the Quantum, it was stiffer in the rear & more harsh in ride. Obviously the longer stays were to help lessen some of this. My distant point being that, materials, size, type, shape, thickness etc, all are taken into account. All things equal, I had a very nice high end merckx with longer chainstays, which was similar to build & tubing type to other frames Ive had. It was very forgiving when you stomped on it. A longer ride with such comfort, i have never had.
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Old 08-27-15, 01:08 PM
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I was thinking some more about this. I'm not sure what the motivation for the OP is, but if someone were to desire to make a living in bicycle design, the actual physics stemming from small changes in tubing length is not going to do anything for you. The macro aspects of bike design is where all the magic is.
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Old 08-27-15, 05:21 PM
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Originally Posted by justinzane
I know that you are speaking from a position of far more knowledge and experience than I have. I also know that there are many ways to change the ride characteristics of a bike. But I am trying really hard to limit this discussion to only chainstay length.
Why are you so singularly focused on just the chainstay length differences? I think that the answer is the effect is very small if you're only going to change the length of the chainstays 5 or 10mm. Probably almost imperceptible to most people. There are other things that have a larger effect on how a bike rides.
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Old 08-27-15, 07:41 PM
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Originally Posted by taras0000
There are other things that have a larger effect on how a bike rides.
According to "The Geometry of Bike Handling" from the Cycling Tips website, describing the principles of the Australian framebuilder Darren Baum...

The Geometry of Bike Handling | CyclingTips

Handling is related to four factors: Trail; Bottom bracket drop; Chainstay length; and Stem length and position.

Here's what it says about chainstay length...

In Darren’s opinion, longer chain stays help deliver a better quality ride. When you climb, the bike has more traction. When you go through a corner, the bike trails further and you can hop on the pedals earlier. The intended use of the bike is a big consideration however.
When chainstays started getting shorter throughout history (late 60’s, early 70’s), it was when riders started getting more powerful and the technology didn’t exist to make the materials strong enough for the desired stiffness. Therefore the chainstays were designed shorter in order to make the bike stiffer. A good bike was considered one that you could barely fit a Tally-Ho cigarette paper in between the rear wheel and the seat tube. This design had nothing to do with handling. It was all about making the bike stiffer. People started identifying this small rear triangle as a “race bike”, and therefore a race bike must handle better. This never changed as materials progressed.
These days the materials exist to make a long chainstay that is still very stiff. However if you have a longer rear end, the bike naturally needs to be manufactured with more material and therefore will be heavier. These days in the industry there is a race for the lightest spec’d bike. What does Baum do with their bikes? They recommend making the rear end as long as acceptable by the customer.
If you’re flexible and can bend forward, 412mm is what Baum will recommend. If the rider sits more upright, the chainstay might go as long as 420mm. If the rider is really tall (i.e. over 6’3″), and the femur is very long, 430mm might be required. The reason for this starts to relate back to seat tube angle and pedalling technique, however I think we might leave that one for another discussion.

But like taras0000 says, that really has to be read in conjunction with the rest.

The great race car driver Ayrton Senna was once asked what was the key to a race car's handling. I think the interviewer expected him to launch into a long spiel about turn-in, pitch, roll, understeer, oversteer, etc. - Senna was an intensely analytical character - but he answered with one word: "Balance." Nothing in isolation, everything talking to everything else.

This was an eye-opener, though: a video showing carbon chainstay flex...
https://www.youtube.com/watch?v=cAz5wOBxuMI

Lateral movement isn't just loss of forward propulsion, it's tyre scrub. We obsess about low rolling resistance but that's assuming the tyres are tracking straight when a lot of the time - front and rear - they aren't. I figure the key is to limit lateral tyre scrub through geometry, handling and stiffness, even when travelling straight, or trying to - I think trail, low or high, has a big effect on the front end - but I don't know enough to know how you achieve that. It sure is complicated.
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Old 08-28-15, 01:28 PM
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@unterhausen, @taras0000: I'm trying to focus on chainstay length specifically because it is one of the more independent variables in frame geometry. If one tweaks, say head angle, there are dependent changes in top tube length, down tube length, trail, reach, etc. Stays, on the other hand, can be lengthened out from minimum clearance lengths for a considerable distance without mandating changes in the front triangle at all.

One of the reasons I like to understand the functionality of parts of a bike independently is that it makes it possible to more clearly understand a bike as a whole without resorting to possibly inappropriate generalizations. I know that this is a pedantic question. I also know that getting to grips with the physics of stay lengths is likely irrelevant to the vast majority of cyclists. Learning about the details of bikes, though, is fun to me.

I've seen numerous posts about the friggin' weight saving of alloy spoke nipples, and responses detailing the difference in wheel moment of inertia. I'm pretty sure that this is at least as relevant to bike performance and comfort as nipples. ;**
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