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Wheels: Static vs. dynamic balance
I've made one of my typical, lengthy replies here, which may be of broader interest, so I've reposted it below. This also gives me the option to proofread and edit, as I'm sure I'll spot errors when I revisit it.
@redfoxrun:
”Said differently: If you are proposing different spoke diameters and/or spoke counts as a means to mitigate tension imbalance, wouldn't there be less to mitigate if the hub inherently built a less imbalanced wheel?”
Said differently: Wouldn't there be less strength available if the flanges were unnecessarily close together?
Perhaps a thought experiment would help:
Imagine a hub with a single, central flange. Zero static bracing angle makes a terribly weak wheel, despite zero imbalance. Intuitively, we know a wheel with some bracing angle would be stronger, even if there's a tension imbalance. Now imagine a highly asymmetric frame and wheel with a dramatically extended hub on the disc side and normal geometry on the cassette side. Intuitively, we know this is stronger than the single flange, will deform in unconventional ways under load, and is an inefficient use of materials.
Hopefully this thought experiment establishes that it is possible for bracing angle to be more beneficial than tension balance. Whether this is true within the range of geometries, weights, and materials relevant to bike design is a separate question, but the fact that balanced static tension is not intrinsically superior is the first principle to keep in mind.
The second is why and how tension balance can be beneficial. The forces are balanced in a static wheel – that's why it's static, after all – even if there is a significant disparity in bracing angle and tension on either side. As Shook notes, the problems begin when the wheel is stressed out of this state. If the wheel is built with symmetric spokes and spoke count, the stressed wheel quickly develops an asymmetric response to certain loads.
An extension of the second concept is that static tension isn't even necessary. Think about a molded carbon wheel, like the Bike Ahead Biturbo, a zero-tension spoked wheel like the Mavic Tracomp family, or even a cast automotive wheel. Zero static tension, yet the wheel can be light, stiff, and strong (the Tracomp design is most relevant to our discussion).
As such, it's not really the tension that matters, it's the stresses and strains that result from the static and dynamic loads – whether it's the light load and modest deformation of cruising along smooth terrain or the maximum load the wheel can sustain.
Taken together, we see:
• The asymmetric widths of the disc (if present) and cassette are the source of all the wheel asymmetry problems (assuming a centered hub, which isn't necessary)
• Static tension doesn't intrinsically matter.
• High, uniform static tension producing a better wheel is just a "rule of thumb" correlation that applies to typical bicycle wheel construction, including the traditional and low-effort techniques of symmetric spoke diameters, symmetric spoke counts, and symmetric rim profile – and let's throw in symmetric frame profile, too.
• Dynamic behaviour is what matters.
Let's look at how the design elements I've suggested fit into this framework:
1. Asymmetric rim profile
Displacing the spoke attachment away from the source of our asymmetry problems (the cassette) produces a greater bracing angle on the side with greater restrictions on bracing angle. If we were striving for balanced spoke tension at static conditions (again, this is unnecessary), we could achieve it with greater bracing angle. As such you will surely see how asymmetric wheel elements can improve wheel performance. This is why asymmetric rims are common on extremely high-end wheels for which weight is a top priority and aerodynamic considerations are minimal.
If we accept this at face value, though, we would be ignoring the potential asymmetric dynamic properties of the asymmetric rim. The rim can be designed and constructed with asymmetric material placement to balance this, which is analogous to the wheel as a whole, which can also be designed and constructed in an asymmetric fashion to produce largely symmetrical dynamic properties with more efficient use of materials.
2. Asymmetric spoke properties
When asymmetric bracing angles exist, asymmetric forces will develop as the wheel deforms. No problem: we can compensate via proportionately asymmetric spoke properties, such as cross-section and/or material (ex. titanium vs. steel). As discussed above, the objective is not to balance the stress – since this is not what matters – but to balance the dynamic stress and strains.
Obviously, the stresses on various wheel components under all deformation cases will produce a complex set of load cases on the spokes, so the asymmetric spoke properties will not balance across the range of load cases, but there is a net benefit to the greater bracing angle afforded by asymmetric spoke properties because this produces dynamic deformation that is approximately as stable as produced via a fully symmetric design with either:
• lighter spokes on the side with greater bracing angle for comparable strength and stiffness at lower weight
• slightly lighter spokes on one side and slightly heavier on the other for greater strength and stiffness and comparable weight
3. Asymmetric spoke count
This functions in the same way as asymmetric spoke properties. It’s another way to use materials in an asymmetric manner to balance asymmetric geometry. Many major companies (ex. Shimano, Campagnolo / Fulcrum, Specialized, Giant / Cadex, DT, Hunt, FSA / Vision) have used or currently use 2:1 spoke counts on flagship products. Approximately half of the exotic wheelsets that use fully proprietary and model-specific hubs have 2:1 spoke counts with maximized flange spacing, despite the considerable static tension imbalance that results.
While this many not prove the case, I hope it persuades you that when manufacturing efficiency is not a top priority, companies use advanced design to make a better wheel without the constraint of symmetric static spoke tension.
4. Asymmetric frame profile
If we expand the scope beyond the wheel and consider the whole vehicle, we can include the option for an asymmetric frame. A simple example would be to create a hub with maximum possible flange spacing and use symmetric spoke materials and dimensions, symmetric spoke count, and symmetric rim; this would produce a wheel with perfectly balanced spoke tension and maximum spoke bracing angles for a given hub width. Surely, we can agree this would be a stronger and stiffer wheel than one with balanced tension, similarly symmetric components, and a symmetric frame that forced narrower flange spacing to achieve the balanced spoke tension. This is yet another example of asymmetric geometry aiding the optimization of the wheel. Of course, it raises questions of how to ensure optimal properties of the entire vehicle. While far beyond the scope of our discussion, the design process involves the same principles of geometry, material volume, and material properties.
To recap:
• Design for dynamic, not static
• Balance stress and strain, stiffness and strength, not tension
• Exploit the available dimensions and geometry via material selection and application
• Asymmetries can balance each other, therefore asymmetric designs can produce symmetric behaviour
Finally, a note on weight: You mentioned a weight increase of 5-15 g for a 157 mm hub vs. 148 mm. I don’t know the source of that data, but it seems reasonable, so let’s use those numbers. That represents an increase of approximately 1% per wheel. The increase in bracing angle afforded by the wider hub is far greater than 1%. The numbers provided in your sources for the relationships between wheel strength and stiffness did not account for stress- and strain-balancing the wheel via the asymmetric design elements discussed above. Implementing these elements will allow the designer to fully exploit the geometric advantages of wider flange spacing, producing a net positive “return on investment” for the slight increase in weight.
@redfoxrun:
”Said differently: If you are proposing different spoke diameters and/or spoke counts as a means to mitigate tension imbalance, wouldn't there be less to mitigate if the hub inherently built a less imbalanced wheel?”
Said differently: Wouldn't there be less strength available if the flanges were unnecessarily close together?
Perhaps a thought experiment would help:
Imagine a hub with a single, central flange. Zero static bracing angle makes a terribly weak wheel, despite zero imbalance. Intuitively, we know a wheel with some bracing angle would be stronger, even if there's a tension imbalance. Now imagine a highly asymmetric frame and wheel with a dramatically extended hub on the disc side and normal geometry on the cassette side. Intuitively, we know this is stronger than the single flange, will deform in unconventional ways under load, and is an inefficient use of materials.
Hopefully this thought experiment establishes that it is possible for bracing angle to be more beneficial than tension balance. Whether this is true within the range of geometries, weights, and materials relevant to bike design is a separate question, but the fact that balanced static tension is not intrinsically superior is the first principle to keep in mind.
The second is why and how tension balance can be beneficial. The forces are balanced in a static wheel – that's why it's static, after all – even if there is a significant disparity in bracing angle and tension on either side. As Shook notes, the problems begin when the wheel is stressed out of this state. If the wheel is built with symmetric spokes and spoke count, the stressed wheel quickly develops an asymmetric response to certain loads.
An extension of the second concept is that static tension isn't even necessary. Think about a molded carbon wheel, like the Bike Ahead Biturbo, a zero-tension spoked wheel like the Mavic Tracomp family, or even a cast automotive wheel. Zero static tension, yet the wheel can be light, stiff, and strong (the Tracomp design is most relevant to our discussion).
As such, it's not really the tension that matters, it's the stresses and strains that result from the static and dynamic loads – whether it's the light load and modest deformation of cruising along smooth terrain or the maximum load the wheel can sustain.
Taken together, we see:
• The asymmetric widths of the disc (if present) and cassette are the source of all the wheel asymmetry problems (assuming a centered hub, which isn't necessary)
• Static tension doesn't intrinsically matter.
• High, uniform static tension producing a better wheel is just a "rule of thumb" correlation that applies to typical bicycle wheel construction, including the traditional and low-effort techniques of symmetric spoke diameters, symmetric spoke counts, and symmetric rim profile – and let's throw in symmetric frame profile, too.
• Dynamic behaviour is what matters.
Let's look at how the design elements I've suggested fit into this framework:
1. Asymmetric rim profile
Displacing the spoke attachment away from the source of our asymmetry problems (the cassette) produces a greater bracing angle on the side with greater restrictions on bracing angle. If we were striving for balanced spoke tension at static conditions (again, this is unnecessary), we could achieve it with greater bracing angle. As such you will surely see how asymmetric wheel elements can improve wheel performance. This is why asymmetric rims are common on extremely high-end wheels for which weight is a top priority and aerodynamic considerations are minimal.
If we accept this at face value, though, we would be ignoring the potential asymmetric dynamic properties of the asymmetric rim. The rim can be designed and constructed with asymmetric material placement to balance this, which is analogous to the wheel as a whole, which can also be designed and constructed in an asymmetric fashion to produce largely symmetrical dynamic properties with more efficient use of materials.
2. Asymmetric spoke properties
When asymmetric bracing angles exist, asymmetric forces will develop as the wheel deforms. No problem: we can compensate via proportionately asymmetric spoke properties, such as cross-section and/or material (ex. titanium vs. steel). As discussed above, the objective is not to balance the stress – since this is not what matters – but to balance the dynamic stress and strains.
Obviously, the stresses on various wheel components under all deformation cases will produce a complex set of load cases on the spokes, so the asymmetric spoke properties will not balance across the range of load cases, but there is a net benefit to the greater bracing angle afforded by asymmetric spoke properties because this produces dynamic deformation that is approximately as stable as produced via a fully symmetric design with either:
• lighter spokes on the side with greater bracing angle for comparable strength and stiffness at lower weight
• slightly lighter spokes on one side and slightly heavier on the other for greater strength and stiffness and comparable weight
3. Asymmetric spoke count
This functions in the same way as asymmetric spoke properties. It’s another way to use materials in an asymmetric manner to balance asymmetric geometry. Many major companies (ex. Shimano, Campagnolo / Fulcrum, Specialized, Giant / Cadex, DT, Hunt, FSA / Vision) have used or currently use 2:1 spoke counts on flagship products. Approximately half of the exotic wheelsets that use fully proprietary and model-specific hubs have 2:1 spoke counts with maximized flange spacing, despite the considerable static tension imbalance that results.
While this many not prove the case, I hope it persuades you that when manufacturing efficiency is not a top priority, companies use advanced design to make a better wheel without the constraint of symmetric static spoke tension.
4. Asymmetric frame profile
If we expand the scope beyond the wheel and consider the whole vehicle, we can include the option for an asymmetric frame. A simple example would be to create a hub with maximum possible flange spacing and use symmetric spoke materials and dimensions, symmetric spoke count, and symmetric rim; this would produce a wheel with perfectly balanced spoke tension and maximum spoke bracing angles for a given hub width. Surely, we can agree this would be a stronger and stiffer wheel than one with balanced tension, similarly symmetric components, and a symmetric frame that forced narrower flange spacing to achieve the balanced spoke tension. This is yet another example of asymmetric geometry aiding the optimization of the wheel. Of course, it raises questions of how to ensure optimal properties of the entire vehicle. While far beyond the scope of our discussion, the design process involves the same principles of geometry, material volume, and material properties.
To recap:
• Design for dynamic, not static
• Balance stress and strain, stiffness and strength, not tension
• Exploit the available dimensions and geometry via material selection and application
• Asymmetries can balance each other, therefore asymmetric designs can produce symmetric behaviour
Finally, a note on weight: You mentioned a weight increase of 5-15 g for a 157 mm hub vs. 148 mm. I don’t know the source of that data, but it seems reasonable, so let’s use those numbers. That represents an increase of approximately 1% per wheel. The increase in bracing angle afforded by the wider hub is far greater than 1%. The numbers provided in your sources for the relationships between wheel strength and stiffness did not account for stress- and strain-balancing the wheel via the asymmetric design elements discussed above. Implementing these elements will allow the designer to fully exploit the geometric advantages of wider flange spacing, producing a net positive “return on investment” for the slight increase in weight.
Author Info:
Calgary, AB, Canada
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I’d love to see a link that describes this in practice: “ slightly lighter spokes on one side and slightly heavier on the other”
There's no link available or necessary for "slightly lighter spokes on one side and slightly heavier on the other". It describes one of the many possible ways to configure an asymmetric spoke spec to balance asymmetric flange offsets and you can easily verify this for yourself with simple geometry.
As an example, 24 mm is a typical flange offset on the drive side of a rear hub. Assuming a symmetric rim and spokes, we might use spokes with 2.0 - 1.8 - 2.0 profile on the both sides of the wheel and a symmetric 24 mm flange offset on the non-drive side to produce a balanced wheel.
Alternatively, we could use the same offset and spokes on the drive side with 2.0 - 1.5 - 2.0 spokes on the non-drive side with 34.5 mm flange offset to produce an equivalent wheel with less mass.
Alternatively - and pertaining to the quote you cited - we could again use the 24 mm offset on the drive side with 2.0 mm spokes and balance this with 2.0 - 1.6 - 2.0 spokes and 37.7 mm offset on the non-drive side for a stronger wheel at roughly equal mass.
Just simple geometry - try it for yourself and see.