Zipp 88/188 Version 9 Hub Flange Design
Below is a direct comparison of hub flange geometry between the Zipp 088/188 Version 9 hubs and an industry leading hub manufacturer. Diameter measurements were taken where the spoke head attaches to the hub.
The 088/188 V9 hub was designed by systematically deriving lateral and torsional force calculations using the framework of the leading competitor’s hub. These calculations were then used in predicting their impact on overall wheel stiffness. Both hubs were theoretically laced into a Firecrest 404 Carbon Clincher for mathematical comparison. The spoke count for the front wheel was 18 with straight pull spokes radially laced. The spoke count for the rear wheel was 24 with straight pull spokes laced in a two cross pattern on both the drive and non-drive hub flanges (2X/2X). This spoke pattern is commonly referred to as a virtual three cross, as a traditional J-bend hub has the spokes crossing three times. Nominal spoke tension was set at 100 kgf for the front spokes, with the rear at 100 kgf drive side, and 60 kgf non-drive side.
Resolving spoke forces – Lateral Loading
Figure 1: Posterior
For the Zipp 088/188 V9 as well as the competitor’s front and rear hubs, the included angle θ is generated graphically by modeling the hub using the dimensions listed in table 1. For the sake of simplicity, the hub’s spoke attachment diameters are modeled as cylinders and the spoke is modeled as a line extending from the rim’s internal diameter to the hub’s spoke attachment diameter. This is easily visualized for front wheels which are radially laced. The same process can be used on the rears even with crossed spoke patterns. However rear wheels also transmit torque to the pavement, so the torsional aspect of the rear hub needs to be taken into consideration and will be analyzed later when the spoke forces are resolved in their torsional components.
Figure 2: Competitor Front Hub
Figure 3: 088 V9
Once this included angle is determined, trigonometry can be applied to resolve the spoke tension force into its axial and radial components. The competitor calculations are shown in blue, while the 088 V9 calculations are shown in red.
The 088 V9 front hub is 2.8% stronger laterally when comparing the industry leading competitor’s lateral force component (1) to the Zipp hub (3). This force directly influences the lateral stability of the wheel. The larger this lateral component is on a wheel, the more lateral load it can withstand per unit of deflection. This means the wheel will feel more stable, more responsive, and best of all eliminate any system waste slowing the bike down.
The same logic can be applied to the rear hub. However, analysis has to be done on each flange as the dish of a wheel is pushed to the drive side to allow for the gears. Therefore, the included angles are different for both the drive side and non-drive side.
Figure 4: Competitor Rear
Figure 5: 188 V9
The same trigonometric equations are used to solve for the rear lateral loading. The equations below are for the non-drive side. The competitor calculations are shown in blue, while the 188 V9 calculations are shown in red.
Looking at the results for the non-drive side competitor (5) and 188 V9 (7), the Zipp hub is 3.4% stronger laterally. The following set of equations is for the drive side.
Comparing the results for the drive side competitor (9) and 188 V9 (11), the Zipp hub is 13.37% stronger laterally. This number is arguably the most important when analyzing the lateral component of a wheel due to the fact that the rear drive side spokes are the first to see input torque from the rider. If the wheel is not stable enough to adequately resist laterally loading, wheel deflection occurs due to these external loading conditions. In this situation the tension of the spoke can decrease, and potentially become fully unloaded. This is very counterproductive when you are trying to transmit effort from the rider to forward propulsion. As the rider applies torque to the rear wheel, the pulling spokes (spokes which have a tension vector opposite the direction of torque being applied) become loaded as they try to equalize the torsional forces of the wheel. If the wheel is not laterally stable and spokes have become unloaded, the rear wheel will have to wind up more in order to create enough spoke tension to equalize the torque on the wheel. The result of this additional wind up is a sluggish, non-responsive wheel, as well as wasted rider effort.
Figure 6: Lateral Wheel
Wind up View
Resolving spoke forces – Torsional Loading
Continuing the comparison between the two hub models dealing specifically with torsional loading, the hubs are generated graphically and modeled using the information listed in Table 1 and the theoretical wheel using a 2X/2X lacing pattern, in order to determine the angle of the spoke coming out of the hub flange with respect to tangent. The angle is crucial in determining the hubs effectiveness at converting the torque applied to the hub by the rider into forward rotation of the wheel on the pavement. The two figures below represent the two wheels looking down the rotational axis, with only the pulling drive side spokes shown. The angle measured was the first pulling spoke with respect to tangent.
Figure 7: Competitor Front Hub
Figure 8: 188 V9/10
Figure 9: Lateral Torque View
Before proceeding it is important to discuss the details of a wheel laced with crossing spokes and highlight the benefits of a 2X/2X laced wheel. Like previously mentioned, the rear wheel has the extra responsibility of converting torque from the rear cogs into forward propulsion. When torque is applied to the hub, the pulling spokes of the wheel resist the hub’s rotation. However, it is only the tangential component of spoke force which directly resists the hubs rotation. The graphic to the left represents a hub flange. The radial component (FRadial) of the spoke tension vector is represented by the black arrow, while the tangential component (FTangential) is represented by the orange arrow. The angle of interest is identified in red (θ). The steeper the spoke exits the hub flange (i.e. the smaller the spoke angle with respect to tangent) the larger the tangential component of the spoke force is and the stiffer the wheel becomes torsionally. This is why radial lacing essentially provides zero resistance to hub rotation. Furthermore, if we were to analyze this system in a perfect world with no rotational inertia or any other losses, one can assume the torque seen on the drive side is equal to the torque seen on the non-drive side; however in the real world we know this to be inaccurate. Angular deflection of the hub shell, rim stiffness, spoke tension, tire traction and pressure; all of these factors affect the forward propulsion of a wheel. Lab testing was conducted where spoke tensions were measured while the wheel was in its free state, as well as torsionally loaded. It was discovered that only about 20% of the torque seen on the drive side gets transmitted to the non-drive side. This is why many rear wheels opt to lace the non-drive side radially. However, when designing the 188 V9 hubs, torsional stiffness was a priority. For example, if there is even 5% torque transferred to the non-drive side flange for any bike rider set-up, that rider’s input torque should be harnessed to drive the wheel forward. This is why the design of the 188 V9 hub includes a 2X lacing pattern on the drive and non-drive side to generate every last bit of performance out of the hub. This extra complexity however comes at a price. Machine time of the hub shell increases and the wheel itself requires more time and precision to lace and build. Factors like these directly influence the overall cost of the wheel.
Referring back to Figure 7 and Figure 8, trigonometry can be used to calculate the tangential component of the spoke force. We need to reference the radial component of the spoke tension we previous calculated in the lateral loading section in order to properly calculate the tangential component of the spoke force. The results of the radial force component can be found in lines (6), (8), (10) and (12).
Looking at the results on the drive side for the competitor (13) and 188 V9 (14), the Zipp hub is almost 1% stronger torsionally. The strength on the non-drive side is slightly less however the calculations are not conducted due to redundancy but the results listed in Table 2.