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Broadening the Scope
Broadening the Scope
Once this proof of concept was tested on the Go-Bikes, we are able to apply our process for finding a filter range to bike spokes of several different gauges and any spoke length. We used the same tensiometer source, and noticed that the upper and lower bounds for tension are roughly the same regardless of spoke gauge for steel spokes. From here, we can use the spoke gauge and length inputs along with the resonant frequency equation to calculate the upper and lower frequency bound that can then be used for filtering. We limited the scope of our app to stainless steel, round spokes of gauges between 13 gauge and 17 gauge in order to keep things relatively simple (and because they are the most commonly used spokes in both home-builds and commercially available wheels). To the right is a visualization of the expected peak frequencies of 13,14,15,16, and 17 gauge spokes between 150 and 300mm in length. This added capability brings our app's potential usability outside of the Olin bike shop, and hopefully onto the computers of DIY bike mechanics everywhere.
Further Testing of Spoke Combinations
Further Testing of Spoke Combinations
While the capability to check tension of a wider range of spokes theoretically increases the usefulness of our app, we were only able to validate results for a single spoke and gauge combination. Further, we only tested straight gauge spokes, which are a common choice in affordable wheel builds, but tend not to be used in custom builds, where single or double butted spokes are more commonly used. In a butted spoke, the section closest to the rim will be the thickest, and the thickness will decrease near the middle. A visualization of butted spokes is shown to the left. Butting allows for stronger, lighter, and more wheels, but throws a (spoke) wrench into our calculator. In theory, the dominant frequency will be that of the thinnest section, as it will have a greater displacement than the thicker parts near the rim and hub. This is supported by the chart above, which demonstrates that as the spoke gauge increases (and diameter decreases), peak frequencies will also increase. However, field testing of this, along with data validation using a real tensiometer, would make that hypothesis more concrete and could potentially give us insight into more accurate filtering methods.
Limitations
Limitations
Although we are very happy with the results of our app, there are certain limitations of our algorithm. One of the most significant is the fact that all of our testing and validation was done with a wheel that had a tube and tire mounted. Due to the compressive force exerted on the rim and spokes by the tube, we expect that our calculator is actually slightly under-estimating spoke tension. While this method of spoke tension testing is more convenient, we would have to figure out the extent to which it under-estimates in order to make the results more accurate, something which is probably too variable to accomplish. Another potential issue we did limited testing with was checking the tension while the wheel is in a truing stand or on a bike. The extra vibrations introduced in these cases impact the reliability of the calculator, and more filtering techniques would need to be implemented in order to resolve this. In general, the calculator has some reliability issues related to the data collection. Specifically, if the user opts to have the app record the sound, unless they have an external mic, it can be difficult to ensure the pluck is recorded well. This issue is harder for us to resolve, and the variance will be mostly on the end-user. Further, it will be the responsibility of the end-user to interpret results and intuit how realistic they are. Finally, given the mathematical model we are using, if a user has crossed spokes (see example at right) in a 1x, 2x, 3x, or 4x configuration, the calculator's output is really the average of the tensions of all spokes being crossed. However, due to how a tensiometer is normally used in practice, which is to ensure even tension, we believe this should have minimal effects on the usability of our app.
A simplified example of a 2x laced wheel. If one was to pluck the blue spoke, the resulting tension calculation on our app would be the average of the red spoke it crosses and the blue spoke's tension.
retreived from sheldonbrown.com
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