Skateboard physics: squeezing bushings

Introduction

Occasionally, people claim that TKP trucks (i.e., trucks with significant forward rake) turn “progressively,” while RKP trucks (i.e., trucks with minimal rake) turn more “linearly”. That, at first glance, can only mean that the trucks resist turning in such ways,1 because, as the reader must be already aware, rake does not change the tilt/turn relation (if you find this bit hard to follow, see here first). What is different is that usually RKP trucks have their kingpin (KP) built perpendicular to their pivot axis (PA) (e.g., Randal, Paris, and indeed, 99% of what is labeled “RKP trucks”; I can only think of Carver’s CX as an exception), while “TKP trucks” (e.g., Bennett, Indys etc) have a KP not perpendicular to the PA2 (for a discussion on the relevance of these categories, see here). So, I had to check for patterns in the way trucks resist when a rider leans on a skateboard. To do that, I recorded how much the bushings are deformed (being aware that the force with which they resist is not always entirely on the turning plane, but I talk about this in my TKPs article).

A note before I explain how I investigated this is required. Other posts in this blog are about abstract geometrical constructs; in a sense, they are about making models. In this one, however, the topic is simply a computational/experimental exercise; based, to be sure, on a theoretically consistent model of a truck. The thing is, as I explain also below, that the function between deck tilt and bushing deformation still eludes me. I will return to the problem some other day.

The nitty-gritty

I decided to investigate the volume of the bushing compression/deflection3 under different deck tilts, which would give an indication of the differences between perpendicular and non-perpendicular PA/KP configurations. I run a model of a truck turning with a single cylindrical bushing intersecting a plane (representing the hanger) 1st. at 90°, 2nd. at 60° and 3rd. at 30° with the pivot axis of the truck. In other words, I got a 60° PA truck and three different angles between KP and PA: 30°, 60° and 90°. The deck tilt goes from 0° up to 40°.

The “experiment”

As intimated above, it’s not too easy to figure out the function between deck tilt and bushing squeeze and since I’m not a big fan of bushings (because elastic metal would surely provide a more energy-efficient return-to-center mechanism in a serious sport; but I digress, that’s a topic briefly discussed here), I abandoned the effort to discover it and decided that I just need to plot the results. I only needed to know the volume of the cylinder that is intersecting with the plane (i.e., the compression/deflection of the bushing on the truck hanger). I used the equation for this volume from Wolfram (which actually isn’t necessary because the volume in question is directly proportional to the height of the intersection and that’s given by the model). I charted the results out:

I was surprised: I was expecting (hoping, even) that the 30° would initially diverge from the 90° and then start catching up again. Nope: it keeps diverging. Then again, I should have known: it is just wishful thinking to expect that miraculously the volumes would converge again (“progressively”), neatly right when a rider had leaned her deck enough to pull her back up.

What is interesting however is that, whichever function this is, it has a positive second derivative for the 90°, a negative one for the 30° and a ~0 one for the 60° (at least within this range of tilts). So there should be a PA/KP angle for which (at least approximately) the bushing deformation could be said to be “linear.” Was it for me in the 60° because that was also my PA angle? To investigate this, I plotted the graph for a 45° PA truck this time with the KP at 15°, 45° and 90° with the PA. The graph on the right is what I got. You can see that at 45° KP/PA it looks “linear”. I need to investigate this thing: it seems that for every degree of tilt we get a constant amount of additional bushing deformation. This seems congruent with a short, passing statement I saw in a paper, namely that bushing resistance is directly proportional to deck tilt (Rosatello et al., 2015).

Finally, I plotted the bushing deformation against the axle turn (not tilt). I only did this for a 60° PA angle. There’s nothing to see here really, nor would it be relevant for this problem (as sketched out in the first paragraph). But in any case, here it is (on the right).

Results in a nutshell

When a truck is mounted to have a PA of 60° (as is usual in slalom and LDP), then: if it is a typical RKP, the bushing is deformed not only more (which I believe isn’t surprising for anyone), but also with an increasing rate, than if the truck were a typical TKP, whose rate of bushing deformation per tilt is either diminishing or is almost constant (see first graph – the orange curve shouldn’t be far from what a TKP looks like, while the blue line pretty much is what an RKP looks like). When PA angle=KP/PA angle, the volume of bushing deformation seems to be directly proportional to the deck tilt angle (yellow line in first graph).

Conclusion

There is certainly a significant difference in how the bushings deform in these two cases (i.e., RKP and TKP trucks). But could it rescue the idea that an RKP is “linear” and a TKP is “progressive”? Hardly, it seems. Ironically, the other way around would have been closer to the truth. Personally, I think we need accurate terms, not aesthetic metaphors, and the physical world provides patterns we can use to gain some clarity in how we understand and communicate our sensations.


References:

PSI Urethanes Inc. (n.d.). Calculating Compression/Deflection Of Polyurethane.
Polyurethane. (2021). In Wikipedia.
Rosatello, M., et al. (2015). The Skateboard Speed Wobble.
Weisstein, E. W. (n.d.). Cylindrical Hoof. Wolfram Research, Inc.


1. Of course it can also mean that some folks -not all- merely echo other people’s experiences, for validation. But, that’s internet forums for you…
2. For the KP/PA angles of a couple of popular trucks, check here.
3. Thanks to Brad Miller for pointing out PU doesn’t get compressed, but it’s deflected when squeezed.

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