So how much are you into the mono wheels right now dude. The build videos were really nice!!!
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Not a crazy amount haha I built the whole vescwheel on paternity leave - however, I do enjoy it quite a bit. More videos on the way!
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Still waiting on pt 3ā:eyes:
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Cheers mate!
Havenāt worked out what Iāll be using as the IMU yet. I anticipate that will be one of the trickier parts as my VESC doesnāt have one built in. Open to ant suggestions.
Not sure what you mean about the float package?
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Havent seen that one! Will definitely watch. Thatās one chunky board.
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I mean at that point you may as well go back to using a hub motor! Not sure what relevance the thin tyre has?
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Interested to learn more about this. Does the PID operate on current feedback? Surely the PID response would be independent of the current if tuned correctly?
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As in very little sidewall to make up for a large rim, so I donāt just mean just a huge wheel.
It would still be light and powerful from the small high kv motor but it would take some less than ideal engineering.
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The PID controls the board angle (motor position, and eventually velocity) based on motor torque (current), so the more current the loop can apply the faster the system responds, which means the board will change speed before it accumulates a lot of position error (tilt)
Think of the current as how stiff the āspringā itās using to pull the board level, low current means a soft āspringā so it will wiggle around a lot
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So, Iāve spent some time this evening running a few preliminary calculationsā¦
Iāve definitely gone wrong somewhere as Iām getting bending stresses over 1000x the yield strength of steel under my dynamic load case. Iād appreciate if someone could have a look. I suspect itās because Iām assuming a very short time period for the impact and a very high stiffness for the tyreā¦
Edit: I also think my estimate for tyre stiffness is far too stiff which is leading to extremely high impact force in the calculations.
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I would buy one of the onewheel friendly Vescsā¦
Not sure if external imus play Niceā¦
Float Package is stuff in the Vesc tool specific to onewheels.
Have you seen the vescify discord?
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I think the nonphysical results are starting with your linear spring assumption. Tires are pneumatic springs, and the deflection of the contact patch is small compared to tire volume, so they can be treated as constant pressure springs. So the force applied to the ground is proportional to the contact patch area, which will grow quickly at first, but become closer to constant at large tire deflections. The linear model you put together probably over-predicts the reaction force.
You also estimated the impact duration using the formula for the natural frequency of the mass-spring system. This would only describe the system accurately if the human body was perfectly rigid, but itās actually got its own springyness. If I performed a 1m drop with my knees locked, I would also pull a 100g landing and snap my bones. As the rider bends to absorb the impact, theyāll absorb the majority of the energy that would go into snapping your frame rails.
I would start with data about how much force humans exert when jumping, seems to be ~10g for a half meter drop. But those are gymnasts doing stiff landings, so maybe thereās a better source that could match our sport better.
https://www.sciencedirect.com/science/article/abs/pii/0021929088902527
Then once you have a G factor, just treat the frame loading like a statics problem. I donāt think thereās a need to bring kinematics of the tire into it, since the rider has so much more mass and āsuspension travelā than the vehicle. The vehicle might vibrate a bit as it gets jostled, but compared to its natural frequency, the force of the rider standing on it is a slow-moving boundary condition that it will settle into an equilibrium around. The tire will just smooth out the initial instant of contact until the system reaches the real point of maximum load, when the rider bottoms out their legs.
Oh, also you need to set one reaction force in the beam calculator as a roller support. setting both as pinned can produce weird results.
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Thank you so much for your in depth response, I truly appreciate it.
I will take your feedback on board and look into this later today 
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Good luck with the build! Iām staying tuned
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I have not but Iāll check it out. I want to avoid buying a new VESC if possible thoughā¦
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As promised @Flyboy I took your feedback into consideration.
I began by attempting to work out the impact force using the same methodology as the one in the paper you cited:
We can model the human body as a 2DOF mass-spring-damper system, whereby the impact force applied by the rider and Onewheel to the ground is given by:
To estimate k1, we can extrapolate the linear relationship between stiffness and mass demonstrated by ĆzgĆ¼ven et. al. which gives us an approximate relationship:
k1 = 2.1m - 26
In our case, m = 135 kg, therefore k1 = 257.5 kN/m.
To estimate c1, we can follow in their footsteps and use the stiffness proportional damping assumption:
We will assume the damping ratio, Ī¾1 to be 0.5.
Ļ1 is the undamped natural frequency of the system, which is given by:
Therefore, c1 = 5896.5 Ns/m.
To calculate the peak impact force we can use constant acceleration kinematic equations in place of x1:
Assuming an initial velocity of 0, this simplifies to:
And, working out the time taken to fall 1m:
Putting all these puzzle pieces together, we get:
Plugging in the value of t gives us a peak impact force of 284189.40N.
Now we can return back to the beam bending calculations. Using a shaft length of 241.3mm, OD of 25mm and ID of 20mm, we get a cross sectional area of 176.71mm2 and second moment of area 11320.78mm4. Assuming the shaft is made from generic steel, the Youngās modulus is 200GPa. Modelling the impact as a UDL as it is transmitted to the shaft via. the wheel hub:
We end up with a peak stress of 17752MPa which is 68 times the yield strength of steel. This is because the load case is still incorrect. No wonder the shaft is failing if it is subjected to over 2100gās of acceleration!
Letās take a different approach.
The gravitational potential energy of the Onewheel and rider combined is:
If we assume all GPE converts to KE (i.e. in typical engineering fashion we neglect air resistance), the average force required for us to come to a stop over a given deformation distance is governed by the work-energy principle such that:
Where Īx encompasses the deformation of both the rider and the board. When a person drops from a height, they crouch to absorb the impact. Letās assume the total deformation of person + tyre comes to just 10cm:
Assuming a triangular impulse profile, this gives us a peak impact force of 26485N.
From here, I explored a few different combinations of hollow/solid shafts, with 30mm or 60mm long hubs. It became apparent that increasing the hub length to 60mm has a very minimal impact on the bending stress. I wouldnāt want to go much higher than that otherwise I risk pushing the sprocket a significant distance from the wheel, and will end up with a comically wide board.
None of the hollow shafts are able to survive the peak impact force without yielding, and only solid steel shafts with a 40mm OD or greater will survive (regardless of the hub length).
A solid steel shaft that is 240mm long and 40mm diameter weights approximately 2.4kg. Thatās pretty hefty and is beginning to raise alarm bells as Iām aiming to keep the overall mass of this build below 15kg. To make matters worse, using a keyed steel shaft may end up being too cost prohibitive:
This leaves me with three options at this stage:
- Find out if my friend that has access to a CNC mill and lathe has the capability to mill keyways in steel shafts.
- Accept a lower and more forgiving load case at my own risk.
- Re-architect the design by introducing some sort of shock absorption or redirecting the radial load somehow.
Iām hoping number 1 works out, otherwise Iāll probably go with option 2ā¦
Also on a side note, today is my birthday 
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More work than i have ever put into anything holy fuck dude
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I warned you.
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Happy birthday! I appreciate your enthusiasm, but these results are still nonphysical.
Youāre coming up with a 20g impact, which you typically have to crash a car into a tree to experience. Consider that ~60g is the start of the lethal range. A rider wouldnāt be able to transmit that much force to the vehicle, since they would crumple and fall off the board.
Youāre predicting that a 40mm bar will fail in double shear, when similar jumps are landed by MTB riders all the time using 4x 12mm cantilever axles, which take the easier route of bending failure when overloaded.
These numbers donāt pass the smell test, which should indicate faulty assumptions. Please, put down the graphing calculator and back away slowly.
In general, you should define and solve physics problems using pathways that start from constants you are fully confident in, and build outward from there. The first time, you treated the tire spring model as the center of attention, and perfectly predicted the springās response to an unrealistic boundary condition (a perfectly incompressible rider bolted to the deck). The second time, you used a better spring model, but the result was still wacky because you were still considering the core response of the physical system before you considered the boundary conditions is has to obey. Will the rider utilize their full muscle power for every size of impact? Hard to say, that would need a lot of empirical data to confirm.
And so using the energy method is the correct choice here. Iām glad you went for it! Your chosen problem statement is to figure out the loads generated by a 1m drop. So the amount of impact energy is fixed. The length of the riderās legs is also a known constant. Since these values are part of the problem statement itself, theyāre the perfect point to jump off of. Weāve defined them to be true, so thereās no speculation needed.
However, you chose to assume 10cm of leg compression. This sounds like speculation to me, which you should avoid because this choice of value has a strong effect on your final result. It doesnāt match up with my personal experience mountain biking, where a 1m huck to flat on a hardtail would 100% slam my ass into the seat, meaning we could expect at least 30cm of compression. These folks seem to agree that you need a lot of compression to land a huck this big:
If the riderās legs compress by 50cm instead of 10cm, the impact would be 4g instead of 20g. If you really want to get an accurate prediction of the loads on your board Iād suggest trying to get real world riding data to pin that deflection number down more tightly.
But it probably doesnāt matter since I think you also missed the mark on axle strength. Are you still analyzing it like a bending beam with a load at the center and pinned supports at the ends? If so, I donāt think that itās a good representation. Your rear wheel hubs bolt onto the rim, and therefore have significant bending stiffness. If the length of axle between the frame rails is stacked up with these hubs, then (1) the load will be distributed, not just applied at the center and (2) the axle will be insulated from bending stress by the hubās higher bending stiffness. If you stack most of the axle, it will primarily experience shear stress between the hubs and the frame rails.
Chromoly, (or any other similar medium-strength steel) has a tensile strength of ~400MPa. The rule of thumb for steel is that the shear strength is half the tensile, and letās throw in a safety factor of 2 for good measure. So the allowable shear stress is 100MPa.
Your overkill 20g impact scenario has a load of 26500N in double shear, so the axle needs 132mm2 of cross section, or a 13mm diameter steel rod.
This passes the smell test since my old hardtail bike used 5mm diameter x 120mm axles. If they were under bending stress they would have been destroyed instantly, but the wheel hubs stacked the whole axles, so they only experienced shear, and therefore lasted for years taking nasty impacts.
TLDR: no need to overthink it, just copy the build of any random dirt bike and youāll have an overkill structure.
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So science communication and education is my day jobā¦ Iām loving this thread! So much theory and practice and knowledge and wisdom. Canāt wait to see the actual results! You would be (might actually be?) a fine teacher @Flyboy !
Would it be worth looking at the onewheel specs, adding some leeway, and going from there? You cold also get some tube, put it on a lever, jump on both sides, see what happens (and could vary these loads) - could even brace and unbrace legs if youāre a true experimentalist!
Anyway I am genuinely enjoying your quest and wish you well. As someone who regularly wishes they had a worked out plan before starting, time to get on the tools!
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