# How do I know when I'm reaching the limits of my wheel?

## Recommended Posts

36 minutes ago, Chriull said:

It's the same acceleration, as long as the HMotW does not overlean

Lets say he only has 300kg, the child 30kg - factor 10 between the weights. With the "same lean" the man puts a ten times higher force on the pedal - this torque has to be countered by an equal torque putting 10 times the force from the wheel on the road. As F = m * a this 10 times greater force accelerates the 10 times bigger mass at exactly the same rate.

Excellent. Thank you!

##### Share on other sites
36 minutes ago, Chriull said:

Lets say he only has 300kg, the child 30kg - factor 10 between the weights. With the "same lean" the man puts a ten times higher force on the pedal - this torque has to be countered by an equal torque putting 10 times the force from the wheel on the road. As F = m * a this 10 times greater force accelerates the 10 times bigger mass at exactly the same rate.

The wheel isn't weightless. The equation is closer to F = (M + m) * a1, where M is the mass of the wheel, and m is the mass of the child. 10x heavier rider would convey 10x torque, causing 10x linear force, i.e. 10F = (M + 10m) * a2. Substitute in a sufficiently large value of M (Gotway Monster, 32kg), and you'll realize that a2 is larger than a1:

$F=(M+m)*a_{child} \\ a_{child}=\frac{F}{M+m} \\ a_{child}=\frac{F}{32+30} \\ a_{child}=\frac{F}{62} \\ a_{child}=0.0161F \\ \\ 10F=(M+10m)*a_{man} \\ a_{man}=\frac{10F}{M+10m} \\ a_{man}=\frac{10F}{32+10*30} \\ a_{man}=\frac{10}{72}F \\ a_{man}=0.1389F$

The actual equations are a lot more complicated than this, but riders of a different mass don't get the same amount of acceleration from the same amount of lean on the same wheel.

• 1
• 1

##### Share on other sites
1 hour ago, hyperair said:

The actual equations are a lot more complicated than this, but riders of a different mass don't get the same amount of acceleration from the same amount of lean on the same wheel.﻿

Are you saying the inverted pendulum is not a correct model to describe the situation? Why not?

##### Share on other sites

Inverse pendulum equations are more complicated as he says

##### Share on other sites

I love how the math clears up what objectively happens.

• The pedals being closer to the axle effectively gives you a harder ride mode. Now I'm wondering if different ride modes (e.g. my old softie ACM vs. the harder MSX or Tesla) are actual firmware differences or merely caused by geometry.
• Never realized a heavier rider gets more acceleration. Essentially it's like riding a lighter wheel for him in comparison to a lighter rider.

That still doesn't answer the question what one actually feels when a wheel has oomph or not in a certain situation.

• The forward acceleration?
• The forward force the wheel has to exert? Maybe scaled by rider mass or something? As we've seen, it's not proportional to the acceleration.
• The "personal effort" one has to exert in getting the wheel going? How far one has to lean etc.
• The resistance of the pedals? The delay of the pedal/wheel reaction?

What is it?

-

On the original topic:

On 6/2/2019 at 11:31 PM, erk1024 said:

What does the wheel do if you are using too much current? Tiltback? I'm assuming that no alarms will go off because those are specifically for speed.

You didn't really get an answer to this. What does the wheel do if you are using too much current?

Hopefully, overheat (with warning, no damage to the wheel, good!) - or if it doesn't do that: blow a mosfet (no warning), fry some cables (no warning, only seen on Gotways for now), blow a fuse (no warning, only seen on Kingsongs for now, I think they are 60A or 80A or something fuses).

In other words, in theory there are a lot of no-warning situations here, which really isn't what you want. From reality we know that these extreme stresses are so far removed from normal riding that you can just expect an overheat alarm or the wheel just works. Or you just have an overlean for non-current related reasons (low battery or near top speed where there isn't enough voltage to power through something).

A cell can even do 20A for a short time, so the 6p 18XL battery can do 120A without problem. So battery current doesn't seem to be a limiting thing in practice. It's either the electronics or a lack of voltage that might cause a crash. Or you know, cars and potholes

##### Share on other sites
25 minutes ago, meepmeepmayer said:

I love how the math clears up what objectively happens.

• The pedals being closer to the axle effectively gives you a harder ride mode. Now I'm wondering if different ride modes (e.g. my old softie ACM vs. the harder MSX or Tesla) are actual firmware differences or merely caused by geometry.﻿
• Never realized a heavier rider gets more acceleration. Essentially it's like riding a lighter wheel for him in comparison to a lighter rider.

The pedals being closer to axle IMO give a better lever so should allow easier lean control albeit you will be more unstable

Heavier rider have better acceleration as long wheel power is unlimited which is not a case  But he would gain more acceleration for given lean (and over-lean sooner too)

##### Share on other sites
4 hours ago, LucasD said:

Inverse pendulum equations are more complicated as he says

Are you just pasting equations or do you actually understand them?

My previous question was: why do you think that the inverted pendulum does not model the lean-vs-acceleration situation accurately? I don't see any reason why it would not, but I am always happy to learn what I don't understand.

##### Share on other sites

@Mono Nobody says that the inverted pendulum isn't the right model. What was said is that the real equations (for the inverted pendulum, which were subsequently posted) are more complicated than the approximation that was posted first, F=(m+M)a , which is just the stationary (intransient) case of the inverted pendulum.

##### Share on other sites
Posted (edited)
1 hour ago, meepmeepmayer said:

the approximation that was posted first, F=(m+M)a , which is just the stationary (intransient) case of the inverted pendulum.

I guess that this equation describes the inverted pendulum, transient or stationary, must be a misunderstanding. The equation just connects force with acceleration, AKA Second Law of Motion. An inverted pendulum equation system without the angle of the pendulum is a meaningless exercise.

Edited by Mono

##### Share on other sites
On 6/5/2019 at 2:38 PM, mrelwood said:

The wheel responds only to the location of the rider’s Center of Gravity.﻿ If the CoG is placed too much forward, you crash due to over-lean. Up to that point the wheel uses as much power that is needed to keep you upright. This is an universal rule with all EUCs.

I think there is an important additional degree of freedom: how much pressure the rider applies to the pedal at any given point in time (set apart from where the pressure is applied, which is obviously relevant as well). It is possible to release pressure for a short (but long enough) period of time such that the wheel can catch up under the rider even from an out-of-balance overlean situation.

To my experience this is an important conception for riding safely: to intuitively understand how to "actively steer" the wheel under the body quickly to any (other) desired place under the body. This again requires in particular flexible knees in the first place.

##### Share on other sites

The point of the post was that different weight riders get different accelerations at a given tilt (constant angle, if you care only about a very short time frame).  For that you don't need any more than the second law of motion. Which is what's left of the inverted pendulum if you have a constant angle (angle derivatives vanish) and ignore the second "vertical" equation.

I guess you can argue that it is no longer an inverted pendulum if it's too degenerate

##### Share on other sites

It is kind of meaningless because for a given tilt/ angle a heavier one exerts more force.

But by the same token to get to the same lean he need to exert more force one wheel

##### Share on other sites
9 hours ago, Mono said:

I think there is an important additional degree of freedom: how much pressure the rider applies to the pedal at any given point in time (set apart from where the pressure is applied, which is obviously relevant as well).

Very true, and this is exactly why I hop a bit even for smaller curbs, roots and other obstacles; to decrease the required power from the wheel. In addition the riding mode and firmware behaviour affect how fast and how strongly the destabilitioning of the CoG is counteracted, making the whole system a constantly varying entity of forces. To which the rider again reacts based on his experience, reflexes, foolishness, etc. But as my point wasn’t understood as is, I tried to spare on the details.

9 hours ago, Mono said:

It is possible to release pressure for a short (but long enough) period of time such that the wheel can catch up under the rider even from an out-of-balance overlean situation.

Should be, yes. On the other hand, when the pressure is released, the wheel receives a smaller rotational moment of force, meaning the wheel will accelerate less. But I don’t know wether this could be an issue in said situation or not.

9 hours ago, Mono said:

To my experience this is an important conception for riding safely: to intuitively understand how to "actively steer" the wheel under the body quickly to any (other) desired place under the body. This again requires in particular flexible knees in the first place.

Free hands being another. Our arms are heavy enough to be useful for fast weight shifts. Which we already do when we are learning to ride (or manoeuvre between roots and rocks on the MSX) and swing our arms for balance. Which makes riding with hands in the pockets (with wrist guards that get stuck in the fabric) an even worse of an idea.

New safety trend: Ride with your hands up horizontally to the sides! You get the best weight shifting and rotational potential in all directional axes!

##### Share on other sites
5 hours ago, mrelwood said:

Should be, yes. On the other hand, when the pressure is released, the wheel receives a smaller rotational moment of force, meaning the wheel will accelerate less. But I don’t know wether this could be an issue in said situation or not.

Right, I think it is an issue. To move the wheel quickly under the body one wants to apply pedal tilt force. I think this is mainly done with ankle movements, such that there is a good separation between releasing weight by knee actions and steering/pushing the wheel by ankle movements. Much easier said than done though.

##### Share on other sites
19 hours ago, meepmeepmayer said:

That still doesn't answer the question what one actually feels w﻿hen a wheel has oomph or not in a certain situation.

• The forward acceleration?
• ﻿ The forward force the wheel has to exert? Maybe scaled by rider mass or something? As we've seen, it's not proportional to the acceleration.
• The "personal effort" one has to exert in getting the wheel going? How far one has to lean etc.
• ﻿ The resistance of the pedals? The delay of the pedal/wheel reaction?

What is it?

I think what you actually feel can be boiled down to "I've leaned this much, but the wheel isn't responding", and this happens in two ways: the pedal dips forward (motor can't match the rider's torque), or the rider falls off the front of the wheel, e.g. when a lightweight rider rides a Monster.

In the first case, your wheel can't keep up with your body. This is an overlean where you've gone beyond your wheel's torque margin, causing the motor to lose the "push of war" against you on the EUC body, causing the EUC body to tilt forwards. If you arch your back to take your CG offline from the vector that your wheel is pushing you, and keep the pressure on your toes, you can occasionally recover from this, especially if you approached the torque limit slowly, so you have time to react.

In the second case, you haven't managed to request the correct amount of torque from the motor. It's like standing straight up (as opposed to bracing yourself properly against the ground), and trying to push a heavy rock. The rock doesn't budge, but you've pushed yourself backwards. In this case, the pedals feel rock-solid, but you've fallen off the front of your wheel. But this doesn't only depend on the weight of the wheel. A few other things matter as well, like you realized -- if your pedal arms are shorter, it pushes against you harder. Then there's also the balance of the EUC body/placement of its centre of mass:

• EUC body CG above the axle (e.g. Inmotion V5, V8, V10): Creates a negative feedback loop where an accelerating wheel causes the EUC body's CG to pull back and resist the rider's torque on the EUC body, like a seesaw.
• EUC body CG below the axle (e.g. Rockwheel GT16): Creates a positive feedback loop where an accelerating wheel assists the rider in torqueing the EUC body forward.
• EUC body CG in front of the axle: Biases the wheel towards accelerating
• EUC body CG behind the axle (Gotway Monster): Biases the wheel towards braking/reversing

Then there's also the rotational inertia of the hub motor's rotor -- it's basically a flywheel with significant mass and radius, so you need some amount of torque to change its angular velocity as well.

So an interesting, low-effort mod to make to make your wheel feel snappier would be to stick weights below your pedals, or use heavier pedals.

14 hours ago, meepmeepmayer said:

﻿﻿ I guess you can argue that it is no longer an inverted pendulum if it's too degenerate

You're right about it being quite degenerate. A wheel without a rider is an inverted pendulum. The rider is an external body that manipulates the pendulum to control the wheel. And if the rider fails to manipulate the pendulum, then the pendulum just does whatever it wants but the rider falls off.

##### Share on other sites
Posted (edited)
1 hour ago, hyperair said:

So an interesting, low-effort mod to make to make your wheel feel snappier would be to stick weights below your pedals, or use heavier pedals.

Nice suggestion. I see the point, but would be surprised if adding weight to the pedals would work to make any wheel snappier. So we have a relatively easy way to falsify one view or the other.

1 hour ago, hyperair said:

Then there's also the balance of the EUC body/placement of its centre of mass:

• EUC body CG above the axle (e.g. Inmotion V5, V8, V10): Creates a negative feedback loop where an accelerating wheel causes the EUC body's CG to pull back and resist the rider's torque on the EUC body, like a seesaw.
• EUC body CG below the axle (e.g. Rockwheel GT16): Creates a positive feedback loop where an accelerating wheel assists the rider in torqueing the EUC body forward.

I am surprised that there is a wheel where the EUC body CG is below the axle. How did you confirm this?

On 6/7/2019 at 9:19 AM, hyperair said:

WIth the understanding that the rider torque must be equal to the motor torque to maintain balance, and that torque is tangential force multiplied by the lever arm, a few things start to stand out:

• Larger pedal clearances decrease the distance from pedal to axle, so you convey more torque to your wheel for a given amount of "lean"
• Larger wheel diameters increase the torque required to induce the same linear acceleration, so you need to push harder to make a larger wheel accelerate in the same way
• Powerpads or cushions with sufficient friction allow you to use your knees to convey torque to the EUC body, allowing you to lean harder without falling off

Indeed interesting points. Though decreasing the distance from the pedal to the axle (first bullet) should lead to less torque, not more torque applied to the wheel. On the other hand, elevating the pedal brings the angle at which the force is applied closer to 90º, hence increasing the torque, which may dominate the distance decrease.

Edited by Mono

##### Share on other sites
Posted (edited)
5 hours ago, Mono said:

Nice suggestion. I see the point, but would be surprised if adding weight to the pedals would work to make any wheel snappier. So we have a relatively easy way to falsify one view or the other.

I haven't actually tried this, but I am quite interested in finding a viable solution to do this that doesn't make me more likely to clip my pedals on something. This was a theory that I came up with while trying to work out the physics for this sometime back.

Quote

I am surprised that there is a wheel where the EUC body CG is below the axle. How did you confirm this?

I didn't actually manage to confirm this -- this was my estimation based on how the batteries are mounted, and also the fact that the GT16 stock pedals are much heavier than anything else I've held (700g from my vague memory). The GT16 is also a really zippy wheel, feeling about as zippy as the V8 despite being ~20kg with the trolley handle compared to the ~15kg of the V8, and much zippier than the V10 which is of similar weight and wheel diameter. I attribute this to V8's high CG (battery above motor) and the V10's even higher CG (both the larger battery as well as the heavy extended handle) as well.

Quote

Indeed interesting points. Though decreasing the distance from the pedal to the axle (first bullet) should lead to less torque, not more torque applied to the wheel. On the other hand, elevating the pedal brings the angle at which the force is applied closer to 90º, hence increasing the torque, which may dominate the distance decrease.

Oh yeah you're right, whoops. I haven't actually worked through the math for how the angle change works yet, but I suspect that the angle at which force is applied gets closer to the tangential direction once the wheel starts accelerating, due to the positive feedback loop I mentioned earlier.

Edited by hyperair
Mentioning the V10

##### Share on other sites
On 6/8/2019 at 3:46 PM, Mono said:

I see﻿ the point, but would be surprised if adding weight to the pedals would work to make any﻿ wheel snappier. So we have a relatively easy way to falsify one view or the other.﻿

I am doubtful as well. Weight of 3-5 times the whole wheel’s weight is already standing on the pedals (with the CoG well above the wheel top). How much additional weight would the pedals require to have a noticeable effect? We might be talking in pounds, not ounces.

##### Share on other sites

Very interesting thread in many ways!

When it comes to applying force on the front half of my MSX I can do it in the following ways:

• Standing straight and standing on my toes
• Placing my feet further forward
• Calibrating forward tilt
• Sitting and leaning my upper body forward
• Bending my knees and leaning forward by hinging at the hips and for even more acceleration stretch out an arm
• Having straight legs and leaning forward while yelling Shamone
• Doing a front shoulder raise with grocery bags without leaning backwards
• Raising my heels while doing some of the above
• Using soft mode

Some of the above movements will still allow me to brake evenly with my acceleration and some will not.
In some cases I have simply moved my feet forward or tilted the pedals forward and this will cost me braking power.
I prefer to use my whole body as the lever but sometimes I will inch my feet forward if I know I am going to be playing with acceleration and speed. At the same time aware that I have reduced braking power compared to when I have my body in the middle of the EUC.

The soft pedal mode will make the pedals do a short inclination when you shift your weight forward in front of the center of the wheel. It won't last forever so you won't magically accelerate forever but it will yield at the beginning allowing for a faster takeoff.

Basically we're tightening a nut or opening a door. Longer wrench = more force applied to nut. Open door far away from hinge = easier to open.
Bigger wheel = bigger nut / door. So we will need a bigger wrench and we will also need to move the door handle out some more.

I have a weighted vest that weighs 10kg. I'll give that a try tomorrow. Since the weight distribution will be above my waist I imagine it will improve my leverage. I can only imagine what that + 3 degree forward incline + soft mode would feel like. And then raise my heels.

• 1
• 1

##### Share on other sites

I was out grocery shopping with my wife. On the way home I had a 5kg bag of groceries. I carry it in front of me and close to my body with a bent arm (basically doing a short bicep static curl). I asked her to match my speed. I held the bag out in front of me with both arms and the MSX accelerated. I brought it back close to me and I slowed down. I held it out with one arm and same thing but there were some shearing forces on my torso making it a bit uncomfortable. We got to a hill and I did the same; outstretched in front of me with both arms. I also leaned forward. There was a huge difference in acceleration as well as maintained speed and much less leaning required than I normally need to get up that hill.

I then held the bag to my chest and shifting forward and backwards. Improved acceleration and worsened braking (as the weight is in front of me).

I'm sure I have some weighted wrist bands and ankle bands lying around somewhere...

##### Share on other sites
1 hour ago, Mike Sacristan said:

I'm﻿ sure I have some weighted wrist bands and ankle bands lying around somewhere...﻿﻿

Or maybe start buying more chips and soda...

##### Share on other sites
2 hours ago, mrelwood said:

Or maybe start buying more chips and soda...

## Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.
Note: Your post will require moderator approval before it will be visible.

×   Pasted as rich text.   Paste as plain text instead

Only 75 emoji are allowed.

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

×

×