Mounting your battery, Center of Gravity.

[safe]

Bicycle / Motorcycle Comparison

The laws of physics are the same for both, obviously, so in order to compare them we have to think in terms of relative proportions.

On a motorcycle (or an ebike with 60 lbs of batteries) the weight is significant enough to seriously effect the handling behavior. Add speed and you get a multiplication effect. So when you are dealing with really high speed (100+ mph) the ability to get the bike to roll (countersteer) is so critical that if you get it wrong your motorcycle will continue in a straight line while you fight with it. Most of the concentrated efforts in motorcycle geometry designs have focused on reducing the difficulty in getting the bike to turn. For a while I remember a period of time when many motorcycles were trying out smaller front wheels with the logic being that it would have lower frontal area (better aerodynamics) and would be easier to steer at speed. I know from my old road racing motorcycle days (RD400 street racing) that at about 80-100 mph the bikes already feel really heavy. It's hard to imagine the really high speed riding (upwards of 180+ mph) and how hard it would be to steer.

On the opposite extreme... a bicycle traveling at a top speed of 15 mph (typically) has almost zero weight and so little speed and momentum that you could do just about anything with the weight placement and not suffer any serious negative effects.

This is the irony about all this...

As long as you go slow and are lightweight you are protected from all the complex issues of motorcycle type geometry.

So in effect "anything" is correct on a bicycle at slow speed! :lol:

 

[John in CR]

Tiberius,

This is an occasion where center of gravity is different that center of mass. You guys all seem to be stuck on center of mass, when in the case of a bicycle with its wheels on the ground CG is what's important. Pick the bike up to put it on a car rack and CG and center of mass become one in the same. What I've been talking about would obviously change the weight distribution toward the rear and I'm sure has an effect on traction as you pull more G's in curves.


Safe,

Speed is not the issue. The detrimental impact of this placement is going to depend on how strong you countersteer like in doing a slalom course and also how tight your turning radius is relative to speed. It's exactly because the added weight wouldn't be part of the combined bike+rider CG, that it could cause the rear end to slip in a high performance turn. Change it your position from speed to performance riding then we can agree, but that's really the traction issue that I've been dancing around, because you've got the deep lean as if there's no weight but extra weight at the outside radius of your turn so the centrifugal force on that weight is greater. My e-bike is no 15mpher and goes 35 now and soon 40 or more, but that doesn't mean I'll ever try to push the limits in turns. For this errands bike I want to keep it light and nimble in handling, and save the motorcycle-like design for the offroad bike I plan.

John

 

[johnrobholmes]

Uhg, un-subscribing.

 

[Tiberius]

Uhg, un-subscribing.

Yes, life is too short to deal with this.

 

[safe]

Momentum

Speed is not the issue.

Speed effects steering geometry.

If you are going zero mph then countersteer would pivot the frame around the rear contact patch. At zero mph all the rear contact patch theories are valid and correct.

At infinite speed the momentum of the bike becomes infinite as well in the forward direction. I hope you get that part... forward momentum INCREASES with speed but rotational inertia DOES NOT CHANGE.

Did the lightbulb go off?

(one of these days we will agree on the same laws of physics)

Exclude issues about bicycles and motorcycles and get back to the basics of bodies in motion. Let's do a thought experiment:

"If you fire a bullet out of a gun it travels at extremely high speed. In order to change it's direction it requires considerable force because the momentum of the bullet wants to travel in a straight line. However, if we were to place some little spiral grooves into the bullet that small frictional effect would make the bullet spin. The forward momentum would be largely unchanged."

You could make the same thought experiment with a bow and arrow.

Basically you have to multiply the effects of forward momentum as the bike goes faster. Anyone that has ever ridden anything at speed (80mph) knows that the bike tends to want to go straight and it's difficult to fight the forward momentum. 100 lbs might feel light at 20 mph, but can feel heavy at 40 mph, this is because you need to multiply the mass by the speed.

Strictly speaking:

Momentum = Mass * Velocity

 

[John in CR]

Safe, stating the obvious doesn't support your argument. The only things "rotating" on a bike are the tires, crank and the headset. Your drawing with balls and arrows makes no sense. You demonstrated quite a few pages back how countersteer angles are smaller at higher speed with the tire track divergence being smaller, so while momentum obviously increases with speed the angles decrease. Explain what happens in a way that contradicts what I've said, which now even includes my discussion of the traction detriment in a curve that comes with a very low battery placement and is probably what TD meant long ago by "wagging the dog".

The concept of roll axis relative to a bike is erroneous, because there is no roll. A plane rolls because it's not on the ground, and it's CG is the same as it's CM. A car has some roll in a turn only because of it's suspension and flexible tires. If you want to talk about adding weight with a choice of placement for performance riding on two wheels, then it needs to be at the point that travels in the straightest line, which is at the CG of the rider+bike. For those who want to call what occurs with the a bike relative to the CG of the rider+bike "roll", then I'll just agree to disagree about the terminology since its use seems to be widespread. On a typical bicycle this point is outside of the erroneous line Safe drew and repeated the image a number of times. Also, it is a point, not a longitudinal axis, because any axis you try to draw on a bike will be an ever changing one. Plus to the front or rear of the "point" will require extra force to create a turn.

Any placement will have detrimental effects. Attached to the rider will have the least effect in terms of handling, but those who've carried their batteries in backpacks can't wait to get them off their back due to comfort and the convenience issue of wires going from you to the bike. To me the next logical place for typical riding on a paved surface is as close to the rear contact patch as possible, because the bike will feel and steer most like it does without the added weight. Some extra care is needed not to have your rear tire slide out due to the centrifugal force laterally on that mass during aggressive turns, but for the typical e-bike rider the ability to brake harder without going end-over-end that a low rearward placement permits is probably a far greater safety benefit than the performance limitation in turns. The only other detriments I see are that the batteries are more exposed than in the triangle, and you run a greater risk of getting clipped in the achilles while walking the bike around. Otherwise, a low and rearward placement will be the easiest to maneuver when off the bike. I may give SteveCA's front wheel placement a go some day, since a bit heavier steering may be worth getting the batteries completely out of the way without making the bike top heavy, which can be a bear to move around. If I ever do a short range performance pack, it will probably go on in a backpack. When I build an off-road bike the batteries will go in the triangle, because I see it as the best compromise, and it will be ridden much more like a motorcycle anyway.

All this discussion and I'm still putting one of my packs in the triangle, since it and the controller fit, out of convenience more than any other reason. It's only 12lbs total, so it doesn't have a big impact. I can feel it though, and even if 40lbs of lead fit in the triangle no way would I place it there, because I like the light nimble feeling of a bike, and a significant weight in the center of a bike will force a more motorcycle-like riding style.

I've learned some good stuff in this thread and it forced me to really think through the issues of battery placement. I'm just sorry that I couldn't explain myself well enough about the point that once tires are on the ground CG and CM can be different, and the lower the added weight is placed the less effect it has on CG. I believe this is an important point related to battery placement. Too bad the unfelt weight of rear contact patch placement shows up at the wrong time in the form of centrifugal force laterally well away from the CG during a curve, because otherwise it would be the perfect placement. The performance guys were right that it is an issue and knew it intuitively, but I believe they were too tangled up in the idea of roll axis and an incorrect definition of CG to correctly explain why it is an issue. It's exactly because it's not part of the CG that it creates a traction issue deep in a turn. Lastly, the reason the calculators are invalid for below axle addition of weight is because as weight is moved lower below the axle height it actually raises the height of the CG, not the CM, just the CG with tires on the ground. I really wish you motorcycle guys would get that, because then I think we'd come to a consensus, though I doubt Safe could ever include himself in a consensus about anything.

I'm exhausted by this thread too. It reminds me exactly of an uproar in high school that was also gravity related. In physics class I made the observation that if you roll a ball down a frictionless plane, at the bottom it would be traveling the same velocity when it reached the end as one dropped straight down from the same height. 2 of my classmates stayed on my side, but only because they could tell that I knew I was right. The rest of the class, then all of the faculty in the science department, and eventually the entire school were all against me, but I stuck to my guns and found the uproar hilarious. My h.s. level course didn't provide the math to prove it, but one of the early sections of my college Physics 101 textbook provided the proof.

John

 

[John in CR]

One quick proof related to CG. Remove a rider's mass from the bike and split it in half. Put one half at the rear contact patch and place the other half up high enough to where the CM is the same as it was originally, so according to your definition of CG it hasn't changed. If CG hasn't changed and front/rear weight distribution hasn't changed, then the bike would handle exactly the same, however the handling wouldn't be even remotely similar, much less unchanged.

If that doesn't get you out of the Safe Zone then nothing will.

John

 

[SamSpeed]

John, please help me understand.

What is the difference between the center of gravity and center of mass? As far as I understand, they are different terms for the almost the same thing. Here are some quotes from article from a google search (the search was center of gravity "center of mass"). The only distinction I can find only applies in extreme circumstances. And these quotes are remarkably consistent.


"The point of an extended body at which the force of gravity can be considered to act and which undergoes no internal motion. The center of gravity corresponds to the center of mass (a.k.a. centroid)."

" The terms "center of mass" and "center of gravity" are interchangeable as long as their is no discernible difference in the pull of gravity from one part of the object to another."

"The terms "center of mass" and "center of gravity" are used synonymously in a uniform gravity field to represent the unique point in an object or system which can be used to describe the system's response to external forces and torques. The concept of the center of mass is that of an average of the masses factored by their distances from a reference point. In one plane, that is like the balancing of a seesaw about a pivot point with respect to the torques produced."

"In the context of an entirely uniform gravitational field, the center of mass is often called the center of gravity — the point where gravity can be said to act."


So. The only difference I can see according to these quotes is when the gravitational field affecting the object is *not* uniform. That implies a very large object (planetary size) or where the gravitational field is very strong (like a black hole). I can't see how these distinctions apply to something as small as a bicycle.

What am I missing?

 

[safe]

Your drawing with balls and arrows makes no sense.

Well let's start by getting you to understand it.

First I read that you made it through High School, but it's unclear if you completed a physics class. My first question is whether you understand the idea of "Vectors"?

Vectors are the way that a force, distance or even momentum are expressed visually.

http://en.wikipedia.org/wiki/Vector_(spatial)

In my drawing the first arrow represents the vector that corresponds to the momentum of the bike. We know that momentum has two components:

Momentum = Mass * Velocity

...so as the speed is increased the length of the vector increases in length.

Now I drew the three black lines to represent the XYZ coordinate system. It might be hard to understand the three dimensional aspect of the picture, but the idea was to represent the second arrow (pointing straight down) as the distance between the center of mass and the ground. The third line represents the force that the tire exerts on the torque vector. Notice that the second and third vectors are constant because the height of the center of mass never changes (the torque vector) and the traction is also a constant.

http://www.physics.uoguelph.ca/tutorials/torque/Q.torque.intro.html

I was a Mechanical Engineer for some of my college years before getting a Physical Sciences (all the sciences) degree followed by a second degree in Computer Science a few years later. Mechanical and Civil Engineers use vectors all day long, so for me it's sort of the basic way to communicate.

So "John in CR" do you understand what a "Vector" is? Is this in your knowledge base or is the idea sort of fuzzy and alien to you? Be honest, no sense in wasting time pretending you know if you really don't.

Are you comfortable with using vectors?

Let's try to elevate this to a discussion using strictly scientific terminology about a mass in motion and a torque effecting it at a distance using formal vectors. Eliminate all the "feels like" and "seems like to me" logic and let's just stick to the science... nothing but the science... we could just as easily be discussing particle physics using the same vector terminology.

(vectors are the universal language of engineers)

 

[safe]

Some Vector Review

http://hyperphysics.phy-astr.gsu.edu/Hbase/vect.html

Just to jog the memory of those who know about vectors but are a little rusty on them. One of the best things about vectors in a three dimensional space is that you can "decompose" any vector that is not parallel to an axis by breaking it up into parts. So a single vector that goes off in a weird direction can be broken down into three separate components to represent the X, Y and Z axis.

Vectors are the easiest thing to use if you know them... but I remember when they were new and how hard it was to grasp the concepts.

Getting back to the core idea of a mass in motion being acted on by a torque out on the end of a distance (wheelbase) we can add vectors together to get the final vector as well. So it works both ways. (decomposition and composition) 8)

All similiar vectors can be added or subtracted with each other.

 

[John in CR]

Sam,

I agree it is confusing because the terms are generally interchangeable. This is the definition that I found useful, because I knew the effect I was thinking about and when everyone was talking about CG I went to go look up the definition, and there are many of them.

center of gravity.
1. (Abbr. CG) The point in or near a body at which the gravitational potential energy of the body is equal to that of a single particle of the same mass located at that point and through which the resultant of the gravitational forces on the component particles of the body acts.

The key wording that got me was gravitational potential energy of the body. If an infinitely small mass is laying on the ground, as far as the perspective that it remains on the ground, has no remaining gravitational potential energy. ie it can't fall any more, so it can't affect the balance of the bike.

This also means that the lower it is the less gravitational potential energy it has, so even though it's mass doesn't change, the lower batteries are placed the less it affects the original CG. Because the batteries are a concentrated mass, I believe we should look at them in 2 ways to determine their effect:
1. How they affect the overall CG, because that's what determines how the bike balances overall, including the lean angle for a given curve and speed.
2. As this concentrated mass is separate from the original CG it starts to exert forces on the bike differently than if the new CG was concentrated all in one location, so this mass has to be looked at separately as well. This is the "wag the dog" behavior that TD mentioned. It's also why the performance guys were so opposed to low placement, because they knew intuitively that placement down low puts that mass at the outside radius of the curve resulting in more centrifugal force, which if you're riding near the limits could make the tire slide right out from under you. This is a very different result than if we added the batteries at the rider and lowered him a bit to come to the same CG.

John

 

[John in CR]

Safe,

Definitely fuzzy and alien, but I understand momentum just fine.

John

 

[safe]

What is Traction?

Given that "John in CR" is still new to vectors I'm going to have to in effect give a physics class in order to build up enough of a knowledge base here (online) to be able to even prove my point. So for people that weren't lucky enough to have suffered long hours studying physics this will act as a beginner course and I'll do my best to make it so that anyone can follow.


Before we can get to understanding how weight effects bicycle handling we need to understand the basics of how forces work. Forces were the main theory that Newton introduced and prior to that people thought in very vague terms about how things behaved. The most well know equation from Newton (though there are several) is:

Force = Mass * Accelleration

...now for our purposes we want to know how much traction a tire is able to give our bicycle so that we can calculate how much steering torque is possible. Braking force and steering force are both examples of traction. The limit of traction is the force of gravity. So let's introduce some numbers:

Mass - 100 kg
Acceleration - (gravity) 9.8 m/s*s or for our purposes 10 m/s*s

...the force is then:

Force = 100 kg * 10 m/s*s = 1000 kg*m/s*s

But we have a convenient standard called the "Newton" that can be substituted so that we get:

Force = 1000 Newtons = 1000 N

http://en.wikipedia.org/wiki/Newton

In the diagram above the vector pointing downward is the force vector of the mass due to the effect of gravity.

This is the maximum force possible for traction for either a turning force or a stopping force. They cannot combine to a total amount more than 1000 Newtons and in most cases would be far less than this. (steering forces tend to be a small fraction compared to braking forces, but we will deal with simplified pure forms to make things easier)

Any questions?

 

[John in CR]

Safe,

Please don't even bother. Look at my last 2 posts of significance. If you see something you want to debate then fire away, but don't bother trying to explain bicycle behavior with numbers. Too many have tried and came up short, and I have no inclination to brush up on the math to even attempt it. I can ride a bike, and feel and visualize what it does and how weight added to different locations affects its behavior all without a single calculation. Yes, early in this thread I had never thought the matter through, and it's possible there's still something I haven't considered, but I challenge you to find something incorrect in my recent few posts. Clarification or refinement is welcome too, just please don't revert to your usual change-the-subject arguments.

John

 

[lostcoyote]

This is the maximum force possible for traction for either a turning force or a stopping force.

oh really? a 25,000 pound truck is headed for a solid wall at 70mph and hits the brakes. it begins to skid. do ya have 25,000 pounds of force as traction? what if it's in sand?, black ice? pavement? furthermore, how about if the speeds is difverent,,, say, 10mph verses 70mph in the above pavement conditions.

Any questions?

yeah, why is your vector diagram so incomplete?
if it was accurate, you would have not made the above statement.

better study up on frictional forces and kinetic energy once again. traction isn't a vertical force but weight of an object does play a role.

oh, wait a minute, ya almost got me... you're simply trying to change the subject from cg to now, traction - lolol

 

[safe]

...traction isn't a vertical force but weight of an object does play a role.

You raise a good point.

In drag racing there was a time where they had not yet passed the "1G" speed for the 1/4 mile. Some even suggested that is was impossible to surpass 1G because the argument was that you cannot accellerate faster than gravity.

But in drag racing they have started to make better use of aerodynamic "ground effects" that press the car to the ground. There is also the effect of the rear wheels expanding as they increase in rpm, so this raises the rear end which is where they place most of the weight. (this gives an extra downforce on the rear wheels)

Ironically the dragster is sort of the perfect example of the "rear bias" machine... they have done everything to create a dragster that goes in a straight line and to do that you move all the weight to the rear. :wink:

For bicycles or motorcycles without ground effects you can effectively set the upper limit as being 1G.

It's not such a big deal what the traction really is (because it's a variable thing) but I was trying to get us out of the vague "gee wiz it seems like" thinking into some more realistic facts about physics.

If we can't transition to "science" then it's just human opinion driving this thread...

 

[safe]

Please don't even bother.

Oh don't worry... it's okay... I actually know how the laws of physics work, so it's fun for me.

I will continue to slooooooooowly present the fundamental physics of the matter and you will have plenty of chances to dispute what is presented... it will be like a physics class for steering geometry. :wink:

 

[lostcoyote]

Oh don't worry... it's okay... I actually know how the laws of physics work, so it's fun for me.

well, if that's truly the case, then properly explain traction and draw a proper vector diagram for a bike going through a turn.
(hint, draw the forces exerted upon the bike at the contact points by the earth)

I will continue to slooooooooowly present the fundamental physics of the matter and you will have plenty of chances to dispute what is presented... it will be like a physics class for steering geometry.

please spare us the agony of having to sift through it all.

 

[safe]

well, if that's truly the case, then properly explain traction and draw a proper vector diagram.

I try to be a good teacher... eventually I will post new diagrams that include what you want if you really need them. Being a teacher is hard because you are constantly being asked to alter the study material to suit the individual student.

Seriously though... are you unable to make the intellectual leap to a vector for traction?

There can be either braking force traction or steering force traction... the very fact that it's complex made me skip it. (are you just being a "pain in the ass" or are you really confused.... come on.... be honest)

I haven't even got to the orthographic drawing issue (that's going to be next) so I was hoping not to get stuck here.

http://en.wikipedia.org/wiki/Orthographic_projection

 

[lostcoyote]

Seriously though... are you unable to make the intellectual leap to a vector for traction?

nice try safe.
but your attempt to manipulate yourself into a teacher position is failing when you can't even get the vector diagram correct.

you see safe, when you make condenscending remarks like this:
"(are you just being a "pain in the ass" or are you really confused.... come on.... be honest)"
i end up just laughing cuz i know something that you don't know.
you want me to be confused, don'tcha?
tell me, when you make condenscending remarks like this, does it give your ego an erection or something of the sort?
(there, how's that for being a pain in the ass)



hint: you talk quite a bit about one of newtons laws... for every action, there is a reaction....

so why not start including the reaction vectors in your diagrams to make them more complete?

is wikipedia your "bible?"
you reference it so much so why not look up friction forces as applied to rotation and centrifugal forces and start mapping these force vectors into your oversimplified and incomplete diagram(s).

 

[Papa]

The only things "rotating" on a bike are the tires, crank and the headset.

This simply is NOT true, John

Image "A" shows a static 'single track vehicle' at rest (i.e. no forward motion, but is simply leaned to the left). The bike's pivoting point (as shown in image "A"), is at the tire's contact patch. We can indeed verify this by simply tilting the motionless bike to the left or right.

Because the bike's vertical CoG position is fixed, and is higher than the static bike's contact patch (or pivoting point), the bike, understandably, will feel 'top heavy' when at rest or when walking the bike.

Image "B" reflects the dynamics when bike is in motion and is being "rotated" to the left and around the bike's "dynamic pivot point", or "longitudinal roll axis".

When the bike is put in forward motion, and the rider initiates steering or counter steering, the front tire's contact is steered laterally beneath the CoG - followed immediately by a lateral movement of the rear contact patch. And because the greater concentration of mass (or weight) is at the CoG, the CoG resists lateral movement and it essentially 'stays put' while the much lighter outer perimeter of the bike's mass "rotates" around the bike's CoG.

ALL knowledgable bicycle/motorcycle theorist, designers and pro riders, refer to the bikes "rotating" and or "rotation", because that's exactly what is happening when the bike is leaned into a turn.

 

[lostcoyote]

... your diagrams ....

consider that in a turn, the wheel axis are not parallel.
your diagram is 2-d and does not reflect reality

 

[Papa]

... your diagrams ....

consider that in a turn, the wheel axis are not parallel.
your diagram is 2-d and does not reflect reality

The diagrams above, intentionally represent "longitudinal roll axis" ONLY, because that is where much of the confussion (for at least one individual) seems to be. The point is specific to "rotation and/or roll axis - nothing else.

 

[John in CR]

Papa,

I can't see the image, but I don't really need it. I've understood all along what you guys meant by roll axis, and disagree with the use of the term. Its far more applicable to a motorcycle than a bike. A typical bicycle is much more top heavy. Because of this the countersteer that gets the contact patch out from under the mass is typically almost imperceptible, so much so that an experienced rider like Johnrob didn't thing he countersteers at all. Only during the countersteer does your "roll axis" come into play, and I'm not even 100% certain that it occurs at the CG. A typical bicycle turn still isn't fully set up during countersteer. That is just the very beginning. It just creates an imbalance that enables the weight to start falling in the direction of the turn, with the bike and rider actually rotating around the contact patches during this "fall". Then during turn the centrifugal force and the traction of tires reach an equilibrium with gravity to stop you from falling all the way over.

That's a lot closer to "exactly what is happening" with a bike going around a curve. Feed that into your roll axis model and watch it fall apart, because the majority of a bicycle lean is often this "fall", which is the bike and rider rotating around the axis represented by a line connecting the contact patches, and this doesn't even begin to get into the other things that can occur in a turn as the rider shifts position relative to the bike.

John

 

[lostcoyote]

Then during turn the centrifugal force and the traction of tires reach an equilibrium with gravity to stop you from falling all the way over.

bingo!

(challenge to safe: let's see if safe can draw a PROPER 2-d vector diagram of this.)