Mounting your battery, Center of Gravity.

lostcoyote said:
john,

have you taken any physics courses?

center of gravity has to do with mass distribution and specifically, the balancing point (fulcrum or centroid)) of that volume of mass integrated over 3 dimensions..
furthermore, it is independant of whether the body of mass rests on the ground at 2,3, or 4 points or if it floats above a cloud.

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

try this simple exeriment:
support a 12 inch ruler on each end with a glass or aluminum can. put your finger on the 6 inch mark and lift. the ruler is more or less balanced on your finger at this point, which marks the rulers center of gravity.

rest the ruler back on the cans or glasses. add a quarter to the 10 inch mark. place your finger back under the 6 inch mark and lift it up again. guess what? the cnetr of gravity of the ruler has shifted away from the 6 inch mark as the 12 inch side tips down.

the bike is no different. center of gravity is determined by spatial mass distribution.
study the link provided above and understand the simple math equations as well as the concept presented.

to add to the experiemnt outlined above, get a 6 long 2x6 board and 2 bathroom scales. place each end of the wood board on the scales.
next, put a 10 pound bag of sugar at the center of the board (the 3 foot point) and measure the scale. assuming a 5 pound board, each scale would record 7.5 pounds.

next, shift the bag of sugar to about the 5 foot position. note that the scale closer to the bag of sugar increases in weight while the scale further away decreases (but each scale adds up to 15 pounds still)

try it.
this is high school physics.
i don't mean to come across as being arrogant here, but your statement that the center of gravity does not change when you add weight over the rear wheel is simply not correct just because it makes contact with the ground. if that was true, then part 2 of the experiment with the 2x6 would indicate that no matter where you place the sugar bag along the 2x6, each scale would always indicate 7.5 pounds.

Lostcoyote,

Yes it is elementary. You forgot to anchor one end of the ruler on the ground. Then it doesn't matter how much weight is added at that point. The rear wheel is the same. Gravity can have no effect once it's already on the ground, and I've been pretty clear about that point all along. I'll give up once it actually clicks for you guys.

John
 
For those who wish to do it manually:

cog02eo8.jpg
 
say wot?

anchoring the rear wheel to the ground?

with a chain?
bolted to a bike rack or a boat anchor?

last time i checked, bike tires were not anchored to the ground.... ever do a jump?
or like, um, move the bike forward such that the wheels actually rotate?

an anchored tire ain't gonna rotate or jump....

"Gravity can have no effect once it's already on the ground"

sure it does. it's the reason bikes weigh this or that. it's the reason you make footprints when you walk upon the sand. it's the reason you can't walk on water or a bike make tire tracks.

-coyote scratchin' his flea bites upon his kunfuzzed brain cuz you ain't makin' no sense to me here.
 
Coyote,

I was head scratching too about why we can't agree on something seemingly straight forward. Then after searching for definitions of CG, I see that our argument is pointless because we're using different definitions. All along I've been looking at bike handling only from the frame of reference of riding on a road with both tires on the ground, not jumping or ever becoming airborne, which opens other cans of worms. The best definition I found for the conditions I'm looking at is:

n., pl. centers 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 word in our different points of view is "potential", because I'm looking at it as the potential energy being zero with the weight on the ground. From that point of view adding weight at the rear contact patch has zero effect on CG. It also means that if you lift the bike off the ground the CG changes to the point encompassed by the unrestricted definition of CG you and Papa use in your points of view. In essence I'm trying to analyze the effect of weight placement only with both wheels always on the ground, and you guys are looking at it in all conditions.

I have to apologize again for getting suckered into a debate with Safe, and even worse this time I permitted some of that to get slung toward you guys, so now I really am done.

John
 
John in CR said:
In essence I'm trying to analyze the effect of weight placement only with both wheels always on the ground, and you guys are looking at it in all conditions.

in that case, you can go back to the 2x6 experiment and place a scale at each end. then distrubute a load along the board and see the effect directly on the readouts.
 
Center of Gravity not Center of Mass. With tires on the ground, add weight at rear contact patch changes nothing in the movement of the frame other than dragging the added weight along with you. This is because there is no energy potential of that mass relative to the frame. Just change your point of reference, and don't think about picking the bike up, just moving it around on its wheels. Wiggle the frame side to side, and turn the frame with the front tire, and that weight at the contact patch has no effect on how the frame moves.

John
 
I'm gonna give it a shot.

John says that,
Gravity can have no effect once it's already on the ground

Hey John, there is a wee bit of sense to that. Sure, if you add weight to the rear axle, it will not affect the weight at the front axle. And as long as the bike is parked, it won't really matter much.

And I see the point about the rear wheel being anchored to the ground. The example of the pencil, with the eraser pressed against the table bears that out. One way to look at it is to think of a hinge -- a mechanical attachment point acting as a fulcrum.

But I think a lot of the confusion here has to do with the notion of weight as opposed to mass. The Wikipedia article on center of gravity (which I presume everyone has read by now) notes that "center of mass" is a preferred term. The distinction between weight and mass becomes important when you consider acceleration. And turning involves acceleration.

Think about wheelies. A bike or car that has a high CoG will do a wheelie more easily than if the center is lower. I hope that's obvious. The reason is during acceleration, the g-forces act on that center and the distance between the center and the axle (the hing point) forms a lever arm. The longer the lever, the easier the wheelie.

Going around a turn involves lateral acceleration. It's more noticable in your car because the acceleration pushes you to the side. On a bike (or airplane) it just pushes you down in the seat. That sideways acceleration acts on the CoG. And that is why a Porsche handles so much differently than a front engine car. If the CoG matches the geometric center, the handling will be neutral, move the CoG fore or aft and you will get understeer or oversteer.

So, and I think this is what this thread is all about, the "flickability" or rate of roll will be affected by the height of the CoG. The hinge point will be the contact point of the tire, as you point out. The higher the CoG, the longer the lever arm. During countersteer, when you turn the front wheel, the bike accelerates sideways just as in a car. Only it responds to the acceleration by leaning. And yes it will rotate around the contact point or hinge. But the force of acceleration is acting on the CoG.

Hope I'm not just adding more fuel to this fire.
 
John in CR said:
Center of Gravity not Center of Mass. John

okay....
for practical purposes, the bike is in a uniform gravitational field, yes?

if so, then very often, the two terms, center of G and center of M are used interchangebly.
 
John in CR said:
Center of Gravity not Center of Mass. With tires on the ground, add weight at rear contact patch changes nothing in the movement of the frame other than dragging the added weight along with you.
John


When stationary, the bike would be easy to lean to and fro and the added mass (implies weight) would not be noticable. When moving, the lower CoG would make a given turn need a larger lean. Much like how a chopper is lower than a street bike, and requires more lean to turn the same radius at the same speed. I can offer no math nor science here, only my own experience. I moved my batteries all around on my version two bike, since I didn't need to pedal there was no place I could not move them. I found out that the lower I mounted the packs the worse my handling got as speed increased, I needed more and more lean for the same turns- not safe for the tires I use. I do ride with speed, not walking pace. The best position was in the middle of the bike frame, with weight as high as my own CoG. This made the bike handle more or less the same no matter how many packs I put on. The lean angles didn't change with more weight, my effort to countersteer didn't change with more weight. It was as if the CoG stayed the same and my contact patch merely pivoted underneath to keep myself and the bike balance. At super low speeds (1 or 2mph) the increased weight was noticeable in the middle of the bike, I could feel the momentum of the packs swing around the rear contact patch. I would MUCH prefer a bike that handles well at speed instead of at walking pace. I ride, not walk my bikes.


For this reason I mounted my batteries around the top tube on v3. I constructed them to not interfere with my pedaling, and the weight centered around the top tube is as close to my belly button as possible. It also balances the bike the bike front to rear, which is top priority for having a bike handle well in sketchy conditions. Offroad, low traction, snow, and any tire slipping situation is not a problem with my current setup. The worst setup I can imagine has all of the weight on either front or rear contact patch. If one tire looses traction it is almost impossible to recover.


As an experiment, change your seat height. The lower you put your seat, the more you have to lean to execute a turn at a given speed.
 
Sam,

We seem to have much the same POV. The only clarification I would make is that it's not just a low CG, because a low CG toward the front will have an effect on "flickability" that is felt, which one of the experienced guys explained quite well some pages back. The point that I've been pressing is that, if it was possible, adding weight at the rear contact patch won't change the flick at all and leave the bike "feeling" as nimble and light in terms of flicking as it did before the weight was added, because the "flick" is anchored at the rear patch. This tells me that getting as close to that point as possible is a good target.

Before Safe jumps in, yes there is a less than ideal change in the arc path of that mass during countersteer, but I believe the angular changes in momentum are so shallow that the difference vs any other placement would be negligible. Place that mass up near the CG and it will be felt in the "flick", because batteries will often weigh as much as the unladen bike, and the "feel" will change toward the feel of a motorcycle. I'm not saying whether that's good or bad. In fact, riding around road racer style like Safe or for off road riding, then such a low rearward placement will likely be detrimental, but zipping around on paved streets I don't think so. Personally I want my errands to stay as light nimble and flickable as possible. I do want to also build a motocross type E-bike, and I'll definitely want its added weight to go up in the center.

John
 
Johnrobholmes,

You bring up a point I hadn't considered, and I'll be riding at much higher speed than is typically legal for ebikes. Do I really want it to ride like a regular bike is a significant question, so I'll have to experiment with placement. I've already modified my seat to be lower and toward the rear, and thinking about the motorcycles I've had, I really liked leaning in those turns on the ones that were lower, so lower may be the place for me. I think Safe may have made the same point before and my brain immediately rejected it as coming from Safe.

John
 
Leaning low into a corner sure is fun, but the turn does take longer to initiate and you are depending more upon the tire sidewalls for traction. Leaning more for turning is less flickability, since you have to execute more movement of roll to get the same turn. I'm not saying a lower CoG is bad, but the handling difference is something to consider. Anything over a few MPH will make noticeable difference in CoG change, and the faster you go the more lean you will need for a defined arc. This means that the lower your CoG , the less a given bike can turn at speed before the tire loses traction.


It is like balancing a weight on a stick, like a circus clown. With a long stick it doesn't take much movement (roll of the stick) to keep it balanced. With a short stick it takes a lot more movement (roll of the stick) to keep things in balance.
 
johnrobholmes said:
When stationary, the bike would be easy to lean to and fro and the added mass (implies weight) would not be noticable. When moving, the lower CoG would make a given turn need a larger lean. Much like how a chopper is lower than a street bike, and requires more lean to turn the same radius at the same speed. I can offer no math nor science here, only my own experience. I moved my batteries all around on my version two bike, since I didn't need to pedal there was no place I could not move them. I found out that the lower I mounted the packs the worse my handling got as speed increased, I needed more and more lean for the same turns- not safe for the tires I use. I do ride with speed, not walking pace. The best position was in the middle of the bike frame, with weight as high as my own CoG. This made the bike handle more or less the same no matter how many packs I put on. The lean angles didn't change with more weight, my effort to countersteer didn't change with more weight. It was as if the CoG stayed the same and my contact patch merely pivoted underneath to keep myself and the bike balance. At super low speeds (1 or 2mph) the increased weight was noticeable in the middle of the bike, I could feel the momentum of the packs swing around the rear contact patch. I would MUCH prefer a bike that handles well at speed instead of at walking pace. I ride, not walk my bikes.


For this reason I mounted my batteries around the top tube on v3. I constructed them to not interfere with my pedaling, and the weight centered around the top tube is as close to my belly button as possible. It also balances the bike the bike front to rear, which is top priority for having a bike handle well in sketchy conditions. Offroad, low traction, snow, and any tire slipping situation is not a problem with my current setup.
An excellent example of finding and maintaining the laden bike's dynamic equilibrium. A bike whos mass is unequally distributed, is not unlike a bowling ball with one of its finger holes filled with lead.

johnrobholmes said:
The worst setup I can imagine has all of the weight on either front or rear contact patch. If one tire looses traction it is almost impossible to recover.
Yup,... we certainly agree.

Thanks for the excellent post.
 
Further reading....


In the Cycle World "Service" column in which they answer technical questions from readers Paul Dean had this to say in response to a question about the center of gravity of bikes and how this affects motorcycle design [specifically about the Yamaha R1]:

"Yamaha's engineers didn't change the laws of physics with the new
R1, they merely abided by them. Remember that demonstration in
high-school physics class that showed you can swing a broom
back-and-forth more easily and quickly if you hold it close to the
bristles rather than at the very end of the handle? The broom has a
greater 'polar moment' when the pivot point is at the end of the
handle; grabbing it closer to the bristles moves the pivot point
nearer the greatest mass, reducing the polar moment. It doesn't
matter if you move the mass closer to the pivot point or the pivot
point closer to the mass; both have the same effect, which is to
centralize the mass.

"Motorcycles have a pivot point, called the 'roll center,' which is
the longitudinal (front-to-rear) axis along which the bike rotates
when leaning into a turn. That axis is not located where the tires
make contact with the road; it's considerably higher, somewhere closer
to the middle of the motorcycle/rider package, depending on the
physical attributes of the bike and rider. When the bike banks over
to, say, the left, the part of it that is above the roll center tilts
over to the left while the part below it swings out to the right. As
a result, any mass that is located below the roll center has
essentially the same inertial effect-or polar moment-as an equal
amount of mass located above it. Thus, the designers try to lower
anything that is above the roll center to get it closer to that axis,
and raise any significant mass located below the roll center for the
same reason."


Who is Paul Dean? http://www.motorcyclemuseum.org/halloffame/hofbiopage.asp?id=336
 
johnrobholmes said:
Leaning low into a corner sure is fun, but the turn does take longer to initiate and you are depending more upon the tire sidewalls for traction. Leaning more for turning is less flickability, since you have to execute more movement of roll to get the same turn. I'm not saying a lower CoG is bad, but the handling difference is something to consider. Anything over a few MPH will make noticeable difference in CoG change, and the faster you go the more lean you will need for a defined arc. This means that the lower your CoG , the less a given bike can turn at speed before the tire loses traction.


It is like balancing a weight on a stick, like a circus clown. With a long stick it doesn't take much movement (roll of the stick) to keep it balanced. With a short stick it takes a lot more movement (roll of the stick) to keep things in balance.

Johnrob,

I'll need to mull some of this over, since you're bringing up CG. My question is this, given a nice smooth curve at speed, does added weight at the rear contact patch increase the lean angle required compared to an unladen bike, and I believe the answer is no, but it's going to require some experimentation to fully believe it one way or the other.

John
 
Increased weight on the rear does not make the lean angle greater, it only affects the front to rear weight bias. Lower weight on the rear (or anywhere) would affect the lean angle, and the lower the weight is located the further apart the total bike/rider mass becomes. This will cause sluggish turn in unless the rider weight is also lowered. Having both low rider and battery weight can have a very nimble lean rate, but still the lean angle will be further than a bike with higher center of mass.


One example of why I would not run an extreme rear weight bias- Going through a turn I may tap the brakes. The rear end will want to drift out upon front braking, because of inertia. This gets exaggerated as the rear weight bias increases. Get into low traction situations and the front brake becomes useless at anything except straight line travel, the bike tries to "jack" the rear end around when the front slows down. I personally use the front brake for almost ALL stopping, unless I am in the middle of a hard turn and traction is near the limits.


Now a question for other motorcycle riders. Do you prefer a forward, neutral, or rearward weight bias for drifting?
 
johnrobholmes said:
Now a question for other motorcycle riders. Do you prefer a forward, neutral, or rearward weight bias for drifting?
A question not easily answered IMHO. A "drift" usually implies the vehicle is under power - enough power to control wheel spin. Many other elements must also be considerd. The cornering force is usually provided from two sources. (1.) Camber thrust and slip angle. And (2.) The engine supplied driving force that acts toward the apex of corner. And depending on CoG height and whether or not suspension is involved, the amount pitch occuring during acceleration and deceleration can dramatically alter entry and exit of the drift. Further still, rider insensitivity and poor technic, can, and often does,.. scramble the whole wretched mess.
 
And John says,
adding weight at the rear contact patch won't change the flick at all ... because the "flick" is anchored at the rear patch.

Yes, the tire contact points are anchored to the ground in the sense of a hinge. And I think that's a useful point of view. But the forces that cause the "flick" or roll, will be affected by the distribution of mass. And yes, I sortof see your point of view.

But as you pointed out, the CoG is a single point in space that is affected by gravity or acceleration. And that is not the same as the hinge point. The forces of acceleration act on that singular center of gravity. The turning, or rolling, or torque effect of that is a function of the distance between the two points. Adding weight (or mass as I like to think of it) at the rear contact point *will* move that single point, the CG, lower and to the rear. Thus, the center of gravity will change. The point of rotation, which is the hinge point or contact point, will not. For emphasis, will not. My point is that the relation between the forces from acceleration acting on the mass of the bike and the geometry, will change due to the change of CG. Anytime you add mass (or weight) to a point other than the exact center of gravity will change the center of gravity.

The good thing about this thread is that it has got me thinking, and more aware of what really happens. If I ride straight ahead but weaving left and right, I can sense, can feel that longitudinal roll center. And it is not at the contact points. Now this is subjective as can be, and I'm not looking at my actual ground track. But If you do it just right, kindof like "lazy eights" in an airplane, that roll center becomes apparent. At least to me.

I used to fly a Piper Pawnee -- a cropduster. In that airplane the motor is at the front with a hopper and fuel tank behind, leaving the pilot seat way behing the CG. In most light aircraft, the CG is real near the pilot's seat, so it took a while to get used to my whole body swinging back and forth with the rudders. But the important thing there is to be able to feel that center of rotation. Some call it "seat of the pants" flying. And in an airplane, free to move in all axes, all rotations occur around the center of gravity.

I've also got to thinking about the notion of the unladen CoG. On a bicycle there are numerous techniques for cornering. I have long had this tendency to like to power my way out of a turn, but it is so easy to hit a pedal in a steep bank (or lean). I've gone ass over teakettle a couple of times doing that. Some say to coast through turns but that's no fun. So I've adopted a technique of leaning my body to the inside of the turn so the bike frame will stay more upright. That sortof works but is not real comfortable.

Likewise, you can plant yourself on the saddle and clamp your thighs and then your body mass becomes closely coupled to the bike. That's more motorcycle style. Otherwise if you stand on the pedals (or pegs), letting the bike move around below you, and just use countersteering technique (no leaning now), the bike will move underneath you in quite a different way. This latter case, I think, is about as close as you can come to experiencing the unladen CG as you can get -- unless you're riding freestyle.

And again, I hope this is a contribution and not more fodder for wattless controversy.

respectfully.........
 
SamSpeed said:
And John says,
adding weight at the rear contact patch won't change the flick at all ... because the "flick" is anchored at the rear patch.

Yes, the tire contact points are anchored to the ground in the sense of a hinge.

No. This point has been made over and over again. Papa has just posted an article that explains it.
The roll axis is not through the tyre contact patches.

Nick
 
Papa said:
"Yamaha's engineers didn't change the laws of physics...

Motorcycles have a pivot point, called the 'roll center,' which is the longitudinal (front-to-rear) axis along which the bike rotates when leaning into a turn. That axis is not located where the tires make contact with the road; it's considerably higher, somewhere closer to the middle of the motorcycle / rider package, depending on the physical attributes of the bike and rider. When the bike banks over to, say, the left, the part of it that is above the roll center tilts over to the left while the part below it swings out to the right."

Who is Paul Dean? http://www.motorcyclemuseum.org/halloffame/hofbiopage.asp?id=336
Yeah, but Yamaha doesn't know anything about steering geometry!

(sarcastic humor :lol: )


I'm wondering if now "the change" is about to happen? Will "John in CR" finally get it?

Stay tuned... :wink:

(note I was stubburn about PWM "current multiplication" so I've had to admit being wrong before too... so we are all imperfect beings. We will still accept you afterwards. :) )
 
Tiberius said:
SamSpeed said:
And John says,
adding weight at the rear contact patch won't change the flick at all ... because the "flick" is anchored at the rear patch.

Yes, the tire contact points are anchored to the ground in the sense of a hinge.

No. This point has been made over and over again. Papa has just posted an article that explains it.
The roll axis is not through the tyre contact patches.

Nick
I noticed that too, Nick. I just assumed it was in reference to a "high side". Such as what occurs when a laterally drifting rear tire decides to suddenly hook-up... "flicking" the rider off. If in fact, that was the point of reference, then yes, the resulting 'flick' pivots at the contact patch. Otherwise, under normal riding, the contact patches do indeed move laterally as the bike rotates during a turn.
 
Yep Tiberius, you caught me in a big fat contradiction.

You know I was riding aimlessly the other day thinking about this thread. In a parking lot, just riding in a steady constant radius circle going faster and faster and noticing the bank angle, and really trying to sense the forces in action. And it occured to me that what was really happening was that I was not moving at all, the earth was spinning beneath me like a top. Add a little throttle and lean a bit more and it would spin all the more!

So motionless as I was, nothing moving but the earth beneath my wheels I closed my eyes and with my mind drew a graph on the inside of my eyelids, and drew the vectors just like that motorcycle picture someone put up a few pages back. The whole thing is truly marvelous.

When you are doing linear algebra, vector analysis, it's usually best to translate the vector to the origin. Then rotations or any other transforms are a lot easier. Just shift the point of view, the point of reference. Of course shift it back at the end to avoid upsetting the balance of nature.

It's a lot like like people. Sometimes there are folks that'll follow along and listen to you all the time. The best way I know to get 'em to stop listening is to tell them they are wrong. That usually works. But if you want to get 'em to listen, it sometimes helps to shift to their POV.


Maintain thy flying speed, lest the earth rise up and smite thee!
 
now take your imagination further and view this within your mind in a spherical coordinate system.
 
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