Center of Gravity, why does it matter on a bike?

Yes, and no. Top-heavy can very much be top heavy, compare a Katana or Sportster to a Harley big twin. The big twin is much easier to handle at low speed despite being 150lbs heavier than the other to, both the sporty and kat carry their weight very high.

While geometry is certainly huge the higher the CG the easier the bike is to tip side to side. Ever notice that the bike is easier to tip in when you have it loaded to hell or carry a passenger, this almost always causes an increase in rake and trail, so in theory the bike would handle slower.

....Yet it doesn't, getting it off a lean takes more energy, but it falls in easier.

Likewise you won't have to lean as much to complete the same arc, when you turn the bike you are balancing gravity (from the center of gravity) against the centripetal force from the cornering arch trying to stand the bike back up. This is because the the higher the CG, the further from the contact patch the CG moves, this means that there is more downward force presented to the chassis with the load carried higher than there would be otherwise.

Its all vector sums, and it can certainly get very complicated very quickly.

So, back in the 1900's a guy could post a question and the inmates would have a civilized discussion on it?

Not quite...

Someone a little further down mentioned a hammer.
A hammer's centre of gravity is close to one end (the head!), but its moment of inertia about its centre of gravity is constant, regardless of orientation.

Its moment of inertia about one end (bottom of handle), IS however very different from its moment of inertia about the other end (top of the head). The further the axis of rotation is from the centre of gravity, the higher the moment of inertia about that axis.

So for a given mass of motorcycle, the higher the centre of mass is off the road, the greater the moment of inertia about a longitudinal axis through the tyre contact patches will be.

Ooh, another one.

Yes, but keep in mind that a motorcycle does not rotate about its tire contact patches as it leans into a turn. It rotates about its CG - the tire contact patches actually are driven out from under the bike by countersteering. If you look at the tracks on the road, to turn left the contact patches first move to the right.

This is the reason that the current trend is towards mass centralization, not low or high CG. The objective is to reduce the moment of inertia with respect to the CG, not with respect to the contact patches.

- Mark

im not going to overthink this . ,just trust the engineers on this .they put alot of thought into what works best and where to locate the weight.
The bike owner usually starts bolting weight out away from mass center and then wonder why their bikes handles so bad.

I think this is about the best description I've seen, simple and to the point, It's all about leverage, That simple. No matter what else is said, the higher the weight is from the ground the higher the leverage factor when moving in any direction regardless of speed, weight or direction. A simple and succinct explanation without killing it with details.

It is a great analogy for holding up a bike at rest and almost anyone would agree that a cruiser is easier to hold at rest at a stoplight than something like a KTM 990. But whether it has an relevence to a moving two-wheel vehicle is an open question.

- Mark

Hi Mark, may I jump in here? Maybe I can help. First a quick review. There are three centers of gravity (center of mass is more precise) on a motorcycle/rider combination. The bike, the rider and what I call the combined center of mass. The C-CofM is the most important because it's your balance point.

What you are calling leverage is sometimes referred to as moment. Moment is the distance between the tip-over line between the contact patches of your tires and the C-CofM. The longer the moment the slower the fall. Slower is my way of saying rotation rate. That's why tightrope walkers carry a pole.

When you get on a taller bike or stand on the pegs you fall slower into turns. That's one reason why roadracers stay low and drag knees-- shorter moment allows then to flick back and forth faster. Same if you are doing a seated wheelie vs. standing wheelie only then the rotation is around an axel.

The big payoff for a longer moment off-road is that the required lean angle for any given turn is less. Stand-up on the pegs and your don't have to lean over as far for a given turn radius at a give turn speed. The reason this is so is a little complicated so maybe not for here.

Hope this helps,
Coach

I agree. My current road bike has a high CoG and it's very easy to tip into a corner. Makes city riding more fun.


I don't disagree with what Coach is saying above, but I think CoG has a different effect as between 240 km/h and 40 km/h.

For road riding this wouldn't be true, although I can see that it might be for off-road riding, especially in a slide situation.

If you are staying within the verticle line of the center of mass than my gut says that the amount of lean (on street riding non-sliding) will be almost totally dependant on the speed and radius of the corner. (Of course the width of the tires will have some effect but I suspect it wouldn't be a major one.) If you are leaning out (i.e. dragging a knee) then a lower Center of Mass will be affected more by the same amount of rider leaning out.

..Tom

Hi, The same physics apply to both on and off-road turns. What varies is the coefficient of friction (traction) and how we handle slip angles. Lean angle is determined by the amount of centripetal force generated in the turn. It is inversely proportional to the radius and speed. If you double the speed CF increases by a power of four. Cut the turn radius in half, same thing, 4x. It's why picking a line through the turn is so important and why a few RPM can make the difference between pulling the turn or going down.

CF works though the C-CofM. So does gravity. CF lifts up (to a high slide fall), gravity down (to a low side fall). Lean angle is the balance between the two. If you raise the C-CofM the required lean angle is reduced for any given motorcycle turn. A lower C-CofM means more lean angle is required for any given turn. That (among other reasons) is why we stand up on the pegs in loose traction like sand.

Raising the C-CofM also decreases rotational speed because the moment is increased. Thus the bike flicks back and forth through the twisties slower. Want a faster handling bike? Lower the C-CofM. We can go in to how bike set-up and rake/trail effect fast/slow handling also but this thread it's about center of mass.

I've been racing and teaching this stuff for many decades. Won lots of championships both on and off-road. It's not opinion but rather just applied physics. Just hard to get into lots of detail here without drawings and video to illustrate.

Hope this helps,
Coach

Yep, as per Cocco ("Motorcycle Design and Technology")....

"There is only one precise angle of inclintion that allows you to maintain your balance at any particular speed when cornering:

angle of lean = arctan (V^2 / R x G)

Where V is velocity of the motorycle, R is the radius of the corner, and G is the gravity constant."​

Nothing about mass, moments, CG, etc. in this equation. Just speed and turn radius. This is basically the same equation for a turning/banked airplane. And if they flying at the same speed, a Cessna 150 and a Boeing 747 will require EXACTLY the same lean/bank to fly in a circle of a given radius.

Assuming a rider remains centered on the bike, a V-Rod and a KTM 990 Adventure (the most widely varying CG examples I can think of) are going to use EXACTLY the same lean angle to go around a corner at the same speed.

Now if the rider is "hanging off" you can start getting into complications that may allow a rider to move the CG of the bike/rider system more or less depending on the CG of the bike itself. Haven't given this much thought. But the idea that the height of a bike's CG affects how much lean is required to negotiate a turn is erroneous. Sorry Coach.

- Mark

Hi Mark, This is where plain physics and applied physics depart. An aircraft is not in contact with support force, it moves in pitch, roll and yaw in the air. And your quote assumes a fixed C-CofM on a given bike in a given turn. This discussion is about different bikes and different rider positions in the same turn. More variables.

A bike on the ground tips from the contact patches (assuming both wheels are on the ground). The lean angle starts there and is a straight line through the C-CofM. If the C-CofM is higher (further away from the tip-over line) then the lean angle is reduced for given turn. We adjust the location of the C-CofM in race practice to accommodate tires, track banking, ground clearance, available traction, etc. Wish I could post some drawings to illustrate what we do in everyday racing. This is pretty basic stuff.

Coach​

This quote says that the lean angle between the CoM and the ground of a single-track vehicle is a function of speed and turn radius. Period. It doesn't matter whether the CoM is one inch above the pavement or 50' above the pavement. The lean angle is the same.

I think the confusion here might be stemming form the idea that a higher CoM is further from the contact patches and therefore the "leverage" forces are different. While this may be true, the "leverage" of gravity is also increased the same and everything stays in balance.

I know there is a tendency to think that simple physics don't explain enough here and I'll readily admit that when a rider starts moving around on the bike and thus changing the bike's lean angle with respect to the CoM things get more complicated. And we're talking only steady state physics here, not dynamic changes.

But.....the idea that the height of the bike's CoM affects the steady state cornering lean angle for a given speed and turn radius is simply incorrect. If you can't accept this, then let's agree to disagree.

- Mark

I think that equation is wrong, or a gross simplification.

Otherwise why the divergence in motorcycle design, by that equation we could essentially ride bikes with 70" wheelbases and the weight wherever and it wouldn't matter.

Except that anyone who has ridden more than one bike knows it doesn't work that way.

I agree with what you are saying except for the complication of the width of the tires. This does change where the force is appled to the ground and will have some effect on lean angle, although I suspect that for relatively "normal" tire sizes the effect isn't huge in normal riding and would tend to have less effect with a higher center of mass.

..Tom

I would expect that a bike with a lower CofM would tend to react quicker to steering inputs and be more desirable for a sport bike, but would tend to feel less stable. (Assuming steering geometry is similar.)

..Tom

Yep, right Tom, there is some influence associated with the roll center of the tire (the fact that when rolled over the tire contact patch does not remain directly on the center line of the bike), and what we've been discussing has been steady-state cornering, not transients. In reality, cornering is a constant series of corrections and changes, where the affects of CG location may have some effect, perhaps major.

- Mark

Because motorcycles are complex beasts and don't corner in steady state conditions. And there is a lot more to motorcycle handling than simply required lean angle. Nevertheless, everything being equal and in steady state conditions, a Harley cruiser will negotiate a given corner at a given speed at about the same lean angle as a MotoGP bike. (Cornering clearance will, obviously, be dramatically different.)

Wheelbase is another complex series of tradeoffs that have nothing to do with lean angle. Here, shorter wheelbase is generally better for handling because it reduces the moment of inertia of the chassis around the up/down axis. It's easier to quickly yaw (turn around a vertical axis) something that is shorter.

Look at it another way - if moving the CG of a motorcycle up/down changed the required lean angle, why don't we see the designers making hurculean efforts to either lower (or raise) the CG to reduce the lean angle? Instead, we see a huge variety of bikes out there with all sorts of designs without any clearcut push towards having either a high or low CG - in fact, it is quite controversial in racing what is optimal. Does this sound like there is a clear-cut lean-angle advantage to putting the CG high (or low)?

It's all spelled out quite clearly in Cocco. This is basic motorcycle dynamics 101.

- Mark