Why don't race bikes have a high CoG?

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Spikeywan
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It seems to me that motorbikes are built to have a low centre of gravity.

I can understand this, having dropped mine twice. Once it gets away from you, there's no stopping it, and having a low CoG helps to make the bike easier to handle in the garage.

However, once you're riding it, then all those issues go away.

I went out for the day with someone on an identical bike to mine. He was a small, light chap, and took nothing else with him. I weigh at least 2 stone more than him, had my girlfriend on the back, and had a fully loaded top box.

He commented that I didn't seem to be leaning much, whereas he felt like he had his ear on the ground following me.

This made me think thusly...

Take two identical bikes, but make one with a very low CoG and one with a very high CoG.

The bike with the high CoG would be able to move more weight over for the same amount of lean. This extra weight transfer would mean that the HCoG bike would have to corner faster than the LCoG bike in order to balance the forces for the same amount of lean.

So, why don't race bikes have a really high centre of gravity?
 
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If the rider and passenger aren't hanging off relatitve to the bike, then center of mass doesn't have a significant effect on lean angle (except for the minor effect of riding on the side of the tires when leaned over).

Race bikes tend to locate the mass somewhat "centrally" in order to reduce angular inertia, which increases the roll (lean) response for the same steering inputs. It's not that critical, as ground clearance when cornernig prevents the engine from being too low.

A low center of mass may help when walking a bike around, but it increases angular inertia, making the bike slow to respond to steering inputs. It's an issue for the very low center of mass motorcycles used for land speed records.
 
Jeff Reid said:
A low center of mass may help when walking a bike around, but it increases angular inertia, making the bike slow to respond to steering inputs.

I don't understand that bit. The moment of inertia is a function of the square of the distance of the mass from the pivot. I would have thought things would have gone the other way and that lowering the mass would decrease the moment of inertia. (The pivot being at ground level). Have I got this wrong?