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coughing skunk · April 24th, 2013, 12:18 PM

totally not trying to hate right now, but why cafe the ninja? One thing to think about if trying to run larger wheels on the ninja is rotational inertia and the energy required to turn the wheel.

I'll try not to get too science-y..

Angular Kinetic Energy (KE) = 1/2 * I * w^2
where I is the moment of inertia for an object and w is the angular velocity

I for a hollow cylinder, which we can approximate our wheels to be for simplicity, is 1/2 * m * r^2
where m is mass of the wheel and r is the radius of the wheel

This means that for the 16 inch wheels, r is .2032 (meters, SI units), and KE equals 1/2 * 1/2 * m * .2032^2 * w^2
= 1/4 * m * w^2 * .041

For the 21 inch wheel, r is .2667, and the resulting KE is
= 1/4 * m * w^2 * .071

Assuming everything else equal (which really isn't, the 21 inch wheel will likely be heavier), if we divide the KE required for the 21 inch wheel by the KE required for the 16 inch wheel we get .071/.041 = 1.7. That means to turn both wheels at the same speed, the energy required to turn the 21 inch wheel is ~1.7 times the amount needed for the 16 inch wheel!

Moreover, how will this affect the overall acceleration of you and your bike?

Well, if you can believe some hand waving in lieu of trying to type of the derivation of how angular velocity relates to a constant linear acceleration then we get:
w^2 = 2*a*theta/r
where a is linear acceleration, theta is how far the wheel has rotated and r is the radius of the wheel

Plugging this into our equation for KE, we get KE = 1/4*m*r*a*theta
We want to know how fast you'd accelerate with the larger wheels, so we'll solve that KE equation for a:
a = 2*KE/(m*r*theta)

Since the energy output of your motor won't change by swapping wheels, KE will be the constant, along with m and theta at any given time during acceleration. Note, this means at any 'snapshot' in time, not that your engine doesn't change its energy output based on revs.

So, to find the relative acceleration difference, we divide the acceleration from the 21 inch wheel, a21, but the acceleration of the 16 inch wheel, a16.
a21/a16 = (1/r21)/(1/r16)=r16/r21 = .76

With the larger wheels, in an ideal world (real world would be worse), you are effectively accelerating %24 slower than with the 16 inch wheels! The same effect happens when kids put 18's on their civics with the 90hp 1.5L motors..

Anyways, enough of that. Not trying to kill a dream just spread some knowledge.

One of my other bikes is an early model XS650 with 19" in front and 18" in rear spoked wheels and more than twice the cc's of the ninja. Not that a small, light, high-revving spoked wheel bike wouldnt be cool.. Just sayin, I got my XS for $1000 running with good chrome. I know there are older larger displacement KZ's for just as cheap or cheaper.

April 24th, 2013, 12:18 PM	#15
coughing skunk ninjette.org member Name: chris Location: northern colorado Join Date: Oct 2012 Motorcycle(s): 07 ninja250r 73 xs650 70 honda cl100 Posts: 17	totally not trying to hate right now, but why cafe the ninja? One thing to think about if trying to run larger wheels on the ninja is rotational inertia and the energy required to turn the wheel. I'll try not to get too science-y.. Angular Kinetic Energy (KE) = 1/2 * I * w^2 where I is the moment of inertia for an object and w is the angular velocity I for a hollow cylinder, which we can approximate our wheels to be for simplicity, is 1/2 * m * r^2 where m is mass of the wheel and r is the radius of the wheel This means that for the 16 inch wheels, r is .2032 (meters, SI units), and KE equals 1/2 * 1/2 * m * .2032^2 * w^2 = 1/4 * m * w^2 * .041 For the 21 inch wheel, r is .2667, and the resulting KE is = 1/4 * m * w^2 * .071 Assuming everything else equal (which really isn't, the 21 inch wheel will likely be heavier), if we divide the KE required for the 21 inch wheel by the KE required for the 16 inch wheel we get .071/.041 = 1.7. That means to turn both wheels at the same speed, the energy required to turn the 21 inch wheel is ~1.7 times the amount needed for the 16 inch wheel! Moreover, how will this affect the overall acceleration of you and your bike? Well, if you can believe some hand waving in lieu of trying to type of the derivation of how angular velocity relates to a constant linear acceleration then we get: w^2 = 2atheta/r where a is linear acceleration, theta is how far the wheel has rotated and r is the radius of the wheel Plugging this into our equation for KE, we get KE = 1/4mratheta We want to know how fast you'd accelerate with the larger wheels, so we'll solve that KE equation for a: a = 2KE/(mr*theta) Since the energy output of your motor won't change by swapping wheels, KE will be the constant, along with m and theta at any given time during acceleration. Note, this means at any 'snapshot' in time, not that your engine doesn't change its energy output based on revs. So, to find the relative acceleration difference, we divide the acceleration from the 21 inch wheel, a21, but the acceleration of the 16 inch wheel, a16. a21/a16 = (1/r21)/(1/r16)=r16/r21 = .76 With the larger wheels, in an ideal world (real world would be worse), you are effectively accelerating %24 slower than with the 16 inch wheels! The same effect happens when kids put 18's on their civics with the 90hp 1.5L motors.. Anyways, enough of that. Not trying to kill a dream just spread some knowledge. One of my other bikes is an early model XS650 with 19" in front and 18" in rear spoked wheels and more than twice the cc's of the ninja. Not that a small, light, high-revving spoked wheel bike wouldnt be cool.. Just sayin, I got my XS for $1000 running with good chrome. I know there are older larger displacement KZ's for just as cheap or cheaper.