Fuel Consumption Question - Rims - Please look

To attack the physics of this situation:



If we assume, for simplicity's sake, that the rim is made of a tube with a disc on one side, with 75% of the weight in the tube portion, we can calculate the rotational inertia for each one.



I for tube = mass*radius^2

I for disc = 1/2 mass*radius^2



16" rim @ 6 kg: I = (.75*6kg)*(.2032 m)^2 + 1/2(.25*6kg)*(.2032 m)^2 = .216



15" rim @ 8 kg: I = (.75*8kg)*(.1905 m)^2 + 1/2(.25*8kg)*(.1905 m)^2 = .254



In this very rough calculation, the larger diameter rim actually is easier to turn. We could also analyze the tire, but assuming the sidewall hieght varies to maintain the same circumference, the majority of the weight in the tread will be at the same place and have the same rotational inertia anyway.



Again, with out knowing where the weight is specifically placed in a wheel, it is hard to say exactly what the rotational inertia is. The higher the neumber, the greater the torque required to accelerate the wheel at the same rate. Multiplied by 4 wheels can make a difference if you race from stoplight to stop light I guess, but it shouldn't make much difference for normal highway driving.



As one more note, if you plan on doing any sort of autocrossing, a higher rotational inertia also leads to longer and slower braking.



P.S. - Only one more class to go for that physics degree. Anyways, back to my quantum electrodynamics calculations. ;)
 
RemmoSi said:
To attack the physics of this situation:



If we assume, for simplicity's sake, that the rim is made of a tube with a disc on one side, with 75% of the weight in the tube portion, we can calculate the rotational inertia for each one.



I for tube = mass*radius^2

I for disc = 1/2 mass*radius^2



16" rim @ 6 kg: I = (.75*6kg)*(.4064 m)^2 + 1/2(.25*6kg)*(.4064 m)^2 = .216



15" rim @ 8 kg: I = (.75*8kg)*(.1905 m)^2 + 1/2(.25*8kg)*(.1905 m)^2 = .254



In this very rough calculation, the larger diameter rim actually is easier to turn. We could also analyze the tire, but assuming the sidewall hieght varies to maintain the same circumference, the majority of the weight in the tread will be at the same place and have the same rotational inertia anyway.



Again, with out knowing where the weight is specifically placed in a wheel, it is hard to say exactly what the rotational inertia is. The higher the neumber, the greater the torque required to accelerate the wheel at the same rate. Multiplied by 4 wheels can make a difference if you race from stoplight to stop light I guess, but it shouldn't make much difference for normal highway driving.



As one more note, if you plan on doing any sort of autocrossing, a higher rotational inertia also leads to longer and slower braking.



P.S. - Only one more class to go for that physics degree. Anyways, back to my quantum electrodynamics calculations. ;)



nerd :D
 
:shocked



The next time I run into the question that starts off, "Two trains leave from New York and Chicago at the same time, one travelling at 50 kph, the other....." I'll know who to go to. :D
 
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