The more mass an object has, the more energy it takes to accelerate it.
To accelerate a rolling object such as a wheel, you must both accelerate
its mass plus overcome its rotational inertia.
Because of this, the weight of rotating mass such as wheels and tires on
a car have a bigger effect on acceleration than static weight such as on
the chassis on a car. When purchasing new wheels and tires for a performance
car, it can be useful to compare the effects of different wheel and tire
combinations. This is especially true when considering upgrading to
larger wheels or tires on a car.
In many cases, car handling can be improved by increasing the diameter
of your car's wheels matched with a lower aspect ratio tire. The drawback
of this is that most plus sized wheel and tire combinations are heavier
than the stock smaller wheel size with a taller tire sidewall. This
can make for slower 0-60mph and 1/4 mile times.
In order to help make this tradeoff decision, I have put together a spread
sheet that calculates the amount of torque needed to accelerate two different
wheel and tire combinations at a given rate. This rate is determined
by the 0-60mph acceleration time of the car in question.
In order to use this spreadsheet, you will need to know the diameter of
the two wheels and size of the two tires in question, plus you will need to
know the rough 0-60mph time, torque, and weight of the car you are dealing
with. The spreadsheet will then calculate the amount of torque needed
to accelerate the wheel and tire combination at the same rate that the car
accelerates at. The spreadsheet will also compare the effects of wheel
weight to chassis weight by calculating the number of pounds of car weight
per foot pound of engine torque on the car. You can compare two different
wheels and tires of the same or different sizes.
I am not an engineer, and it has been over 15 years since I took my last
physics class, so if you spot any errors in my spreadsheet, please drop
me a line. (rocksandracing @ the-welters.com) I used the web site listed below
to refresh my memory of physics. It explains things in a pretty straight
forward manner, and is a good resource.
My spreadsheet
for calculating rotational inertia and acceleration.
NOTES
My spreadsheet does not use any macros, but you should always virus scan
things like spreadsheets and word docs when you download them.
My spreadsheet contains three different models for calculating the rotational
inertia of a wheel and tire combination. I believe that "model 3"
is the most accurate, but the other two are included as a way of showing
how I arrived at model 3.
"Unsprung" weight of wheels and suspension components has effects on handling
in addition to the effects of rotating mass on acceleration. This
spreadsheet does not address any of these issues. But increased weight
on unsprung components makes shocks and springs have to work harder, and
also diminishes car handling with other things being equal. The trade
off of lower aspect ratio or wider tires verses their increased weight is
beyond the scope of this page.