[home][rumors and news][model release matrix][dealer network][desktop calendar][exhaust notes][tov forums][links][search][sponsors][garage][login]

Tire Rack Upgrade Garage
 Search for a Dealer:
 Canadian Flag US Flag
 Honda Acura
 ZIP  
Acura
There are currently no active Acura promotions
Honda
There are currently no active Honda promotions
First impressions and some background info on the 2019 Acura RDX Prototype
More.......................
2019 Acura RDX Prototype Debuts with Evocative Styling, Higher Performance, New Tech and Luxury Appo
More.......................
Live from Detroit! 2019 Acura RDX Reveal
More.......................
Honda releases more information on the 2019 Insight
More.......................
American Honda Sets 3rd Straight Annual Sales Record with Best-Ever December
More.......................
HONDATA Dyno Test: 2018 Accord Sport 2.0T 6MT
More.......................
All-new Acura RDX Prototype Teased Ahead of Detroit World Debut
More.......................
Honda Takes New Approach with Insight Prototype Debuting at 2018 NAIAS
More.......................
Civic --> Re: Horn upgrades for 2017 Civic Si and Type R?
Join Discussion......
Audio & Electronics --> Re: What's your favorite dashcam?
Join Discussion......
Today's Reading Links --> Re: Honda's downfall in Europe continues :(
Join Discussion......
Professional Motorsports --> Re: 2018 Honda F1 PU
Join Discussion......
Integra --> How the Integra Changed the Sport Compact Scence
Join Discussion......
General Talk --> Re: What do you want from a modern Type-S?
Join Discussion......
RLX --> Re: Acura RLX Reviews
Join Discussion......
IMA/Hybrids --> Re: waiting for '18 Accord Hybrid
Join Discussion......
Strictly Technical --> Re: Acura V6 Turbo Engine
Join Discussion......
ILX --> Re: 2019 ILX - FMC?
Join Discussion......
Civic --> Re: Just bought a new 2017 Si Sedan!
Join Discussion......
Civic --> Re: Civic Si, $199 lease offer
Join Discussion......
RDX --> Re: 3rd Generation Acura RDX Reviews
Join Discussion......
General Talk --> Re: Veloster N coming to the States
Join Discussion......
Sales Experiences --> Re: Joke of an experience in PHX
Join Discussion......
Jump to:
article details
Author Ryan Leecock
Categories All Honda/Acura
Create Date January 18, 2002 18:06
Last Update February 08, 2005 18:23
Theory of a Rotational Mass

by Jerome Soh

What is the physical relationship between an increase in wheel/tire = weight (rotating mass) and static weight?

It depends on how the weight of the wheel/tire is distributed.

Actually, there is a relationship between rotating and static weight. For the purposes of a car,

a=T(2/md+d/2I)

a = acceleration
T = torque driving the wheel
m = mass the wheel must "tow" from the center of rotation (COR)
d = diameter of tire
I = polar moment of inertia of wheel/tire combination

This was derived from first principles. The first term comes from F=ma where F = T/(d/2) --> d/2 is the moment arm at which the force from the ground on the tire acts. The 2nd term comes from a = alpha*(d/2) where alpha is angular acceleration. T=alpha*I.

(I) is not easy to calculate for complicated shapes like wheels... it is usually measured. The general form is (I) = sum (mi*di^2). (mi) is the "lump" of mass at a distance (di) from the COR. Break up your wheel into a zillion parts, measure the distance from the COR to each part, sum them all up using the above equation, and you get (I) :-). As an example, let's take a simple shape: for a uniformly distributed disk, (I) = md^2/8. Plugging into the above equation for (a), we get:

a=T(2/md+4/m_wd) where m_w is the weight of the wheel. Thus, we can see that for a uniformly distributed disk (like a hockey puck), the importance of rotational weight is 2x that of static weight (if the weight was static, it would contribute to the first term with the "2" factor, if it was rotational, it would contribute to the 2nd term with the "4" factor). However, a typical wheel/tire combination has most of it's weight at the outer edges, which increases (I). Thus, rotational weight is more than 2x the equivalent static weight.... probably near 3x or more (for really heavy tires with light wheels).

> things to rotate, you need a torque.  Simply put, heavier wheels require
> more torque to get them rotating at the same speed as lighter wheels.

No and no. You seem to have the right idea, but please let me clarify. Wheels with a larger moment of inertia (I) require more torque to _accelerate_ at the same rate as a wheel with a smaller I. For a given horsepower output, both wheels will eventually reach the same terminal velocity, but the wheel with the larger I will take longer to reach it. It is possible for a heavier wheel to accelerate at a faster rate than a lighter wheel for a given torque. As an example, let's say we have 2 identical 15" wheels. Now let's add 1 lb to wheel #1 at the very edge of the wheel, and 2 lbs to wheel #2 near the center of the wheel. Even though wheel #2 is heavier, it has a smaller polar moment of inertia (I) and thus will accelerate at a faster rate for a given torque than wheel #1.

You can, of course, calculate the acceleration, then work your way backwards and simply define an "effective mass" as the proportionality constant between F and a. In this case you'd arrive at

M_effective = (M + 4I/d^2)

However, such a definition is neither physical, nor possibly even useful. The problem is that, as you stated,

>(I) is not easy to calculate for complicated shapes like wheels

so that, eventually, you'll have to take a guess at (I), like,

>.... probably near 3x
>or more (for really heavy tires with light wheels).

I think this might be helpful in an FAQ, provided that a warning is added that it is not quantitatively accurate. It would, however, provide a good conceptual insight for why adding 10 pounds of wheel is worse than driving around with a 10 pound sandbag.

reader's comments
Click Here to Submit Your Comments
Jump to:
TOV Video: 2019 Acura RDX Walk-around with LPL Steve Hansen
Read Article....................
TOV Photo Gallery: 2018 North American International Auto Show
Read Article....................
2018 Acura RLX PR Photo Gallery
Read Article....................
TOV First Drive: 2018 Honda Accord
Read Article....................
2018 Honda Accord Specifications and Features (FINAL)
Read Article....................
2018 Honda Accord Hybrid PR Photo Gallery
Read Article....................
Contact TOV | Submit Your Article | Submit Your Link | Advertise | TOV Shop | Events | Our Sponsors | TOV Archives
Copyright © 2017 Velocitech Inc. All information contained herein remains the property of Velocitech Inc.
The Temple of VTEC is not affiliated with American Honda Motor Co., Inc. TOV Policies and Guidelines - Credits - Privacy Policy