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post #1 of (permalink) Old 05-01-2015, 05:21 AM Thread Starter
Peaty
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Join Date: Jan 2006
Location: Lawrence, KS - Rock Chalk
Posts: 8,097
Car Year: 2016
Car Model: BRZ Limited - Manual
Transmission: 6 Speed Manual
Wheel / Tire Weights and Rotational Inertia

I was looking around for something on my hard drive and found this again. I did not make the attachment, just passing it on. Thought it might be of interest to someone. The spreadsheet has all sorts of cool calculations. I'm not sure if the formatting will hold up but here is a partial cut and paste:
Quote:
Wheel / Tire Weights and Rotational Inertia
Car and Wheel Dimensions: wheel 1 wheel 2 Derived dimensions wheel 1 wheel 2
Wheel size (inches) 16 17 Wheel Radius (feet) 0.67 0.71
Tire width (mm) 215 225 Tire sidewall height (feet) 0.42 0.33
aspect ratio 60 45 Tire radius (feet) 1.090 1.041 (~same)

wheel weight (lbs) 22.0 19.0 wheel mass (slugs) 0.68 0.59
tire weight (lbs) 21.0 25.5 tire mass (slugs) 0.65 0.79
Total wheel weight 43.0 44.5 total mass (slugs) 1.34 1.38

Car 0-60mph time 5.3 Linear Acceleration in ft/sec^2 16.60
Wheel rotat'l accel'n radians/sec^2 15.23
Note: Units for inertia are slug feet^2
Formulas Implied Radius of Gyration
I1=Rotational Inertia 1, single uniform density disk 0.793 0.748 I=1/2 (MR^2) Rgy = .71Rt

I2=Rotational Inertia 2, Tire Disc + Wheel Disc 0.684 0.775 I=Iw+It
wheel alone (solid disc) 0.152 0.148 Iw=1/2(MR^2) Rgy = .71Rw
tire alone (hollow disc) 0.532 0.627 It=1/2M (Ra^2+Rb^2) Rgy = Rw + .54(Rt-Rw) approx

I3=Rotational Inertia 3, Two Discs, Edge Weighted 0.861 0.949 I=Iw+It
wheel alone 0.202 0.197 Iw=2/3(MR^2) Rgy = .82Rw
tire alone 0.659 0.751 It=M (Rg^2) Rgy = Rw + .8(Rt-Rw)

Rotational Torque G=IW Torque Loss Per Wheel, Ft-lbs Tq difference Per Wheel Torque difference * 4 wheels Torque Diff, rot'l+linear Total Added Chassis Weight Equiv, W2 vs W1
Uniform density disk, Tire + Wheel 12.1 11.4 0.7 2.7 -0.6 -1.1 lbs
Tire Disc + Wheel Disc 10.4 11.8 -1.4 -5.6 -8.9 -15.9 lbs
Tire Disc+ Wheel Disc, Edge Weighted 13.1 14.5 -1.3 -5.3 -8.7 -15.5 lbs

Torque devoted to linear acceleration 24.2 25.0 -0.8 -3.4 -6.0 lbs ( linear only )


LIMITATIONS:
All rotational inertia models are approximations, but model 3 may be the most accurate.
The two wheel / tire combos are assumed to have the same total radius (wheel1) when calculating the acceleration rates and torques.


Attached Files
File Type: zip wheel_inertia.zip (9.0 KB, 8 views)

Peaty

2016 BRZ, 2010 Leg 3.6 R, 2013 OB, 2001 Forester S and 1999 Miata
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