Adding Radius of Gyration values?

[Nugget12]

Hi There
I am doing a little test program for some tire testing and just need to make sure I am doing something right, I am calculating the radius of gyration of my tire and wheel separately using the formulas from Dunlop http://www.dunlopaircrafttyres.com/tech_support/dunlop-engineering-data.aspx So I have a value of k for the tire and wheel, do I just add those two together to get the combined radius? I do that currently but it leaves me with a value of k that is outside the radius of the tyre, ie for a tire whose diameter is 0.36m I get a k value for the rim of 0.201 and for the tire of 0.239 so combined it comes to 0.44 which feels wrong to me. Can anyone see where I am going wrong?
Chris

 

[SteamKing]

Hi Ther
I am doing a little test program for some tire testing and just need to make sure I am doing something right, I am calculating the radius of gyration of my tire and wheel separately using the formulas from Dunlop http://www.dunlopaircrafttyres.com/tech_support/dunlop-engineering-data.aspx So I have a value of k for the tire and wheel, do I just add those two together to get the combined radius? I do that currently but it leaves me with a value of k that is outside the radius of the tyre, ie for a tire whose diameter is 0.36m I get a k value for the rim of 0.201 and for the tire of 0.239 so combined it comes to 0.44 which feels wrong to me. Can anyone see where I am going wrong?
Chris

The gyradius r is based on the mass of a rotating object and its moment of inertia about the axis of rotation, such that:

r² = I / M

where

I - moment of inertia
M - mass of the object

Your tire and wheel probably have two different masses, so the proper calculation would be to convert the gyradius of each component to a moment of inertia, using the correct masses, add the moments together, and then calculate the gyradius of the combined assembly, like so:

I_tire = M_tire*r_tire²
I_wheel = M_wheel*r_wheel²

I_total = I_tire + I_wheel

M_total = M_tire + M_wheel

r_total = (I_total / M_total)^1/2

 

[Nugget12]

Many thanks for the quick reply, that looks more sensible, will give that a try. Thanks.