# Radius of Gyration

Started by
CWA
, Apr 29 2012 16:35

7 replies to this topic

### #1

Posted 29 April 2012 - 16:35

I'm using calculations from Dixon's Shock Absorber Handbook on Roll & Pitch Vibrations (Undamped 1DOF) in the Vibration Theory chapter. I'm studying an FSAE car, and I've got an ADAMS model and extracted eigenvalues and have natural frequencies:

Heave 1.8Hz

Pitch 3.9Hz

Roll 5.5Hz

Using calculations from Dixon's equatons, I get the Pitch Dynamic Index to be 8.39 and Roll Dynamic Index to be 5.95. Resulting radii of gyration are 3.42m for roll and 6.84m for pitch. I used spruing mass (276kg) and the sum of all four wheel rates (not spring rates).

Taking roll as an example, how is it possible to have a radius of gyration larger than half the track width of the car, where there is no overhang past the track width? Do the natural frequencies listed seem realistic (particularly roll and pitch compared to the heave), making the error due to calculations? Or are the frequencies for pitch and roll incorrect, based on an inaccurate model?

Thoughts would be appreciated, thanks in advance

Heave 1.8Hz

Pitch 3.9Hz

Roll 5.5Hz

Using calculations from Dixon's equatons, I get the Pitch Dynamic Index to be 8.39 and Roll Dynamic Index to be 5.95. Resulting radii of gyration are 3.42m for roll and 6.84m for pitch. I used spruing mass (276kg) and the sum of all four wheel rates (not spring rates).

Taking roll as an example, how is it possible to have a radius of gyration larger than half the track width of the car, where there is no overhang past the track width? Do the natural frequencies listed seem realistic (particularly roll and pitch compared to the heave), making the error due to calculations? Or are the frequencies for pitch and roll incorrect, based on an inaccurate model?

Thoughts would be appreciated, thanks in advance

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### #2

Posted 29 April 2012 - 22:18

It can't be. The formula for I is M*R^2=sigma m*r^2+i and M=sigma m where r is the distance from the axis and m,i is the inertia of each component, and you can ignore i if you make m small enough. Since no r can be more than the length of the vehicle then R must always be less than that.

In practice for a full size car R for pitch and yaw are about the same, say 1m or so, and roll is a lot less.

In practice for a full size car R for pitch and yaw are about the same, say 1m or so, and roll is a lot less.

### #3

Posted 01 May 2012 - 09:18

Greg is correct (of course).

I am currently a long way from my copy of Dixon. Perhaps you could define "dynamic index" for me, & perhaps state the wheelbase of your vehicle.

That aside, pitch radius of gyration is a very useful way of thinking about pitch inertia. Pitch radius of gyration normalized by wheelbase varies (according to my estimates) from between 0.31 (F3), 0.325 (F1) to 0.425 (touring car) & 0.443 (front engine/transaxle). For reference, a pure constant section beam would be sqrt(1/12). My guess for your vehicle would be around 0.38...

I am currently a long way from my copy of Dixon. Perhaps you could define "dynamic index" for me, & perhaps state the wheelbase of your vehicle.

That aside, pitch radius of gyration is a very useful way of thinking about pitch inertia. Pitch radius of gyration normalized by wheelbase varies (according to my estimates) from between 0.31 (F3), 0.325 (F1) to 0.425 (touring car) & 0.443 (front engine/transaxle). For reference, a pure constant section beam would be sqrt(1/12). My guess for your vehicle would be around 0.38...

### #4

Posted 01 May 2012 - 17:29

Perhaps you could define "dynamic index" for me,

as for Dixon's definition:

**Edited by TC3000, 01 May 2012 - 17:31.**

### #5

Posted 01 May 2012 - 19:07

Thank's TC. On that basis it would appear that something is not quite right with CWA's calculations.

### #6

Posted 01 May 2012 - 20:39

Thank's TC. On that basis it would appear that something is not quite right with CWA's calculations.

Just for confirmation, what Dixon is defining as the "pitch dynamic index" is exactly twice the values you were quoting, correct?

### #7

Posted 01 May 2012 - 21:31

That was my conclusion.

### #8

Posted 10 May 2012 - 21:30

I've now made contact with my copy of Dixon (actually two, the "Shock Absorber Handbook" & "Tyres Suspension & Handling").

The definition of "Dynamic Index" appears to differ between the two books. The "TSH" version appears to be to square of the "SAH" version. In "SAH" he opines that the normalised pitch radius of gyration is around 0.5 for a road car, "often more for a large car, less for small cars which tend to have less overhang".

All very convincing, but worth checking, I thought.

Over a number of years I have assembled rig data acquired from a range of road vehicles, largely on an ad hoc basis, with the objective of assembling a (more or less useful) compendium of background information. After reading Dixon's notes, I processed my estimates of normalised pitch radius of gyration (Kr) to obtain this histogram. Interestingly (or otherwise), the only vehicles for which my estimates of Kr exceeded 0.5 were a Landrover & a few Porsches.

It would be fair to note that my estimates are "dynamic", notionally covering the heave & pitch modes, and a "non-monolithic" sprung mass (they all are) would reduce the effective value of Kr (I think). I leave you to decide the implications of that.

The definition of "Dynamic Index" appears to differ between the two books. The "TSH" version appears to be to square of the "SAH" version. In "SAH" he opines that the normalised pitch radius of gyration is around 0.5 for a road car, "often more for a large car, less for small cars which tend to have less overhang".

All very convincing, but worth checking, I thought.

Over a number of years I have assembled rig data acquired from a range of road vehicles, largely on an ad hoc basis, with the objective of assembling a (more or less useful) compendium of background information. After reading Dixon's notes, I processed my estimates of normalised pitch radius of gyration (Kr) to obtain this histogram. Interestingly (or otherwise), the only vehicles for which my estimates of Kr exceeded 0.5 were a Landrover & a few Porsches.

It would be fair to note that my estimates are "dynamic", notionally covering the heave & pitch modes, and a "non-monolithic" sprung mass (they all are) would reduce the effective value of Kr (I think). I leave you to decide the implications of that.

**Edited by DaveW, 10 May 2012 - 21:36.**