I was looking into the unsprung mass distribution of cars to try find an error on a program that MonkOnHotTinRoof is programming for us (tristancliffe, BobSmith and myself do the work from the physics point of view). The problem was that at some points in time we were getting a negative tyre normal load against the surface (long calculation - won't bore you with it now) and I assumed that the error may be from the unsprung mass being unevenly distributed. Here is a calculation I did based on some data that ColCob gave me.

Variable Names

mTotal - Total Mass
mUnsprung - Unsprung Mass
mSprung - Sprung Mass
distrTotalF - Total Mass distribution on front wheels
distrSprungF - Sprung Mass distribution on front wheels
distrUnsprungF - Unsprung Mass % of front wheels of total mass

Calculation

mTotal = mSprung + mUnsprung
W = mg (Weight = mass * gravity)
Therefore when the car is not accelerating perpendicular to the road surface:
F = mTotal * g
F = (mSprung + mUnsprung) * g
F is the total force against the road exerted by all the tyres

When the car is stationary the force exerted against the road by both front wheels is:
FTotalFront = distrTotalF * (mSprung + mUnsprung) * g

distrTotalF * mTotal = distrSprungF * mSprung + distrUnsprungF * mUnsprung
distrTotalF * mTotal - distrSprungF * mSprung = distrUnsprungF * mUnsprung

Therefore the force exerted by the unsprung mass on the front wheels is:
FUnsprungFront = (distrTotalF * mTotal - distrSprungF * mSprung) * g

The total force exerted by the unsprung mass is:
FUnsprungTotal = mUnsprung * g

Therefore the percentage distribution of that mass on the front wheels is:
distrUnsprungF = [(distrTotalF * mTotal - distrSprungF * mSprung) * g] / (mUnsprung * g)
distrUnsprungF = (distrTotalF * mTotal - distrSprungF * mSprung) / (mUnsprung * g)

Results




If you consider the fact that all those values come from a long calcuation with some slightly rounded-off values, they are probably considered 50:50 in LFS. This is inaccurate. A rear wheel should be much heavier than a front one on the FZ50 for instance and this could make quite a big difference as to the way cars handle. Seing as Scawen is busy on physics updates now, perhaps this can be added in the patch? It shouldn't take that long but it is something that would change the cars under certain conditions (high vertical acceleration) handle quite differently. Or do I have something wrong in my calculation...

Quote from axus :

When the car is stationary the force exerted against the road by both front wheels is:
FTotalFront = distrTotalF * (mSprung + mUnsprung) * g

Wrong. You're assuming here that the unsprung masses are distributed the same as the sprung mass for each car. The correct expression should be:

FTotalFront = ( (distrTotalF * mSprung) + mUnsprungFront ) * g

The rear unsprung mass acts directly through the rear wheels/tyres and has no effect on the weight supported by the front wheels.
Haven't looked through the rest of your maths, but when I did a similar thing a while ago I found that the front and rear unsprung masses for the cars are different. I'll try to find the values I have and post them here to see if it helps you.

OK, I just found the values I calculated. They are expressed as kg per wheel FRONT / REAR.

XFG: 11.38 / 14.07
XRG: 13.38 / 16.71
XRT: 16.04 / 17.74
RB4: 14.75 / 15.79

I've got more but I'll have to wait until later to post them...let me know if you think I'm miles off
OK, here are the others:

FXO: 14.11 / 18.21
LX4: 12.82 / 13.01
LX6: 14.07 / 14.77
RAC: 14.95 / 16.98
FOX: 13.35 / 16.51
FO8: 17.51 / 22.01
FXR: 23.68 / 23.29

That's all I've got round to doing. If you want some info on how I got to those numbers I'll try to explain but I might have to spend a while looking through the spreadsheet to remind myself

Quote from StewartFisher :

Wrong. You're assuming here that the unsprung masses are distributed the same as the sprung mass for each car. The correct expression should be:

FTotalFront = ( (distrTotalF * mSprung) + mUnsprungFront ) * g

The rear unsprung mass acts directly through the rear wheels/tyres and has no effect on the weight supported by the front wheels.
Haven't looked through the rest of your maths, but when I did a similar thing a while ago I found that the front and rear unsprung masses for the cars are different. I'll try to find the values I have and post them here to see if it helps you.

OK, I just found the values I calculated. They are expressed as kg per wheel FRONT / REAR.

XFG: 11.38 / 14.07
XRG: 13.38 / 16.71
XRT: 16.04 / 17.74
RB4: 14.75 / 15.79

I've got more but I'll have to wait until later to post them...let me know if you think I'm miles off

I'm afraid you are wrong.

mTotal = mSprung + mUnsprung
FTotalFront = distrTotalF * mTotal * g
FTotalFront = distrTotalF * (mSprung + mUnsprung) * g

I have the distribution for the total mass and the distribution for the sprung mass. You are confusing distrTotalF with distrSprungF.

EDIT: For a more elaborate explaination, visit http://monkster.hopto.org/cgi- ... nsprung_mass_distribution

Quote from axus :

I'm afraid you are wrong.

mTotal = mSprung + mUnsprung
FTotalFront = distrTotalF * mTotal * g
FTotalFront = distrTotalF * (mSprung + mUnsprung) * g

I have the distribution for the total mass and the distribution for the sprung mass. You are confusing distrTotalF with distrSprungF.

Ah...oops! Sorry, I'll have to lok at it again!

Looking at Colcob's data that I gave you, the unsprung mass distributions are close to even, but not always. That is of course assuming that it is accurate. I'll do something with the data in a bit and get back to you.

Sorry about this, but you've been wasting your time. There is no way from the data we have to determine the unsprung mass distributions or the sprung mass distributions.

I needed to have some kind of figure for sprung mass distributions to do any kind of calcs for the suspension analyser (ie you need a figure for what mass is on your spring) so I just had to take the unsprung mass distribution as being 50:50 in the absense of any other data to derive some usable sprung masses.

So unfortunately, because you've taken the sprung mass figures as gospel, all thats happened is that you've proved to within 0.1% that I'd assumed an unsprung mass dis of 50:50. Which I had.

Just to clarify, raf file data includes the total sprung mass, and the total overall mass (both including driver), from which you can accurately derive the total unsprung mass.

It also includes dimensions from the individual wheels to the centre of gravity of the whole car (including driver). From this you can accurately derive the overall weight distribution at the contact patch.

However, from that data alone, I dont see how you can derive the individual unsprung masses.

If it weren't for a long standing bug in the raf output, we'd be able to easily derive it by comparing the vertical tyre load with the suspension deflection*spring stiffness, and working out the difference in load.

Unfortunately, the values that the raf output reports as being vertical tyre load are actually vertical spring load, so you cant do that.

Quote from colcob :

Sorry about this, but you've been wasting your time. There is no way from the data we have to determine the unsprung mass distributions or the sprung mass distributions.

Sprung mass distribution may be obtained from raf (vertical loads) provided that there is a moment when the car is standing still on a flat surface. Total mass distribution may be taken from garage view (with driver and fuel). I hope the two distributions are not equal. The calculation from the first post seems reasonable, though I'll check it one more time.

Yes, I was thinking about that a second ago but the thought never quite fully developed. Its midnight - I should be getting to bed. I'll look into this tomorrow. Thanks again for the help w126! You've already helped with the development of our little app quite a lot. Feel free to visit our wiki and look at how development is going. It almost has everything that f1prefview does (albiet not as user friendly for now) and some extended diagrams available. It should soon have the output made by RAFTyreExtract covered too - not sure if you have taken into account only acceleration of the wheel perpendicular to the road surface or just along the Z axis, we are working away on a few things. The final version should allow you to enter custom equations in the fields for X and Y axes... The latest binaries are available to download from the wiki. There seem to be a few bugs lurking around though but development is coming along nicely and they should be sorted soon.

Quote from axus :

not sure if you have taken into account only acceleration of the wheel perpendicular to the road surface or just along the Z axis

I take full wheel acceleration vector into account in my current development version of RAFTyreExtract and when using this version lateral and longitudinal tyre forces differ slightly (around 1 %) from the values shown by previous released version. I have been trying to extend RAFTyreExtract to work with front wheels lately, but to do that I still need to research what is the meaning of steer from RAF dynamic wheel info in all possible cases.

Quote from w126 :

Sprung mass distribution may be obtained from raf (vertical loads) provided that there is a moment when the car is standing still on a flat surface. Total mass distribution may be taken from garage view (with driver and fuel). I hope the two distributions are not equal. The calculation from the first post seems reasonable, though I'll check it one more time.

Ah, good point, I hadnt thought it all the way through. So what you need to do is park up on a guaranteed flat surface during the run (not sure whether one exists though to be honest), take the spring deflection readings from that point, and you should be good to go.
Although the flatness issue is a problem, if the surface isnt dead level it will mess up your sprung distribution and be a waste of time. I suppose that the garages at kyoto are probably as near dead flat as anywhere.

Quote from colcob :

Ah, good point, I hadnt thought it all the way through. So what you need to do is park up on a guaranteed flat surface during the run (not sure whether one exists though to be honest), take the spring deflection readings from that point, and you should be good to go.
Although the flatness issue is a problem, if the surface isnt dead level it will mess up your sprung distribution and be a waste of time. I suppose that the garages at kyoto are probably as near dead flat as anywhere.

Autocross is dead flat

Quote from w126 :

I take full wheel acceleration vector into account in my current development version of RAFTyreExtract and when using this version lateral and longitudinal tyre forces differ slightly (around 1 %) from the values shown by previous released version. I have been trying to extend RAFTyreExtract to work with front wheels lately, but to do that I still need to research what is the meaning of steer from RAF dynamic wheel info in all possible cases.

Surely, you only need to take the perpendicular force... and that goes for g too - you only should take into account its effect in the direction perpendicular to the surface - which is the next thing on the list for our development - finding the slope of the surface. You should be able to work out 3 points on it atleast by using the forward-vector, right-vector and suspension travel... haven't looked it much yet though. Our version does give front tyre info aswell, albiet we don't have the coeficient of friction in there yet. As soon as we get reliable values for the force between the tyre and the road, it will be in there.

EDIT: I just looked at RAF output from the autocross to see if I get a different figure for the sprung mass distribution. I first did the XF GTi and the value looked very close to ColCob's so I put my new value in there and it seemed that the XF GTi does indeed have 50:50 unsprung mass distribution. That wasn't too strange because the XF GTi has same wheel sizes front and rear. Then I did the same for the XR GT and I got a 50:50 unsprung mass distribution again. This seemed odd because the XR GT has wider rear tyres. I decided to do it for the car that seems least likely to have such an unsprung mass distribution - the FZ50 with 295's on the back and 235's on the front - and I got a 50:50 unsprung mass distribution again. It appears that they are indeed distributed in this way. If someone can be bothered to do this for the rest of the cars and prove me wrong, go ahead - I don't have enough time to do this now. I'm pretty sure all the cars are like this. This should be changed for the physics patch IMO.

That's odd because changing the wheel / tyre sizes in LFS tweak does (did) alter the cars mass & weight distribution.

Hmmm, perhaps something is wrong with my equations. Surely though, the "Tyre Load" from the two front tyres devided by the total tyre load should give you the sprung mass distribution. Maybe there is something wrong with my equations but I did check them with my physics lecturer and he said they seemed fine.