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Can we put the unsprung mass thing to rest? Skip to the bold part at the end if you don't care.
The physics of it are not hard, you can model it as two masses with a spring and a damper in between. Those who have taken upper level engineering courses will recognize this as a second order dynamic system:
If you're really interested watch some youtube videos on LTI systems.
The response of the unsprung mass to an input will have a larger magnitude if it has a smaller mass, all else held constant.
Here's a simplistic model of a spring-mass-damper system, I'm going to make the assumption that the mass of the car is much more than the mass of any wheel. It's just to make a point, read this for a more developed model.
Let's say the spring constant is 250# and damper coefficient is 50. I actually have no clue what damper coeff most automobile struts are but it's going to be a constant in all cases anyway so who cares. The x-axis will just go for almost 30 seconds, for better resolution.
We'll use a few different unsprung masses, 80 lbs, 130 lbs, 180 lbs.
This plot shows position versus time. As unsprung mass increases, the response magnitude decreases and the time it takes to dampen out increases. That's it. That's why racers go for smaller wheels and run stiff suspension.
Forces on the ball joints are a matter of mass, and momentum. Newton's 2nd law states the force is equal to the first time derivative of momentum. Same thing as mass x acceleration. So the unsprung mass will have more momentum if it's heavier, therefore imparting more force on the ball joints, right?
...but remember, the heavier unsprung mass travels less distance and has lower response frequency - refer to plot, which graphs position versus time. The second derivative of position is acceleration, and the higher unsprung mass will have substantially lower acceleration than the lighter mass. This is because the magnitude of the position sine wave and its frequency are both lower than those of the lighter mass. Basic calc I.
Therefore higher unsprung mass leads to lower acceleration of the mass. Force is mass x acceleration, but as you can now see, it isn't as clear. Although you may have a large mass, you have a low acceleration term. And if you install a lighter mass, the acceleration will increase.
Here's the punchline. The acceleration of the unsprung mass is tied to the springs and struts you run...it's 2 out of 3 inputs for the transfer function. That will determine the forces that the unsprung mass exerts on the ball joints. Just run suspension that is a good match for your wheels and your ball joints will be fine.
Awesome! Thanks for some actual discussion on the topic.
Based on what I read there you would have to know the working limits of the ball joints and other supporting parts to actually see if the added weight translates to an issue or not. Which, since people don't seem to be replacing ball joints at an alarming rate with big wheels it would seem that the wheels at within the limits of the joints they are running.
At rest, the force(s) applied to the ball joint and other suspension components(bjosc) will be static. Rolling in a straight line across a completely flat surface, the forces applied to the bjosc should be static as well.
When the tire impacts any bump, the tire/wheel will experience a change in the forces applied to it while the mass of the car will attempt to remain moving in the same direction it was before the tire/wheel impacted the bump. These two forces will change the amount of force applied to the bjosc.
Assuming I have the car sitting with the tires/wheels on four hydraulic posts and I can change the amount of upward force and height these post exert at will.
If three of the posts have the same upward force and the fourth one has an extra 100 pounds of force compared to the others, the bjosc of that tire/wheel will experience more force than the other three(because it is now supporting more of the weight of the car compared to the other three). How would a change in the mass of the tire/wheel change the amount of force being applied to the bjosc? In this controlled situation, I don't see how the mass of the tire/wheel would have any effect on the forces applied to the bjosc.
In a dynamic environment where the car is moving over an uneven surface, how would things change? At impact with a bump, a wheel with heavier mass is going to resist moving out of it's path of travel more than a lighter wheel. Will this very small difference be enough to change the forces applied to the ball joint? It would seem to me that the mass of the car resisting the change in direction would have a much greater effect on the forces applied to the bjosc than slight changes to the mass of the tire/wheel.
OTOH, I would think that a change in the friction coefficient caused by tires with more grip would create much more of an effect on the forces applied to the bjosc than changes in wheel size.
Two tires of different sizes but equal lateral grip should exert the same forces on the bjosc while cornering at their limits of adhesion. Two tires with different levels of lateral grip but equal size should exert different levels of force on the bjosc at their limits of adhesion.
For you trained engineers, please explain if my WAGs are completely off track.
Did a mod do it or did he figure out that he was acting like a 4 year old on a sugar high and decide to delete the posts that made him look bad?
Hahahahahahahahahaha
Mod did it.
Thanks for the laughs, it was fun.
Some great advice. I Only needed to hear it from someone other than Cole.
Take care out there.
Azbanks: nothing wrong with that analysis. There's a static portion (weight of car) and dynamic portion. The dynamic portion can either work in the same direction as the weight, or the opposite.
Think of a yo-yo, when it reaches the bottom and starts to come back up you feel a little tug on the string. That's Newton, because force is equal to the time-rate change of momentum. As momentum is conserved, but reversed in direction, it exerts a tension force through the string. That force is dynamic, and the weight of the yo-yo is static.
In the same way, the changing momentum of the unsprung mass demands a matching reaction force from the ball joints. The good news is that the rate of that change can be controlled via well-chosen suspension parts, so the magnitude of the reaction force (which is equivalent to the time-rate change of the momentum) can be kept within the fatigue limit.
Your thoughts on friction are really interesting actually, and you're right, probably just as much if not more of a contributor.
And also....when calculating the dampening rates for the spring rate and mass....the tire is also part of the spring rate....thinner sidewall:higher spring rate which is calculated in series not parallel. (If I remember correctly)
I drive in the real world....larger rims look cool but potholes are everywhere. I don't want to be fixing tires and rims all the time nor drive a car that vibrates. If one of my kids borrows a car, they have to buy it if they curb it....that's a rule))
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Originally Posted by refresh951
I have deleted several posts. No room on RL for personal insults.
Just deleted the posts? What happened to John D's policy?
Zero Tolerance In the Forums
There is now a zero-tolerance policy in effect for harassment and off-topic bickering in the Forums. It’s fine to “disagree”. It’s fine to debate. It is fine to argue in a mature manner.
It is NOT fine to cast third-party suspicions, as a 3rd party or competing supplier - calling a vendor “shady”, and/or slandering a supplier or person in any public forum. Rennlist is certainly no exception.
So – here is some advice… If you are thinking about posting a reply which you wonder “will John D. ban me for this?” – presume the answer is YES – and don’t post it.
If someone is harassing you in technical threads report them and never respond to them. If you participate even to defend yourself you are part of the problem and are just as guilty.
This is your only warning. If you participate in off-topic bickering, slander or harassment in the technical forums you will be banned from Rennlist.com
Let’s keep the Forums technical.
John D.
I know many who have left RL for other sites due to member immaturity / harassment / unnecessary bickering, maybe enforcement of the policies would help?
07-02-2015, 02:57 PM
Doug go get a mod, quick! We need to bring on the ban hammer!!! 
