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Unsprung vs sprung weight – going to a larger wheel on the JK

15K views 81 replies 23 participants last post by  Captain Ahab 
#1 ·
I have been thinking of going from the stock BFG 32’1” tires to 35” and in my reading on the forums I keep running into often repeated information that 1lb of unsprung weight is equal to 10lbs of sprung weight. Using that notion, if my new wheels and tires add 10lbs of weight at each corner, that would be a total of 40lbs of added unsprung weight which would equate to the equivalent of carrying 2 substantial people around all the time weighing in at 400lbs. This formula crops up all the time, is repeated as gospel as it gets into more and more threads and seems to me to be simplistic and completely bogus.

My notes from reading about this stuff are below (disclaimer - I am not an engineer – I would be interested to hear from anyone who is!). They are a bit long winded – but I do think the 1lb : 10lb rule needs some serious debunking.

As a rule, lighter wheels will allow the suspension to respond more quickly to the terrain. In street driving they will hop less, allow the suspension to react more quickly and maintain contact with the road more effectively. Heavier wheels will bounce more and for longer over bumps, potentially impacting ride quality.

Increased rotational mass of larger wheels and tires will slow acceleration and affect mpg. (Mpg will be more impacted in lots of start / stop driving than on the highway – so how badly mpg is impacted will depend on the amount of highway vs city driving). Weight of the tires is more important than weight of the wheels when thinking about rotational mass – the weight at the edge of the circle is more difficult to turn (has more leverage) than weight nearer the hub. So any increase in tire weight is more significant pound for pound than any increase in wheel weight. Rotational mass also has a bearing on braking – stopping that increased rotational mass is harder.

That said – the Jeep still weighs 4-5,000lbs so while a lighter tire / wheel combination would accelerate noticeably faster if jacked up in the air, it all changes when you put the Jeep on the ground and factor in the huge mass it has to start moving – the ratio of unsprung to sprung weight has not changed that much even with the larger wheels and tires. Ten pounds of additional weight at each corner of a lightweight Lotus Elise (1,950lbs curb weight) would be more obviously detrimental to acceleration than on a four door JK loaded with steel bumpers, winch and recovery gear etc. Right there you can tell there is no one size fits all rule of thumb that will work when considering unsprung weight.

A bigger impact in terms of acceleration is not the wheel weight, but the increased circumference of the tire which will impact the gearing – a bigger wheel will make for a taller gear ratio. There is no getting around this without re-gearing the final drive. So going to 35” tires from stock will impact acceleration from a stoplight and hill climbing on high elevation mountain passes. (It will also increase speed / change engine braking in 4wd low rock crawling).

So - just as I am thinking well, the suspension does not have to react that quickly in a slow moving rock crawling situation and I can go and buy those Hutchinson beadlocks at 48lbs a corner and add some BFG KM2s at 68lbs, there is also the wear and tear aspect (and increased potential for bending something) of having all that additional mass bouncing up and down at the end of the axles. The stock wheel/tire on a Rubicon is a 26lb Moab wheel plus BFG KO 46.4lbs = 72 lbs. That Hutchinson combo would be 116lbs – an increase of 44lbs a corner or 176lbs total unsprung weight. While I absolutely do not believe the formula of 10:1 cited above, (that would mean the equivalent added weight would be 1,760lbs!) there is no getting around adding 176lbs of unsprung weight has to impact wear and tear and affect street handling.

My conclusion? The 1lb : 10lbs formula is bogus and not a reason to get hung up on lighter wheels and tires. It may be nearer 1lb : 2lbs but whatever that ratio is (and despite the fact the large sprung mass of the JK will diminish the effects on acceleration between different wheel / tire combos) it is still smart to go with lighter components for overall wear and tear, braking, and grip in on road situations. If our Jeep was going to be driven mostly off road, then I might approach things differently, but I’ll be looking at lighter alloy wheels (probably AEV Pintlers at around 26lbs) and good all round tires that have some siping for icy winter roads and less weight – Duratracs at 60lbs are looking promising. Those Hutchinson beadlocks are some of the best looking wheels out there but…

I have driven Lotus cars and the founder, Colin Chapman, was famous for saying “just add lightness” to increase performance rather than adding bigger engines to get more hp with the knock on effect of bigger, heavier components in the drive train, brakes, tires etc. I think the physics behind this outlook are just as applicable in the off road world. I believe I may have got it wrong with some of my Jeeping mods – my steel bumpers and heavy recovery gear would be less necessary if I just “added lightness.” I perhaps should have looked longer at the aluminum offerings. Look at the Jeep Stitch as an extreme example – it performs spectacularly. Paying more attention to weight rather than beefing everything up might help ride height, improve suspension performance, acceleration and braking and get us stuck less often!

Some guys at the BMW forum got into debating the physics/math on unsprung weight here:
Reducing Rotating Mass: Ditching Dead Weight

OK – enough of my amateur ruminations – I am keen to hear where I may have got it all wrong… ☺
 
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#6 ·
Before upgrading the wheels and tires, what is the need, or is it a want? I won't be upgrading anything, unless its needed, about the only thing I see missing on the Rubicon is adequate skid plates.
 
#7 ·
You are probably right - our Rubicon was very capable out of the box but I added a modest 2.5 AEV lift with geometry correction brackets to maintain handling. Our tires at two years old are now at the point of needing replacement. Also we just came back from Moab Easter Jeep Safari - and that always makes you want to tinker :)

No I did not buy the wheels and tires yet. We have the Teraflex tailgate hinge which looked to me to be the most elegant solution to the spare wheel thing if you ever go to bigger wheels.

The truck just dropped off my rear bumper - Easter Safari purchase - so I am going to go attach that (more weight!) before I go buying wheels and tires :)
 
#9 ·
It's been a while since I did any dynamics work, but here's what I came up with:
Adding 1 lb of rotational mass requires the same energy to accelerate to a given speed as adding 1.013 lb of non-rotational mass*

*Assuming the mass of the wheel is evenly distributed

It turns out the diameter of the wheel is not actually a factor, as the terms cancel in the equations.
 
#10 ·
It's been a while since I did any dynamics work, but here's what I came up with:
Adding 1 lb of rotational mass requires the same energy to accelerate to a given speed as adding 1.013 lb of non-rotational mass*

*Assuming the mass of the wheel is evenly distributed

It turns out the diameter of the wheel is not actually a factor, as the terms cancel in the equations.
Very interesting! I have argued many times that bigger tires are NOT the massive inertial issue that so many claim; and it appears you just proved it.
 
#11 ·
I went through this whole thing recently too. I raced motorcycles and it's hard to get out of the frame of mind that you need to find the lightest possible combination. I've had fast cars as well and getting rid of 10lbs a corner does amazing things for your acceleration and braking...so initially i was set out to go lighter than stock, but after more reading realized for my Jeep it was a silly proposition and needless.

With that said I came to the conclusion that for me staying as close to the stock wheel/tire weight was desirable for obvious reasons, wear and tear, MPG, acceleration etc...

I didn't understand why a lot of jeepers were running around with E rated tires either...adds so much unnecessary weight to a vehicle that could never possible come close to the load rating. Yes I know, several people will say the are tougher, etc...and maybe in some special applications you could make an argument for it, but in the real world I just don't see it.

I researched for a solid month before I purchased my set up. At first the 15" route seemed a no brainer because the wheel and tire combo's are so light, however for me the backspacing required to clear stock components just sets the tire too far out from the Jeep causing even more wear on suspension. Tires for 16" wheels are almost all D and E rated so I settled on 17".

I ended up with procomp 7069's 17X9 and 285/70/17 Toyo AT2 in a passenger tire vs light truck. Even at the passenger tire rating the AT2's load rating are 2800lbs a tire...still overkill for the jeep, but in a 285/70/17 they weighed 48lbs...

The same tire is available in an E rated tire...that weighs 56lbs. Why add 8lbs of unnecessary weight for a rougher ride and more wear and tear on components.

In the end my stock setup on my scale at home was 68.8lbs. My new setup with larger sidewall and width was 69.8lbs. Very happy, took a lot of research, but for me it was well worth it.





 
#12 ·
Before I got back into Jeeps, I owned a '04 F150 FX4. For it I had a set of winter wheels and tires (stock wheels, stock tire size of 275/75/18) and a set of 20x10 Ford Racing wheels shod with 305/50/20 all season performance tires for summer use. Overall height on both sets were ~32".

The summer set with the larger wheels were a tad heavier and acceleration, braking, and fuel economy were noticeably worse than with the stockers. They actually seemed to act like flywheels on the road. However, since the summer tires were low-profile, the handling improved. I wouldn't say I would have autocrossed it or anything, but you could tear up an on-ramp. And they sure looked cool.

But for me, an off-road vehicle benefits from a tire with a taller sidewall. Less chance of destroying a wheel out in the bush.
 
#13 ·
Thanks Skippy77 - I'll take a look at that setup. I would think E rated tires might flex less around rocks with their stiffer sidewall when aired down off road (although I am still relatively new to this and may be wrong) so I was rejecting those for that reason as well.
 
#15 ·
Like I said I think E rated may have applications for jeeping, but for the majority of us it's extremely unnecessary. Good luck with your search. I found 3 or 4 good A/T tires in passenger rated vs LT. Check out treaddepot.com I ordered from their and they have weights listed for everything.
 
#18 ·
I will say this about stiff sidewalls. I have military tires designed for HMV's and there is no such thing as a sweet spot for inflation due to the fact that my Jeep weighs half the HMV. At 22 psi with my setup, I get perfect flat contact but corning on pavement is squirrely. At 35 psi they handle great but am going to wear out the center of the tread prematurely.
 
#30 ·
All of my ruminations are equally amateur, as my last physics class was a LONG time ago and I don’t feel like doing any complicated math right now to try and prove a point. I do believe that you are mostly correct with a few flaws in reasoning. As you point out, unsprung weight and rotational mass are different, although in vehicles they are frequently referring to the same thing—the wheels and tires. Unsprung weight, however, only affects the responsiveness of the suspension, rotational mass affects the performance of the vehicle (probably somewhere between a 7:1 and 10:1 ratio’s that I have always heard). Let’s look at two components to illustrate the difference:

Half of the weight of the lower control arm is unsprung in that half attaches to the spindle and the other half attaches to the vehicle. If we increased the weight of the lower control arm by something ridiculous, say 1000 lbs, we have increased the unsprung weight by 500. When you hit a bump in the rode, the force that the tire translates to the shock and spring will be muted by the fact that the tire must first move 500 of the 1000 lbs control arm before the force gets to the suspension and allows the suspension to do the job it was intended to do. Furthermore, the spring will continue to compress under the constant force of the upward traveling control arm before the springs own energy can stop the control arm and move it in the other direction in an attempt to keep the tire in contact with the uneven surface of the road. However, the acceleration force of the tire remains constant, as the control arm’s weight has no bearing on the engines ability to turn the wheel so the overall acceleration of the vehicle is only affected by the burden of accelerating and stopping an extra 1000 lbs load. 1 pound of unsprung weight = 1 pound of sprung weight (to everything but the suspension) because the wheels do not care where the extra weight is.

Now, rotational Mass is a force that must be overcome by the engine (or brakes) before the energy is delivered to the wheels. The contact patch between tire and pavement is the only place where any fore is exerted that transfers into acceleration of movement of the vehicle. However, just because the force of the engine is constant doesn’t mean that the linear force of the tire is constant. To demonstrate, let’s change something that is sprung weight, but still rotational—the flywheel. Let’s make the flywheel 1000lbs. Before the wheel’s see the force of the engine, the engine must first overcome the force of the 1000lbs flywheel and start rotating that. The remaining energy continues to the wheel’s, where it is transferred into linear energy that accelerates the vehicle forward. However, because the engine is first moving the 1000lbs flywheel, there will be less horsepower seen at the wheel due to the increased parasitic losses. Now, the reduced force that the tire is able to generate has to start overcoming the force of a vehicle that is also 1000lbs heavier, so a reduced force (lower Rwhp) has to attempt to move a heavier load.
You can see why the effect of rotational mass has a much greater than 1:1 ratio on the overall performance of the vehicle, but it not because the vehicle thinks it is 10 times heavier, it is because the added weight is both robbing power AND increasing the load. To oversimplify, we have the rule of thumb that the perceived affect of roating an extra 1 lbs is similar to hauling an extra 7-10 lbs. However, I believe that you are mistaken in your reasoning that the ratio changes based on the vehicle. The Lotus in your argument is still impacted by the same ratio (let’s call it 10:0 for simplicity sake) as the 5000 lbs jeep, it’s just that the change in perceived weight has a much larger impact on the Lotuses power to weight ratio.

Let’s do some math, and say that a 2000 lbs Lotus has 200 hp, while your 5000+ lbs has 285 HP. The lotus is faster because it only has to move 10 lbs per horsepower while the jeep is sluggishly pushing around 17.5 per hp. If we add wheels on each that add 40 lbs, and say that this is the equivalent to 400 lbs of perceived weight, then the lotus now feels like it is moving 12 lbs per horse (a 20% difference) while the jeep feels like it is moving 18.9 lbs per horse, an 8% change in power to weight ratio. So the ratio of adding the rotational mass was the same for each vehicle (1 lbs of rotational mass is like adding 10 lbs of non-rotational mass), but both vehicles respond differently to the extra 400lbs of perceived weight.

So, I’m not sure that we really disagree that much in the end, except for the comment that “Right there you can tell there is no one size fits all rule of thumb that will work when considering unsprung weight.” First, unsprung weight only affects the responsiveness of the suspension, more correctly we are talking about rotational mass. And the rule of thumb that is in question here still seems to affect both equally; it is the effect of the rules impact on overall perceived power-to-weight ratio. Since the Added rotational mass actually affect both the power (at the wheels) and the weight, it is much more costly than just weight. I believe that this ratio will remain fairly constant between all vehicles. However, your ultimate conclusion that the jeep will take on the 400 lbs of perceived weight and still roll down the road just fine is still true. So get them big ‘ol wheels ordered! Besides, if you don’t like the new power to weight ratio with the big wheels, I hear they make a supercharger now!!! :action-smiley:
 
#31 ·
So my experience over the past 7 years and 3 sets of 35" tires.

First tires were 35" Xtreme terrain on ProComp 7089. Approx tire weight 79lb. After 60,000klm I switched to 35" Duratracs 64lb same wheels.

Instant / consistent result was 2mpg increase in mileage with the Duratracs and rolling resistance difference could be felt.

Later I switched wheels and went to 35" Pitbulls at 86lb per tire. Mileage dropped on average 3mpg.

I also see a difference in mileage when I reduce weight by removing the hardtop. So whether you call it unsprung vs sprung weight or just power to weight ratio, I would bet that If I put the stock tires on and add a few extra hundred pounds of people or gear I would see about the same difference.

To the OP some tires/sizes can not be had in anything other then E rated. That's what you get when you want 3ply sidewall and rock proof tread.
162,000+ klm on stock drivetrain DD with moderate wheeling and have yet to break or bend anything.
So, I say each to his own. If light duty 285s work for you stay with it, it's your rig. Personally I am going up to 90lb 37s..
 
#32 ·
Eric T - thanks for that. I am going to have to re-read the details but I get what you are saying - and you probably got LedZep_06 eyes crossed with that post :)

JTPhoto - nothing beats real world experience. Too often people post opinions when they only have experience with one setup - thanks for your post using different tires and weights.
 
#33 ·
I actually already have some code written to calculate effective linear mass of a wheel and tire (the equivalent amount of non-rotational mass on the vehicle that would have the same effect on acceleration).

To calculate moment of inertia of the wheel, I assume the wheel is composed of a simple thin disc surrounded by a simple thin-walled cylinder, both parts the same thickness. It's a simplification, but much closer than a simple assumption of evenly distributed mass (a wheel is more biased to the outer radius).

For the tire, I assume a thin-walled cylinder for the tread and two thick-walled cylindrical tubes (inner radius is the wheel radius). I assume even distribution of mass through the material of the tread and the sidewalls. Again, not perfect, but good enough for an estimate.

(formulas for moment of inertia: List of moments of inertia - Wikipedia, the free encyclopedia)

Some examples of specific rotational:non-rotational equivalent ratios:

17x9 wheel, 1:1.21
15x8 wheel, 1:1.16

33x12.5x17 tire, 1.1.82
33x12.5x15 tire, 1:1.80

I'd like to know where this 1:10 ratio came from, because that seems WAY off!
 
#36 ·
It's amazing how much different 'math' there is to figure out the whole unsprung weight thing. A buddy of mine did the 'math' when I upgraded to a 62.5 lb BFG AT/KO in a 315/70/17. He had me at the equivalent of just shy of 2000 lbs because I went from a 32" to a light 35" on factory wheels.
 
#38 ·
Not necessarily - anecdotes from the same driver using the same setup and driving style with actual experience with different wheels and tires are useful - like JT-Photo post above. It's anecdotes from people who have only used one tire or people comparing tires not on the same platform or in the same environment - they amount to pretty much just opinion and aren't much use.

I agree it would be cool if a suspension designer / engineer got into this discussion and told us where we are all wrong though!
 
#40 ·
Um...an anecdote is an oppinion without imperical data to prove it. Essentially everything said on this thread including my own is anecdotal.
Yes, I agree. Even this 'rule of thumb' comes from anecdotal evidence to begin with. I have always heard this argument in the form of drag racing calculations where drag racers know what the effect of a pound is on their car. Anecdotally and you could make the argument for empirically, since it is repeatable), drag racers know that 100 lbs is worth about 1/10th of a second in the quarter mile (on a light weight drag car). But they can also prove that when those pounds are on the wheels or tires, ~10 lbs can reduce the ET by the same 1/10th of a second as 100 lbs on the frame. From this, the assumption began that 1 lbs of rotating weight is equal to 10 pounds of weight on the frame. (Not to be confused with unsprung weight although the term is often mis-used here).

So, does this ratio change when we go from a lightweight drag car to a 5000+ Jeep? I don’t believe so. The 100Lbs=1/10th of a second DOES change because of the power to weight ratio is completely different; that 100lbs is only 2% of the jeeps weight, but 4% of a 2500 lbs race car. But the effect that this added weight has (probably something closer to .05 seconds per 100lbs) is the same whether it is 100lbs on the frame or 10lbs in the wheel. I see no reason why this ratio would change, because you still have a similarly weakened force (due to increased parasitic losses) pushing a heavier object. Therefore, the results of the added rotational mass are still compounded compared to mass on the frame.

The real question is though, can you deal with it. Using the anecdotal ‘evidence’ of drag racing that started this rule let’s make some wild assumptions: assuming 10 lbs of added rotational mass is equal to 100lbs of sprung mass, and 100 lbs of sprung mass in a 2500 lbs drag car is worth 1/10 of a second over a ¼ mile. Because our jeeps are roughly twice as heavy as the drag car, the difference in power to weight ratio (which is really the measurement of how fast we will reach the ¼ mile) will be about half, so very roughly, 10 lbs of rotational weight is equal to 0.05 seconds in the quarter mile. If each of your tires weighs an additional 10 lbs, you will be completing the standing quarter mile in approximately 0.2 seconds slower, in the quarter mile, at full throttle. Unless you are asking the internet for advice on how to power shift a truck transmission at redline for ‘emergency situations’, chances are you are not even driving your jeep under these conditions to begin with.

I can tell you from experience, a 0.2 second difference shows up on an E.T. slip, but this hardly translates into a ‘seat of the pants’ difference. Your mileage may change, but gearing and the effect that your new, larger tires have on your final drive ratio will have much more impact to your ‘seat of the pants’ feel than an extra 40lbs of rotating mass.
 
#41 ·
I've been an engineer for 35+ years, albeit a EE. Nevertheless, there's one thing I've learned about math/theoretical estimates; and that is they are just estimates, particularly in multi-variable scenarios such as this. Sometimes estimates are good for establishing baseline assumptions, but empirical evidence is always a powerful voice.

Having said that, I would pay close attention to JTPhoto JK's post. I think he presents an excellent use case, which many people fall into. If, on the other hand, you are running your rig to it's limits, then it stands to reason that stuff will bend and break. The question becomes how much money are you willing to spend in order to mitigate that risk??

BTW & FWIW, I have a 2014 JKURX with 35s on 20" fuel wheels. My wheel/tire combo weighs 102.8 lbs. Also, I have an automatic with 3.73 ratio. So far things are working out well. But admittedly, I haven't done any hard core wheelin yet. So we'll have to wait and see what happens after I get a winch on her and get serious.

Great thread folks with lots of smart people! It gets the neurons working. :)

-tc-
 
#42 ·
I found a website that explains the effect of rotating mass much better than I could have done (warning: lots of math and physics formulas!): The Effects of Rotational Inertia on Automotive Acceleration

His simplified models are nearly identical to the simplified models I use for calculating moment of inertia for the tire and wheel. His derivation of formulas also agrees with the formulas I came up with for getting the "equivalent static weight", and helps confirm the ratios I posted as being good estimates.

He also gets into flywheels, where he mentions that it can be as much as a 1:10 ratio! (but in low gears only). Maybe this is where the incorrect 1:10 rule of thumb came from for rotating mass in general?
 
#44 ·
Although the same laws of physics apply to both a drag racer and JK the relevant performance metrics are quite different.

Drag racing is about max acceleration while maintaining traction and Jeeps in general are about larger tires for a variety of reasons (obstacle/tire ratio, ground clearance, traction, appearance), ride quality and fuel economy. The 1:10 ratio for unsprung mass has been around for a long time and it is based on empirical data which is validated by some engineering models.

The impact of this guideline is very different due to the range in tire size involved with Jeeps which is between a stock 29" all the way to a 42" in most cases. The moment of inertia varies as the square of the tire radius so the impact is very significant when it comes to angular acceleration which translates to power requirements. The weight of these tires also varies considerably and the amount of the weight on the tread where it makes it most impact also varies greatly with highly aggressive and tread patterns.

I have run up to 37" tires and two member of my family have run 40" tires on JKs. My anecdotal observation tracks with JTPhotos 1-2 MPG drop. Off road the increase in fuel consumption is even greater.

On the ride and handling, I don't understand how anyone can argue that an increase in unsprung weight will not be detrimental. It does however have the benefit of decreasing the potential for rollover.

Are we trying to convince ourselves that there is no down side to bigger wheels and tires?

If that is the case, we should address lift kits next. :D
 
#50 ·
The 1:10 ratio for unsprung mass has been around for a long time and it is based on empirical data which is validated by some engineering models.
Can you provide any references to back up that statement (not the "been around for a long time" part, but the "validated by engineering models" part).

I've done calculations, and also provided a link to an explanation, formulas, etc. that agree with my calculations. It's nowhere near 1:10.

I'd also like to know what was actually being measured to get the empirical data that brought about the 1:10 ratio. Any info on that?
 
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