Maximum Tractive Force [Archive]

Spetsnazos

09-08-2011, 05:16 PM

Can someone confirm that I am doing this correctly? Fairly certain that I am, just want to make sure.

The car is a FSAE RWD with a T2 Diff. Looking at page 39 of "Fundamentals of Vehicle Dynamics" by Thomas D. Gillespie, it states that for a solid rear axle with a locking differential the maximum tractive force is

Fx=u*(W*b/L)/(1-(h/L)*u)

and thus the maximum longitudinal acceleration is

axMAX=Fx/(Vehicle Weight/g)

Correct??

Spetsnazos

09-08-2011, 05:16 PM

Schmidt

09-09-2011, 02:02 AM

Hey,
I don't know about the first equation because I can't find what all symbols mean.
The second one is definitely inaccurate. Weight/g is just fancy-shmancy for "mass", but not exactly the same for a car. According to a = Fx/(W/g), if you have aerodynamic lift, you would suddenly have less mass to accelerate.

But more importantly there is no drag/rolling resistance (front wheels..) in your model.
Maybe you can list the symbols of that first equation.

Best,
Erik

murpia

09-09-2011, 05:18 AM

Gillespie uses some very basic assumptions in his analyses. This is because his book is "Fundamentals" not "Advanced".

I think one of the assumptions in the tractive force example will be tyre mu = 1. For the maximum acceleration, aero drag may have been neglected as Erik points out.

Aero lift is probably also neglected.

The assumptions are clearly stated, so you should be able to work out for yourself whether they are valid for your case.

Regards, Ian

Spetsnazos

09-09-2011, 11:13 AM

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by murpia:
Gillespie uses some very basic assumptions in his analyses. This is because his book is "Fundamentals" not "Advanced".

I think one of the assumptions in the tractive force example will be tyre mu = 1. For the maximum acceleration, aero drag may have been neglected as Erik points out.

Aero lift is probably also neglected.

The assumptions are clearly stated, so you should be able to work out for yourself whether they are valid for your case.

Regards, Ian </div></BLOCKQUOTE>

Actually the assumptions are not clearly stated in the book. The only thing I can find is u=peak coefficient of friction and instead of using that, I am using instantaneous coefficient of friction based on my tire model.

b=longitudinal distance from the front axle to center of gravity
u=peak coefficient of friction
W=weight of the vehicle
L=wheelbase
Fx=force in the x-direction(tractive force)

There is no assumption about mu=1, that doesn't even make sense because why put it into the tractive force equation if its equal to 1?

Mike Cook

09-09-2011, 11:35 AM

Fx = mu * dynamic rear weight (for a rwd car)

dynamic rear weight = W * a / (a+b-h*mu)

a = distance from front axle to cg
b = distance from rear axle to cg
h = cg height
mu = coefficient of friction
W = total weight

Adding Downforce can increase your dynamic rear weight and increase your Fx. However, it doesn't change your mass, so your acceleration will still be force/mass.

Spetsnazos

09-09-2011, 01:26 PM

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by Mike Cook:
Fx = mu * dynamic rear weight (for a rwd car)

dynamic rear weight = W * a / (a+b-h*mu)

a = distance from front axle to cg
b = distance from rear axle to cg
h = cg height
mu = coefficient of friction
W = total weight

Adding Downforce can increase your dynamic rear weight and increase your Fx. However, it doesn't change your mass, so your acceleration will still be force/mass. </div></BLOCKQUOTE>

Thanks man, what I was looking for.

Spetsnazos

09-09-2011, 01:43 PM

Mike Cook

09-09-2011, 06:05 PM

Well, technically, it would be the coefficient of friction for the tire with the dynamic weight on it. But you would probably need a good deal of tire data to figure that out (and it would still be wrong).

With our tires, I usually use about 1.4 as a good starting point.

Spetsnazos

09-10-2011, 06:44 PM

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by Mike Cook:
Well, technically, it would be the coefficient of friction for the tire with the dynamic weight on it. But you would probably need a good deal of tire data to figure that out (and it would still be wrong).

With our tires, I usually use about 1.4 as a good starting point. </div></BLOCKQUOTE>

Why would it still be wrong? I am using tire data from the tire consortium

Edward M. Kasprzak

09-11-2011, 04:39 AM

Strictly speaking, every calculation we do as engineers is wrong. We always make assumptions and apply equations which are a simplification of reality. The key is to make assumptions and use equations which give results that are "close enough" to reality. How close is "close enough" is up to the engineer to decide.

Speaking specifically about the TTC tire data (or any laboratory tire data for that matter), we know tire performance is a function of both the tire and the road surface. Since the test machine and the road have different surfaces, the results will be somewhat different. Also, lab conditions do not exactly match on-vehicle conditions. Lab data is still useful (if "wrong"), and its accuracy can be improved through comparison with real-world performance (e.g., a change of friction coefficient).

Mike Cook

09-11-2011, 07:49 AM

Dr. Kasprzak,

I appreciate all you have done for the FSAE community. But to start out a post with 'every calculation we do as engineers is wrong' is a little disingenuous.

If you look at the tire data you can see Coefficient of Friction values up to about 3. This is almost off by a factor of 2 from what we generally see in the field. Most of the calculations I make as an engineer, may not be 100% accurate, but are pretty darn close. I wouldn't consider this pretty darn close. The tire data may be useful, but without a lot of research on relating tire test results to on track results the ttc data is difficult to use and have confidence. It is also difficult to compare one tire to another, since different tire compounds may behave differently on the sand paper belt.

Tire data is fun. It gives us more answers to the questions surrounding racecar dynamics. Engineers love answers. But, they should be a little more concerned with if the answers are right.

Instead of spending more and more money on laboratory testing, why don't we figure a way to test the tires on real asphalt.

Mike

Jersey Tom

09-11-2011, 04:42 PM

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Instead of spending more and more money on laboratory testing, why don't we figure a way to test the tires on real asphalt.

Mike </div></BLOCKQUOTE>

As if lab tire data wasn't a difficult can of worms as it is... I'm not sure whether taking it to that level is the best call.

That said, there is nothing preventing teams from doing their own track correlation of the data.

Admittedly I have been out of the loop for a bit, but I got the impression that few if any teams were really using the lab data to the most of its potential... or even doing back-to-back construction/compound/manufacturer evaluations.

In my not so humble opinion, I think the best thing is more education on application (albeit hard to come by!) and focusing on basics rather than adding additional complexity.

flavorPacket

09-11-2011, 09:55 PM

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by Jersey Tom:

In my not so humble opinion, I think the best thing is more education on application (albeit hard to come by!) and focusing on basics rather than adding additional complexity. </div></BLOCKQUOTE>

+1. There is a LOT you can do to make a car faster without ANY tire data.

Edward M. Kasprzak

09-13-2011, 05:26 AM

Mike: The respect is mutual. I'm familiar with your contributions to these forums--they are appreciated.

I will note, however, that the TTC has not tried to mislead anyone. The discrepancy in grip between the TTC data and on-track performance is documented, with most feedback placing the grip at Calspan about 35-40% higher than on-track. Whether its the TTC or our (MRA) professional customers, everyone faces the challenge of applying lab data to the road. The size of the discrepancies vary depending on the tire and the real-world road surface. Sometimes the correlation can be essentially 1:1 (non-FSAE tires).

I certainly agree that the TTC data is not easy to use, and that comparing tires to one another is difficult. Nothing is easy when it comes to tires. The TTC fills a hole by providing some engineering data on tires. This can be supplemented by student tests (driving their vehicle) and correlation work.

On-road testing has its own set of challenges. The resulting data is just as difficult to use. The TTC could look into running some on-road tests. We're always open to suggestions.

Spetsnazos

09-13-2011, 10:45 AM

If we know for a fact that it is 30-40% off, generally speaking, then can we give it a correction factor based on the surface the tire will be used on?

As a future engineer, I rather have something that is 40% off that I can analyze with some kind of correction factor than nothing other than "how it feels".

Good discussion though Mike, if we could keep it going I think more people could learn about how to apply the data correctly http://fsae.com/groupee_common/emoticons/icon_smile.gif

Hector

09-13-2011, 12:40 PM

RobbyObby

09-13-2011, 07:26 PM

I personally believe the TTC data is merely meant to be a starting point. Due to the nature of the tests (any laboratory tests for that matter), which try to minimize the total variables throughout the process, and include many assumptions, there will also be some difference between real world situations. For students/teams just beginning to grasp the complexities of vehicle dynamics, it is a great tool. However, once you move past that point and start to look for more realistic real world correlations, it forces you to start running your own tests, so you can start comparing results and determine certain correlation factors. This is where the top engineers excel and differentiate themselves from the rest.

Just my $0.02.

Adambomb

09-13-2011, 07:39 PM

IMHO track testing and lab data are two entirely different things. Lab data is nice because the conditions are much better controlled, although looking at TTC data you can begin to appreciate different thermal effects, etc. by looking at the variation and funny effects that exist even under such controlled conditions. Based on what little testing experience I have I can appreciate how hard it is to get a test that is simple enough to not be blown away by un-intentional factors yet still provide meaningful results.

However, TTC is lab data, and absolutely can not be taken as gospel tire behavior. Anyone with any seat time knows the tremendous amount of variation between, say, a 30 year old asphalt parking lot in March and a completely sanitary concrete airstrip in July.

TTC data has its place, but I'd say that there are a very very small number of teams that know enough about their car's behavior (ie actual, not just what you designed it to do) to even make full use of TTC data. And clearly for 99% of the teams out there (including us), there are much larger gains to be had with track testing than with TTC data. That being said, TTC is great when trying to decide which tires you want to run, as I know that there is no way our team would be able to just plain buy that many different types of tires to do that testing, let alone put resources towards the actual testing (although that video Hector posted did look pretty awesome). It is also good for the "intellectual masturbation" half of the competition, in showing how your analysis of TTC data influenced your suspension design and what the results were.

Just my $0.02.

RobbyObby

09-13-2011, 07:43 PM

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by Adambomb:
IMHO track testing and lab data are two entirely different things. Lab data is nice because the conditions are much better controlled, although looking at TTC data you can begin to appreciate different thermal effects, etc. by looking at the variation and funny effects that exist even under such controlled conditions. Based on what little testing experience I have I can appreciate how hard it is to get a test that is simple enough to not be blown away by un-intentional factors yet still provide meaningful results.

However, TTC is lab data, and absolutely can not be taken as gospel tire behavior. Anyone with any seat time knows the tremendous amount of variation between, say, a 30 year old asphalt parking lot in March and a completely sanitary concrete airstrip in July.

TTC data has its place, but I'd say that there are a very very small number of teams that know enough about their car's behavior (ie actual, not just what you designed it to do) to even make full use of TTC data. And clearly for 99% of the teams out there (including us), there are much larger gains to be had with track testing than with TTC data. That being said, TTC is great when trying to decide which tires you want to run, as I know that there is no way our team would be able to just plain buy that many different types of tires to do that testing, let alone put resources towards the actual testing (although that video Hector posted did look pretty awesome). It is also good for the "intellectual masturbation" half of the competition, in showing how your analysis of TTC data influenced your suspension design and what the results were.

Just my $0.02. </div></BLOCKQUOTE>

+1
Completely agree.

Mike Cook

09-14-2011, 05:40 AM

Spet,

You have to be careful about just scaling the tire data by some constant mu. Consider this:

We all know that as load increases on tire the mu generally goes down. But is this sensitivity due to the normal load OR due to the cornering force the tire is producing? In other words, since the tire is producing much more cornering force on the belt than asphalt, are these huge cornering forces actually what is producing the 'load sensitivity'?

Similarly, perhaps the slip angle that maximum cornering force is produced is at least partly a function of the cornering force you are producing. So if you reduce the amount of cornering force you are producing (be scaling mu), your true slip angle may migrate.

I don't have answers for these questions, but the thoughts have been rattling around in my head for awhile.

Dr. Kasprzak is 100% right in that tire data is only a piece of the puzzle. I just don't want some of the newer guys thinking TTC is a holy grail and spend all of their time on it. As others have pointed out, track testing is probably a much quicker way to get results. My team has consistently scored well in the last several years and have borderline been one of the fastest teams every year. We haven't honestly used the tire data to improve our performance at all. Just food for thought.

Mike

Edward M. Kasprzak

09-14-2011, 06:21 AM

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">I just don't want some of the newer guys thinking TTC is a holy grail and spend all of their time on it. </div></BLOCKQUOTE>

Amen. Fundamentals first, and you can't beat seat time with a test plan (not just for tires, but for everything). Complete the "theory, design, build, test, evaluate against theory" loop.

One nice aspect of the TTC data is that students can use it to whatever level they see fit. Some teams just want tire spring rates, or they look at the general shape of the various plots. Others study surface temperature response, use it for suspension calculations, do skidpad & acceleration simulations, do suspension parameter sensitivity analyses, do force-moment diagram analyses, compare different tires, etc. The list goes on, and all *can* be perfectly good uses of the data if it fits into a properly closed design & development process.

The TTC data doesn't cover every scenario, but what's there enables many different kinds of exploration and analysis. In short, that's the role of the TTC--to produce affordable FSAE tire data for engineering analysis. Like any tool or resource, it needs to be used appropriately. Reminders to do so are always appreciated.

ben

09-14-2011, 06:30 AM

I'll preface this post with a declaration of respect for the contributions of Dr Kasprzak and Mr Cook.

When it comes to constrained testing of tyres you can get into trouble pretty fast because the load is adjusted by the feedback loop on the machine to whatever you ask it to do. On a real car the load is in no small part due to the weight transfer caused by the grip of the tyre itself. What this means in practice is that a nice stiff tyre will generally look better on a flat track than it will in practice. It might grip when it's loaded, but it might not have enough grip to load it in the first place - gets lots of people confused often when developing tyres :-)

That's a long-winded way of saying that I don't think investing heavily on track-based constrained F&M tyre data would automatically give you a massive step forward.

Jan Zuijdijk makes a similar point in his damper book regarding constrained testing of dampers vs. how they actually behave on the car.

Ben

Mike Cook

09-15-2011, 10:02 AM

Good point Ben. I will look up Mr. Zuijdijk's book.

While actually field testing tires would be very difficult, I think strain gauged suspension links can probably offer a lot of insight to what the tire is doing on the car. We recently strain gauged our pushrods and I thought that was one of the best bang for the buck measurements we made in years. I noticed instrumented links on GFR's car this year. I wonder if Dr. Pasch will chime in on whether he thought that was good investment of time and if they learned a lot from it.

bob.paasch

09-15-2011, 11:57 AM

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by Mike Cook:
I noticed instrumented links on GFR's car this year. I wonder if Dr. Pasch will chime in on whether he thought that was good investment of time and if they learned a lot from it. </div></BLOCKQUOTE>

We think so Mike. We should know for sure by the end of fall, Chris Patton will be using the data to validate his tire, vehicle dynamics and lap sim models. We will be publishing at least some of that in a couple technical papers.

bob.paasch

09-15-2011, 12:01 PM

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by Mike Cook:
Dr. Kasprzak is 100% right in that tire data is only a piece of the puzzle. I just don't want some of the newer guys thinking TTC is a holy grail and spend all of their time on it. As others have pointed out, track testing is probably a much quicker way to get results. My team has consistently scored well in the last several years and have borderline been one of the fastest teams every year. We haven't honestly used the tire data to improve our performance at all. Just food for thought.

Mike </div></BLOCKQUOTE>

I agree with all of this. Of course there is no TTC data on the Hoosier LC0. Yet http://fsae.com/groupee_common/emoticons/icon_smile.gif

Edward M. Kasprzak

09-15-2011, 04:56 PM

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Yet </div></BLOCKQUOTE>

Look for the LC0 in TTC Round 5, early 2012.

ben

09-16-2011, 02:58 AM

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by Mike Cook:
Good point Ben. I will look up Mr. Zuijdijk's book.

While actually field testing tires would be very difficult, I think strain gauged suspension links can probably offer a lot of insight to what the tire is doing on the car. We recently strain gauged our pushrods and I thought that was one of the best bang for the buck measurements we made in years. I noticed instrumented links on GFR's car this year. I wonder if Dr. Pasch will chime in on whether he thought that was good investment of time and if they learned a lot from it. </div></BLOCKQUOTE>

I'd totally agree on that Mike. One of the hardest things to do at our level is impact the car to that extent by running a custom set of suspension links with strain gauges installed or Kistler wheels. It's rarely practical in a racing environment.

If I was back at Uni I'd be trying to do it - a great project IMHO.

Ben

CameronBeaton

10-10-2011, 04:06 AM

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by Schmidt:
Say you have aerodynamic lift, you would suddenly have less mass to accelerate </div></BLOCKQUOTE>

Say what?

theTTshark

10-10-2011, 12:49 PM

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by CameronBeaton:
<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by Schmidt:
Say you have aerodynamic lift, you would suddenly have less mass to accelerate </div></BLOCKQUOTE>

Say what? </div></BLOCKQUOTE>

You'd still have to accelerate the mass, you just wouldn't have the same normal loading on the tire.

Schmidt

10-10-2011, 05:45 PM

Uhmm... if you take partial quotes it is very easy to manipulate someones statement. I was merely pointing out that weight/g is not the same as mass. And using the example of aerodynamic lift to show how......

CameronBeaton

10-11-2011, 12:18 AM

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by Schmidt:
Uhmm... if you take partial quotes it is very easy to manipulate someones statement. I was merely pointing out that weight/g is not the same as mass. And using the example of aerodynamic lift to show how...... </div></BLOCKQUOTE>

What you said it still wrong, F=ma regardless of lift. theTTshark has it right