1M Diff and Transmission Specs

[tarheel91]

Originally Posted by Kurt_OH

The definition of Horsepower.

Wrong. Horsepower uses engine torque and does not consider gearing between it and the wheels.

Horsepower = Engine torque * RPM/5252.

[Kurt_OH]

Originally Posted by Pete_vB

You may be referring to me? Start a now thread and we can discuss...

You posted a mountain of charts and graphs, and if I'm reading them and understanding your statements correctly, it appears that you allege that even WITHIN a specific gear, that the amount of torque applied to the wheels can be lower with a higher numerical gear ratio at certain RPM. Is that one of your points?

Also, I believe you stated that the amount of power being applied to the wheels was (more or less) at the limit of traction. If that's so, then are you saying that NO car with similar tire size, vehicle weight/distribution can possibly out-accelerate the 1M, in at least 1st gear?

Thanks in advance for your reply.

Kurt

[swamp2]

Originally Posted by tarheel91

No. Power to weight gives you only an instant value, that is, power to weight at max power. You can derive power to weight throughout the entire RPM band using the horsepower curve. What's most important is definitely the effective torque under the curve, mostly in the upper part of the rev range (i.e. from whatever RPM you shift into 2nd at on).

Effective torque at the wheels is actually more useful than horsepower, as it considers the actual gearing and tire size. Horsepower is great for a rough idea of how a car with a given weight will accelerate, but it's not as precise as torque at the wheels.

Uhhh, yes. I used to think much the same way that peak torque to the wheels per weight was the most important factor. Although it is a pretty reasonable one, hp (per weight) is still better.

All values that are single numbers are indeed just that - single numbers. If you talk about integrating a curve you actually will get the exact same type of information from integrating torque or power after all they are inextricably related by T = P/ω (in SI units...). You are sort of comparing apples to oranges in this regards. You can't say one number is better but then demand you have the full curve!

Either way power is much more useful than torque at the wheels. There a variety of reasons. hp is basically a shortcut calculation of torque at the wheel. Why? Because high reving engines with more gear torque multiplication typically have less torque but more power. What you loose in torque you make up for with high rpm and high hp. Taller relative gears are optimal for such high rpm engines and thus the pair naturally acompany each other. All bets are totally off if a manufacturer completely screws up on the choice of optimal gears...

The other reason why torque at the wheels (specifically the one figure of peak torque) is less accurate is because when driven at the limits of max acceleration an engine typically spends almost no time at the rpms where peak torque occurs. All of the relevant time is spent when the engine is at or near peak power (similarly at or near redline).

hp/weight has another small, but very practical advantage. hp is more commonly reported (although certainly I am not saying peak torque figures are hard to get) and the torque to the wheels requires THREE additional pieces of data, 1st gear ratio, FD ratio and wheel size. That alone, makes it quite a bit more burdensome to calculate compared to hp/weight. Simple, effective, accurate. One number based on two of the most common specifications available.

Last but not least hp is a much better indicator of top speed. Sure aerodynamics is cirtical here especially up above the 150 mph mark but given roughly constant Cd and frontal areas top speed is goverened almost exclusively by peak hp. Peak wheel torque is not useful here (nor peak wheel Force for that matter).

If you want a more detailed "proof" of what I have explained above see this post and the long discussion after it.

Originally Posted by tarheel91

P.S. Early on you were talking about centrifugal forces causing tire diameter to expand, but that has no where near the effect that deformation from the weight of the car (i.e. contact patch) and the longitudinal slip ratio (The tire bunches up right before the contact patch and stretches after it when being acted on by a longitudinal force). The tire size is actually always smaller than it's static diameter (although it gets closer the higher the speed). Calculating this stuff, though, requires much more info than you have, and ultimately it's not worth it when you're using such a basic simulator.

You're better off making sure you've got the basic stuff right; worry about the complicated stuff much later (same goes for parasitic loss; it's much more complicated than you're assuming it to be, and you'll probably be way off).

I also disagree here - on both points.

When a tire is properly inflated to a manufacturers spec the revs/mile (which is the same thing as an effective radius) precisely describes the tire. Sure it does not give you an exact time dependent tire shape but that is entirely irrelevant from the perspective of vehicle acceleration simulation. Such effects you mentioned of a "bunching" tire are relevant only during burn outs and with tires than deform dramatically (drag tires) under torque and road reaction forces. The effect of a tire growing with the cars speed is a pretty well recognized effect (again seen in a very dramatic case with top fuel dragsters). Either way it makes intuitive sense that a tire is more or less a spring and the a centrifugal force will stretch the spring. Sure you can argue that the spring is non-linear as I am sure it is but it is certainly not highly non-linear and this the simply spring analogy is just fine. Again the errors from this expansion effect are on the same order as the errors from using a tire formula vs revs per mile to calculate a cars speed at a given axle rpm and both can indeed be completely ignored to get a basic acceleration simulation correct. The tire expansion is turned of by default in CarTest and I have chosen to leave it enabled.

As for parasitic losses: These can indeed be complicated. However, you can easily account for 1st order effects accurately enough with simple linearly dependent loss percentages vs rpm. What is "accurate" enough. In the simplest terms I'd say if 1. Your simulator produces results within the range of reported values AND 2. You can simulate the absolute difference in performance from a variety of changes to inputs that correspond to realistic physical changes you might make when modifying a car, then your simulator is "accurate enough". Obviously a "hobbyist" (or recovering physicist) interested in simulating production cars will have a very different definition of accuracy than say a professional race team. In my experience the loss formulations in CarTest are indeed thorough and accurate enough. CarTest computes engine, transmission, wheel/axle speeds as an explicit function of time, along with vehicle speed and then uses speed dependent losses for the following components: transmission, differential, axles (drive shafts, U-joints and wheel bearings). Of course determining how to modify the default loss values in CarTest so that they are "good enough" is another matter which I already provided some warning about.

[Pete_vB]

Originally Posted by Kurt_OH

You posted a mountain of charts and graphs, and if I'm reading them and understanding your statements correctly, it appears that you allege that even WITHIN a specific gear, that the amount of torque applied to the wheels can be lower with a higher numerical gear ratio at certain RPM. Is that one of your points?

What statement makes you think that? No, that's not one of my points. The formula I posted earlier:

Engine Torque (ft lbs) x Gear Ratio x Final Drive Ratio / Tire Radius (ft) * Drivetrain Efficiency

For the 1M:
370 (ft lbs) x 4.11 (1st gear ratio) x 3.154 (Final Drive) / 1.06 ft x 85% = 3846 lbs

So at any given engine RPM (and hence TQ) a higher ratio will put more torque to the wheels. This will make the car faster within that gear until the torque exceeds traction (wheelspin).

Originally Posted by Kurt_OH

Also, I believe you stated that the amount of power being applied to the wheels was (more or less) at the limit of traction. If that's so, then are you saying that NO car with similar tire size, vehicle weight/distribution can possibly out-accelerate the 1M, in at least 1st gear?

No, not exactly what I'm saying. If we calculate that 1 G of acceleration is the peak for a given setup, then gearing for more than this is pointless, and will likely slow you down in practice due to the lower sliding friction of a wheelspinning tire.

So if you can't pull more Gs all you can do is hold those peak Gs for longer. The 1M hits that peak G point for an instant, but a different torque curve, etc might hold those Gs everywhere in 1st gear. If it made more torque it could also be geared taller to hold 1st for longer without exceeding the traction limit- either of those would make it accelerate faster.

[swamp2]

Originally Posted by Kurt_OH

BUT, we're kinda headed off topic anyway. Originally the discussion was about the gearing specs of the 1M. Then I commented regarding my preference for a higher numerical final drive ratio.

I've participated as much as anyone else in the tangent, but I'd prefer to get back to the prior discussion if possible. Another poster stated that the higher numerical gear would result in slower acceleration. I continue to disagree, especially when we're talking about WITHIN a gear, or across a contrived set of time/speed/distance measurements that favor the lower numerical gearing.

I guess I need to be the first to apologize for getting OT here in the thread, However, the two topics are in fact VERY closely related. If you understand both you'll be far better informed.

You should have a look here at this extensive debate and discussion on FD ratios. Both myself and another astute forum member came to the exact same conclusion. The shortened version of the conclusion from that long thread is that FD ratio tweaks will affect in gear results providing what feels like more peak thrust (well it is indeed more peak thrust, you will be able to feel it and measure it). However, there is no such thing as a free lunch - the improved peak acceleration comes at the price of less time in each gear. The effects mostly cancel each other! This is very closely related to the torque vs. hp discussion. Changing the FD absolutely bumps torque at the wheels through simple torque multiplication. However, it absolutely does not increase your engines power (obviously). Being in gear n-1 has SO much more acceleration than being in gear n. From 1st to 2nd might be about a factor of 2 in average acceleration and that is huge. Too miss out on that because you got to redline earlier and had to shift if a big disadvantage. To maximize acceleration you want to maximize your time spent in lower gears (obviosuly assuming you can stay below redline).

A caveat here is the case where a manufacturer chose a poor FD ratio or one not all all optimized for acceleration. In some cases you can get some small benefits for both in gear thrust and gains in metrics that require shifts, but again intuitively you are not getting more power from the engine!

Hope this helps.

[Pete_vB]

Originally Posted by swamp2

Sure it does not give you an exact time dependent tire shape but that is entirely irrelevant from the perspective of vehicle acceleration simulation. Such effects you mentioned of a "bunching" tire are relevant only during burn outs and with tires than deform dramatically (drag tires) under torque and road reaction forces.

This is not true.

A tire generates force only when operating at a slip angle, either in a straight line or in a corner. The tire's design, construction and use all define what that slip angle is, but it often generates peak force in the range of 5% to 8% slip. This means that near the limit of traction the wheel is actually spinning 5-8% faster than the road, even though it does not appear to be spinning. As the torque goes down the amount of slip also goes down, but it remains a significant effect. The Bosch lapsim simulator I mentioned has inputs for this- you can define longitudinal and lateral slip angle separately. Unfortunately for us, the tire data needed to do this accurately is a highly guarded secret not available to mere mortals.

The point being that for a radial street tire with a belt package specifically designed to resist this deflection at speed (and hence internal friction and tire heating, which is what limits speed rating) this slip angle is a bigger factor than centrifugal tire growth- it cancels it out and then some.

[swamp2]

Originally Posted by technik330

I've read several of your posts, in various threads, and it appears you're extremely skeptical of the 1M, even insecure about its very existence.

Well my dad can beat up your dad. Get real. I'm as excited about a "return to roots" M car as much as any red blooded M ethusiast. I owned 3 different M3 models and have very loosely considerd other non M3 Ms as well. There is absolutely no insecurity going on here. I'm always skeptical but insecure, nope. In case you missed it I think my most thorough expression of opinion on the 1M is here in "Are you disappointed..." thread. My clear answer was "no".

[swamp2]

Where to start...

Originally Posted by Kurt_OH

So to say "torque matters for X, whereas HP matters more for Y" is absolute nonsense.

I firmly disagree. For a load hauling or pulling vehicle in fact torque is a more useful engine specification. It does not get biased by high rpm which is not important for pulling. You need massive torque, right at very low rpm. Again you should always make the qualification that to the wheels is more important or a better/more informative spec, but generally when gearing is done properly this extra piece of info is not so critical. For a performance car when WOT acceleration is important, and things like 0-100, 60-130 and 1/4 mi times, hp is a more informative stat (again power to the wheels if you have it) but peak hp/weight is the best simple predictor of performance.

But then you go on to say

Originally Posted by Kurt_OH

I won't say your statement is wrong, but it's misleading/misled. HP is what matters at ALL RPM, at ALL speeds, and at ALL gearings. IN fact, HP is a MORE accurate measure - you don't even have to worry about, estimate or concern yourself with gearing - it is a constant from the crank right through to the tire.

The ONLY curve you need bother with is HP; torque naturally relates, but isn't "it".

Which is EXACTLY the right way to see things. I couldn't agree more.

Originally Posted by tarheel91

Nope. Horsepower is a made up value. It holds no real meaning. Horsepower is simply a trick way to take into consideration gearing (without actually knowing the gearing) because the higher the rpm "y" amount of torque is achieved at, the higher the gearing that can be used to achieve that torque at speed z. It's a relative measure of power, that's it. If you want to oversimplify things and argue that work/time is all that matters, that ignores that you're not just trying make power. You're trying to accelerate as fast as possible within a certain ranges of speeds.

hp is simply a form of power and to call power a "made up" quantity is absurd. Don't tell your big insight to the automotive companies, the power companies or generator companies. You can go back to physics 101 and find a variety of definitions of power that are real and quite useful. Power is simply the rate at which work is peformed or energy converted. P = dW/dt or P = F x V. Power is no more nor less made up than torque.

hp absolutely is not a "relative measure of power" it can be linearly converted to SI power in watts/kW and that is as meaningful a concept and specification as any.

I do agree that power will tell you about a cars performance without having to know gearing. That is exactly the bloody point, you've finally said it. If you can have one and only one number. And it is a VALUE, not a full CURVE of data, hp (again obviously) hp/weight reigns supreme.

Have you even seen a good drag racing scaling formula that uses torque to the wheels to predict 1/4 mi times and traps? No, it does not exists because folks have found the following empirical relationship to work surprisingly well:

trap in MPH = 231.3027 (hp/weight)^(1/3) and
ET in seconds = 6.1178 (weight/hp)^(1/3)

(power and weight in common US units)

Although a constant power approximation (very crude) is used you might appreciate the fidelity of such models with very high R^2 values. See here.

It seems abundantly clear you did not bother to read my lengthy "proof" of why power to weight is more important than torque/weight as referenced in my post #74?

Let me also correct one more statement you've made,

Originally Posted by tarheel91

You're trying to accelerate as fast as possible across a certain ranges of speeds.

Well at least that is what most straight line contests are all about...

Originally Posted by tarheel91

F=ma. In a rotational sense, T=m*alpha (angular acceleration). For a given mass, it is instantaneous torque that determines how fast that object accelerates at any given second. Torque at the wheels = engine torque * gearing/tire size. Torque at the wheels, which is directly related to acceleration, is directly related to gearing. That means acceleration is directly related to gearing. Ultimately it's the area under the torque at the wheels curve vs. speed which determines how fast something accelerates.

Wrong formula, T=I*α where I is the moment of inertia. Anyway...

"For a given mass, it is instantaneous torque that determines how fast that object accelerates at any given second."

I agree, exactly AT ANY GIVEN second. Torque is fine for determining what happens at an instant (although if you know the velocity then hp is just as good since P=Fxv (SI units!)). So of course if you know a torque curve that indeed gives you the needed vs. time information that a single point is missing. hp, the peak figure informs you more about a cars ability to maintain that torque over a longer period of time.

You really seem to be missing the point. Sure for full knowledge we need a simulation, we need a full torque or hp curve, either is actually fine. But to SIMPLIFY and choose a single value (ratio specifically) that is going to be the most telling about a cars ability under WOT, ACROSS MULTIPLE GEARS then hp/weight is still king. Did you bother to read any of my post #74???

Hmmm what's next...

Originally Posted by Pete_vB

This is not true.

A tire generates force only when operating at a slip angle, either in a straight line or in a corner. The tire's design, construction and use all define what that slip angle is, but it often generates peak force in the range of 5% to 8% slip. This means that near the limit of traction the wheel is actually spinning 5-8% faster than the road, even though it does not appear to be spinning. As the torque goes down the amount of slip also goes down, but it remains a significant effect. The Bosch lapsim simulator I mentioned has inputs for this- you can define longitudinal and lateral slip angle separately. Unfortunately for us, the tire data needed to do this accurately is a highly guarded secret not available to mere mortals.

The point being that for a radial street tire with a belt package specifically designed to resist this deflection at speed (and hence internal friction and tire heating, which is what limits speed rating) this slip angle is a bigger factor than centrifugal tire growth- it cancels it out and then some.

So you are saying that an physics based computer simulation software for modeling street or even "exotic car" acceleration can not predict accurately without modeling these effects? Rubbish, pure rubbish buddy. You better stop using CarTest yourself if you think this.

You've noted it yourself "near the limit of traction" then.... Sure that's all fine. But this is the stuff that matters for an overall small portion of the total time in a given run (say a 1/4 mi run, in a street car to insure all assumptions are on the table).

Either way these things are like a couple percent error in tire radius at 200 mph. Not relevant of our purposed here at all. Some very interesting physics for sure but not relevant.

As to your sims in post #44, I seem to have not commented.

1. I was comparing a M-DCT car to the 1M not the 6 MT. There is some significant differences. You need to adjust CarTest integration time steps to handle shifts that are about 30 ms or so. There is a real advantage here for drag racing a M-DCT.

2. No matter how I tried to replicate your 1M simulation, and in particular it being a 10 second flat car from 0-100 mph, I simply can not get anywhere close to that. Did you use a custom torque curve and enter data points one by one? Do you really think the stock 1M is going to be a 10 second car to 100? I don't, period. The best I could find (even using my custom and lowered loss figures) was 11.2 s. Keep in mind CarTest does include a 1 foot roll out as per std. US drag racing and thus an 11.2 appears as about a 10.9 in the tabular view. For the M-DCT M3 I got 9.6 s to 100 on the chart and 10 even on the graph. The best reported time has been from MotorTrend and they got 9.7 seconds. We alway need to ground our simulations in reality!

Whew...

[Madozu]

Originally Posted by tarheel91

Wrong. Horsepower uses engine torque and does not consider gearing between it and the wheels.

Horsepower = Engine torque * RPM/5252.

Yes, agree 100% Just wanted to mention that the number at the end (5252 in this case) heavily depends on the units used (Metric or Amercian).

You can easily check the equation by using the the units for "power", "torque" and "rpm". Unfortunately, I can only easily do that for metric units ... American and British friends, please apalogize If you do that you get:

Power = Torque * RPM

Then fill in the units for power and torque:

                            1
Watt   = Newton * Meter * ------
                          Second

Then substitute the derived units with their definition in base units (see links to Wikipedia)

m*m*kg   m*kg        1
------ = ----  * m * -  
s*s*s    s*s         s

And if you regroup the right side of the equation you get

m*m*kg   m*m*kg
------ = ------
s*s*s    s*s*s

The formula clearly shows how related torque and power are: if you know the engine power at a certain engine speed, you can calculate the torque at that speed and vice versa. This is also the reason why you implicitly change the torque curve in programs like CarTest when changing power at certain engine speeds.

[Pete_vB]

Originally Posted by swamp2

So you are saying that an physics based computer simulation software for modeling street or even "exotic car" acceleration can not predict accurately without modeling these effects?

Well I guess that depends your definition of "accurate". We've seen that your "...accurate, guaranteed" figures were 8% off in gearing, 15% off in torque and who knows what else (because you've refused to post your numbers despite saying you would). So if that's your definition of accurate then sure. Of course if you're a race team that uses a sim for a living rather than an amateur defending their car's pride on a forum, you might want to know that 1st gear ends 2 mph sooner than predicted. Which is why Bosch built it into LapSim...

For a little education, remember you are pushing on the ground with a rubber band (literally). Let's say the limit of traction is 1G, you pull that through 1st, and you get 5% slip. So if 1st ends at 40 mph on paper you actually need to grab the gear 2 mph sooner at 38 mph. Can you fudge that in a sim made for amateurs? Sure, especially if some of your customers think things like torque don't make a practical difference...

Originally Posted by swamp2

1. I was comparing a M-DCT car to the 1M not the 6 MT.

I was comparing it the 6 speed M3 in my original post. The one about which you said:

Originally Posted by swamp2

Your "analysis" and commentary was painting a false picture of the cars being pretty close or advantages going to the 1M at certain speeds. This simply is not the case.... Power to weight is the figure that matters.

Which as we now see is false on many levels. The 1M is very close. It is faster at certain speeds. You have yet to point out a factual error in my numbers, while you made numerous mistakes in your analysis- wrong gearing, tire diameter, low torque, ignoring torque and power curves, and who knows what weights you used as you still won't post your setup.
What I posted corrected your errors and put up an apples to apples comparison with the numbers I used in the first place. If I made a mistake in any of the specs then by all means point it out.

Originally Posted by swamp2

2. No matter how I tried to replicate your 1M simulation, and in particular it being a 10 second flat car from 0-100 mph, I simply can not get anywhere close to that. Did you use a custom torque curve and enter data points one by one?

Obviously, for both the M3 and 1M. I posted the curves.

Originally Posted by swamp2

Do you really think the stock 1M is going to be a 10 second car to 100? I don't, period. The best I could find (even using my custom and lowered loss figures) was 11.2 s. Keep in mind CarTest does include a 1 foot roll out as per std. US drag racing and thus an 11.2 appears as about a 10.9 in the tabular view. For the M-DCT M3 I got 9.6 s to 100 on the chart and 10 even on the graph. The best reported time has been from MotorTrend and they got 9.7 seconds. We alway need to ground our simulations in reality!

That's funny. Road and Track's test has the 6MT M3 at 9.4 seconds 0-100, 1/4 mile in 12.5 @114.8. Perhaps you're doing something wrong, like not entering a torque curve?

Seriously though, I believe both cars to be on the fast side, though matching faster published tests. As I said I don't put a ton of stock in cartest being accurate, and I'm not saying the 1M is going to be a 10 second to 100 car. I am simply comparing one to the other under identical conditions with the realistic/ published specs, which is where this started.

[tarheel91]

Originally Posted by swamp2

Uhhh, yes. I used to think much the same way that peak torque to the wheels per weight was the most important factor. Although it is a pretty reasonable one, hp (per weight) is still better.

All values that are single numbers are indeed just that - single numbers. If you talk about integrating a curve you actually will get the exact same type of information from integrating torque or power after all they are inextricably related by T = P/ω (in SI units...). You are sort of comparing apples to oranges in this regards. You can't say one number is better but then demand you have the full curve!

Either way power is much more useful than torque at the wheels. There a variety of reasons. hp is basically a shortcut calculation of torque at the wheel. Why? Because high reving engines with more gear torque multiplication typically have less torque but more power. What you loose in torque you make up for with high rpm and high hp. Taller relative gears are optimal for such high rpm engines and thus the pair naturally acompany each other. All bets are totally off if a manufacturer completely screws up on the choice of optimal gears...

The other reason why torque at the wheels (specifically the one figure of peak torque) is less accurate is because when driven at the limits of max acceleration an engine typically spends almost no time at the rpms where peak torque occurs. All of the relevant time is spent when the engine is at or near peak power (similarly at or near redline).

hp/weight has another small, but very practical advantage. hp is more commonly reported (although certainly I am not saying peak torque figures are hard to get) and the torque to the wheels requires THREE additional pieces of data, 1st gear ratio, FD ratio and wheel size. That alone, makes it quite a bit more burdensome to calculate compared to hp/weight. Simple, effective, accurate. One number based on two of the most common specifications available.

Last but not least hp is a much better indicator of top speed. Sure aerodynamics is cirtical here especially up above the 150 mph mark but given roughly constant Cd and frontal areas top speed is goverened almost exclusively by peak hp. Peak wheel torque is not useful here (nor peak wheel Force for that matter).

If you want a more detailed "proof" of what I have explained above see this post and the long discussion after it.

So you admit single numbers are just peaks but you don't see the value in looking at that value over the whole rev band (i.e. the area under the curve, the integral, etc.)? That makes no sense.

Let me put this as simply as possible. If you want to look at acceleration, the simplest way to do that is use torque = mass * linear acceleration / radius. Yes, you can do plenty of conversions to get the same thing from power, but it's a waste of time and it's much less intuitive when looking at a graph or something.

Horsepower is convenient because it is easy to calculate (as you said) and it gives us a pretty good idea of how a car will perform. However, as you yourself admit, it essentially estimates the effects of gearing based upon the rpm the torque is made at. This is in NO WAY more accurate than using the actual gearing figures.

At the end of the day, it is torque that is directly related to acceleration, not power. Not just peak numbers, either. The whole curve matters. Different engines make power in different ways (the curve on an I6 is very different from a curve on a V6). FI engines have curves that are COMPLETELY different from NA engines. My supercharged Z4 makes within 50 ft-lbs of peak torque from 2000-7000RPM (horsepower actually peaks at 6700, but torque is closer to 4200). I have slightly less peak power than a C6, but I will walk away from him in a straight line like it's nothing. Why? My torque curve is much flatter up top. I make peak torque all the way through the rev range, it's not just some point I assend to and then rapidly descend from. The shape of the curve is essential. Period. That's basic calculus, come on.

Originally Posted by swamp2

I also disagree here - on both points.

When a tire is properly inflated to a manufacturers spec the revs/mile (which is the same thing as an effective radius) precisely describes the tire. Sure it does not give you an exact time dependent tire shape but that is entirely irrelevant from the perspective of vehicle acceleration simulation. Such effects you mentioned of a "bunching" tire are relevant only during burn outs and with tires than deform dramatically (drag tires) under torque and road reaction forces. The effect of a tire growing with the cars speed is a pretty well recognized effect (again seen in a very dramatic case with top fuel dragsters). Either way it makes intuitive sense that a tire is more or less a spring and the a centrifugal force will stretch the spring. Sure you can argue that the spring is non-linear as I am sure it is but it is certainly not highly non-linear and this the simply spring analogy is just fine. Again the errors from this expansion effect are on the same order as the errors from using a tire formula vs revs per mile to calculate a cars speed at a given axle rpm and both can indeed be completely ignored to get a basic acceleration simulation correct. The tire expansion is turned of by default in CarTest and I have chosen to leave it enabled.

As for parasitic losses: These can indeed be complicated. However, you can easily account for 1st order effects accurately enough with simple linearly dependent loss percentages vs rpm. What is "accurate" enough. In the simplest terms I'd say if 1. Your simulator produces results within the range of reported values AND 2. You can simulate the absolute difference in performance from a variety of changes to inputs that correspond to realistic physical changes you might make when modifying a car, then your simulator is "accurate enough". Obviously a "hobbyist" (or recovering physicist) interested in simulating production cars will have a very different definition of accuracy than say a professional race team. In my experience the loss formulations in CarTest are indeed thorough and accurate enough. CarTest computes engine, transmission, wheel/axle speeds as an explicit function of time, along with vehicle speed and then uses speed dependent losses for the following components: transmission, differential, axles (drive shafts, U-joints and wheel bearings). Of course determining how to modify the default loss values in CarTest so that they are "good enough" is another matter which I already provided some warning about.

You can disagree all you want, but you're not just disagreeing with me, you're disagreeing with all of vehicle dynamics. Go pick up any book on the subject by any of the masters, and you'll see you're completely wrong. Effective radius is less than rolling radius, for the myriad of reasons I presented to you before. The first person who taught this to me was a race engineer with over 30 years of experience, many of which at the top of the business. Yes, centripedal forces to tend to push the tire out, but it doesn't have the effects you think it does. 1) It's not actually pushing it directly out. It's the momentum of the rotating mass that is creating this force, and the velocity is tangent to the side of the tire. Thus, it's at 90 degrees, not 180. It's not pushing directly out, it's pushing it at an angle. Thus, no where near the full effects of the forces are felt. At the same time, this force pales in comparison to the load the tire is under from the car and, at high speeds, downforce. The idea that a wheel deforms is basic Statics. It's not even really a part of Vehicle Dynamics, to be honest.

I've tested vehicles with wheel speed sensors, and it always worked out that actual speed is lower than what you'd assume for a given number of rotations and a given diameter tire.

[technik330]

Originally Posted by swamp2

Well my dad can beat up your dad. Get real. I'm as excited about a "return to roots" M car as much as any red blooded M ethusiast. I owned 3 different M3 models and have very loosely considerd other non M3 Ms as well. There is absolutely no insecurity going on here. I'm always skeptical but insecure, nope. In case you missed it I think my most thorough expression of opinion on the 1M is here in "Are you disappointed..." thread. My clear answer was "no".

You're joking right...?

Have you taken the time to re-read half of your posts in this thread alone?

The comment I made was based on reading several of your posts, in various threads. I wasn't reading in to your posts, just reading them, and believed them to exude insecurity, that's all.

I bet you're stoked that ///M is returning to its roots; I'm just baffled by your way of demonstrating it, by marginalizing the 1M.

[Pete_vB]

Originally Posted by swamp2

Power to weight is the key metric in determining a cars performance.

Tarheel91 makes a good case for why this is far too over-simplified above, and I think we've shown that well elsewhere in the thread as well, but for another illustration of why this is too simplistic and leads to errors I did the following simulation to illustrate the point. I used the 911 turbo because huge area under the power curve and gearing makes for a dramatic comparison:

Car 1- I took the "Porsche Turbo 1988" in carsim, which you have, and change hp to 400 at 7000 rpm, tq to 400 at 5000 rpm- typical modified 911 turbo numbers.

Car 2- Same car, I left 400 hp at 7000, but I put torque at 300 at 3000 rpm. The flat torque curve looks like an M3 motor with the top 1000 rpm cut off, or a high revving toyota/ lotus motor that makes peak power at redline. For car 2 I also removed 500 lbs.

Car 1 has 3025 lbs / 400 hp = 7.6 lbs per hp.
Car 2 has 2525 / 400 hp = 6.3 lbs per hp.

This contest shouldn't even be close according to your simplistic evaluation, but car 1 wins every acceleration test. That's the problem with ignoring area under the curve. Obviously this is an extreme example, but it's the same error you made in evaluating the 1M and it seems the message still hasn't gotten through. Again, garbage in, garbage out- if you're not evaluating the the important numbers the results are worthless, and the torque/ power curve is important.

[swamp2]

Originally Posted by tarheel91

So you admit single numbers are just peaks but you don't see the value in looking at that value over the whole rev band (i.e. the area under the curve, the integral, etc.)? That makes no sense.

Let me put this as simply as possible. If you want to look at acceleration, the simplest way to do that is use torque = mass * linear acceleration / radius. Yes, you can do plenty of conversions to get the same thing from power, but it's a waste of time and it's much less intuitive when looking at a graph or something.

Horsepower is convenient because it is easy to calculate (as you said) and it gives us a pretty good idea of how a car will perform. However, as you yourself admit, it essentially estimates the effects of gearing based upon the rpm the torque is made at. This is in NO WAY more accurate than using the actual gearing figures.

At the end of the day, it is torque that is directly related to acceleration, not power. Not just peak numbers, either. The whole curve matters. Different engines make power in different ways (the curve on an I6 is very different from a curve on a V6). FI engines have curves that are COMPLETELY different from NA engines. My supercharged Z4 makes within 50 ft-lbs of peak torque from 2000-7000RPM (horsepower actually peaks at 6700, but torque is closer to 4200). I have slightly less peak power than a C6, but I will walk away from him in a straight line like it's nothing. Why? My torque curve is much flatter up top. I make peak torque all the way through the rev range, it's not just some point I assend to and then rapidly descend from. The shape of the curve is essential. Period. That's basic calculus, come on.

You seem to be missing my point over and over and over again. Being familiar with vehicle simulation I'll be the first acknowledge that a full engine curve (either torque or hp, it's totally irrelevant which you use since they are linearly related - come on that's just algebra a lot easier than calculus) is required to accurately simulate a vehicle. HOWEVER, for most of this discussion I have been talking about the most important SIMPLE parameter there is. Now even if you want to bother with gearing and weight and wheel diameter, I still contend that hp/weight is more important. You've already agreed that hp is more convenient. So there are three levels of information here we have been discussing. 1. Peak single value hp vs. peak single value torque. 2. Then there is one step beyond that to a calculation that adds drivetrain information but still uses a single engine value. 3. Lastly there is the level of having the full curve (and gearing obviously). It is my contention that in order of simplest (that is still highly informative) to ultimately informative, but substantially more complex (certainly for the average enthusiast) this is the list:

1. Power to weight. That is peak power or course, perhaps minus losses if you have that, divided by weight. Since losses don't vary too radically you can to 1st order leave those out. As almost anyone knows you can not get peak hp from peak torque nor vise versa since they happen at different rpm. You've already agreed that hp basically is a shortcut to torque+gearing information. Why make it more complex.
2. Examine a full curve of data, hp and torque and 100% interchangeable here, each tells you EXACTLY the same information about the engines characteristics. Perhaps one intermediate step even beyond this is looking at the same results across all gears.
3. A full blown transient vehicle simulation of which a key ingredient is a full rpm engine curve.

You continue to compare apples to oranges yourself when you say #2 is "better" or more informative than #1. Sure its better but it "costs" a lot more too.

I'm quite keen to hear the peak torque, peak hp, redline and weight of your car vs. a C6. Also by what margin you best this car? Can you accurately simulate this besting you have observed? Although there are exceptions to rules I don't contend that a single number can ever capture exactly every case of which car bests which other one. Its just that if I had to place a bet, and could only know one simple value, I'd choose power to weight. Man, I am beating me head against a wall on this...

Once we settle this one we can move on to a topic I know you'll love. You can even compute track times given a data set of multiple cars on that track and their lap times and nothing other than, you guessed it, power to weight ratio. Sure the R^2 is not 1 for such a prediction. This is nothing like what would be useful for a race team either. I'm aware of what they use. Given the simplicity of such a regression over a full blown dynamic lap simulation it is remarkable how well power/weight predicts!

Why don't we see any successes like this or like the prior drag racing ones I referred to for peak torque to weight or peak torque times gearing ratios/weight or other such "useful" numbers you like so well?

Originally Posted by tarheel91

You can disagree all you want, but you're not just disagreeing with me, you're disagreeing with all of vehicle dynamics. Go pick up any book on the subject by any of the masters, and you'll see you're completely wrong. Effective radius is less than rolling radius, for the myriad of reasons I presented to you before. The first person who taught this to me was a race engineer with over 30 years of experience, many of which at the top of the business. Yes, centripedal forces to tend to push the tire out, but it doesn't have the effects you think it does. 1) It's not actually pushing it directly out. It's the momentum of the rotating mass that is creating this force, and the velocity is tangent to the side of the tire. Thus, it's at 90 degrees, not 180. It's not pushing directly out, it's pushing it at an angle. Thus, no where near the full effects of the forces are felt. At the same time, this force pales in comparison to the load the tire is under from the car and, at high speeds, downforce. The idea that a wheel deforms is basic Statics. It's not even really a part of Vehicle Dynamics, to be honest.

I've tested vehicles with wheel speed sensors, and it always worked out that actual speed is lower than what you'd assume for a given number of rotations and a given diameter tire.

Again we are not going to see eye to eye. Tire dynamics is surely not my specialty. Your appeal to experts is not going to buy much with me though either. And my point is not really to debate this particular topic. However, as I've already stated, in order to get all common performance metrics we all care about such as things like 0-60, 0-100, 60-130, quarter mile (times and traps) within a couple tenths of a second and within a couple mph you ABSOLUTELY do not need advanced tires dynamics models in a simulator. If you really felt otherwise, you should not be using CarTest yourself. Come on you can't have your cake and eat it too.

Do you have any idea between the difference between a "1st order effect" and a "2nd order effect". It means the sized or variation in results you see from 2nd order is an order of magnitude or perhaps some other "power law" amount smaller. Might even be that "x" is small so x^2 and x^3 in some expansion are then really small. This is the case with tires in simulators. With no advanced 2nd order effects, either a model based on the ideal size from the nominal tire size OR on the diameter from the revs/mi spec a simulator will deliver sufficient accuracy. In either case for "A-B" relative predictions the tires will be modeled the same way. As is typical with most physics based simulators (my profession by the way, nothing like CarTest but very loosely similar) relative results are easier to get and get accurately since computers offer perfectly controlled "experiments" between different inputs. If the tires are mis-modeled by a small 2nd order effect at least they are mis-modeled the exact same way in both simulations.

And no, just so you can stop getting you physics equations and terms wrong, it is cetrifugal forces that tend to expand a tire not centripetal (nor centripedal [sic] which you apparently just invented by misspelling). Maybe you might want to revise your entire description there above keeping in mind that for any part moving in a circle at constant rpm the SUM of all of the forces acting on it must be exactly toward the center of rotation and equal to mrω^2 (SI units or course). You can't cover all of the advanced stuff with the basics so clearly screwed up.

[swamp2]

Originally Posted by technik330

You're joking right...?

Have you taken the time to re-read half of your posts in this thread alone?

The comment I made was based on reading several of your posts, in various threads. I wasn't reading in to your posts, just reading them, and believed them to exude insecurity, that's all.

I bet you're stoked that ///M is returning to its roots; I'm just baffled by your way of demonstrating it, by marginalizing the 1M.

I was being sarcastic. You obviously missed it. Your should not need to resort to some psychology or meta analysis to make your point. Whether I like, hate, compliment or dis a car precious to you has no impact on the value of my statement.

To humor me if you can please point of my "exuding of insecurity" that would be useful. You are reading way too much into things here buddy.

[swamp2]

Originally Posted by Pete_vB

Well I guess that depends your definition of "accurate". We've seen that your "...accurate, guaranteed" figures were 8% off in gearing, 15% off in torque and who knows what else (because you've refused to post your numbers despite saying you would). So if that's your definition of accurate then sure.

1. Tires. After comparing the tires size from nominal tire sizes based on a formula to a effective circumference calculated from revs/mi I agree that my initial 1M sims were off in top speed by about 8%. Based on my further simulations this does not come even close to changing my ultimate conclusions about the relative performance between the M3 M-DCT and 1M.
2. Torque: My simulations here absolutely were not off 15%. I was simply using maufacturers stated values. That being said I agree the 1M is likely to be underrated both on power and torque. Again even running some new simulations based on those results it does not make a big difference in my qualitative predictions.

Originally Posted by Pete_vB

Of course if you're a race team that uses a sim for a living rather than an amateur defending their car's pride on a forum, you might want to know that 1st gear ends 2 mph sooner than predicted. Which is why Bosch built it into LapSim...

For a little education, remember you are pushing on the ground with a rubber band (literally). Let's say the limit of traction is 1G, you pull that through 1st, and you get 5% slip. So if 1st ends at 40 mph on paper you actually need to grab the gear 2 mph sooner at 38 mph. Can you fudge that in a sim made for amateurs? Sure, especially if some of your customers think things like torque don't make a practical difference...
...
That's funny. Road and Track's test has the 6MT M3 at 9.4 seconds 0-100, 1/4 mile in 12.5 @114.8. Perhaps you're doing something wrong, like not entering a torque curve?

Seriously neither you nor I do this professionally. The idea is to be able to make some realistic real world predictions. Most interestingly if you can do this before there are real world test results that is of some value. If you want to focus on all of the tiny effects that can have a negative effect on a simulators accuracy you'll never get anywhere. If you like LapSim so much you should definitely switch to it for any future posts. Then we can really have some arguments...

For reference as to "accuracy" have a look at this nice M3 performance "database". Your really fast magazine prediction is already there. The point here is that there is so much variation even in real world testing. To compare such results to a simulator indeed requires some judgement about the plethora of test results. Sure some of these can be accounted for by variables like 1 ft roll out in the US but not in Europe, or perhaps temperature or air density. Unfortunately, there are far too many random variations to account for them all. Hence we see natural varation. Magazines nor "hobbyists" with a Vbox have the sophistication and dedication to test in the way a race team can and does. When you get to values of uncertainty in your sim, smaller than a reasonable observed range, you are certainly good enough for the perspectives of a "hobbyist".

Originally Posted by Pete_vB

The 1M is very close. It is faster at certain speeds. You have yet to point out a factual error in my numbers, while you made numerous mistakes in your analysis- wrong gearing, tire diameter, low torque, ignoring torque and power curves, and who knows what weights you used as you still won't post your setup.
What I posted corrected your errors and put up an apples to apples comparison with the numbers I used in the first place. If I made a mistake in any of the specs then by all means point it out.

Seriously though, I believe both cars to be on the fast side, though matching faster published tests. As I said I don't put a ton of stock in cartest being accurate, and I'm not saying the 1M is going to be a 10 second to 100 car. I am simply comparing one to the other under identical conditions with the realistic/ published specs, which is where this started.

I will post my full simulation inputs shortly. My results still show that its only close to 60 or 70. The margin of lead shown by the M3 in my original simulations has narrowed but my qualitative conclusion has not. The changes I am seeing are almost entirely due to these higher peak torque and hp results. I've simply given you the benefit of the doubt on the peak values and their locations. I do also think those are entirely reasonable. Ultimately I still stick to my contention that the real car, 1M underrated or not, will not be as close to the M3 M-DCT as you have shown. No break throughs here. Other than the 6MT VS. M-DCT don't know why your results are so close. I don't think the M-DCT makes up the difference.

[Pete_vB]

Originally Posted by swamp2

2. Torque: My simulations here absolutely were not off 15%. I was simply using maufacturers stated values.

The 1M will run 370 ft lbs for up to 10 seconds at a time. At no time in these runs we are posting do you see 10 seconds of wide open throttle. Hence if you're using any less than 370 you're fooling yourself.

Originally Posted by swamp2

I will post my full simulation inputs shortly. My results still show that its only close to 60 or 70. The margin of lead shown by the M3 in my original simulations has narrowed but my qualitative conclusion has not. The changes I am seeing are almost entirely due to these higher peak torque and hp results. I've simply given you the benefit of the doubt on the peak values and their locations. I do also think those are entirely reasonable. Ultimately I still stick to my contention that the real car, 1M underrated or not, will not be as close to the M3 M-DCT as you have shown. No break throughs here. Other than the 6MT VS. M-DCT don't know why your results are so close. I don't think the M-DCT makes up the difference.

I have not shown any results vs an M3-DCT. Every sim I have done has been vs a manual. Please also post a run vs a 6MT for comparison. Please keep in mind my original statement on the 1M vs the 6MT M3, to which you objected so strongly:

"the 1M is clearly going to kick hard when the boost hits, pulling harder than the M3 until about 35 mph when the torque rolls off and the M3 keeps pulling. The 1M is again slightly ahead up until about 60 mph in 2nd. In the higher gears, however, the M3 spends more and more time in front, and it's always in front above about 115 mph due to the higher top end power. "

[M3 Adjuster]

Originally Posted by Pete_vB

Car 1- I took the "Porsche Turbo 1988" in carsim, which you have, and change hp to 400 at 7000 rpm, tq to 400 at 5000 rpm- typical modified 911 turbo numbers.

Car 2- Same car, I left 400 hp at 7000, but I put torque at 300 at 3000 rpm. The flat torque curve looks like an M3 motor with the top 1000 rpm cut off, or a high revving toyota/ lotus motor that makes peak power at redline. For car 2 I also removed 500 lbs.

Car 1 has 3025 lbs / 400 hp = 7.6 lbs per hp.
Car 2 has 2525 / 400 hp = 6.3 lbs per hp.

This contest shouldn't even be close according to your simplistic evaluation, but car 1 wins every acceleration test. That's the problem with ignoring area under the curve.

pictures are pretty.....

[swamp2]

OK here are some revised sims in full gory detail...

Notes:

• I have no idea why my prior M3 sims are so bad. They are. I must have grabbed the wrong car from a huge list of a bunch of levels of refinement to my M3 sims. The numbers I have here should have been what I posted all along. Why I did not notice 106 mph traps and top speeds of 168 mph I don't know. Please excuse the big screw up on this. Careless, careless.
• Losses are custom for both the 1M and M3. My loss values are based on some comments in "Fundamentals of vehicle dynamics" (Gillespie text) along with much discussion among knowledgeable forum members here on M3post.com. The standard losses are way too high for a modern high performance car and they don't match rototest.com results either, hence my adjustments.
• M-DCT shift times: I've actually measured these and they are about 30 ms (best case). To get them to appear as about 30 ms in graphs I simply used the 20 and 10 ms results for a MT.
• Integration time steps: These must be reduced to at least 30 ms to capture these M-DCT shift times. I've run the 1M and M3 with the exact same integration time step. You will see changes between running at 50 (default) and 30 ms. Generally speaking results will converge the lower and lower the time step gets. Prior experimentation has show 30 ms to be fairly well converged even for a M-DCT car.
• 1M 6MT shift times: To get a roughly 250 ms shift time. Which is probably about the best a really fast shifting driver can do I used the 200 and 50 ms times respectively. In the time domain I got shifts that appear to take just about 250 ms.
• Like Pete I've assumed 15 hp and 15 torque underrated AND that the overboost torque is always available. That is extremely generous for predicting better performance that real world since this is known not to be true.

Results:

• It is hard to see on such small graphs. The 1M might get 5 feet on the M3 up to about 5 seconds, 60-70 mph. From there the M3 steadily pulls away. By 120 mph the M3 shows 4 car lengths on the 1M.
• M3 results are consistent with the better results in this informal database of results posted here.
• I don't really believe the 1M will get a 4.1 0-60. Perhaps a couple tenths worse. Meaning the torque or power used here is too liberal. Either way a ver nice result.
• As mentioned earlier despite some problems with my earlier sims my qualitative conclusion is the same.
• I did also use a custom torque curve widening it but preserving the maximum values shown in the main set screen. It did not result in any qualitative changes in the graphs. A couple tenths here or there, nothing significant.

[swamp2]

Originally Posted by Pete_vB

The 1M will run 370 ft lbs for up to 10 seconds at a time. At no time in these runs we are posting do you see 10 seconds of wide open throttle. Hence if you're using any less than 370 you're fooling yourself.

Sounds reasonable. However the 384 peak due to under rating is still nothing more than informed guessing.

Originally Posted by Pete_vB

I have not shown any results vs an M3-DCT. Every sim I have done has been vs a manual. Please also post a run vs a 6MT for comparison. Please keep in mind my original statement on the 1M vs the 6MT M3, to which you objected so strongly:

"the 1M is clearly going to kick hard when the boost hits, pulling harder than the M3 until about 35 mph when the torque rolls off and the M3 keeps pulling. The 1M is again slightly ahead up until about 60 mph in 2nd. In the higher gears, however, the M3 spends more and more time in front, and it's always in front above about 115 mph due to the higher top end power. "

Yes, in part I've been doing apples to oranges with M3 6MT vs. M-DCT.

My conclusion is that the M-DCT will be always in front well below 115.

Let me see how "mature" me 6MT M3 sims are.

[swamp2]

Pete, my 6MT simulations vs. revised 1M simulations now look qualitatively very similar to yours. The difference in our simulations now stems almost entirely from the short 250ms shift times I have used for both the M3 and the 1M. Optimistic but not unreasonable times. Have a look at the M-DCT in CarTest using my suggested advise above. Do we get some close qualitative agreement there?

Sorry about that. I should have gotten on the M3 6MT vs. M-DCT thing much earlier.

However, back to a remaining point of contention. I can not show significant differences between 1M simulations by tweaking the torque curve. No matter what you do you can't alter the curve in the higher rpms much and still have a reasonably shaped set of curves and ALSO get the right peak power. That's is also related to my whole point about for a single number power to weight is more important.

[Pete_vB]

Originally Posted by swamp2

OK here are some revised sims in full gory detail...

Notes:

• I have no idea why my prior M3 sims are so bad. They are. I must have grabbed the wrong car from a huge list of a bunch of levels of refinement to my M3 sims. The numbers I have here should have been what I posted all along. Why I did not notice 106 mph traps and top speeds of 168 mph I don't know. Please excuse the big screw up on this. Careless, careless.
• Losses are custom for both the 1M and M3. My loss values are based on some comments in "Fundamentals of vehicle dynamics" (Gillespie text) along with much discussion among knowledgeable forum members here on M3post.com. The standard losses are way too high for a modern high performance car and they don't match rototest.com results either, hence my adjustments.
• M-DCT shift times: I've actually measured these and they are about 30 ms (best case). To get them to appear as about 30 ms in graphs I simply used the 20 and 10 ms results for a MT.
• Integration time steps: These must be reduced to at least 30 ms to capture these M-DCT shift times. I've run the 1M and M3 with the exact same integration time step. You will see changes between running at 50 (default) and 30 ms. Generally speaking results will converge the lower and lower the time step gets. Prior experimentation has show 30 ms to be fairly well converged even for a M-DCT car.
• 1M 6MT shift times: To get a roughly 250 ms shift time. Which is probably about the best a really fast shifting driver can do I used the 200 and 50 ms times respectively. In the time domain I got shifts that appear to take just about 250 ms.
• Like Pete I've assumed 15 hp and 15 torque underrated AND that the overboost torque is always available. That is extremely generous for predicting better performance that real world since this is known not to be true.

Looks fairly reasonable so far, but where are you getting your M3 weights from? BMW USA is listing unladen weight at 3704 lbs on the website? And DCT is supposed to add 45 lbs... Or is that wrong? You have 3581...

By the way, the unrealistically low loss required to get good speeds is one reason I'm not so sure about cartest. I needed to do something similar, but it doesn't look right vs lapsim.