The advantages of a NA engine?

Serious wrote

(low gears you pedal crazy fast but don't have to use much strength; whereas in high gears you pedal slowly but use a lot of energy pushing the pedals.)

IMO, and is often shared, you want to maintain pedal speed in the 70 - 90 RPM range regardless of road speed. That is why the gears are used; to maintain cadence but vary speed. So, no, you don't pedal crazy fast in the low gears and slower in the higher gears. You pedal the same and let gearing do what it is supposed to do.

I understand what you were tryiong to point out though but wanted to clarify.

Edward wrote

BTW, someone needs to throw in a real engineer's anwer to torque multiplication. I'm no engineer or physicist, but I do realize that the gearing on the M3 allows it to deliver much more torque to the rear tires than the same amount of torque in a 335 (if it had the same engine flywheel torque) would deliver through the powertrain.

Hmmm if I understand your point you want the short simple formula based way to see/understand gearing torque multiplication (under approximations suitable to the discussion)? We could write the equation for rear wheel torque but ultimately it is vehicle acceleration anyone cares about. If two cars have the same wheel size and weight then you can just compare rear wheel torque to rear wheel torque.

a = (loss x g x FD x Te)/(rw x m)

This simply comes from F = m x a and T = r x F (torque = radius x force) - basically Newton's law and the definition of torque. In plain english:

accelerative force at rear wheels =( drivetrain loss (torque loss) x gear ratio x final drive ratio x engine torque )/ ( rear wheel radius x vehicle mass )

(Note: you must use ALL SI units for these formulae if you want to put some numbers in - plug in common US units and you will get nonsensically sized results)

Of course some terms are rpm dependent such at Te and even the loss, but the key factor here for understanding torque multiplication is simply the g and FD terms. g as well is gear dependent (obviously).

Just for example:

1st gear M3: g x FD = 4.78 x 3.15 = 15.1
1st gear 335i: g x FD = 4.06 x 3.08 = 12.5

That is a whopping 21% advantage for the M3. A 335i needs about 360 ft lb just to make up the difference in 1st gear. Many other posts have plotted this out across gear and across rpm to see the entire picture. This has been done for a variety of cars not just the 335i and M3 actually right here in the forum. Without more graphs, which seem to scare some folks off this should suffice to demonstrate the principal.

Lastly as Bruce always points out you don't really need to do this calculation anyway. As hp more or less does the calculation for you. It it not perfect nor precise but engine torque combined with gearing is basically hp. Here we don't mean mathematically, just from understanding the performance of a car.

Hope that is useful to some folks.

swamp2 wrote

Hmmm if I understand your point you want the short simple formula based way to see/understand gearing torque multiplication (under approximations suitable to the discussion)? We could write the equation for rear wheel torque but ultimately it is vehicle acceleration anyone cares about. If two cars have the same wheel size and weight then you can just compare rear wheel torque to rear wheel torque.

a = (loss x g x FD x Te)/(rw x m)

This simply comes from F = m x a and T = r x F (torque = radius x force) - basically Newton's law and the definition of torque. In plain english:

accelerative force at rear wheels =( drivetrain loss (torque loss) x gear ratio x final drive ratio x engine torque )/ ( rear wheel radius x vehicle mass )

(Note: you must use ALL SI units for these formulae if you want to put some numbers in - plug in common US units and you will get nonsensically sized results)

Of course some terms are rpm dependent such at Te and even the loss, but the key factor here for understanding torque multiplication is simply the g and FD terms. g as well is gear dependent (obviously).

Just for example:

1st gear M3: g x FD = 4.78 x 3.15 = 15.1
1st gear 335i: g x FD = 4.06 x 3.08 = 12.5

That is a whopping 21% advantage for the M3. A 335i needs about 360 ft lb just to make up the difference in 1st gear. Many other posts have plotted this out across gear and across rpm to see the entire picture. This has been done for a variety of cars not just the 335i and M3 actually right here in the forum. Without more graphs, which seem to scare some folks off this should suffice to demonstrate the principal.

Lastly as Bruce always points out you don't really need to do this calculation anyway. As hp more or less does the calculation for you. It it not perfect nor precise but engine torque combined with gearing is basically hp. Here we don't mean mathematically, just from understanding the performance of a car.

Hope that is useful to some folks.

Thanks swamp. Wow, so in reality, the 335i doesn't really have the advantage in any gear.

Guys, Bruce is correct here. It indeed takes some serious thought for "car guys" to see it is true. Most of you will not like the simplest proof I will offer but it is simply that:

P = F x v

Power is force x velocity. So two systems at the same speed (their speed, not their wheels, their engines, or anything else) will have a accelerative force that is directly related to the power the system can exert at that speed (power is absolutely a function of speed by the way in a car - probably obvious but worth stating).

This works for a bicycle, a diesel semi, a M3, an electric car, whatever. It is physics and physics is simply correct and predictive.

Here is another way to think about this that complements the above, since few will "buy" the proof above. Contrary to some rumblings in some prior post formulae and physics are VERY meaningful and precise and as long as folks understand and agree on equations they greatly enhance understanding. They can greatly increase confusion as well...

This alternate way to understand is back to gearing. If you floor your car at a low speed in a high gear you get very poor acceleration - it "bogs" as we say. If at the exact same speed you simply put the car into the lowest gear possible (with just a bit of rpm left before redline of course) the car accelerates much more, probably drastically more. Why does the car accelerate so much better? It is because you force the engine rpm higher which makes the engine produce much more power and there you have it. Same speed more power. Do recall that power = torque x rpm (the extra 5252 factor you typically see is just for our terrible english units...).

You can also think in terms of torque multiplication as I talked about just above. The lower gear makes much more torque multiplication. Thus more torque and more force at the drive wheels. Even if your torque curve was dead flat the lower gear and accompanying higher rpm gives you more power.

What tends to complicate this is the "at the same velocity" requirement. We all know as any race or comparison proceeds the two vehicles will not always be at the same speed at the same time. It would be awfully boring if they were. Thus you can only really use this argument for a whole series of imagined rolling drag races each time with the contenders starting at the exact same speed (gear selection and hence power level up to the driver). This can be repeated over and over at slightly increasing starting speeds. But as soon as one contender is going much faster than the other you can not use the basic relationship.

To get around this minor limitation (and the complications of different torque and power curves, and gearing and wheel sizes and redlines and drivetrain loss, etc., etc. etc.) one must actually do a full "transient analysis" and compute the actual force at the wheels, the losses and resistive drag force and the resulting instantaneous acceleration, the resultant increase in velocity from that instantaneous acceleration and then repeat this in very small time steps. This is what CarTest and similar software tools accomplish and that is where my results came from many posts back.

Think hard, ponder it, you will have so much more insight into how and why cars perform and which things are key for more performance (well straight line performance at least...).

The next challenge is final drive modifications. If you also understand why final drive modifications typically increase in gear results but not results across multiple gear you really get it.

Sedan_Clan wrote

Thanks swamp. Wow, so in reality, the 335i doesn't really have the advantage in any gear.

No, it does. It a bit more complicated than that. It is rpm dependent since the torque varies by rpm. But the advantage is at such low rpm for such a small window it is mostly irrelevant.

Also complicating things is that the 335i is most likely underrated buy about 20-30 hp. For a true 300 hp 300 ft lb 335i the advantage is almost universally with the M3 (again assuming you are driving in the right gear for the best acceleration at WOT). For a real 335i there are some points in a drag race where it will put down more wheel force than the M3.

Have a look at the very last graph in this post. This removes the any possible overrating issue since it used actual dyno results (as does the post linked below).

You will also like this one. The M3 vs. close competitors factoring in actual dyno data, gearing and weight. Link. Unfortunately the 335i was not included. The only problems here with displaying the information in this fashion are: 1. Way too much data to look at, and, 2. What you probably really want are graphs vs. time like the ones I posted in post #213 in this thread.

In the end, the key take away is simply this: Power to weight rules. And of course I mean peak power...

pbonsalb wrote

It is OK that some people's knowledge is book or internet or simulation based. I can read also and have bench-raced plenty, but my real car learning came from working on them, modifying them, dyno testing them, tuning them, and driving them. We obviously have different approaches and I will leave the spreadsheets to you.

Indeed to each their own. The absolute best combination is to do both. Nonetheless, when taking an approach like the one above you do almost always end up with some huge and important misconceptions. You continue to have multiple key misconceptions about how and why cars do what they do.

pbonsalb wrote

You have to beat the piss out of the high horsepower low torque car to run with the high torque lower horsepower car.

High rpm production engines may have a bit shorter life than lower rpm ones however, in either style of car with a quality engine you can count on a similar lifetime before a major failure. Even with an motor like the S65 you are probably likely to have a head failure before something directly related to the stress from its redline and use at that level. Thus I disagree with the extremity of the "beat the piss" comment. You simply have to choose the right gear and press the throttle far. Some don't like to do this, that is fine. Some do.

pbonsalb wrote

This is why the N54 makes for the better daily driver in the 500 to 4000 rpm range where it shines.

I still disagree, it is the better "lazy driver". If simply mean it produces more wheel torque at those rpms that is incorrect. Please have a look here. This is the same link I just provided just above.

pbonsalb wrote

Your small sliver of automobile enlightenment is the S65 and what you gather from the internet that everyone else looks at as well. I have your holy grail S65. I also have the N54. I had a supercharged M3 with 460 rwhp and 360 lbs rwtq with a 3.64 diff that is now turbocharged to over 500/500 and faster with a 3.15 diff. What I find to be enlighteing is enlightening to drive such different cars with such different power curves on a regular basis. It gives me the ability to appreciate one more than another in certain situations.

Ugh, spare me the braggadocio. I don't give a rats a$$ what you own nor what you drive. To me understanding is much more important than amateur hot rodding experience. Furthermore you know nothing about what I own, have owned, admire, driven nor where I get my information. Most of it is created be me rather then recycled. Sure I am not inventing new engineering nor science but it is my effort. I completely stand behind my reputation and history here on this forum especially in regards to dispelling rumors and false beliefs and doing just a small but to bring some science to car guys. That being said I do indeed think the E9x/S65 is very special car (as do most with any gear head tendencies at all) but I have many other favorites as well. Your hyperbole of the/my S65 "holy grail" is just that.

pbonsalb wrote

I am just not close-minded to the reality of getting outsquirted on the street in daily driving by modded 135/335s. It has happened to far better drivers than me.

I would think nothing less of myself, my car nor my understanding of them getting bested in a street race by a modded 335i.

Please let's try to get back on topic. Everyone. This is not another 335i nor modded 335i vs. M3 thread.

swamp2 wrote

No, it does. It a bit more complicated than that. It is rpm dependent since the torque varies by rpm. But the advantage is at such low rpm for such a small window it is mostly irrelevant.

Also complicating things is that the 335i is most likely underrated buy about 20-30 hp. For a true 300 hp 300 ft lb 335i the advantage is almost universally with the M3 (again assuming you are driving in the right gear for the best acceleration at WOT). For a real 335i there are some points in a drag race where it will put down more wheel force than the M3.

Have a look at the very last graph in this post. This removes the any possible overrating issue since it used actual dyno results (as does the post linked below).

You will also like this one. The M3 vs. close competitors factoring in actual dyno data, gearing and weight. Link. Unfortunately the 335i was not included. The only problems here with displaying the information in this fashion are: 1. Way too much data to look at, and, 2. What you probably really want are graphs vs. time like the ones I posted in post #213 in this thread.

In the end, the key take away is simply this: Power to weight rules. And of course I mean peak power...

Right, the 25% gearing advantage of the M3 is diminished by the 10% underrating of the 135/335 torque, making the real world differences smaller than the spreadsheeters and simulators see. Then you consider that part throttle torque of the responsive twin turbo engine is greater than that of the S65 and the daily driving advantage tilts towards the 135/335, which is also a little lighter. That full boost at part throttle is also hard for the spreadsheeters and simulators to grasp, since only full throttle numbers show up. Certainly, drive the piss out of the M3 and it is the faster car even at low rpm -- all the magazine 0-60 times demonstrate this. But a lot of those test drivers also comment that the 135/335 is the better daily driver. In the 500 to 4000 rpm range in daily driving, it does incredibly well. The power is a split second away and it will outsquirt the mighty M3 in many daily driving situations in which the M3 does not have the space to rev up and catch up (and pass).

Put a $250 to $500 tune in the 135/335 and the M3 gearing torque advantage is all gone except at very high rpm. The 335is with a slightly uprated factory tune is putting out 340 lbs at the rear wheels. Most M3 put out 250-260 lbs while most 135/335 are doing 275-285 lbs at the rear wheels. Add your 25% advantage to that and you have 312-325, but remember the M3 torque peak is 3900 and the 135/335 torque peak is half that (less according to BMW), which really helps in daily driving though not on the dragstrip. I'd do a spreadsheet/simulation, but I'd rather go drive one of my cars -- maybe the one with the high horsepower low torque S65, maybe the one with the high torque moderate horsepower N54 or maybe the one with the massive torque and horsepower turbo S52.

bruce.augenstein@comcast. wrote

You're missing what I didn't originally state, but have now added to my post. Sorry.

The missing item was that the two cars are side by side, i.e., the same speed.

Ok, fair enough then. Thanks for the correction.

So, let me see how that effects my example. So, then, we start with two identical M3s. We then modify one of them with a power adder such that it now makes as much power in second gear at 25mph (@ whatever RPM that happens to be - I don't know off the top of my head, and it would differ between 6MT to DCT anyway) as the still-stock one does in 1st gear at 25mph (again, whatever RPM that happens to be - it will definitely be a higher RPM than the other car though). Now, if we put them next to each other traveling at 25mph, and punch it, they will accelerate at the same speed. Well, this is true only for the initial instant the throttle is pushed. After that, presumably, the power curves no longer mirror each other @ the respective engine RPMs so one car will start to pull. But if the curves somehow matched up identically throughout the rest of the rev range, until the car in first gear hits redline, then indeed they would be neck and neck the whole time to that point.

This I am more apt to accept. It does make you shake your head a little though.

pbonsalb wrote

But a lot of those test drivers also comment that the 135/335 is the better daily driver. In the 500 to 4000 rpm range in daily driving, it does incredibly well. The power is a split second away and it will outsquirt the mighty M3 in many daily driving situations in which the M3 does not have the space to rev up and catch up (and pass).

How much "power" does a car really need to make a great daily driver? <--That was a rhetorical question! Like I stated in an earlier post, claiming one is better than the other sounds silly to me. Both the 335i and the M3 have MORE than enough power (...MORE power than a car needs).

I have one question. We always say high revving engine is better. This way we can have shorter gear ratios and take advantage of torque multiplication.

BUT, let say we have two cars with perfectly flat torque curves. Car1 has 200lb-ft torque, 305hp, and revvs to 8000rpm. Car2 on the other hand has 400lb-ft torque, 305hp, and revvs to 4000rpm. For the sake of example, assume the engines idle at 0rpm.

The cars weigh same, use same tires etc. They have the same gearbox, but the differentials are 2x different (or differentials are same but the gear ratios are 2x different) such that they put the same torque to the wheels.

Are these cars will have the same acceleration?

Sedan_Clan wrote

How much "power" does a car really need to make a great daily driver? <--That was a rhetorical question! Like I stated in an earlier post, claiming one is better than the other sounds silly to me. Both the 335i and the M3 have MORE than enough power (...MORE power than a car needs).

I don't get that either. Folks in europe drive around with <2litre cars...

Well, if you buy into what Bruce has said above (I do since I think he's correct ), then the answer to your question depends on the power curves. So I don't believe there's enough information here to make a conclusion. Power and torque curves do inter-relate, however, I still believe you need to supply an actual power curve here to reach an answer. You've only given a peak power spec (not even a peak power RPM), or so it seems if I've understood you properly.

erhanh wrote

I have one question. We always say high revving engine is better. This way we can have shorter gear ratios and take advantage of torque multiplication.

BUT, let say we have two cars with perfectly flat torque curves. Car1 has 200lb-ft torque, 305hp, and revvs to 8000rpm. Car2 on the other hand has 400lb-ft torque, 305hp, and revvs to 4000rpm. For the sake of example, assume the engines idle at 0rpm.

The cars weigh same, use same tires etc. They have the same gearbox, but the differentials are 2x different (or differentials are same but the gear ratios are 2x different) such that they put the same torque to the wheels.

Are these cars will have the same acceleration?

mkoesel wrote

Well, if you buy into what Bruce has said above (I do since I think he's correct ), then the answer to your question depends on the power curves. So I don't believe there's enough information here to make a conclusion. Power and torque curves do inter-relate, however, I still believe you need to supply an actual power curve here to reach an answer. You've only given a peak power spec (not even a peak power RPM), or so it seems if I've understood you properly.

My first assumption that I pointed out in my post is that the torque curve is perfectly flat for both cars, from 0rpm to max rpm. For both cars, maximum power comes at redline.

erhanh wrote

I don't get that either.

Well, you see, it is another example of the contradictory logic that seems to win a lot of mindshare on automotive forums.

On the one hand, people want a manual gearbox because they insist on very finite control over the gear ratios that their transmission provides. But on the other hand, they want a car that doesn't really need those ratios to provide a good sensation of speed an performance to begin with.

Of course, the irony here is that, even with a 335i, obviously the car accelerates best when in the lowest gear fro the current speed (below 100 mph anyway). And, as a corollary you need to wind the thing to 7000 RPM to get the best acceleration anyway (in lower gears).

I suppose what it comes down to the fact is that, people care most about how the car feels, not how it actually performs. Low end torque makes a car feel faster, even when it isn't. Similarly having a manual gearbox makes a person feel like they are driving fast, even if they are not (in fact, even if they aren't even using it effectively).

erhanh wrote

My first assumption that I pointed out in my post is that the torque curve is perfectly flat for both cars, from 0rpm to max rpm.

Right. But I was talking about the power curve, not the torque curve.

mkoesel wrote

Right. But I was talking about the power curve, not the torque curve.

What is a power curve then? Power is hp, right? If so, then the power will increase from 0 (@ 0rpm) to 305hp at redline. Since one of the cars have redline at 4krpm, its power curve will be steeper.

mkoesel wrote

I suppose what it comes down to the fact is that, people care most about how the car feels, not how it actually performs. Low end torque makes a car feel faster, even when it isn't. Similarly having a manual gearbox makes a person feel like they are driving fast, even if they are not.

Agreed.

erhanh wrote

What is a power curve then? Power is hp, right? If so, then the power will increase from 0 (@ 0rpm) to 305hp at redline. Since one of the cars have redline at 4krpm, its power curve will be steeper.

Well, but that still doesn't tell us the shape of the curve.

Also, you didn't say initially that the cars made maximum power at redline. Not all cars do, you know. In fact most don't. The M3 doesn't (though it's close @8300 RPM, IIRC).

mkoesel wrote

Well, but that still doesn't tell us the shape of the curve.

Also, you didn't say initially that the cars made maximum power at redline. Not all cars do, you know. In fact most don't. The M3 doesn't (though it's close @8300 RPM, IIRC).

If the torque is constant, wouldn't the power increase (linearly) all the way to redline and have its max value? Anyways, I made a quick graph of it. No units, so sorry about that.



So again, the cars weigh same, use same tires etc. They have the same gearbox, but the differentials are 2x different (or differentials are same but the gear ratios are 2x different) such that they put the same torque to the wheels.

Are these cars will have the same acceleration?


And yes, you're right that M3 has its max power at 100rpm shy of redline. I believe same was true for S54 engine.

erhanh wrote

If the torque is constant, wouldn't the power increase (linearly) all the way to redline and have its max value?

Actually, yes, that's correct. Power = Torque X RPM / 5252 (when using horsepower and ft-lbs for the units).

So I recalled correctly that power and torque are interrelated earlier, but I forgot that the above formula makes it explicit.

Are these cars will have the same acceleration?

No idea. I'm guessing yes.

mkoesel wrote

No idea. I'm guessing yes.

I'm guessing they'll have same acceleration too, but than the "high revving engine is better because you can take advantage of gearing" argument is gone now...

erhanh wrote

I'm guessing they'll have same acceleration too, but than the "high revving engine is better because you can take advantage of gearing" argument is gone now...

I believe that counter-argument only holds if you have a transmission with zero shift time. Don't quote me on that.