[SteveC]

I've had my '09 330D MT since December and have been enormously impressed with its performance, expecially acceleration and overtaking punch

A while ago I had the opportunity to test drive a 635d Sport. The 6 Series is 115kg heavier than my 3 Series, but packs an extra 41hp and 60 Nm of torque, which overall equates to a 0-62 mph of 6.3 seconds.

The performance however feels remarkably different. The 6 is very fast and linear, building speed quickly in a seamless rush. Upshifts are extremely fast, much quicker than can be achieved manually.

By comparison, the 330D has far greater 'punch' and out of the blocks speed. In terms of dynamics, overtaking in the 6 Series is a fairly normal, if very rapid affair, whereas in the 330D you need to make sure you've got enough space ahead when you nail it. In the 0-60 sprint, the 6 Series loses a lot less time shifting gears, but does not equal the in-gear thrust of the 330d.

I was quite surprised by subjectively how much faster the 330d felt, which got me sitting down with the numbers to try and understand why.

First I calculated how much impact weight has on performance (all other factors being equal, which they aren't, but bear with me)

To calculate weight/time, I used a comparison between the 653d and 335d. Same drive train but 70kg weight difference

So 70kg equates to an 0.3 time difference or 0.43sec per 100kg

Next I tried to calculate the effect of horsepower and torque on sprint times

Since its impossible to know their individual contributions, I used the factor of hp + torque. which works reasonably well as long as we're comparing only diesels with very similar power : torque ratios

I compared the 330d with its 245/520 with the 325d's 197/400

The repective weights are 1625 and 1610, which equates to a time correction of 0.065 seconds

So the 330d's power factor is 765 while the 325d punches out 597, a difference of 168

With a weight corrected time difference of 1.34 seconds this translates into a power/time factor of 0.008 seconds per hp+torque unit

Next I tried to understand the contribution of Efficient Dynamics. For this I needed to compare 2 cars, one with Efficient Dynamics, the other without. The 330d and 335d work nicely

The 330d Auto does 0-60 in 6.2 seconds, while the '35d is 0.2 seconds quicker.

Weight difference is 30kgs in favour of the '30d, which translates to 0.129 seconds.

Power factors are 765 for the '30d and 866 for the '35d, a difference of 101which translates to a theoretical time of 0.81 seconds

Subtract the weight difference advantage and the difference becomes 0.68 secs.

If we then subtract the actual difference of 0.2 seconds, what we are (theoretically) left with is the difference attributable to efficient dynamics; 0.48 seconds

If we then express that time difference in terms of power factor, it comes to 60 (hp + torque)

If we then divide the power factor by the '30d's hp:torque ratio, we get a factor of 1:2.12, which gives the equivalent of 19.23hp and 40.77 Nm Torque.

In terms of Efficient Dynamics, what we can say is that the 330d is 8% more efficient at delivering its 245 flywheel horsepower and 520Nm of torque to the rear wheels, compared to the 635d and 335d. This almost exactly agrees with increases in fuel efficiency and explains why 0-60 times are almost the same even though the 330d has less flywheel hp and torque.

Take into account the 7% weight advantage, 8% better power efficiency and lack of torque convertor vs. the 635d and its easy to understand why the 330d MT feels subjectively quite a bit faster.

[hmi1750]

wow! excellent analysis...

[dagjohnsen]

Very impresive indeed!!!

Saw you commented in my thread re. new 330d vs 335d, seems like 330d is the way to go these days.

I have a e92 325d manual. 1590 kilos. Dynoed 245 rear wheel horsepower on a dynojet dyno. (if the drivetrain powerloss is 15% it should equal 288 hp)
I calculated peak torque 660 NM @ 2800 rpm.

My car does not have Efficient Dynamics.

How would that leave my car compared to the new 330d?

My math is not like yours, so if you could do the math it would be great.

Best regards
Dag Johnsen

[SteveC]

Originally Posted by dagjohnsen

Very impresive indeed!!!

Saw you commented in my thread re. new 330d vs 335d, seems like 330d is the way to go these days.

I have a e92 325d manual. 1590 kilos. Dynoed 245 rear wheel horsepower on a dynojet dyno. (if the drivetrain powerloss is 15% it should equal 288 hp)
I calculated peak torque 660 NM @ 2800 rpm.

My car does not have Efficient Dynamics.

How would that leave my car compared to the new 330d?

My math is not like yours, so if you could do the math it would be great.

Best regards
Dag Johnsen

According to your calculations, your car makes almost the same bhp as a 335d, makes 80 nm more torque and weighs 65kg less

Using those numbers, your car's weight advantage should be worth around 0.28 sec and its extra power and torque about 0.66 secs. which means that in theory your car should be nearly 1 second faster than a stock 335d in the 0-60 sprint

While this is unlikely due to traction issues (with 660nm of torque), your car should be blisteringly quick over the 50-80mph sprint

If we compare the bhp:torque ratios of the 335d and 330d you get 1:2.03 and 1:2.12 respectively so I believe your calculated torque at 660nm (1:2.29) may be a little high and is probably more realistically somewhere around 590nm, which would still make your car around 0.3 -0.4 seconds quicker than a stock 335d due to similar poke and less pork

Of course we're comparing tuned vs. stock. Remap a '35d and you're back in the weeds again

In summary, a 330d is not going to feel as fast as your car and you'd need to have it remapped to get slightly superior performance

[NFS]

It's an interesting question, but I really don't see the relevance of any analysis based on adding peak torque and horsepower figures together. Unfortunately that data is pretty much meaningless as a way of understanding relative differences in performance.

[SteveC]

Originally Posted by NFS

It's an interesting question, but I really don't see the relevance of any analysis based on adding peak torque and horsepower figures together. Unfortunately that data is pretty much meaningless as a way of understanding relative differences in performance.

Using published statistics, there is no easy way to calculate how BHP and Torque values individually contribute to 0-60 performance values.

However, for 2 similar cars, where their ratios of BHP:Nm are within 5% of one another (for example 330D and 335D), then summing and correlating the sum with weight corrected acceleration performance is reasonably valid, all other things being equal.

I agree that the sum of BHP and Torque would be meaningless in comparing say a 335d with a 335i, since their BHP:Nm ratios are altogether different

Using the above calculation returned a value of 8% increased efficiency for the 330d's EfficientDynamics which just happened to exactly equal its fuel efficiency gains, which is what you'd expect. Hardly 'case proven' but a reasonable indication that we're on the right track.

In this end, this is not supposed to be serious maths, just an amusing way of trying to compare 2 similar cars using a limited number of published specs.

[dagjohnsen]

Originally Posted by SteveC

According to your calculations, your car makes almost the same bhp as a 335d, makes 80 nm more torque and weighs 65kg less

Using those numbers, your car's weight advantage should be worth around 0.28 sec and its extra power and torque about 0.66 secs. which means that in theory your car should be nearly 1 second faster than a stock 335d in the 0-60 sprint

While this is unlikely due to traction issues (with 660nm of torque), your car should be blisteringly quick over the 50-80mph sprint

If we compare the bhp:torque ratios of the 335d and 330d you get 1:2.03 and 1:2.12 respectively so I believe your calculated torque at 660nm (1:2.29) may be a little high and is probably more realistically somewhere around 590nm, which would still make your car around 0.3 -0.4 seconds quicker than a stock 335d due to similar poke and less pork

Of course we're comparing tuned vs. stock. Remap a '35d and you're back in the weeds again

In summary, a 330d is not going to feel as fast as your car and you'd need to have it remapped to get slightly superior performance

I think a standard 335d dynos around 255-260 at the wheels and that equals around 313 hp with a 18% drivetrainloss. The torque is probably higher than stated as well so I think my car will be slightly slower than a standard 335d. Its difficult to shift as fast as that autobox.....wonder how the new 330d will do on a dyno, my guess is that it has some serious power when measured

Thank you very much for your calculations, its higly appreachiated!

I did calculate the torque from the reading I see on the dynograph, a certain horsepower at a given rpm gives you the torque.
But if the dynojet measures a little optimistic numbers then horsepower and torque could be a little less than it seems. 13% drivetrainloss is probably more correct on a manual BMW than the 15% that ESS is using, but its quite close anyway
actually I would prefer less torque to have a more progressive powerdelivery, but I guess I have to live with it
the 50-80 is very imressive indeed

[NFS]

Originally Posted by SteveC

Using published statistics, there is no easy way to calculate how BHP and Torque values individually contribute to 0-60 performance values.

However, for 2 similar cars, where their ratios of BHP:Nm are within 5% of one another (for example 330D and 335D), then summing and correlating the sum with weight corrected acceleration performance is reasonably valid, all other things being equal.

I agree that the sum of BHP and Torque would be meaningless in comparing say a 335d with a 335i, since their BHP:Nm ratios are altogether different

Using the above calculation returned a value of 8% increased efficiency for the 330d's EfficientDynamics which just happened to exactly equal its fuel efficiency gains, which is what you'd expect. Hardly 'case proven' but a reasonable indication that we're on the right track.

In this end, this is not supposed to be serious maths, just an amusing way of trying to compare 2 similar cars using a limited number of published specs.

The torque and BHP figures you are summing are peak only. What matters is the torque curve through the rev range.

More fundamentally summing BHP and torque at all just doesn't make sense. The ratio of peak torque to peak HP is equally meaningless.

As an analogy you may as well try adding length and volume together to create a 'size index'. It doesn't give you anything meaningful, because the numbers are not relevant to each other and the data that would actually provide some answers is not there.

If you seriously want to understand the relative acceleration characteristics of both cars you need to know:

1. Torque at the wheels throughout the rev range (i.e. engine torque x gearing less transmission losses).

2. Drag coefficient

3. Weight

The data is available for both cars, you'd just need to dig around to find it. Playing around with a programme like this one might then provide some useful insight into the differences that you have observed in test drives.

http://vlsicad.ucsd.edu/~sharma/Potpourri/perf_est.html

[dagjohnsen]

Originally Posted by NFS

The torque and BHP figures you are summing are peak only. What matters is the torque curve through the rev range.

More fundamentally summing BHP and torque at all just doesn't make sense. The ratio of peak torque to peak HP is equally meaningless.

As an analogy you may as well try adding length and volume together to create a 'size index'. It doesn't give you anything meaningful, because the numbers are not relevant to each other and the data that would actually provide some answers is not there.

If you seriously want to understand the relative acceleration characteristics of both cars you need to know:

1. Torque at the wheels throughout the rev range (i.e. engine torque x gearing less transmission losses).

2. Drag coefficient

3. Weight

The data is available for both cars, you'd just need to dig around to find it. Playing around with a programme like this one might then provide some useful insight into the differences that you have observed in test drives.

http://vlsicad.ucsd.edu/~sharma/Potpourri/perf_est.html

SteveC is right when he says you can use this to compare similar BMW cars with turbo diesel engines. They will have torque and hp curves quite similar.

Nobody said this is accurate, but a tool to do a quick comparison easily.

I agree that the peak numbers can be misleading due to very different powercurves on different engines.

[PhilR]

Originally Posted by SteveC

I've had my '09 330D MT since December and have been enormously impressed with its performance, expecially acceleration and overtaking punch

A while ago I had the opportunity to test drive a 635d Sport. The 6 Series is 115kg heavier than my 3 Series, but packs an extra 41hp and 60 Nm of torque, which overall equates to a 0-62 mph of 6.3 seconds.

The performance however feels remarkably different. The 6 is very fast and linear, building speed quickly in a seamless rush. Upshifts are extremely fast, much quicker than can be achieved manually.

By comparison, the 330D has far greater 'punch' and out of the blocks speed. In terms of dynamics, overtaking in the 6 Series is a fairly normal, if very rapid affair, whereas in the 330D you need to make sure you've got enough space ahead when you nail it. In the 0-60 sprint, the 6 Series loses a lot less time shifting gears, but does not equal the in-gear thrust of the 330d.

I was quite surprised by subjectively how much faster the 330d felt, which got me sitting down with the numbers to try and understand why.

First I calculated how much impact weight has on performance (all other factors being equal, which they aren't, but bear with me)

To calculate weight/time, I used a comparison between the 653d and 335d. Same drive train but 70kg weight difference

So 70kg equates to an 0.3 time difference or 0.43sec per 100kg

Next I tried to calculate the effect of horsepower and torque on sprint times

Since its impossible to know their individual contributions, I used the factor of hp + torque. which works reasonably well as long as we're comparing only diesels with very similar power : torque ratios

I compared the 330d with its 245/520 with the 325d's 197/400

The repective weights are 1625 and 1610, which equates to a time correction of 0.065 seconds

So the 330d's power factor is 765 while the 325d punches out 597, a difference of 168

With a weight corrected time difference of 1.34 seconds this translates into a power/time factor of 0.008 seconds per hp+torque unit

Next I tried to understand the contribution of Efficient Dynamics. For this I needed to compare 2 cars, one with Efficient Dynamics, the other without. The 330d and 335d work nicely

The 330d Auto does 0-60 in 6.2 seconds, while the '35d is 0.2 seconds quicker.

Weight difference is 30kgs in favour of the '30d, which translates to 0.129 seconds.

Power factors are 765 for the '30d and 866 for the '35d, a difference of 101which translates to a theoretical time of 0.81 seconds

Subtract the weight difference advantage and the difference becomes 0.68 secs.

If we then subtract the actual difference of 0.2 seconds, what we are (theoretically) left with is the difference attributable to efficient dynamics; 0.48 seconds

If we then express that time difference in terms of power factor, it comes to 60 (hp + torque)

If we then divide the power factor by the '30d's hp:torque ratio, we get a factor of 1:2.12, which gives the equivalent of 19.23hp and 40.77 Nm Torque.

In terms of Efficient Dynamics, what we can say is that the 330d is 8% more efficient at delivering its 245 flywheel horsepower and 520Nm of torque to the rear wheels, compared to the 635d and 335d. This almost exactly agrees with increases in fuel efficiency and explains why 0-60 times are almost the same even though the 330d has less flywheel hp and torque.

Take into account the 7% weight advantage, 8% better power efficiency and lack of torque convertor vs. the 635d and its easy to understand why the 330d MT feels subjectively quite a bit faster.

You have not considered the effect the added weight of your Anorak in the boot has on your calculations........

[NFS]

Originally Posted by dagjohnsen

SteveC is right when he says you can use this to compare similar BMW cars with turbo diesel engines. They will have torque and hp curves quite similar.

Nobody said this is accurate, but a tool to do a quick comparison easily.

I agree that the peak numbers can be misleading due to very different powercurves on different engines.

Do they have the same gearing though?

And how similar are the torque curves?

Plus (and this is a BIG point) the 635d is an auto and the 330d is a manual, which will make the transmission loss quite different.

What you could do is this:

330d auto saloon: 1625kg, 0-62: 6.2 Secs: Peak Torque: 520nm

Peak Torque Per KG = 0.320

635d sport coupe: 1725kg, 0-62: 6.3 Secs: Peak Torque: 580nm

Peak Torque Per KG = 0.336

330d has 1.8% less torque per KG but is 1.6% quicker from 0-62 mph

This does suggests that the 330d is able to make very slightly better use of it's engine power. Possible explanations are:

1. Torque curve differences
2. Less drivetrain loss
3. Co-efficient of drag
4. Rolling resistance of tyres
5. Gearing differences

[SteveC]

Originally Posted by NFS

The torque and BHP figures you are summing are peak only. What matters is the torque curve through the rev range.

More fundamentally summing BHP and torque at all just doesn't make sense. The ratio of peak torque to peak HP is equally meaningless.

As an analogy you may as well try adding length and volume together to create a 'size index'. It doesn't give you anything meaningful, because the numbers are not relevant to each other and the data that would actually provide some answers is not there.

If you seriously want to understand the relative acceleration characteristics of both cars you need to know:

1. Torque at the wheels throughout the rev range (i.e. engine torque x gearing less transmission losses).

2. Drag coefficient

3. Weight

The data is available for both cars, you'd just need to dig around to find it. Playing around with a programme like this one might then provide some useful insight into the differences that you have observed in test drives.

http://vlsicad.ucsd.edu/~sharma/Potpourri/perf_est.html

I essence, you are correct, when you want to compare different model cars; however:

1. read my last sentence
2. When the bhp:torque ratios of 2 cars are very similar, it is perfectly valid to sum them for comparative purposes
3. When transmission losses and drag coefficients are the same or vary within an acceptable margin of error, they don't need to be considered, since they cancel each other
4. Lets use your analogy of length and volume:

Take 2 boxes with the same ratio of length to volume. Lets say the ratio is 1:5

All you now need is the length or volume of each box.

Lets say that box 1 has a length of 2 and box 2 is 6 long

Based on the L:V ratio of 5, box 1 would have a volume of 10 and box 2 would have a ratio of 30

Using LxWxD for box 1, WxD = 5
On box 2, WxD = 5

Take 2 different boxes with volumes of 25 and 45

box 1 would have a length of 5 and box 2's length would = 9

WxD of box 1 = 5
WxD of box 2 = 5

Take another 2 boxes with volumes of 75 and 85
L Box 1 = 15
L Box 2 = 17

WxD box 1 = 75/15 = 5
WxD box 2 = 85/17 = 5

Now let's use size index and L:V to calculate Length and Volume

Lets say box 1 has a Size Index of 12, while box 2 has a SI of 42

Our L:V ratio is 1:5

so if we divide both SI's by 6 we get 2 and 7

Applying the same ratio, we can say that
for box 1 L= 2 and V=10
for box 2 L=7 and V=35

The point is, as long as you are comparing very similar cars with the same body and very similar drive trains and torque curves, most potential variables can be ignored because they are within an acceptable margin of error and therefore cancel each other

This is why you can use my formula to compare various diesel models within the same series. However the same formula is useless in comparing say petrol and diesel models because their bhp:torque ratios are so different.

[NFS]

Originally Posted by SteveC

When the bhp:torque ratios of 2 cars are very similar, it is perfectly valid to sum them for comparative purposes

By all means compare peak torque / weight for each car AND peak HP / weight for each car.

However, I still feel that adding peak torque and peak hp together or considering them as a ratio just isn't meaningful.

Anyway ... if it makes you happy then fair enough.

[SteveC]

Originally Posted by PhilR

You have not considered the effect the added weight of your Anorak in the boot has on your calculations........

Damn, I knew I was missing something!

[SteveC]

Let me try once more to illustate the mathematical logic of what I'm saying

HP and Torque are related to one another

1 HP = 33,000 foot-pounds of work per minute

HP = Torque x RPM/5252 (5252 is derived by dividing 33,000 by 2xPi)

When you compare 2 values mathematically you typically express 1 as a value of the other i.e as a fraction or a ratio

For example is we compare 2 numbers with one another, say 1 & 6 we can say that the first number is 1/6th of the 2nd number or that the 2 numbers have a ratio of 1:6
Following on, when 2 numbers are the same, say 6 & 6 we can say that the first number equals the second number 1/1 = 1 or that they have a ratio of 1:1

Now lets use that same logic to compare BHP and Torque

Lets say that 1 BHP contributes x to acceleration and torque y

Now take 2 cars, one with 250 HP and 400 ft lbs and the other with 350 HP and 560 ft lbs of torque.

In terms of acceleration, car 1 would have 250x and 400y while car 2 would have 350x and 560y

The ratio of HP:Torque in car 1 is 1:1.6 and in car 2 is 1:1.6

If we compare the ratios, we get 1:1.6/1:1.6 = 1

The relationship of BHP to Torque in car 1 is the same as in car 2

This means that the influence of x and y in car 1 is the same as x and y in car 2 so the 2 expressions cancel, leaving only 250 and 400 in car 1 and 350 and 560 in car 2

To represent and compare the total accelerative forces of each car I can now simply sum the numbers i.e 650 and 910 and call them something like acceleration units

When car 1 accelerates from 0-60 in 6 seconds and car 2 in 5 seconds, all other things being equal (or within acceptable limits of error) I can directly equate the difference in acceleration time with the difference in the 2 car's acceleration units, namely 1 second = 260 au

Lets now say that I make a change to car 1, for example by adding Efficient Dynamics that makes it faster by 0.3 seconds
I can now say that 0.3 seconds = 78 au
and using the ratio 1:1:6 I can now assign equivalent BHP and Torque values to say that Efficient Dynamics is the equivalent of adding 30bhp and 48 ft lbs

Anyway, this started as a fun little exercise to evaluate Efficient Dynamics, so let's move on

[NFS]

Originally Posted by SteveC

Let me try once more to illustate the mathematical logic of what I'm saying

Surely the mathematical relationship between peak BHP and peak torque for a given car is simply going to be determined by the engine speeds at which those peak values are achieved?

Since the engine speed for peak torque is not always the same as for peak HP in the end any differences in this 'ratio' just reflect the fact that there are unknown variables. Beyond that I can't see how it means anything?

As to your mathmatical explanation .. it looks to me as if you are ignoring the fact that peak torque and peak HP don't occur at the same time.

[SteveC]

Originally Posted by NFS

Surely the mathematical relationship between peak BHP and peak torque for a given car is simply going to be determined by the engine speeds at which those peak values are achieved?

Since the engine speed for peak torque is not always the same as for peak HP in the end any differences in this 'ratio' just reflect the fact that there are unknown variables. Beyond that I can't see how it means anything?

As to your mathmatical explanation .. it looks to me as if you are ignoring the fact that peak torque and peak HP don't occur at the same time.

Hi there,

Firstly its important to appreciate that we're not trying to come up with a mathematical model for comparing any 2 model of cars. Only those with very similar BHP:Torque ratios, where all other variables like drag, drive train losses etc are also alkmost identical (since they are not considered. The only other variable we consider is weight, because that has a fairly substantial input

Second.....acceleration is a function of the torque and HP curves, as you rightly stated somewhere else. All we are trying to do here is correlate their peak values with the 0-60 sprint, which we can do when the curves are very similar, which they are in this case

Third....in most cases a 0-60 sprint will be performed by taking the car close to redline. That's because the torque and HP at redline are higher than they would be compared to their values after shifting gear

Four...the torque and HP curves for the cars under comparison are very close. Peak torques rpm are within 8% of one another and peak HP within 13%

That small shift of peak location within the rev range is insignificant for the purpose of this exercise

The point you seem to be missing is that this very simple (and simplistic) calculation only works for very similar engines, where you can afford to ignore most of the variable you are worrying about due to the fact that they are so similar their difference falls within acceptable error limits

[NFS]

Steve - I do understand your points. I just don't think that this tells you anything useful about performance of different cars.

Clearly you've thought it through and are aware of the limitations of the approach you've taken. So if it works for you then great!