m3 brochure Dyno Graph

[anidjare]

This may have been discussed, but I just picked up the new m3 brochure, and the dyno graph on page 36 shows horsepower and torque crossing over each other at about 3900 rpm.

I always thought that was supposed to occur at the constant of 5252 rpm.

Any thoughts?

[Wads]

are the units in bhp and lb/ft? if not maybe Kw and Nm cross at a different point?

[anidjare]

Originally Posted by Wads

are the units in bhp and lb/ft? if not maybe Kw and Nm cross at a different point?

It was bhp and lb/ft at the crank.

[rai]

as far as I know there is not a place where HP and TQ are supposed to cross each other and in fact there are engines where the HP is never more than the TQ.

[bruce.augenstein@comcast.]

Originally Posted by rai

as far as I know there is not a place where HP and TQ are supposed to cross each other and in fact there are engines where the HP is never more than the TQ.

Horsepower and torque always cross at 5252 rpm. That's because the formula to convert one to the other is (torque X rpm)/5252 = horsepower.

The reason they didn't cross at that point on the graph is that there are two different scales on that graph - one on the right and one on the left, with the bottom scale denoting rpm.

Bruce

[lucid]

The two lines do not really cross. Power and torque are different concepts, and thus have different units (I'm not talking metric vs whatever; torque is force x distance, and power is work per unit time). You can't plot data that are expressed in different units on the same graph. Well, you can to present them together in one chart, but that doesn't really mean anything and what you really have is two seperate overlay graphs with different units, scales, etc.

[swamp2]

Originally Posted by lucid

The two lines do not really cross. Power and torque are different concepts, and thus have different units (I'm not talking metric vs whatever; torque is force x distance, and power is work per unit time). You can't plot data that are expressed in different units on the same graph. Well, you can to present them together in one chart, but that doesn't really mean anything and what you really have is two seperate overlay graphs with different units, scales, etc.

Great explanation. I would add that IF you make the "mistake" of plotting them on the same graph where the height of the hp curve is hp and the height of the torque curve is in ft lb then indeed they will always cross based on the definition as Bruce mentioned.

[rai]

my mistake, I was thinking about some engines that have more TQ than HP and the HP never catches the TQ but then those are engines that don't reach the 5252 rpms

[sayemthree]

I think its good to see them on the same graph- if you keep the engine between the torque peak and the HP peak you will get the best performace. can someone attach a pic of the graph in question?

[oneginee]

As usual you can get the exact answer from me in those things :


for a given torque and RPM we all know :

hp = tq(in lbs.ft)* RPM * 2 PI / 33,000

hp = tq(in lbs.ft) * RPM / 5,252


if you look at the torque characteristic on p 36 the torque scale on the left is compressed by a factor of 2X compared to the hp scale on right (plus they made a typo should read HP not kW)

then on top of that they shifted up the zero references by aligning 10 Nm of torque with 10 hp instead of 0 Nm of torque with 0 hp (you will see by the end of this post what difference it makes)

So if you take the hp scale as the reference and using

1 foot = 0.3048 metres
lb = 0.45359237 kg
g = 9.8 m.s^-2

hp_curve = tq (in N.m) / 0.45359237 / 0.304 / 9.81 * RPM * 2 PI / 33,000

and due to the torque scale compression and offset :

tq_curve = tq (in N.m) / 2 + 10


then finding where torque curve and horsepower curves cross
is done by posing hp_curve = tq_curve and solving for RPM

RPM = (tq / 2 + 10 ) / tq * 0.45359237 * 0.304 * 9.81 / 2 PI * 33,000

or after calculating the constant term :

RPM = (tq / 2 + 10) / tq * 7,105

Surprise ! it is not a constant (like 5252 RPM if they had referenced torque and hp on the same axis and used torque in lbs.ft)
This means the speed (RPM) at which torque and hp curves will cross will BE DEPENDENT on the actual torque curve of the car the data is taken from.

if you put 400 N.m of torque in the equation the result is

speed = (400 / 2 + 10 ) / 400 * 7,105 = 3,730 RPM which is what you get on p 36.


BOTTOM LINE : they can use different scales and offset between the two curves plotted on the same graph to MAKE THEM CROSS WHEREVER THEY CHOOSE. Had they not offset the origin the curve would have crossed at 3,552 RPM and had they not doubled the hp scale the crossing point would have been at 7,105 RPM which may not have looked as good.

good marketing !!

[swamp2]

Originally Posted by oneginee

As usual you can get the exact answer from me in those things...

I beg to disagree. I'd say we get the typically overly complicated and not very useful answer. Bruce and Lucid had it covered 110%. You do like to toot your own horn don't you.

[lucid]

Originally Posted by swamp2

I beg to disagree. I'd say we get the typically overly complicated and not very useful answer.

+1. Honestly, I didn't take the time to read through the algebra, but it sure seems unnecessary.

[anidjare]

Originally Posted by bruce.augenstein@comcast.

Horsepower and torque always cross at 5252 rpm. That's because the formula to convert one to the other is (torque X rpm)/5252 = horsepower.

The reason they didn't cross at that point on the graph is that there are two different scales on that graph - one on the right and one on the left, with the bottom scale denoting rpm.

Bruce

Thanks, not sure how I missed that.

[sayemthree]

can someone link to the graph?

[sayemthree]

found it!

[oneginee]

Originally Posted by swamp2

I beg to disagree. I'd say we get the typically overly complicated and not very useful answer. Bruce and Lucid had it covered 110%. You do like to toot your own horn don't you.

Actually it is straightforward and 100% correct. These mathematical results are not open to discussion. I like to get the right answer rather than listen to a few people (but not all) making half guesses and then think they are entitled to diss hard facts backed by mathematical proof. Sorry pal but if you can't follow move to the right lane.

[swamp2]

Originally Posted by oneginee

Actually it is straightforward and 100% correct. These mathematical results are not open to discussion. I like to get the right answer rather than listen to a few people (but not all) making half guesses and then think they are entitled to diss hard facts backed by mathematical proof. Sorry pal but if you can't follow move to the right lane.

I am not necessarily saying your result was incorrect or "non-mathematical". Just that it was way too complicated and again Lucid and Bruce had it covered 100% with much more brevity and eloquence. Others agreed with me.
P.S. you won't get very far trying to "one up" me on the Math side, one of my degrees is in Math. You are not the only mathematically inclined fellow here.

[oneginee]

Originally Posted by swamp2

I am not necessarily saying your result was incorrect or "non-mathematical". Just that it was way too complicated and again Lucid and Bruce had it covered 100% with much more brevity and eloquence. Others agreed with me.
P.S. you won't get very far trying to "one up" me on the Math side, one of my degrees is in Math. You are not the only mathematically inclined fellow here.

I tend to go into details so that there are no doubts left as to how I come to the results.

P.S. you won't get very far trying to "one up" me on the Math side, one of my degrees is in Math. You are not the only mathematically inclined fellow here.

[lucid]

Originally Posted by oneginee

Actually it is straightforward and 100% correct. These mathematical results are not open to discussion. I like to get the right answer rather than listen to a few people (but not all) making half guesses and then think they are entitled to diss hard facts backed by mathematical proof. Sorry pal but if you can't follow move to the right lane.

I am not trying to flame you, but what exactly did you prove with the algebra? What exactly is "correct" in what you posted?

The relationship between torque and power is carved in stone. The rest is just about how one defines the axis and scales and all that. Plus, all of this is pretty much meaningless for the reasons I explained in my previous post.

[oneginee]

Originally Posted by swamp2

I am not necessarily saying your result was incorrect or "non-mathematical". Just that it was way too complicated and again Lucid and Bruce had it covered 100% with much more brevity and eloquence. Others agreed with me.
P.S. you won't get very far trying to "one up" me on the Math side, one of my degrees is in Math. You are not the only mathematically inclined fellow here.

Yes I tend to go overly into details so that there are no doubts left as to how I come to the results.

P.S. you won't get very far trying to "one up" me on the Math side, one of my degrees is in Math. You are not the only mathematically inclined fellow here.

I went through and graduated from superior and special mathematics classes in France (Math sup/ Math spé). If you do not know about these I suggest you search it. You're quite presomptuous, same comment to you about trying to "one up" me.

[oneginee]

Originally Posted by lucid

I am not trying to flame you, but what exactly did you prove with the algebra? What exactly is "correct" in what you posted?

The relationship between torque and power is carved in stone. The rest is just about how one defines the axis and scales and all that. Plus, all of this is pretty much meaningless for the reasons I explained in my previous post.

I gave a full mathematical answer to the original question that leaves no possible doubt. Yes I read your comment and there is nothing meaningless about superimposing two curves even if using different scales, slope signs and monotonicity are still visible which is usefull to interpret the data.

[gasman]

Originally Posted by swamp2

I beg to disagree. I'd say we get the typically overly complicated and not very useful answer. Bruce and Lucid had it covered 110%. You do like to toot your own horn don't you.

Boy...talk about the pot calling the kettle black!!