A topic covered before, but clearly worth covering again…

The author: Georg Kacher, seasoned European bureau chief for Automobile (i.e. not a newb)

The place: page 31, April 2012 issue

The car: Bentley Continental GT V8

The statement: “Alternatively, you can work the shift paddles to keep the engine revving between 4000 and 6300 rpm, where the power and torque curves approach, intersect, and then run almost parallel to the limiter.”

The torque curve and horsepower curve cannot be parallel. If the torque curve is flat across, then the horsepower curve would be a linear line going up.

Are you suggesting that there is some inherent relationship between the two curves, of which Mr. Kacher seems unaware?

In hp and lb-ft,

power = torque*revs/5252

So power can not be parallel to torque when shown against revs. The two are measured in different units, so the point where they intersect is dependent on the scales used to plot.

This. Power is the product of torque and angular velocity, i.e. P = T * RPM *2pi. So if the torque curve is a straight line (regardless of whether its flat), HP should be linearly increasing along the x (RPM) axis.

Torque is the measured value. Horsepower is calculated by the equation [email protected] wrote.

Whether the biggest V16 or the smallest 1 cylinder, Torque in Ft-Lb. is always precisely equal to HP at 5,252 RPM (assuming the engine can rev that high!)

Yes, they can be parallel–if the engine is off.

But a bit of calculus also shows they can be parallel in a non-trivial case as well:

torque curve = f

slope of torque curve = d/dx(f) = f’

power curve = x/5252*f

slope of power curve = d/dx(x/5252*f) = (x*f’ + f)/5252

Thus, they are parallel when f’ = (x*f’ + f)/5252

If we make a up a torque curve, e.g., f = -8/10^6 * (x – 3000)^2 + 200, then we see the torque curve and the power curve are parallel at 6733 rpm. (In this case, they are also parallel at 768 rpm, but that’s obviously not the point we want.)

The lesson here is that when the torque is falling (f’ < 0), the quantity x*f' can be very negative, which also makes the slope of the power curve ((x*f' + f)/5252) negative & potentially parallel.

Beyond trivial, for two reasons:

1. “Parallel” is generally understood to mean that that the lines have the same slope along a non-trivial number of consecutive points, and not just a single point.

2. The points determined by your math are both outside the normal operating range of the engine (which redlines at 6,300).

The curve I made up is made up. (That’s why I said: “If we make a(sic) up a torque curve …”) The math merely represents that it can/does happen. If you’d like to see them parallel at 6000 rpm, that’s hardly a problem; I can make that up, too.

The text “run almost parallel to the limiter” pretty much describes what the made up curve generates to a tee: two curves that run almost parallel to each other (with equal slopes at one point) after the power peak.

Edit: Here’s the plot:

http://i1127.photobucket.com/albums/l634/phytheaux/torque-power.png

Torque is not a mathematical function, it is the force produce by the expansion of burning gases in the cylinder, minus friction. This is determined by the volumetric and combustion efficiency of the engine. Horsepower will rise with rpm until torque is dropping faster than rpm is rising (in terms of proportions).

Parallel does not necessarily mean flat.

No, parallel means they have the same slope. It is impossible because horsepower is a function of torque and time. HP = (torque*RPM)/5252 ergo, any increase in torque will yield a greater increase in power, producing a greater slop for the horsepower curve.

He’s describing the curves along then after the torque peak, and over most of this range the HP curve slopes slightly upward while the torque curve is initially flat then slopes downward. I have’t seen the curves, but from the released figures we can calculate:

4000 RPM: 371 HP, 487 lb-ft

5000 RPM: 463 HP, 487 lb-ft

6000 RPM: 500 HP, 416 lb-ft

Sigh. Playing fast and loose with engineering concepts isn’t exactly rare on the interwebs. On the plus side, it’s a great opportunity for an editor to demonstrate that they don’t know what they’re talking about.

But this is a print magazine. You can’t lie in print.

I don’t think anyone was lying. Nor were they fact checking.

I suppose technically it’s incorrect, but I kind of get the gist of what he is trying to say. To that end if I ever get a chance to drive this car I’ll be sure to keep the revs up!

“the gist of what he is trying to say” is that he has a basic (and rather embarrassing, given his position) misunderstanding of power and torque and how motors produce useful work.

I think that this quote is talking about the old and new engines available in the GT. He is saying that the torque, and also the HP curve of the old and new engines are very similar from 4000rpm to the top. I believe that he is justifying them putting a smaller engine in the car, saying that you can achieve the same performance if you keep the revs up.

Kacher’s comment about “where the power and torque curves approach [and] intersect” is meaningless. Power and torque have different units and are therefore plotted on different y-axes. You can draw them to intersect anywhere you want.

He should know better. I would hope that DEDjr would have caught this error.

Well. Obviously he is not LJK Setright or Karl Ludvigsen. He could, however, be a professional journalist. And thus is ignorant about almost everything.

http://image.automobilemag.com/f/6710880+w750+st0/0610_z+2007_mazdaspeed_3+dyno_chart.jpg

http://www.atpturbo.com/root/releases/images/release112606/mazdaspeed6_dyno1.gif

Take the derivative of p. Take the derivative of t. 0 = p’ – t’

That will tell you where the slopes are equal. You’ll need a mathematician to do the work for you, and an engineer to tell you if the equation is even relevant to production ICEs. The pictures indicate it possible solutions may be production relevant.

If Kacher is wrong, he’s made an inaccurate description of the actual dynograph. Neither math nor engineering appear to exclude the description he gave.

The first chart uses two different y axes, so it’s not relevant.

What we’re seeing with the second chart (which is of essentially the same Mazda 2.3T engine) is that, well after the power peak, the curves will become somewhat parallel. This is also the case at low rpm.

What’s happening? At the extremes the two curves are still necessarily changing at different rates, but this rate is a percentage of a different absolute figure. The differences in the absolute figures and the rates of change can cancel out when both curves are increasing and when both are decreasing. So at low rpm and again well after the power peak. Put another way, a smaller percentage of a larger figure can be equal to a larger percentage of a smaller figure.

Yet this won’t be the case along the range Kacher mentions, because the bulk of this range is between the two peaks, where hp is increasing while torque is falling. And the redline is only 300 rpm after the power peak.

Even where the lines do run parallel this is an arbitrary product of the arbitrary formulas for power and torque. Use kw and nM, but keep the same scale for both, and you’ll have much different slopes to the curves.

In short, even if Kacher’s description were accurate–and it isn’t–then it would be meaningless.

“The first chart uses two different y axes, so it’s not relevant.” — Uh, as you yourself (weren’t you among them?) have pointed out, torque and power are measured in different units, so they HAVE TO use different scales along the Y axis — so how can THAT in and of itself disqualify any particular graph?

I was told that wasn’t going to be any math.

Somebody lied.

Gah, that quote reminds me of the Springfield Civil war reenactment from the Simpsons, commemorating the time they fought for, against and beside the Union.

Kacher has been writing for decades for CAR and Automobile, and probably has as much seat time in high end cars as anyone in the biz. Best English writing German auto journalist. Damn fine review, I thought and gets right to the point with experience the usual auto journo cannot match. So he says what he feels I’ve always thought. If you haven’t read him over the last 20 years or so, then your experience of car reviewing is too limited.

In his mind’s eye, no doubt he knows what he’s nattering about, so maybe he’s got this screwed up, who knows. It’s a bit much musing about this when TTAC is rife with missing words, spelling errors and incorrect usage of apostrophe’s virtually every day! And where Kriendler’s road tests of Hyundais in Nevada no longer follow the “established” TTAC policy of revealing who paid for the junket, and what was received for free, you know to keep the great unwashed informed about who’s dishing out the freebies looking for favors, wind noise be damned.

People in glass houses ….. etc.

That’s nice and all but the point is this –

Do you want to take car advice from someone who

a) knows how torque and horsepower are related but occasionally places an errant apostrophe.

b) doesn’t know how torque and horsepower are related but has Strunk memorized.

I’ll take a.

I’m well aware of Kacher’s experience, hence my surprise at this brainfart.

The print magazines typically run everything through multiple proofreaders–a luxury those of us with lower budgets and multiple responsibilities cannot afford. Kacher’s brainfart slipped past all of them.

I still remember the piece Georg Kacher wrote for Automobile Magazine about the then-new Jaguar XJ40. Best car in the world, he called it, and it was in the same issue with a thorough introduction to the also-new BMW E32 735i, a car which had at least a claim to consideration for best car in the world of 1986. In other words, people who are still taking him seriously 25 years later aren’t paying enough attention.