Area under the curve

When I read about different engines it is always about peak power. 
 

Then when reading about having a good engine it is mentioned that more important that peak power is the "area under the curve" which make sense to me. 
 

Is there any actual measure of area under the curve or rule of thumb? As in a V8 will always have more area under the curve than a turbo 4? 
 

I was comparing these two charts. 

Generally it is torque and where and when and how flat the curve is what defines a good motor or a motors character under the HP curve. 

Somebeach (Forum Supporter) said:

Is there any actual measure of area under the curve or rule of thumb? As in a V8 will always have more area under the curve than a turbo 4? 

How much of the curve do you care about?  Is this a street car where you're expecting to pull away from lights and pass people on the freeway in top gear, or a road race car where you're just looking at the area above the points where it drops to when shifting at redline?  In the latter case it doesn't just depend on the power curve, it also depends on the gear ratios in the transmission.

In the case of the road race car I'm not actually sure it matters that much.  Even the peakiest cars around usually have a torque plateau a few thousand RPM wide at the top end, so as long as the gear ratios are chosen properly it's not going to drop out of that band if you're driving it right.

In the case of a street car, the two numbers peak torque and peak hp will usually tell you the character of the motor.  The use case is going to vary too much for a complex integration of the torque curve defined between arbitrarily-chosen RPM to be meaningful, so the "character" is all you really need.

In calculus, the area under the curve is calculated via "integration". One could do the same for a torque curve, to come up with a comparison but it's still only measuring total area, but the shape of the curve is really probably more important.

In reply to codrus (Forum Supporter) :

It was more of a learning question than a specific application, all that info helps  thanks. I didn't even really think about the transmission playing a big role. 

So here are some numbers to illustrate the issue:

The A15 motor in my Datsun 1200 makes 99whp at 8000 RPM, at 6500 it makes 95hp BUT at 6000 it drops to 88 and by 5300 it drops to 78.

The gearbox (out of a street 210) drops 2900 RPM on the 2/3 shift, 2200 on the 3/4 shift and 1500 on the 4/5 shift (note I don't use 5th) I upshift at 8200RPM.

I lose 20hp on the 2/3 shift.  There is a close ratio gearbox for the car but they are fragile.

My fastest lap at home home track is actually with the wide ratio gearbox; due to the fact that I make fewer shifts per lap.

In my case it would very likely be worth giving up some horsepower in an effort to get a wider powerband. Say if I could get the motor to make 90hp between 5000 & 8200 RPM.

The short answer is yes, the measure of area under the curve is called the integral.  It isn't published though.  

I think it's really important. Even when road racing, if you have a narrow powerband you cannot afford any mistakes. Someone makes a move on you in a corner, you have to drop the throttle and you fall off the power. Or something goes wrong - on the competition debut of the NC Miata, we discovered the gearboxes had a lifespan of 200 laps before the 3-4 shift fork would break. Our drivers had to drive with a minimum number of shifts, and the flexibility of the engine made that possible. Our fastest lap of the race was done with just two gear changes :)

One of our old dynos would pop out data in a very useful format, I was always planning to create an "area under the curve" calculation from it. But everyone knows peak horsepower, so that's what everyone concentrates on. Just like 0-60 is given priority over 30-70 even though the latter is a lot more useful.

Here's an extreme illustration of area under the curve. Very similar peak power levels. One is my car with a 6.2l LS3, the other is a boosted 2.0. 

This is why I loved my old big block forte. Power under the curve? Yes. All of it. 

I'll leave here the comment that a lot of engines have redline too close to the power peak.

You want your time in gear to bracket peak power, not end at it.  With a wide ratio trans you may want to go 1500 or more RPM past power peak.

For an example, look at the 2.0l power curve posted above.  Looks like it ends at 7750rpm or so, at which point it is making about the same power as at 5000.  If the trans ratios drop you to lower than 5000rpm after shifting at 7750, you need to shift later, otherwise you are not maximizing your average horsepower.

I think that's what I didn't like about the centrifugal SC on track - every shift had to be right at the rev limiter because that's where the peak was. Every rpm below that was a decrease in power, so a little lift meant you had to downshift to hopefully end up right at the redline again. I was spending a lot of time managing the power delivery instead of the rest of the car.

Somebeach (Forum Supporter) said:

In reply to codrus (Forum Supporter) :

It was more of a learning question than a specific application, all that info helps  thanks. I didn't even really think about the transmission playing a big role. 

 

It's not only the transmission ratios but also the final drive ratios and tire size. 
    Both for the road and in racing.  Serious racers use transmissions that are easy to change gear ratios's. As well as quick change final drive ratios. When combined with tire diameter every corner can be accounted for. 
    On the road a broader torque band feels more comfortable  and peak power is just for bragging rights.  While a smaller more nimble car feels best with a more narrow and "peaky" power band. Allowing the driver to feel more engaged with the driving experiance. 

I've long been an advocate of the theory that HP sells vehicles while torque wins races. Narrow power bands can be great if you're an expert on the right track (i.e. no chicanes). Otherwise wide power bands are what I'd lean too.

So for fun I will relate this from my days of racing a 125cc GP bike.

Coming off of turn 9 at Willow Springs I ever so slightly bobbled a shift, thought nothing of it until I looked at the lap chart, that lap was .5 slower than all of the others. A 1500 RPM wide powerband is not ideal but when trying to get 30+ horsepower out of 7.5 cubic inches it's inevitable.

Other advantages of not having to rev the nuts off the motor are fewer shifts and the car being far less pitch sensitive when you are on and off the throttle.

I will always remember this wannabe youtuber that was spamming his videos and posts on a local facebook page about his big turbo Supra being fast yet losing to everyone. They dynoed it and his area under the curve was awful, while his car made like 700+ WHP, he only made like 300 or so at around 6000 rpm, then it didn't make peak power until around 8000 RPM lol.

Tom1200 said:

So for fun I will relate this from my days of racing a 125cc GP bike.

Coming off of turn 9 at Willow Springs I ever so slightly bobbled a shift, thought nothing of it until I looked at the lap chart, that lap was .5 slower than all of the others. A 1500 RPM wide powerband is not ideal but when trying to get 30+ horsepower out of 7.5 cubic inches it's inevitable.

Other advantages of not having to rev the nuts off the motor are fewer shifts and the car being far less pitch sensitive when you are on and off the throttle.

 

This is one place why rotaries had traditionally been able to punch above their weight.  Sure if you just looked at PEAK numbers, on a well built engine, peak torque would be like 7000 and peak horsepower around 8000.

But, it would make 90% of peak torque down to around 2500, and the power fell off very gradually.  The actual driving experience is just a big, fat, broad plateau.  They don't "feel" fast because there are no surging rushes.  You could simply avoid a short-lived downshift or upshift and be just as well off.  Maybe even better, because shifting costs acceleration.

Several years ago, I had a conversation with our favorite dyno tuner (hi, Ed) about this very topic. More area under the curve, generally, is good.

But how would you turn that into some kind of universal metric? That's the trick. Let's say that your car redlines at 7000 rpm, so maybe you'd measure the area of the curve between 1000 and 7500 rpm. You could use that a tuning tool: Did your latest change make more or less power under the curve? (Or you could measure between 800 and 8100 rpm--whatever works for you.)

The trick would be coming up with a universal formula that would allow people to compare engines: Where, basically, do you start measuring? 

In reply to David S. Wallens :

Quarter mile times?

Another interesting metric is WRC.  Take a Subaru STi.  The WRCar made about 330-340hp, the street car (with a 2.5l) made 300 peak.  However, the WRC would be MUCH quicker in the quarter mile, IIRC mid-11s.  That is because they made 340hp peak, but they made 340hp everywhere.  The restrictor limited airflow, but (at the time) boost was unlimited, so they'd make around 25-30psi at low RPM and taper to about 7psi at redline.  So the horsepower was pretty flat but the torque was enormous, like 450-500ft-lb at peak.

It's still horsepower that accelerates you, it is ALWAYS horsepower that accelerates you.   The torque peak RPM/level can HELP you correlate powerband width, but not always. 

Another thought that may answer your question some:  Look into the formula that the Engine Masters competition does.  They do look at average horsepower over a certain powerband width, so you can't build a high RPM hero engine and claim dyno queen prize.  That may be a better metric, because that Supra engine could probably belt out some good quarter mile times if it was paired to an automatic trans with a well matched converter.  Basically it would be driving on the converter all the time except right before a shift.

I don't think there is a right answer.  The best thing to do is real world testing, or a focused analysis for that application.  I tend to math out various powerbands w/ the vehicle parameters and ratios accounted for.  For autox you look at accel in a single gear (usually 2nd) from ~20mph to 65mph.  For something on track you would look at the accel in each gear between shift points, maybe +/- a few RPM to account for flexibility.

It's what made TDI manuals feel like they had 2.5 times the power they actually had.

The OPs second post is misleading because the two dyno charts are different scales.

When I look at dyno charts I look at the areas where I actually drive them. Peak means nothing to me if I'm never there. My Jeep is rated at 190 but lord knows I'm not revving it to 4600rpm to find it, but it makes 128 at 3000rpm which is plenty for a 3000lbs car.

A 401 CJ said:

It's what made TDI manuals feel like they had 2.5 times the power they actually had.

Correlating that with what buzzboy just posted, they made a good amount of horsepower at engine speeds most people feel comfortable using on a regular basis.

I probably never make more than 130-150hp with my Volvo on a daily basis.  However, it doesn't need to exceed 3000rpm or half throttle to do that, so it feels a lot more effortless.  You could stick the redline there and the numbers would be hideously unimpressive.... kind of like a TDI.

I like the DSG in the Sportwagen.  I have a regular customer with one, it's a remarkably friendly device.