A question about the relationship between power and torque

[karabiner98k]

The following is the relationship between torque and HP:

HP = Torque (lb-ft) X RPM / 5252

I have used it many times without any problems except for one car, the MC-Laren F1.

Here is it's torque and power:

627hp@7400 RPM
479lb-ft@4000-7000RPM

So, at 7000RPM this car has 479lb-ft of torque but when you calculate the power at 7000RPM, you will end up with 638hp!

How can this be true while the maximum power is 627hp?

 

[cepheid]

Are you sure that your conversion factor is right? Google calc says that:

$$\frac{1~\mathrm{lb}_\mathrm{F} \cdot \mathrm{ft}}{\mathrm{min}} = \frac{1}{33~000}~\mathrm{HP}$$​

and this also agrees with Wikipedia.

 

[94JZA80]

So, at 7000RPM this car has 479lb-ft of torque but when you calculate the power at 7000RPM, you will end up with 638hp!

How can this be true while the maximum power is 627hp?

horse power more or less follows the law of diminishing returns. that is, the higher you push the rpm's, the less of a power gain you will achieve. in other words, if you were to increase the rpm's in equal increments, eventually each corresponding increase in power will be less than the one before it. this is due to heat soak (as well as other factors) that affect an engine's ability to increase power as the revs increase.

so, if you know that the McLaren F1 makes 627hp@7400rpm and 479lb-ft@4000-7000rpm, and if you know that it also makes 638hp@7000rpm via your calculation, then the torque value @ 7400rpm must be less than it was from 4000-7000rpm. this makes sense, as most cars hit their peak torque somewhere in the middle of the revband where it plateaus for a bit, and then tapers off toward redline. so i wouldn't be surprised if torque is in fact less than 479lb-ft after 7000rpm. in fact, you can use your formula in reverse to calculate the actual torque @ 7400rpm:

if HP = (TQ*rpm)/5252, then TQ = (HP*5252)/rpm = (627*5252)/7400 = 445 ft-lb. of torque --> as you can see, torque @ 7400rpm is less than it is @ 7000rpm.

its all in the characteristics of the dyno plot/graph. the horsepower of a car who's dyno plot shows that torque plateaus and hardly drops off near redline will most likely increase up to redline. the horsepower of a car who's dyno plot shows that torque plateaus but then has a moderate drop-off will probably peak before redline and stay that way (plateau) until redline. the horsepower of a car who's dyno plot shows a significant drop-off in torque approaching redline will probably also drop off somewhat before redline. now i understand that forced induction motors have some characteristics that set them apart from naturally aspirated motors on the dyno, but look at some various dyno plots and you'll see the general trend.

 

[94JZA80]

the OP's conversion factor is correct in this instance. so long as the dyno plot measures power in units of horsepower AND measures torque in units of ft-lbs, their graphs will cross @ 5252rpm.

 

[cepheid]

Nevermind. I was just missing a factor of 2*pi:

33000/2*pi = 5252

 

[karabiner98k]

so, if you know that the McLaren F1 makes 627hp@7400rpm and 479lb-ft@4000-7000rpm, and if you know that it also makes 638hp@7000rpm via your calculation, then the torque value @ 7400rpm must be less than it was from 4000-7000rpm. this makes sense, as most cars hit their peak torque somewhere in the middle of the revband where it plateaus for a bit, and then tapers off toward redline.

My question is that if this car can produce 638hp@7000RPM, why they didn't claim a maximum power of 638hp instead of 627hp??

 

[94JZA80]

My question is that if this car can produce 638hp@7000RPM, why they didn't claim a maximum power of 638hp instead of 627hp??

that is a good question my friend...and its impossible to tell for sure without consulting McLaren's marketing and engineering departments themselves. i have a feeling that its just another instance of an automobile manufacturer underrating its car's true power output. take the 03-04 Ford Mustang Cobra's for instance - they were rated at ~390bhp from the factory, but people would dyno them and find that their Cobra's were making closer to 390whp. on the off chance that you're not familiar with the terminology, bhp is brake horse power, and it is a rough measurement of how much power a motor outputs to the drive shaft or flywheel (essentially what an engine dyno connected directly to the drive shaft would measure). whp is the amount of power measured at the wheels (i.e. what a rolling dynamometer measures). b/c a small amount of power is lost through drivetrain components (drive shaft couplings, gear box, differential, etc.) before reaching the wheels, whp is always less than bhp. hence, a 390bhp Mustang Cobra would be making closer to ~330whp had Ford been honest about its car's power output in the first place. in other words, if the Mustang Cobra is putting down ~390whp on the dyno, then it is making closer to ~460bhp (i.e., Ford seriously underrated the Cobra's power output). the Chevy C6 Z06, Nissan GTR, and many others were underrated by the factory regarding power output...not b/c the manufacturer overlooked something, but b/c they use is as a marketing ploy.

 

[karabiner98k]

that is a good question my friend...and its impossible to tell for sure without consulting McLaren's marketing and engineering departments themselves. i have a feeling that its just another instance of an automobile manufacturer underrating its car's true power output. take the 03-04 Ford Mustang Cobra's for instance - they were rated at ~390bhp from the factory, but people would dyno them and find that their Cobra's were making closer to 390whp. on the off chance that you're not familiar with the terminology, bhp is brake horse power, and it is a rough measurement of how much power a motor outputs to the drive shaft or flywheel (essentially what an engine dyno connected directly to the drive shaft would measure). whp is the amount of power measured at the wheels (i.e. what a rolling dynamometer measures). b/c a small amount of power is lost through drivetrain components (drive shaft couplings, gear box, differential, etc.) before reaching the wheels, whp is always less than bhp. hence, a 390bhp Mustang Cobra would be making closer to ~330whp had Ford been honest about its car's power output in the first place. in other words, if the Mustang Cobra is putting down ~390whp on the dyno, then it is making closer to ~460bhp (i.e., Ford seriously underrated the Cobra's power output). the Chevy C6 Z06, Nissan GTR, and many others were underrated by the factory regarding power output...not b/c the manufacturer overlooked something, but b/c they use is as a marketing ploy.

Yes, i knew about Wheel hp and dyno graph and the best example of a recent underrated car is GTR. This could be one of the reasons why Mc-Laren claimed 627hp.

 

[russ_watters]

Perhaps they just didn't want to bother dealing with the 2% deviation from perfectly flat on the torque curve?

 

[94JZA80]

that is a very good possibility as well...

 

[karabiner98k]

Another interesting example is Ascari A10. This seems to be an overrated car.

Max power: 625hp@7500RPM
Max torque: 413lb-ft@5500RPM

When you calculate the torque at 7500RPM (max power RPM), you will end up with 437lb-ft which is more than 413lb-ft (max torque)!

There are 2 possibilities:
1) The max torque claim is underrated.
2) The max power claim is overrated.

What do you think?

 

[Lsos]

Yeah that's just weird. Obviously, for one reason or another, the published numbers are wrong.