Torque and power quiz 4

[yoshimitsuspeed]

I spend a lot of time in the automotive community and a lot of time on car forums and groups.
Ever since I started to learn the actual relationship of torque and power it drove me crazy how few others in the automotive world actually understood this basic formula. People capable of building motors that make 500 hp per liter and who still think that torque is low end power.
I have gotten into enough arguments with people to learn that most would rather argue relentlessly cause that's what theys daddy taught them than sit down and think about the simplicity of the formula long enough to understand the relationship of the two.
I have decided to try a different tact and make a little quiz that gets people thinking about this from a different angle and maybe hoping they will get the point that torque and power can't be compared, and that torque does not mean low end power.
I just started on this tonight and it's 3AM. I want to do more to improve it but I also would love some input from others on ways I could improve it.
I would like it to be as detailed and informative as possible while still being interesting and keeping the person engaged and interested.

Tell me what you think of what I have so far.
What could I do better?
What are other questions I could ask or ways I could put things to get people thinking about the relationship without getting too bogged down in the math to loose too many people?
On that note should I focus more on the math or stay more with the basic relationship and principles?

http://matrixgarage.com/content/think-you-understand-torque-and-power

 

[gruntguru]

. . . . we cannot deny the fact that between 2 engines with the same peak power, the one with the highest peak torque will offer better performance.

Oh yes we can.

So, if you have two identical vehicles traveling side by side, and one has an engine making 75 ft-lbs of torque at 14,000 rpm and the other has a sweet diesel making a cool 500 ft-lbs of torque at 2100 rpm, they'll accelerate at exactly the same rate. They're making the same power, and traveling at the same speed, so they have the same thrust.

From snoopnoon's example it is clear that peak torque has absolutely nothing to do with it. The diesel has 6.6 times the torque but doesn't accelerate any faster.

The fact is (neglecting rotating inertias) if both engines have the same power, the one with the wider "power band" will accelerate better through the gears. That is to say "the engine with the highest average power across the band dictated by the gearbox ratio spacing". Generally speaking, the torque peak will not even be used when shifting at the optimum points - the revs will not drop that low.

je suis charlie

 

[JackAction]

Funny, now I'm getting blasted from two different comments that are exactly the opposite of one another:

*power* people always manage to lose sight of what happens to acceleration when the engine cannot be operating at its peak power rpm; it's as if acceleration at any other rpm does not matter even if running at those rpms cannot be avoided.

Generally speaking, the torque peak will not even be used when shifting at the optimum points - the revs will not drop that low.

Can't we avoid those rpms or will the revs not drop that low? It doesn't really matter because I'll repeat the only important thing I've said that covers it all (I have enlighten the keywords):

«Only the average power in the selected rpm range counts, not the average torque in the selected rpm range.»

Norm, I like the way you started talking about the subject in your first posts and then you began introducing comments about saying that the torque value is somehow more useful than the power, and it's not.

Here's why: If I tell you that I have a car driving at 10 m/s with an engine that produces 500 N.m, it is impossible for you to tell me the tractive force of that car; not even a close estimate. If I tell you that I have a car driving at 10 m/s with an engine that produces 100 kW, I can estimate that the tractive force is 10 000 N. Simple as that. It doesn't even matter if your car is powered by a gas engine or electric motor - or a nuclear reactor for that matter. Anything else doesn't matter (as long as you have traction to support that force): weight (and other rotational inertia effect), drag coefficient & frontal area, rolling resistance, inclination of the road, if it's a FWD, RWD or AWD, or even what song plays on the radio: They have no direct effect whatsoever on the total tractive force you will produce at the wheels (i.e. except for some losses inherent to the different components' design).

If you use the torque, you will need to know the engine rpm (and you will now know the engine power) or the complete geometry of the car where - from the tire diameter - you will find the wheel rpm and - from the gear ratio - you will find the engine rpm and from that you'll get the power of the engine. Very complicated; with no addition of useful information.

This is why simple equations like these ones and this one or even a more complicated simulator like this one only needs the power-to-weight ratio to give an amazingly close estimate of performance. All the resistance forces and inefficiencies are combined in one big constant.

What I wanted to point out is that a statement like «You get a 33% improvement when the car is in the same gear and the engine is at different rpm» - although true - is a misleading information that doesn't take into account the vehicle speed difference and it only fuels the «torque» peoples' theory that torque is more relevant than power. Only power matters, there is no «if», «but» or «it depends». Whatever calculations you can do with torque, I can do it in less steps, and with less information, with power.

 

[BrianPetersen]

Would the people fixated on horsepower numbers and nothing else, and think that everything can be taken care of with gear ratios, please explain to the class why a 9 litre 6 cylinder diesel engine is appropriate for propelling a box truck, and a far smaller and lighter Suzuki Hayabusa engine that makes the same (ish) power is not appropriate ... think of all the extra cargo you could carry if you were not lugging that huge engine around which weighs the better part of a ton on its own.

Perhaps the same people could explain why the reverse is also true ... bearing in mind that the diesel engine weighs twice what the whole bike does.

I've already tried, in this very thread, but obviously something must not be sinking in.

 

[SomptingGuy]

Maybe the class doesn't realise that prime movers aren't perfect power-on-demand devices and have some serious intrinsic design/application trade-offs. It's amazing that most of them actually work and more amazing that we've managed to engineer contraptions that allow useful work to be extracted from them.

A super-efficient 2-stroke ship diesel would be ideal for a motorcycle. If efficiency was more important than driving pleasure. And if the bike was already big to start with.

A bike engine would be ideal for a heavy goods truck. If the tiny additional cargo it allowed offset the drop in efficiency. And the short life-span of the engine when operating at either full or zero load all day.

Steve

 

[140Airpower]

Brian, your point about inconvenient gearing is well taken, but the example introduces even more compelling reasons a Hayabusa can't be used for trucking. You acknowledged this in an earlier post.

When I learned that a then typical long-haul diesel truck engine produced less horsepower than my 327 I wondered what would happen if they used 327s in heavy trucks. I didn't think the gearing for the higher rpms was an issue. I assumed the 327 would overheat on hills and would wear out in a small fraction of the truck engine's service life. I didn't even think about the fuel economy.
The Hayabusa could be geared for the job -as a stunt, but might catch fire or melt on a long grade and if it didn't it might be junk by the top of the hill. Otherwise, it could be a good idea.

Car makers are approaching the challenge of substituting tiny boosted engines for the typical large engines used for heavier vehicles and for meeting the performance of larger engines. It's not just gearing, 9 speed autos can handle it, it takes the water jacketing, cooling system and bottom end strength and wear characteristics of the larger engines being replaced.

 

[BrianPetersen]

It remains to be seen whether those tiny boosted engines will live as long as a slightly larger, though unboosted engine. It sure doesn't seem like they use any less fuel in the real world, as opposed to the fictional, low-speed, light-load, gentle world of the official EPA Federal Test Procedure.

 

[140Airpower]

Brian, good point there. I guess we'll see. Also we'll see if transmissions get more gears or if they have already gone too far.

 

[JackAction]

Would the people fixated on horsepower numbers and nothing else, and think that everything can be taken care of with gear ratios, please explain to the class why a 9 litre 6 cylinder diesel engine is appropriate for propelling a box truck, and a far smaller and lighter Suzuki Hayabusa engine that makes the same (ish) power is not appropriate

Very simple, and it is all related to what has already been said: «average power» over the «selected rpm range».

The useful rpm range for a large truck needs to perform throughout the whole range. Even with a wide power band, they can have like 20 gear ratios; Imagine how many they would need if they had a narrower power band. You miss one shift and you lose your power: Not very practical. So they need high power in the lower rpm range. They are so heavy that they need to perform right from the start (v=0).

The motorcycles can get away with little power at low speed as they are very light and have very low drag resistance to begin with. So you can use an even smaller engine (even less weight and drag resistance) with an equivalent power band in a higher rpm range. You could also use the large truck engine and get the extra power at the starting line, but the extra weight of the engine will probably handicap you throughout the rest of the race.

Here's another way to look at it: Take your 1000-14000 rpm motorcycle engine and install a 5:1 gear reducer between the crankshaft and the clutch. Put the engine on a dyno and measure at the gear reducer. You will have the exact same values for the power curve, except that it will be in the 200-2800 rpm range. The torque values, though, will all be multiplied by 5. Now you can compare it with your diesel engine that have a similar rpm range. And the maximum torque will probably be lower in the case of the motorcycle engine because of the way it is tuned.

People shouldn't fix on the maximum values, but rather the average values over the rpm range that they will use. But if you only have the maximum torque and maximum power of an engine, the maximum power will give you an idea of the power curve over the whole rpm range; The maximum torque doesn't do that. Between an engine that produces maximums of 300 lb.ft and 350 hp and another one that produces 400 lb.ft and 250 hp - if geared appropriately in both cases - the first one will most likely give you better performance. But if, like posted earlier in an example, you have the same maximum power, but have a higher maximum torque in one case, the one with the higher lower end torque has also higher lower end power and that increases the average power over the entire rpm range.

 

[BrianPetersen]

I had a new Chrysler 200 with the newfangled 9-speed as a rental this past Sunday through Tuesday. I never found any circumstance in which it actually uses 9th gear.

For how this transmission has been criticised in the press, I found it to be quite good. (I'm sure FiatChrysler has been working on the calibration.) Smidge reluctant to downshift, but most automatics are like that. My van (also a FiatChrysler product) has the ole 6-speed 62TE, and I'd gladly take the 9-speed in its place, even if it only functions as an 8-speed. The closely-spaced higher gears on the 9-speed are a lot better ... the 62TE has a huge gap between 5th and 6th.

 

[NormPeterson]

This is why simple equations like these ones and this one or even a more complicated simulator like this one only needs the power-to-weight ratio to give an amazingly close estimate of performance. All the resistance forces and inefficiencies are combined in one big constant.

I am aware of the first two, which are essentially curve-fits to a fairly large amount of actual dragstrip results. Good approximations, sure. But they won't give you the acceleration data at any speed at all, so they're pretty much irrelevant to any torque vs HP discussion.

I didn't need to go very far into your third link to find Ft. Ft can just as easily be determined from (crudely) [torque] x [gearing] ÷ [drive tire radius], all of which would be knowns. From a power-centered approach, you still need to know gearing and tire radius, simply to find the point on the HP curve that your engine is operating at in that instant - as is suggested in your later post with "[sub]«average power» over the «selected rpm range»[/sub]". Convince me that working with power in order to determine an acceleration curve between 35 mph and 55 mph and staying in a single gear would be easier.

Forget "effective mass" for rotational effects; do it properly as [torque] = x [alpha], which will remain independent of rpm per se. Isn't it easier to deduct a parasitic torque that's a function only of the torque curve's variability than to deduct a parasitic power that's a function of both HP curve variability and the RPM at that point?

saying that the torque value is somehow more useful than the power, and it's not.

Have you ever tried to construct a general math model of vehicle acceleration from basic vehicle data and first principles yourself? Mine even considers deceleration due to drag during the time it takes to execute each upshift. But hey, I've been at this one off and on since I was in college . . . and I'm now retired.

Funny, now I'm getting blasted from two different comments that are exactly the opposite of one another:

Quote (NormPeterson)
*power* people always manage to lose sight of what happens to acceleration when the engine cannot be operating at its peak power rpm; it's as if acceleration at any other rpm does not matter even if running at those rpms cannot be avoided.

Quote (gruntguru)
Generally speaking, the torque peak will not even be used when shifting at the optimum points - the revs will not drop that low.

Our comments are entirely consistent. If your shifting from at or slightly beyond the power peak is such that you land above peak torque rpm, it's because the gear spacing was close enough to permit this. This is not always the case. In fact one of my cars develops peak torque at 4500 rpm and peak HP at 6000. Fuel cut is said to be 6250 or so. But the step from 2nd gear to 3rd is from 2.00:1 to 1.38:1, so a 2-3 upshift drops the revs to no more than 4312 (closer to 4100 would be safer). The first to second step is wider still . . . as is the 4th to 5th.


Norm

 

[140Airpower]

One thing I was thinking, but haven't mentioned, is that for high speed racing, top end power can absolutely dominate. For high speed ovals this is obvious, but in road racing it's top end power that allows a car to pass on the straights. Trying to pass with grunt coming out of the turns can be defeated by a good opponent. So depending on the track, you may not think low-end torque is very important.

 

[JackAction]

Have you ever tried to construct a general math model of vehicle acceleration from basic vehicle data and first principles yourself? Mine even considers deceleration due to drag during the time it takes to execute each upshift. But hey, I've been at this one off and on since I was in college . . . and I'm now retired.

So I'm gonna stop right here as I'm not gonna go into a «I'm smarter than you are» discussion.

Instead of telling you that I'm smarter than you, I'll show how I smart I am (maybe it's less than you, but I'm still proud of what I accomplished): The simulator from the third link, I wrote it. The theory behind it, I developed it and showed how I did it, up to the last detail. For what I did not do, I cited my sources. It is all there for you to analyze. So trust me when I'm telling you that nowhere in that simulator, the engine torque nor the rpm was needed to determine the acceleration of a vehicle. I only used the power alone.

Instead of telling you that I'm smarter than you, I'll show you how humble I am. If you look at the About page, in the Thanks section, at the very end, you'll find the name Suresh Gopalan. He's one of the few who wrote me to tell me they found a mistake on my work. He's the only one who was actually right. If you find a mistake in my work, I will add your name to this list and I promise that my Thank You will be truly sincere.

All I care about is the knowledge of science and its sharing. All my argumentation is made towards that goal.

 

[LionelHutz]

Would the people fixated on horsepower numbers and nothing else, and think that everything can be taken care of with gear ratios, please explain to the class why a 9 litre 6 cylinder diesel engine is appropriate for propelling a box truck, and a far smaller and lighter Suzuki Hayabusa engine that makes the same (ish) power is not appropriate ... think of all the extra cargo you could carry if you were not lugging that huge engine around which weighs the better part of a ton on its own.

Perhaps the same people could explain why the reverse is also true ... bearing in mind that the diesel engine weighs twice what the whole bike does.

I've already tried, in this very thread, but obviously something must not be sinking in.

The explanation is perfectly simple, as I already pointed out 11 days ago. The topic of this thread is the quiz and the quiz is a THEORETICAL exercise attempting to help people understand the relationship between HP and torque.

 

[NormPeterson]

I developed it and showed how I did it, up to the last detail. For what I did not do, I cited my sources. It is all there for you to analyze. So trust me when I'm telling you that nowhere in that simulator, the engine torque nor the rpm was needed to determine the acceleration of a vehicle. I only used the power alone.

Not too surprisingly, I found that you are considering many of the same things that I have, and you even define top speed in specifically the same language that I do (when a = 0.000...). And a few that I haven't, at least not to date (aero lift, off the top of my head). Unfortunately, in terms of HTML or whatever language those pages were created using, I'm less than a newbie, so it's taking a while.

I do have a question - since you're using power, and since there are plots involving longitudinal acceleration, what are you using for power for determining acceleration at points that would require operating the engine at other than peak power rpm? There's an acceleration curve with a couple of wiggles in it that cannot be explained by anything I've found yet. Oddly enough, I see torque determined before HP, although it is not peak torque.

I think a factor for at least overall powertrain efficiency is in order. As an example, 300 HP engines identical to the one in my Mustang typically dyno something like 265 - 270 at the wheels, this most likely being measured using the direct (1:1) 4th gear, which even if you ignore all the gears in constant mesh not carrying power still leaves U-joint and hypoid axle gear effects absorbing torque/wasting power. About rotational inertia - flywheel, clutch, tire, and wheel weights and diameters are subject to considerable variation and aren't necessarily fitted to a vehicle with optimum acceleration in mind. Hence, it might be useful to keep them independent of total vehicle mass and (better still) separate from each other. If nothing else, it would allow comparisons involving changes to those components (is a 5 lb weight loss per wheel worth doing? how about that aluminum flywheel instead?).

More challenging, and of particular interest to the dragstrip guys, would be a good acceleration model for the first 60 feet. I don't have one, and it's not for not having tried. If I was smarter, maybe I might.


About top speed and the difference between theory and reality . . . if the car is not geared optimally to put the engine right at peak power rpm at that speed, you won't get there. There used to be a magazine that published drag at 100 mph in their data panels (I think it was "Car Life", which ceased publication decades ago). Some constant or other times the cube root of (HP over drag@100) would get you to a theoretical top speed. Whether the car was geared to actually accomplish that feat was of course a separate question, but it was still better than wild guesses and wishful thinking.


Norm

 

[JackAction]

First, you must understand the objective of the simulator, which is closely link to the subject of this thread: Identify the important characteristics of a vehicle to achieve a certain level of performance. What do you need to do the ¼-mile in 11 s, reach 150 mph or go from 0-60 mph in less 4 s? Before fine tuning gear ratio & power curves, before reducing the weight of your wheels, What are the basics? This is where it relates to the OP: You need power and traction. If you don't have enough of either of those thing, you are wasting your time studying any models you are making.

What the program does is giving you a realistic maximum performance level for a given vehicle. No matter what fine tuning you do, it will most likely never be better than what is shown on the graphs.

So it is assumed that the vehicle is at constant power all the time. Knowing that most people who will use this tool will use it for a vehicle with an ICE, I introduced some average inefficiencies (89% for typical drivetrain and 94% for direct drive) and I've assumed the average power that can be maintained is 95% of the maximum power given. More info in the Converting engine power to wheel power section.

The first part of the acceleration curve is limited by traction. The best drivers will maintain enough power to be at this limit in the first part of their acceleration (Of course we assume the drivetrain is designed to reach that limit as well). The «wiggles» are introduced by an assumption I made, that there will be some kind of transmission that is shifting, to make everything more realistic, as explained on the site:

This site assumes an average mass factor of 1.07 for a direct drive. For a typical road vehicle, it assumes a 6-speed transmission shifting every 1/6th of the top speed with the following mass factors for each gear ratio (from first to last): 1.19, 1.12, 1.08, 1.07, 1.06 and 1.05. This will also work with most older vehicles with 3- or 4-speed transmission as well, as such vehicles are usually not set up to reach their potential top speed.

My goal was to quickly compare vehicles, with as little data as possible. If I want to evaluate how a 1964 Corvette, a 1982 mazda RX-7 and 2006 Audi A4 compare to one another, what do I need to know? I've reduced it to 4 variables: Power, weight, traction and vehicle layout, which are data easily available (except for traction; even though it is probably the most important one, performance-wise). I make assumptions for all others and you can input your own aerodynamic, rolling resistance and basic vehicle geometry if you wish. But even if I let the user input them, he will most likely guessed them just like I do, and if he has access to the real numbers, he's probably not looking for free apps on the web to do his calculations.

You can find a «usual» method to do the same calculations on one of my «competitor»' site, blackartdynamics.com. You have to input much more data ... and then the program will do assumptions anyway (For example, the frontal area is calculated based on the width X height, not sure how). The engine power curve is based on max torque and max rpm. Not even max power! You have to enter data to model a torque curve until you reach your max power. Very tedious and you need a lot of data. If your sources are magazine articles and such, good luck!

In the end, you will find that the results are mostly the same with both simulators. IMHO, close enough that, with all the assumptions made, you are probably well within the margins of error.

I guess my point is that there is no point to introduce a lot of precision in your input data, if that data is made of wild guesses anyway. It's just discouraging and that's when everyone sees math & physics as boring and useless.

More challenging, and of particular interest to the dragstrip guys, would be a good acceleration model for the first 60 feet. I don't have one, and it's not for not having tried. If I was smarter, maybe I might.

I feel your pain. But after discussing with some tire engineers, the drag tire has a very special compound which has a friction coefficient that varies a lot, especially at launch. I'm pretty sure some very hard to find data has to be known to have a good precision in that small period of time.

You probably did not notice, but on the different graphs on my simulator, the data appears when you point your cursor on the curves. If you point your cursor on the time curve for the ¼-mile at the 60-ft line, you will have the precise time.

Here's a random case study to show how you can use the simulator for reverse engineering:

Take this Corvette.

I entered the following data (you have to uncheck Simplified version):
[ul]
[li](transmission) Engine power: 887 hp[/li]
[li]Mass: 3300 lb (approx. reference)[/li]
[li]h/L: 0.18 (guessed)[/li]
[li]F/R: 53/47 (reference)[/li]
[li]Friction coeff.: 2.68[/li]
[li]Rolling resistance: 0.02 (guessed)[/li]
[li]CdA: 0.583 m² (approx. reference)[/li]
[li]ClA: 0 m² (guessed)[/li]
[/ul]

I adjusted the friction coeff. to get the 60-ft time and the power to get the ¼-mile time and speed. You'll note that the 1/8-mile time & speed match also.

The friction coefficient seems rather low for a drag slick; So the car/driver probably doesn't maximize its grip for the launch (transmission/suspension/driver?). If I convert to wheel power, I get 789 hp. If the car is known to produce more than that at peak power, the gear ratios or shift points are probably not well selected to fully extract the maximum power from the engine. And that is true power at the track, not «SAE net» standardize.

 

[NormPeterson]

Quick thoughts . . .

I guess it's out of scope for the purposes of your model, but suppose you wanted to see what happens in street settings where you might start out with the engine nowhere near its power peak. Something like acceleration from 30 - 70 starting in 3rd gear as might happen as you accelerate up to highway speed from an unusually slow ramp corner.

I would think that blackart would need to specifically use peak HP and its RPM just to define a second point on a torque curve. Between two points and a pair of slopes you ought to be able to get something usable enough for making comparisons.

Variously, I've played with tire grip and several other parameters for the 60' matter (there are many inputs). To me as a road course guy it's really just to get the sheet to reflect reality as opposed to any performance I'm particularly interested in achieving as a driver, but I would like to get it there eventually.

I did not notice anything pop up when I hovered the mouse over the curves because it comes up very slowly. I have no idea if the slowness is a problem at my end, your end, or with something in between.

FWIW, I recently ran my sheet a couple of times for the new Z/28 and got quarter mile numbers right around 12.3/116. Car and Driver got 12.7/116 and Motor Trend got 12.3/117.2 . . . some of the Camaro5 dragstrip guys want to see an 11.9x out of that car in stock form pretty badly, and I really don't see it happening except by freakish confluence.


Norm

 

[JackAction]

I guess it's out of scope for the purposes of your model, but suppose you wanted to see what happens in street settings where you might start out with the engine nowhere near its power peak. Something like acceleration from 30 - 70 starting in 3rd gear as might happen as you accelerate up to highway speed from an unusually slow ramp corner.

The closest thing the model will tell you is the lowest time you can possibly take to go from 30 to 70, assuming you can get near peak power. You take the time from 0-30 and subtract it from the time 0-70 and you get the 30-70 elapsed time.

I know the situation that you described can happen in real life, but I would think that if someone is looking for performance, he would downshift to get in the peak power rpm range. And that brings us back to the OP and the importance of power vs torque in acceleration.

 

[Nereth1]

Story time:

I remember some years ago, a university lecturer of mine had this misconception in a machine dynamics class. He said to a couple hundred students that if you want your car to go faster you need to buy a car with more torque. He said it multiple times, and this annoyed me because I hate people in positions of authority handing down completely false dogma. I wrote up a really simple bit of maths during the lecture that showed that with power and vehicle mass (engine and vehicle) I could predict acceleration, but with torque and mass I couldn't. Showed it to him during the break. He looked at it for 10 seconds then waved it off and said he couldn't go through it (this is highschool level maths by the way) but he had graduate students that had analysed it and they came to the conclusion that torque was what was important.

Could never take him (or his grad students, apparently) seriously again.

In any case, I have a feeling you will lose most people with that quiz of yours because once the thinking gets tough, they will simply close the tabs and say 'meaningless academic tripe', and won't engage hard enough to realise what you are trying to teach them. You really need to get it through to them in one profound sentence. The quiz feels a bit patronizing to me and it will feel more so to someone struggling with answers and getting told he is wrong.

And if this is your reaction to the torque vs horsepower debate, you're gonna really have a fun time with all the other stuff floating around with the automotive hobby (which is rife with this stuff, because it is just that level of accessible vs complicated where everyone can form an opinion but no one can verify it), all the vehicle dynamics misunderstandings are massive and far harder to explain/prove. At some point you just gotta ask them what happens to an airplane on a treadmill and fade into the distance while they all quote their qualifications at eachother right after completely missing the point.

Good luck!

 

[dicer]

HP is an arbitrary number 33,000 lb ft per minute, it was a number that was settled on as the definition of 1 horse power. Torque is the true quantity measured.
As far as testing an IC engine on any sort of dynamometer or prony brake, there are losses that gum up the accuracy.
Again HP is a calculated value from the measured torque.

 

[JackAction]

HP is an arbitrary number 33,000 lb ft per minute, it was a number that was settled on as the definition of 1 horse power. Torque is the true quantity measured.
As far as testing an IC engine on any sort of dynamometer or prony brake, there are losses that gum up the accuracy.
Again HP is a calculated value from the measured torque.

HP might be an arbitrary number, but it is a unit. What this unit represents is power, and that is a very real thing.

Power is the result of the combined effect of torque AND rpm. That is what is important to understand. Torque by itself doesn't tell the whole picture, neither does the rpm. You need to know both, and that what power is useful for.

Imagine your statement rewritten this way (changes highlighted):

HP is an arbitrary number 33,000 lb ft per minute, it was a number that was settled on as the definition of 1 horse power. rpm is the true quantity measured.
As far as testing an IC engine on any sort of dynamometer or prony brake, there are losses that gum up the accuracy.
Again HP is a calculated value from the measured rpm.

It would still be true, but that doesn't mean that an engine that can reach 10 000 rpm will give better performance than one reaching 5 000 rpm.