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Author torque -> BHP equation?
Rob H
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Registered: 28th Oct 00
Location: Staffordshire Drives: Astra SRi
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25th Mar 04 at 20:38   View User's Profile U2U Member Reply With Quote

Any one know what it is?

Something like (torque*RPM)/5252 i think?
bubble
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Registered: 24th Jan 04
Location: Darwin, NT Australia.
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25th Mar 04 at 20:39   View User's Profile U2U Member Reply With Quote

In the past it has been a great feature of most performance car magazines to quote peak brake horsepower as the most significant measure of a cars ability to perform.

I’m going to tell you why you shouldn’t care less about bHp and why torque is so much more important. Did you know, for instance, that no rolling road in the world has ever ‘measured’ horsepower? They all measure torque, and convert to bHp. Torque is the thing you feel when you accelerate, not horsepower. Infact, as we will see, 85 bHp can be an awful lot more use than 150 bHp in some situations! Does that sound crazy? Well read on.

We’re going to need some basic physics, so stick with it as it eventually all makes sense. I’m also going to stick to ‘old money’ units rather than metric, because despite the best efforts of the bureaucracy in Brussels, that’s what we are still most familiar with over here.

In case you are interested, 1 bHp = 0.7457 kW and 1 lb-ft torque = 1.3827 Nm.

What is horsepower?

‘Horsepower’ (hp) was coined after work done by an engineer called James Watt (1736-1819). He was using horses to pull coal from coal mines and worked out that on average a horse could pull about 33,000 pounds of coal up one foot in one minute. So 33,000 foot pounds of work per minute is 1 horsepower. When the steam engine came along, being vastly more powerful than an individual horse, the unit of ‘horsepower’ became widely used. Your average ‘Thomas the Tank engine’ was able to produce about 1500 Hp!

By the way, Brake horsepower (bHp), as usually quoted for cars, is the actual horsepower measured at the output shaft of an engine, as opposed to the theoretical calculated horsepower for the engine.

So bHp = Hp – frictional losses.

Revolutions per minute

Well, revolutions per minute are pretty obvious, so I figure you get that one. Just look at the tacho in your GTI and blip the throttle a bit, you’ll figure it out!

So tell us about Torque then!

Thirdly we come to torque. Torque is the ‘twisting’ force generated by the output shaft of an engine, we’ll call it the ‘crankshaft’ from now on. Torque is measured in foot-pounds (lb-ft). One foot pound of torque is the twisting force necessary to support a one pound weight one foot away from the crankshaft.

Still with me? Now the kinds of engines we’re interested in produce circular motion. Imagine a one pound bag of sugar on the end of a foot long pole connected to the crankshaft. Move that bag of sugar completely around, making one revolution of the crankshaft. What we have effectly done is move a one pound resistance around a circle of diameter 2 feet. The circumference of the circle is given by the simple formula C=Pi x D (Pi is 3.1416-ish and D=2). So we have moved that bag of sugar a total of 6.2832 feet, and we’ve done 6.2832 foot pounds of ‘work’.

Ok, this is where it starts to make sense.

James Watt said that one horsepower was 33,000 foot pounds of work per minute. If we divide 33,000 foot pounds of work per minute by 6.2832 foot pounds of work, some of the units cancel out and we end up with an equation that relates horsepower and torque. We find that if we could spin that 1 pound bag of sugar round our crankshaft at 5252rpm, we’d be doing 33,000 foot pounds per minute of work, or 1 horsepower. What we get is this…

Horsepower = (Torque * RPM) / 5252

The first thing you can spot from this formula is that at 5252 rpm, torque and hp are equal numerically. So if, as is often the case in the car magazines, you see a horsepower and torque graph where the values for torque and horsepower do not cross at at 5252rpm, you can laugh at it, as it is total ..er.. horse manure! As you can see in the two diagrams, these power and torque plots are correct, showing both horsepower and torque to be equal at 5252rpm. (5252rpm is marked by the red dot)

Out of interest you can see that whilst the mk2 16v has greater peak torque than the mk2 8v, the 8v is generating at least 10 lb-ft more torque between 2000 and 4500 rpm than the 16v, giving the lie to the notion that the 16v is as torquey as the 8v throughout the rev range. Historians may recall that VW published a torque plot trying to prove that the 16v was had more torque throughout than the 8v, but guess what, the figures didn’t cross at 5252rpm!

Some examples

Lets take two point examples in detail to clarify what all this means, using two familiar cars that both generate a peak of 150bhp from the factory; a mk3 Golf GTI 16v and a new Mk4 Golf GTI TDI. Down the pub, both cars have equal kudos on the power and 0-60 fronts, but what about torque? I’ve taken the figures from Volkswagen themselves.

First the mk3. It generates its 150bhp at quite a high rpm, about 6000.

150 = (t*6000)/5252
t=131.5 lb-ft

Secondly the mk4. Being a diesel, it generates its 150 bHp at a much lower rpm, 4000.

150 = (t*4000)/5252
t=196.25 lb-ft

Notice also that these torque figures are not the peak torque figures for these engines. Peak torque and peak horsepower do not usually happen at the same RPM. In the case of the mk3 16v, peak torque is just a little higher at 133 lb-ft @ 4000-5600 rpm, with the mk4 TDI it is a more significant 236 lb-ft @ 1900 rpm.

For the right foot brigade, the point at which a given car will accelerate most strongly from is the peak torque point. So maximum in gear acceleration for the Mk3 16v would be above 4000 rpm, and for the mk4 TDI it would be at a mere 1900 rpm, which you can test at your leisure! By comparison, the 8v Golfs peak torque is generally in and around the 3200-3500 rpm area. Just for comparison, some electric motors generate peak torque at zero rpm and it drops away from there up the rev range, meaning maximum acceleration is available at a stand still, guess why most trains today are electric!

So in summary…

We’ve said that that torque is more important than horsepower, but why? Well, take your trusty Mk4 again. We’ve shown that it accelerates quickest from 1900rpm in any gear, since this is the maximum torque point. However, the calculation shows that at 1900 rpm the TDI is only generating about 85bhp, yet it accelerates far quicker from here than it does at 4000 rpm when it is generating 150bhp. Our electric motor will give maximum acceleration with zero horsepower! So horsepower really means nothing at all in terms of performance, torque is what counts. Arguably, horsepower doesn’t really exist at all, it is merely a calculation derived from measured torque at a given RPM.

It also shows why gearboxes are important. What gearboxes do is change the ratio of RPM at the engine compared with the RPM of the driven wheels. If you half the RPM at the wheels compared with the engine with a 2:1 gearbox ratio, guess what…. you double the torque at the wheels!

Now you can see why diesels (and particularly turbo diesels) are famous for their torque, as they generate their high levels of torque at a low rpm. This also explains why 16v cars tend to have shorter gear ratios in order to multiply their relative lack of torque and take advantage of their greater rev limits. Conversely, diesel cars tend to have much longer gearing to spread that torque out over a larger road speed range.

In a nutshell then, a truly torquey engine is one that produces a large percentage of its maximum torque over the widest possible rev range. A good example of this within the VW group is the Mk4 1.8T, which has virtually constant torque between 1750 and 4500 rpm, it’s also why the mk1 1.8 was so much quicker than the earlier 1.6. By comparison, 16v engines are the not so good at this, as whilst they do in fact produce fairly high torque figures, they only do this in a narrow band towards the top of the rev range.
bubble
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Registered: 24th Jan 04
Location: Darwin, NT Australia.
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25th Mar 04 at 20:43   View User's Profile U2U Member Reply With Quote

take ya 3years read it
J da Silva
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Registered: 10th Apr 03
Location: The FACTory
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25th Mar 04 at 20:46   View User's Profile U2U Member Reply With Quote

where did u copy and past that from then?
sebj
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Registered: 4th Sep 03
Location: Gavesend Kent
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25th Mar 04 at 21:04   View User's Profile U2U Member Reply With Quote

Nice post bubblevaux
MattyB
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Registered: 13th Nov 01
Location: 118.5bhp :D
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25th Mar 04 at 21:04   View User's Profile U2U Member Reply With Quote

still dont get it!

All i know it my TD has more torque than a GTi-6, but still aint a racing car.

Matt
bubble
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Registered: 24th Jan 04
Location: Darwin, NT Australia.
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25th Mar 04 at 21:06   View User's Profile U2U Member Reply With Quote

quote:
Originally posted by VenomTurbo
where did u copy and past that from then?


m8 from fezonline!!!
mike_1.2LS96
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Registered: 23rd Oct 03
Location: Darlington | Mazda 323 1.8 Exec
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25th Mar 04 at 21:49   View User's Profile U2U Member Reply With Quote

quote:
Originally posted by bubblevaux
Horsepower = (Torque * RPM) / 5252



Using data from my car figures:
Max Torque: 86Nm @ 2800rpm
Max Power: 33kW @ 4600rpm

Calculated as:

Hp = ( Tq * RPM ) / 5252

Tq = ( 5252 * Hp ) / RPM

Results

................nm...........kw
4600........37.6.........33
2800........86............45.8492003


= BOLLOX

Rob H
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Registered: 28th Oct 00
Location: Staffordshire Drives: Astra SRi
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25th Mar 04 at 21:54   View User's Profile U2U Member Reply With Quote

Need to convert Nm into lb/ft first mate.

Divide by 1.3827
mike_1.2LS96
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Registered: 23rd Oct 03
Location: Darlington | Mazda 323 1.8 Exec
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25th Mar 04 at 22:17   View User's Profile U2U Member Reply With Quote


..................lb/ft.........hp
4600.........48.9.........42.9
2800.........63.4.........33.8



That seems right but why?

..................Nm.........kW
4600.........66.........31
2800.........86.........25

If Hp and Tq can be converted between kW / BHP and Nm / lb\ft surely using the same formula should reveal the same results..

Rob H
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Registered: 28th Oct 00
Location: Staffordshire Drives: Astra SRi
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25th Mar 04 at 22:22   View User's Profile U2U Member Reply With Quote

All to do with dimentional analysis and other bollocks. I'd explain, but ive just spent the day doing coursework, and i really cant be fucked .
vibrio
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Registered: 28th Feb 01
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25th Mar 04 at 22:56   View User's Profile U2U Member Reply With Quote

your original equaltion is correct
Rob H
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Registered: 28th Oct 00
Location: Staffordshire Drives: Astra SRi
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25th Mar 04 at 23:02   View User's Profile U2U Member Reply With Quote

quote:
Originally posted by vibrio
your original equaltion is correct


Yeah i realised. I was hoping someone knew for deffinate cause i couldnt find anything on Google, but i found it for certain anyway .

 
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