Power to Weight factoring in Torque

[Speedy300]

Normally when comparing cars I initially look at their power to weight ratios as this tends to give a good indication of straight line speed. However, this rules does not seem to apply with very torque biased engines such as diesels.

For example (data per Torque Stats):

E90 BMW 330d ‘09 - 242 bhp / 1610kg = 150 bhp/ton with 383 lbs/ft

0-100mph = 15 Secs


Mazda RX8 ‘03 - 228bhp / 1394kg = 164 bhp/ton with 156 lb/ft

0-100mph = 19 secs

The Mazda has a much higher power to weight ratio but is clearly slower from 0-100 mph then the torque biased BMW.

Does such a calculator exist on the net which realistically factors the torque output into a power to weight calculation? Or can you come up with one?

Edited by Speedy300 on Thursday 7th March 21:51

[McWigglebum4th]

[McSam]

A very realistic calculator already exists, it's called physics, and it applies to the 0-100mph times you quoted. So use those

[GroundEffect]

Where did you get those specs? From fastestlaps.com the two cars are virtually identical to 100mph - with the RX8 being 0.6s faster.

BHP is a measure of torque by speed...basically work done. This measure of work done is a good indicator of accelerative capability.

Torque as an absolute is useless in this comparison.

[Speedy300]

GroundEffect said:

Torque as an absolute is useless in this comparison.

Torque stats

[ging84]

what is missing is the gearbox
if they had cvt transmissions and equal traction the rx8 would accelerate quicker, especially if it was more aerodynamic.
but cvt's don't exist / are st so you need to take account of the torque curve and the gear ratios.
there is something called a thrust chart which plots the available torque vs speed for each gear
this data could be used together with the weight of the vehicle to give it's theoretical max acceleration, but this does not take account traction and you couldn't really do that easily so you are better off looking at real world figures

[mrmr96]

GroundEffect said:

Where did you get those specs? From fastestlaps.com the two cars are virtually identical to 100mph - with the RX8 being 0.6s faster.

BHP is a measure of torque by speed...basically work done. This measure of work done is a good measure of accelerative capability.

Torque as an absolute is useless in this comparison.

+1

[GroundEffect]

Speedy300 said:

GroundEffect said:

Torque as an absolute is useless in this comparison.

Torque stats

http://fastestlaps.com/cars/bmw_330d_e46.html

http://fastestlaps.com/cars/mazda_rx-8.html

Not saying they are perfect, but those numbers make more sense to me.

If you're doing an analysis you stick to one type of calculation, either torque based or power based. When you start mixing the two it gets confusing and comparisons fall apart.

In my line of work I stick to torque-only. This means you need all the gearing ratios but it just makes more sense to me.

[xRIEx]

This might be useful here:

chris182 said:

...a hugely simplified explanation is below. This completely neglects many things such as rotational inertia, drivetrain losses, grip limits, units etc etc but gives a very short and basic explanation of the effects of torque and power on acceleration (performance if you will).

Acceleration = Force / Mass

Force = Wheel torque / Wheel radius

Wheel torque = Instantaneous Engine Torque / ( Gear ratio * Final Drive Ratio )

Instantaneous Engine Torque = Instantaneous Engine Power / Instantaneous Engine Rotational Speed

Instantaneous Engine Rotational Speed = Vehicle Speed / ( Gear Ratio * Final Drive Ratio * Wheel radius * 2 * Pi )

Combining the above and simplifying gives the following result:

Acceleration = ( Instantaneous Engine Power * 2 * Pi ) / ( Mass * Vehicle Speed )

i.e. Acceleration is proportional to instantaneous power not torque. The reason why a layman thinks a 100bhp diesel feels faster than a 100bhp petrol is because a greater percentage of that 100bhp is delivered at the rev range he uses in general driving.

[Speedy300]

Lets not get too bogged down with those specific car stats.

I could have picked loads of cars to demonstrate my point.

[chris182]

mrmr96 said:

GroundEffect said:

Where did you get those specs? From fastestlaps.com the two cars are virtually identical to 100mph - with the RX8 being 0.6s faster.

BHP is a measure of torque by speed...basically work done. This measure of work done is a good measure of accelerative capability.

Torque as an absolute is useless in this comparison.

+1

The spread of torque across the rev range is very important though. Peak power measurements are made at one fixed rpm which with discrete gear ratios is impossible to maintain whilst accelerating. A peaky engine like the RX8 will be developing considerably less than it's peak power for a high percentage of the time, so when you integrate over time to get total energy (which is proportional to the square of velocity) then divide by time to get the average power it will be lower than an engine with the same peak power but a fatter torque curve.

Obviously there are a whole host of other factors at play too in determining 0-60 times.

[GroundEffect]

chris182 said:

mrmr96 said:

GroundEffect said:

Where did you get those specs? From fastestlaps.com the two cars are virtually identical to 100mph - with the RX8 being 0.6s faster.

BHP is a measure of torque by speed...basically work done. This measure of work done is a good measure of accelerative capability.

Torque as an absolute is useless in this comparison.

+1

The spread of torque across the rev range is very important though. Peak power measurements are made at one fixed rpm which with discrete gear ratios is impossible to maintain whilst accelerating. A peaky engine like the RX8 will be developing considerably less than it's peak power for a high percentage of the time, so when you integrate over time to get total energy (which is proportional to the square of velocity) then divide by time to get the average power it will be lower than an engine with the same peak power but a fatter torque curve.

Obviously there are a whole host of other factors at play too in determining 0-60 times.

...hence why I said 'as an absolute' (i.e. a point value)

[chris182]

xRIEx said:

This might be useful here:

Ah yes. I knew I'd answered this one before.

[Kozy]

Speedy300 said:

Does such a calculator exist on the net which realistically factors the torque output into a power to weight calculation? Or can you come up with one?

Edited by Speedy300 on Thursday 7th March 21:51

Yes, I wrote one:



Will do FWD/AWD/RWD traction based on tyre grip, wheelbase and CG. gear ratios and a two stage torque curve model, gear ratios, tyre sizes, aero drag etc.

Will calculate 0-60, 0-100, 40-80, 1/4, 1/2 mile times and speeds. Pretty much any combination of time
And distance you could want.

I would put it online, but the converter software costs £300.

I am open to donations...

Edited by Kozy on Thursday 7th March 22:14

Edited by Kozy on Thursday 7th March 22:15

[paranoid airbag]

McSam said:

A very realistic calculator already exists, it's called physics, and it applies to the 0-100mph times you quoted. So use those

True dat any calculation will be less accurate (and less fun). But easier I suppose.

The next best thing to physics would be to get the torque curve of the engine and gearing data (maybe aero data too), at which point it can be calculated - work out how much torque the engine is producing at a given speed from the gearing data, apply that to the car for some short period of time (the shorter the better), work out the new speed, rinse and repeat. (you may also be able to actually integrate the torque curve, which could be more accurate in theory, but sod it I'm not explaining calculus at this hour). You could make this calculation as accurate as you wished. I'm pretty certain online calculators which do this exist, sorry I can't point you to any.

The next best thing after that (no gearing data, no torque curve) would be to:
-count that number of gearchanges necessary to get to 100
-find out how big the rev range between peak torque and peak power is as a fraction of the revs that give you peak power , i.e.
(peak power revs - peak torque revs)/ peak power revs

-make an assumption about the torque curve - bearing in mind that, at peak power, the torque must be falling away faster than revs are rising (power = torque x rotational speed, so peak power occurs at the revs that maximise torque x rotational speed - sorry but this involves calculus again). A straight line is probably not too awful a guess (considering the other guesses here) and does make things simple.
-go back to the first method with your guessed data.

After that? time = mass x speed x speed / ( 2 x Power x a fudge factor )

(a fudge factor is a number you cram in for no reason other than 'it gives you better answers')

*Waits for any embarassing errors to be made apparent*

[Kozy]

paranoid airbag said:

True dat any calculation will be less accurate (and less fun). But easier I suppose.

The next best thing to physics would be to get the torque curve of the engine and gearing data (maybe aero data too), at which point it can be calculated - work out how much torque the engine is producing at a given speed from the gearing data, apply that to the car for some short period of time (the shorter the better), work out the new speed, rinse and repeat. (you may also be able to actually integrate the torque curve, which could be more accurate in theory, but sod it I'm not explaining calculus at this hour). You could make this calculation as accurate as you wished. I'm pretty certain online calculators which do this exist, sorry I can't point you to any.

That's what mine does. In .1 second intervals. It was truly horrid to write, but it seems to work.

[Gad-Westy]

Speedy300 said:

Lets not get too bogged down with those specific car stats.

I could have picked loads of cars to demonstrate my point.

I can't think of any. Torque is meaningless with out engine speed. And if you know those two, you'll know power. Ultimately it is power that gives you acceleration. You could have a miniscule amount of torque but if you can spin the engine fast enough you'll still have something that goes like st off a shiny shovel. Just take a look at an F1 car's torque figures for an extreme example.

Put it another way, give me a lever long enough and I can generate 500 ft.lb of torque, at maybe 5 rpm, but as yet I haven't had any calls from any major car manufacturers asking me to power their new flagship supercar.

Edited by Gad-Westy on Friday 8th March 07:52

[Krikkit]

Kozy said:

I would put it online, but the converter software costs £300.

I am open to donations...

What on earth is it written in?

[Kozy]

Excel. To put it online in a secure, non-borkable, user friendly format though, I need a pro Flash license of this: http://www.spreadsheetconverter.com/

It's either that, or pay a programmer/web developer a lot more to write it as a web app.

I have some others too, for engine thermodynamics, brake bias, suspension dynamics and a data analysis app: http://www.pistonheads.com/gassing/topic.asp?h=0&a...

If there was enough interest, I'd sort out a website for them all, at the moment though I have better things to spend £300 on.

[Kozy]

Here we go then, ran the 330D and RX8 specs through my calculator.

Here's the thrust curve, though this doesn't take into account weight.



Remarkably similar past 1st gear, and the traction calcs suggest the 330D can't really use all that extra thrust in 1st gear anyway. The great leveller (which is usually unquantifiable) is 'Area under the curve'. Yours truly has integrated those thrust curves and the 330D is 8.4% up on the RX8, but the RX8 has 20% less weight to propel.

The times:

0-60
RX8 5.9
330D 5.8

0-100
RX8 14.8
330D 15.1

1/4 mile
RX8 - 14.4 @ 97.7mph
330D - 14.4 @ 98.5 mph

1/2 mile
RX8 - 22.5 @ 120.4mph
330D - 22.7 @ 116.9 mph

Where ever you got 19 seconds for the RX8s 0-100, it was wrong.

Edited by Kozy on Friday 8th March 10:11