A brief discussion of the RS4 power

[ArthurPE]

I offer this to stir thought and discussion, not to incite
I'll approach it 2 ways, comparative and analytical

comparative, same magazine, same testing regime, same driver, both corrected for temp/atm press
just got a mag today that tested a new Boss Mustang
444 HP @ 7500
380 lb ft @ 4500
5 liter V8
similar to the RS4 engine type
gear ratios are the same, both are doing ~92 mph at HP peak
both shift the same number of times for the 0-100, the 1/4 and 0-120

the RS4 weighs 9% more (3980 vs 3666)
the Boss has >7% more HP and 20% more torque
peak HP/wt 8.25 vs 9.6, 17% more
peak torque/wt, more important, 9.65 vs 12.55, 30% difference!
torque at peak HP (213 vs 266) a 25% difference
so over the power band the Boss has ~27.5% more torque/wt than the RS4...
and since F = ma, accel is proporational to force/torque...

.........RS4....Boss
1/4....13.0...12.8...1.5%
trap...109....113....3.5%
0-120...16....14.9....7%

how can the RS4 be so close despite the power/wt adavantage of 17% to 30% depending on the variable compared?
it gets worse if we assume 380 rather than 414 for the RS4

analytical
assume a loaded wt of 4100
3-8k 8.5 sec
speed 36-96 mph or 53-141 ft/sec (delta 88 ft/sec)
a = 88 ft/sec / 8.5 sec ~ 10.4 ft/sec^2 (average)
F = ma = (4100/32) (10.4) ~ 1330 lb (force) as thrust
T = F x r = 1330 x 13/12 ~ 1440 lb ft at wheels
converted to engine = torque wheels / gear ratios ~ 1440/(4.11 x 1.52) ~ 230 lb ft (after drivetrain and tire losses)
so 230 average and since it makes 90% from 3-8k we can assume peak to be ~ 1.1 x 230 ~ 253 lb ft after losses at the wheels

the engine is rated 317, so 90% or the average would be 285 lb ft (before losses)
if we assume total losses of only 15% (the tires slip 3% alone, so 12% for the drivetrain)
at the wheel average ~ 0.85 x 285 ~ 240 or peak of 1.1 x 240 ~ 265 lb ft (after 15% losses)
calculated average at the wheels (15% losses)...230 vs 240, 4% difference...peak 253 vs 265, ~4-5%
but we know losses are higher than...12% + 3% ~ 15% (it has twice the axles, and 3 vs 1 diffs compared to a 2wd, 2 more diffs, front to rear, and front, the trannies cancel and are efficient, it's the axles and diffs that have losses, they have angles and change directions, so twice the axle and 3 times the diff losses, let's assume 50% more losses)...
if we use the same for tires and adjust the rest (1.5 x 12) + 3 ~ 21%

if we assume only 20% total losses (I believe it to be 20-22%)
rated becomes avg/peak...230/253...the same as calculated

these are some of the 'proofs' I have used to convince myself the car makes rated power

[Dom81]

Far too technical for me Arthur, but a good read nevertheless. The only two answers I have for mystery speed are flux capacitors and dilithium crystals...

[S4Player]

Far too technical for me Arthur, but a good read nevertheless. The only two answers I have for mystery speed are flux capacitors and dilithium crystals...

Flux capacitor lol

[bam_bam]

Arthur's happiness is proportional to the function w2*c (w squared * c), where w stands for the daily expansion of his ego, and c stands for the daily increase of his self-importance. Now, ego expansions costs £3 per pump and self-importance injections cost £2 each. His daily budget for both is £100. How should he divide his money between ego and self-importance to maximize his happiness? Assume he does not have to buy integer numbers of either ego pumps or self-importance jabs.

[amanda1]

I offer this to stir thought and discussion, not to incite
I'll approach it 2 ways, comparative and analytical

comparative, same magazine, same testing regime, same driver, both corrected for temp/atm press
just got a mag today that tested a new Boss Mustang
444 HP @ 7500
380 lb ft @ 4500
5 liter V8
similar to the RS4 engine type
gear ratios are the same, both are doing ~92 mph at HP peak
both shift the same number of times for the 0-100, the 1/4 and 0-120

the RS4 weighs 9% more (3980 vs 3666)
the Boss has >7% more HP and 20% more torque
peak HP/wt 8.25 vs 9.6, 17% more
peak torque/wt, more important, 9.65 vs 12.55, 30% difference!
torque at peak HP (213 vs 266) a 25% difference
so over the power band the Boss has ~27.5% more torque/wt than the RS4...
and since F = ma, accel is proporational to force/torque...

.........RS4....Boss
1/4....13.0...12.8...1.5%
trap...109....113....3.5%
0-120...16....14.9....7%

how can the RS4 be so close despite the power/wt adavantage of 17% to 30% depending on the variable compared?
it gets worse if we assume 380 rather than 414 for the RS4

analytical
assume a loaded wt of 4100
3-8k 8.5 sec
speed 36-96 mph or 53-141 ft/sec (delta 88 ft/sec)
a = 88 ft/sec / 8.5 sec ~ 10.4 ft/sec^2 (average)
F = ma = (4100/32) (10.4) ~ 1330 lb (force) as thrust
T = F x r = 1330 x 13/12 ~ 1440 lb ft at wheels
converted to engine = torque wheels / gear ratios ~ 1440/(4.11 x 1.52) ~ 230 lb ft (after drivetrain and tire losses)
so 230 average and since it makes 90% from 3-8k we can assume peak to be ~ 1.1 x 230 ~ 253 lb ft after losses at the wheels

the engine is rated 317, so 90% or the average would be 285 lb ft (before losses)
if we assume total losses of only 15% (the tires slip 3% alone, so 12% for the drivetrain)
at the wheel average ~ 0.85 x 285 ~ 240 or peak of 1.1 x 240 ~ 265 lb ft (after 15% losses)
calculated average at the wheels (15% losses)...230 vs 240, 4% difference...peak 253 vs 265, ~4-5%
but we know losses are higher than...12% + 3% ~ 15% (it has twice the axles, and 3 vs 1 diffs compared to a 2wd, 2 more diffs, front to rear, and front, the trannies cancel and are efficient, it's the axles and diffs that have losses, they have angles and change directions, so twice the axle and 3 times the diff losses, let's assume 50% more losses)...
if we use the same for tires and adjust the rest (1.5 x 12) + 3 ~ 21%

if we assume only 20% total losses (I believe it to be 20-22%)
rated becomes avg/peak...230/253...the same as calculated

these are some of the 'proofs' I have used to convince myself the car makes rated power

Nice read can you do this for the RS6 v8 v v10???

[bam_bam]

^ agreed. As much as I take the piss Arthur, the B5 RS vs B7 RS and the C5 RS vs C6 RS maths essay question would be a very interesting read, and probably more relevant. I'm excited now!

[duud40]

You`re taking a very complicated way of explaining something very simple. US cars are crap.
Seriously now . Plot a histogram of thrust for both cars vs time . Area under the curve shows you the winner. And it`s graphic and everybody understands pictures.
The car does not make the same power with carbon deposits. Why can`t you get that?
People have dyno tested rs4 before and after carbon cleaning maybe at most a week apart and had 30 ish horsepower difference.

[ArthurPE]

relax guys...simmer down
show me the 'error' of my ways...don't sling insults

I have plotted the curves using mathlab and integrated (numerically) the area under for both torque and power vs rpm and distance and speed vs time...
the car makes ~415 HP and cars cleaned/uncleaned show no statistically signifcant difference

the math I used is simple, F = ma...we know the mass, we know the time and we know the change in speed, hence the avg acceleration can be determined...we can approximate the losses...
show me where the arguement falls down, not personal attacks

[P_G]

You`re taking a very complicated way of explaining something very simple. US cars are crap.
Seriously now . Plot a histogram of thrust for both cars vs time . Area under the curve shows you the winner. And it`s graphic and everybody understands pictures.
The car does not make the same power with carbon deposits. Why can`t you get that?
People have dyno tested rs4 before and after carbon cleaning maybe at most a week apart and had 30 ish horsepower difference.

duud40, whilst I agree with what you have said my concern with every carbon related discussion is the point when people start saying with carbon it had 'x'-power and cleaned it had y-power. How long does it have 'y'-power, about 500-2000 miles max because as has been clearly said in the FSI patent carbon build up is a by product of these engines so it is supposed to be there. And it is present in the engine when rated power was measured for this engine so theoretcially if you clean your car then you could actually have more than rated power for a short period of time but the way you are measuring it only shows near rated figures. How's that for a concept?

If one has the time or more importantly the money to throw £600-1000 to have your IM cleaned every 2-5k miles then best of luck to you, but bang for buck it is one of the least economical mods available and there are plenty of examples out there where a car that has never been touched will run as well or within a close proximity of a cleaned RS4. There are too many variables in every measuring method to pitch one car against another, even dyno testing.

[edge]

duud40, whilst I agree with what you have said my concern with every carbon related discussion is the point when people start saying with carbon it had 'x'-power and cleaned it had y-power. How long does it have 'y'-power, about 500-2000 miles max because as has been clearly said in the FSI patent carbon build up is a by product of these engines so it is supposed to be there. And it is present in the engine when rated power was measured for this engine so theoretcially if you clean your car then you could actually have more than rated power for a short period of time but the way you are measuring it only shows near rated figures. How's that for a concept?

If one has the time or more importantly the money to throw £600-1000 to have your IM cleaned every 2-5k miles then best of luck to you, but bang for buck it is one of the least economical mods available and there are plenty of examples out there where a car that has never been touched will run as well or within a close proximity of a cleaned RS4. There are too many variables in every measuring method to pitch one car against another, even dyno testing.

Does everything think that the return of the deposits could be as soon as 500miles?

[adsgreen]

I've seen a 2011 mustang and like most US cars it's simply huge and built like a barge.
I'd wager cross section area is much higher than the RS4 and probably Cd is too.

Also assuming gear ratios are the same, the RS4 has an advantage of another 600 odd RPM and hanging onto a lower gear can make all the difference if there's one extra gearchange involved for the mustang just in the time taken to switch cogs making things appear closer than they are.

[sonny]

Off topic, that 2011 Mustang looks awesome, I even looked into buying one.

carry on...

[2manytoys]

Did someone call my name?

Q. Does the RS4 make it's claimed power?
A. Probably, but nobody I know has removed the engine to find out? (a bit like the oil discussion that goes on, no one has stripped the engine to know what effect each brand oil has had).

Q. Does Carbon impact power?
A. If you have enough of it, absolutely. It can cause the timing to <beep> more aggressively than normal, and thus reduces power in the higher revs. Do I know how/why? Not really. I can speculate, but all I know for sure is it happens.

Q. Is the RS4 a quick car, and more importantly does it live up to the hype?
A. Sure it's quick, but there are faster cars out there. But show me an AWD V8 convertible (in my case) that's as good value.

Here is a Dyno Graph for the non-believers
Note: The red line is a new RS4 engine after being run-in. The blue is the old engine full of carbon. Notice the Red line (shape) more closely represents the claimed power in Audi's own brochure


Audi's Claimed Power Graph - Look at this brochure, and note the shape
http://www.jlosee.com/images/RS4/PDF/RS4%20Brochure.pdf

Seriously, could I not add my 2c to this thread

[andre3k]

A little off-topic but Arthur I read you were working on something re the deposits, how's that progressing?

[ArthurPE]

I've seen a 2011 mustang and like most US cars it's simply huge and built like a barge.
I'd wager cross section area is much higher than the RS4 and probably Cd is too.

Also assuming gear ratios are the same, the RS4 has an advantage of another 600 odd RPM and hanging onto a lower gear can make all the difference if there's one extra gearchange involved for the mustang just in the time taken to switch cogs making things appear closer than they are.

the aero is similar, and moot until 120
it's a small fraction of the total power expended...
so if it's even 10% at 100 mph and the difference of Cd x area is 10%, you are talking 1% in 20% of the range, or 0.2% total impact...moot

the Boss is faster than an M3 around Leguna Seca
and 300 lbs lighter than an RS4, so both must have fog-horns
the stuff I've read said it's steering is something 'BMW would be proud of', this from BMW grovelers
the engine is all aluminum, port injected, 4V, variable intake/exh cams and makes rated power (something most say Audi can't do, lol)

peak power
Boss 7500
RS4 7600-7800
no point shifting after that

as I stated, the gear changes are the same for 0-120 and for the 1/4 mile, both take 3...1-2, 2-3, 3-4