[Jonn335]

Originally Posted by teknochild

im reading the underlined as in order for the car to generate the same amount of torque the engine has to run faster, im sure thats not what u meant though so would you mind rephrasing this?

Um....

....

I am trying to describe the diference between power and torque, and its tricky stuff...


The point of my post is to try and illustrate that you can predict what the acceleration of a car will be at diferent speeds by using the torque curve of the engine and multiplying by the gear ratios (OK trans losses do throw a bit of a spanner in the works).
Once you know the torque at the wheel, and you know or can estimate the force it is working against (inertia of the car, friction from the tyres, drivetrain friction losses, air resistance) you can predict the acceleration.
When you are comparing like for like, for example the same car with just a diff change, you can predict how it will behave, without having to change it.

My approach is fairly low tech, i am sure the boffins in BMW and the like have all sorts of fancy computer programs to work this sort of stuff out, but from my calculations i have decided that for me a diff change to 3.64 is not going to be worth doing, unless the engine RPM is raised. Then you can have your cake and eat it as you can go with a lower ratio, and still get the speeds in the gears.
(Perfect example is the M3):rocks: this is why turboed M3s are simply rocket ships. Hi RPM+turbo+low gearing=insane speed.
Lots of times people change the diff and the car just feels faster and sounds faster, but really is just about the same.

[teknochild]

i realize what your trying to say, unfortunatly your wrong, i was trying to get you to restate something that was so obviously wrong to make sure you couldnt say "thats not what i meant" afterwards

theres already a lengthy thread in the general car talk forum you might want to go visit, and do NOT post in it until you read the whole thing through either, and snwere the multiple choice question lol

[angshuman]

Hi All,

Out of sheer curiosity, a friend of mine recently performed some first-principles analysis of a car's behavior under acceleration using straightforward Newtonian physics. Using basic input parameters including the full torque curve, gearing and diff ratios, approximate drag coefficients, estimated shift times and of course, weight, he found that it is possible to estimate the acceleration of a car to a surprising level of accuracy.

He has created a web-based frontend where you can enter the input parameters for any car and apply the analysis. Preset input data are available for some cars, and he will be adding more cars as and when he is able to dig up the input parameters. I am attaching a link to his first public post introducing the concept. The link to the actual web application is at the end of his post.

http://twinturbo.net/net/viewmsg.asp...msg_id=1925430

Regards, A.

[chonko]

Originally Posted by Jonn335

Um....

....

I am trying to describe the diference between power and torque, and its tricky stuff...


The point of my post is to try and illustrate that you can predict what the acceleration of a car will be at diferent speeds by using the torque curve of the engine and multiplying by the gear ratios (OK trans losses do throw a bit of a spanner in the works).
Once you know the torque at the wheel, and you know or can estimate the force it is working against (inertia of the car, friction from the tyres, drivetrain friction losses, air resistance) you can predict the acceleration.
When you are comparing like for like, for example the same car with just a diff change, you can predict how it will behave, without having to change it.

My approach is fairly low tech, i am sure the boffins in BMW and the like have all sorts of fancy computer programs to work this sort of stuff out, but from my calculations i have decided that for me a diff change to 3.64 is not going to be worth doing, unless the engine RPM is raised. Then you can have your cake and eat it as you can go with a lower ratio, and still get the speeds in the gears.
(Perfect example is the M3):rocks: this is why turboed M3s are simply rocket ships. Hi RPM+turbo+low gearing=insane speed.
Lots of times people change the diff and the car just feels faster and sounds faster, but really is just about the same.

I use a simple analogy to explain the concept of Torque and Power.

Consider two athletes with different strengths. Say athlete A and B. Athlete A can lift 100kg, while Athlete B can only lift 10kg. Let us say, that the work to be performed is to move 500 kgs over a distance 1000m.
Let us say Athlete A can run with a load of 100 kg at 1km/hr, and Athlete B can run with a load of 10kg at 5km/hr.
For the sake of simplicity, let us discount the return trip, and focus on the trip with both Athletes carring their loads

Athlete A will accomplish the task in 5 trips (500/100=5)
Athlete A will do it in 5 hrs. 1 hr per trip because he can run at 1km/hr.
In terms of work done, Athlete A has done= 5*(100kg X 1000m)* units
=500000 units

Athlete B will accomplish the task in 50 trips (500/10=50)
Athlete B will do accomplish the task in 12 minutes x 50=600 minutes ie 10 hrs.
In terms of work done, Athlete B has done = 50*(10Kg*1000m)*units
=500000 units

Both Athletes have done the same amount of work, however let us consider the Power.
We define Power as the ability to do work. Power is how fast we can get work done.
For Athlete A, the Power = work done/time taken. =500000 work units/5 hrs time unit
=100000 Power units

For Athlete B, the numbers will be 500000/10hrs
=50000 Power units.
Athlete A is more powerful than Athlete B, or we can say Athlete A is more efficient than Athlete B.

How does this relate to Engines: Torque and Horsepower.
The ability to lift a certain amout of load is analagous to the Torque of the engine.
The Power of the Athlete is analagous to the HP of the engine.

Acceleration like you mentioned is governed by Torque. Torque is what you apply to change the state of the car. The engine delivers a force anytime it strokes which is directly proportional to the combustion(bore size and the fuel type). The force is transferred to the gear box as torque through the crankshaft. Diesel engines have more torque because diesels are richer in Carbon and Hydrogen than Petrol, and they revv lower. And that is why Petrol engines have more Torque than Hydrogen, ethanol or other natural gas engines.

Horsepower relates to how efficient the engine is in performing a stroke:
How quickly air and fuel are mixed. The restriction of any of these components affect the engine efficiency.
How fast the piston travels down the cylinder and how fast they return back to their initial state. BMW tries to keep this very short, F1 engines have even shorter stroke distance.
The richness of the air.
How fast you get the gases out of the piston for the next stroke. Diesel engines suffer from this because they have more gases per piston to discharge, thus can't revv as fast a petrol engines
And finally, the torque generated, or the force generated in the psiton chamber.


Gearing. Gears are mechanical devices we use to improve efficiency. You do now want an engine to be revving at the high end because at high revvs, the engine generates little torque, so we use gears to keep the engine within the optimum window.
Low gears are used to make the process of moving the vehicle at lower speeds easier, and allow the engine to operate within the optimum window.
To turn the gears, you need Torque, and if you don't have it, then you will be limited by the gear size, or you better look for a way of getting it.
Because Torque is a function of the combustion size, it is also affected by rpm, and the gears are used brilliantly to keep the engine in the sweek spot.

So, I will add to your earlier comment, Acceleration= Friction(traction:tires & tarmac; weight of car), Inertia(weight of the car),Torque(cylinder bore:volume of fuel mix per stroke, RPM).
HP= how you can manage and sustain the torque at a given RPM or speed.

Enough said

[e36jakeo]

One additional note about gearing is that cars are typically geared to have closer ratios in the upper gears so that as speed increases there is less of a drop in RPMs between shifts.

Case in pont: if I shift my S2000 at the 9000 RPM redline in each gear the next gear's RPMs are as follows:

2nd gear: 6400 RPM
3rd gear: 6750 RPM
4th Gear: 7250 RPM
5th gear: 7500 RPM
6th gear: 7500 RPM

The power peak is at 8300 RPM, and because it is a peaky motor (little torque, requires revs to make HP), each time you shift you have to climb back up to power peak.

By shortening the final drive ratio you would effectively be running in higher gears, which allow you to always be closer to the power peak. Notice how smart Honda is by having the 8300 RPM power peak the midpoint of the 5th and 6th gear RPM range (7500 - 9000) so the car is always making the max average HP in that gear.

The E36 M3 is the same way, as are most performance cars. Close ratios and a short final drive become most important in peaky, high RPM cars that need to be kept close to their power peak (and, thus, redline) in order to make good HP.

One argument for the fact that, even with 150 lbs more weight and less HP (10-30 HP, depending on what you believe the true HP of the 335i to be) the 335i is as fast as the M3 is because the M3 makes its peak power at 7900 RPM, just 100 RPM below the redline and shift point. Thus in every gear, especially 1st, 2nd, and 3rd, the AVERAGE HP in each gear is far below the 333 HP power peak (perhaps 285 Hp average). The 335i, however, makes peak power at 5800 RPM, well below its 7000 RPM redline. Thus, if you shift at 7000, the power peak remains nearly in the center of each gear and therefore the AVERAGE power in each gear is much higher than the 300-320 HP peak power might suggest (perhaps 290 average).

The result is that at peak acceleration (for that brief instant when the E46 M3 is making all 333 HP) the M3 pulls harder than the heavier 310-320 HP 335i. But the 335i pulls almost as hard as it does at 5800 RPM (peak) everywhere in each gear, and the average HP winds up being great than the M3.

Of course, as you get into 4th, 5th, and 6th gears, where the ratios are closer, the drop from the power peak is less in the M3 and the average HP in those gears may be greater than the 335's average. Thus the M3 will probably walk somewhat on the 335i at speeds over 100 MPH.

[2m3]

Originally Posted by e36jakeo

One additional ..... Thus the M3 will probably walk somewhat on the 335i at speeds over 100 MPH.

e36jakeo, I can tell you understand about cars.

In real life when the car is moving, the short gearing/short final drive ratio/close gear ratio/higher rpm peak torque of E46M3 has advantage over the heavier/longer gearing/lower redline rpm of the 335i.

[herbz]

Originally Posted by e36jakeo

One additional note about gearing is that cars are typically geared to have closer ratios in the upper gears so that as speed increases there is less of a drop in RPMs between shifts.

Case in pont: if I shift my S2000 at the 9000 RPM redline in each gear the next gear's RPMs are as follows:

2nd gear: 6400 RPM
3rd gear: 6750 RPM
4th Gear: 7250 RPM
5th gear: 7500 RPM
6th gear: 7500 RPM

The power peak is at 8300 RPM, and because it is a peaky motor (little torque, requires revs to make HP), each time you shift you have to climb back up to power peak.

By shortening the final drive ratio you would effectively be running in higher gears, which allow you to always be closer to the power peak. Notice how smart Honda is by having the 8300 RPM power peak the midpoint of the 5th and 6th gear RPM range (7500 - 9000) so the car is always making the max average HP in that gear.

The E36 M3 is the same way, as are most performance cars. Close ratios and a short final drive become most important in peaky, high RPM cars that need to be kept close to their power peak (and, thus, redline) in order to make good HP.

One argument for the fact that, even with 150 lbs more weight and less HP (10-30 HP, depending on what you believe the true HP of the 335i to be) the 335i is as fast as the M3 is because the M3 makes its peak power at 7900 RPM, just 100 RPM below the redline and shift point. Thus in every gear, especially 1st, 2nd, and 3rd, the AVERAGE HP in each gear is far below the 333 HP power peak (perhaps 285 Hp average). The 335i, however, makes peak power at 5800 RPM, well below its 7000 RPM redline. Thus, if you shift at 7000, the power peak remains nearly in the center of each gear and therefore the AVERAGE power in each gear is much higher than the 300-320 HP peak power might suggest (perhaps 290 average).

The result is that at peak acceleration (for that brief instant when the E46 M3 is making all 333 HP) the M3 pulls harder than the heavier 310-320 HP 335i. But the 335i pulls almost as hard as it does at 5800 RPM (peak) everywhere in each gear, and the average HP winds up being great than the M3.

Of course, as you get into 4th, 5th, and 6th gears, where the ratios are closer, the drop from the power peak is less in the M3 and the average HP in those gears may be greater than the 335's average. Thus the M3 will probably walk somewhat on the 335i at speeds over 100 MPH.

Great post...... reading it makes perfect sense and all the info is accurate. Thanks

[e36jakeo]

Originally Posted by 2m3

e36jakeo, I can tell you understand about cars.

In real life when the car is moving, the short gearing/short final drive ratio/close gear ratio/higher rpm peak torque of E46M3 has advantage over the heavier/longer gearing/lower redline rpm of the 335i.

The average HP per gear is most important, not where the power in each gear is found (high RPM, low RPM, it does not matter). Close ratios help keep a high revving, peakier powerplant closer to its peak power and, thus, helps it to have a higher average HP in each gear. A torquier engine (like the 3.0L turbo in the 335i) does not need as close ratios since its power curve is not as "steep" as a less torquey engine. It's average HP in each gear is closer to its peak power than a less torquey engine.

As I mentioned, the upper ratios in an M3 get closer and closer, so the drop from peak power is less and thus it averages more HP in these gears. But gear 1, 2, and 3 are quite long for an engine that makes peak power at redline (it goes 100 MPH in 3rd gear -- this is not short gearing). That is why a shorter final drive makes a HUGE difference in an E46 M3 - it gets you to the power peak quicker in each gear and allows you to accerlerate in the higher (closer) gears sooner.

Compare the curve for the 335i
http://paultan.org/wp-content/upload...dyno_large.jpg

to the curve for an E46 M3

http://www.m3forum.net/m3forum/showt...ght=dyno+chart

In an E46 M3 when you shift from 1st to 2nd gear the RPMs drop from 8K to below 5K, where you are only making 200 or so WHP, and you have to climb back up toward the power peak.

In a 335i you shift at 7K and drop back down to 4K or so where the car is still making 225 HP (because of the additional torque). This is less of a drop from power peak, and because the peak occurs 1200 RPM before the redline you stay closer to the peak for longer and average more HP (especially in the lower gears, which are more widely spaced.

As you get into 4th, 5th and 6th in the M3 the RPMs only drop to probably around 5500, 5800 and 6000 (guessing here -- any E46 owners want to chime in with exact numbers), so there is less of a drop from the peak HP and thus a high HP average (= better acceleration). The 335i's upper gears also become closer, but it offers less of an advantage since the drop from peak power was so much less than the M3. Thus the M3 "comes into its own" over 100MPH when it is in 4th-6th gear, and would probably begin accelerating away from a stock 335i.

This is the same reason why an E36 M3 (240 HP, 236 lb/ft of torque, 3175 lbs) equaled the 0-60, 0-100, and 1/4 mile times of a Honda S2000 (240 HP, 151 lb/ft of torque, 2800 lbs) even though the S2000 was over 10% lighter, has very short gear ratios and a short final drive. Regardless, every time you shift the S2K it temporarily drops to less HP than the M3's corresponding drop due to the M3's additional TORQUE, and has to pull itself back to the power peak again (where it holds the weight/HP advantage).

This is also why a 335i with the XEDE reflash (appox. 380 HP, 420 lb/ft torque, 3600 lbs) may keep up with the projected E90 M3 (est 420 HP, 315 lb/ft torque, 3600 lbs), at least in the lower gears. The extra 100 lbs of torque will mean it is AVERAGING as much HP in the lower gears as the M3. But I don't mean to start THIS again . . .

[2m3]

Originally Posted by e36jakeo

The average HP per gear is....... But I don't mean to start THIS again . . .

e36jakeo, another good post of yours. This is my favorite subject to read and to learn from anybody.

I agree with you regarding the importance of average HP per gear.

What do you think of the effect that 335i is heavier than e46M3, however, the rear tire of E46 M3 at 255/35/19 or 255/40/18 is taller than the 255/35/18 of the335i. Which one yield more advantage? Is there any formula to calculate this?

So lets say to accelerate from 60 mph 100 mph in 3rd gear with both the
335i and E46m3 side by side, what is the Rpm of each car (from 60 mph to 100 mph)

The torque (from the rpm at 60 mph to 100 mph), then we multiply the torque by the gearing

The time of each car in accelerating from 60 mph to 100 mph

[bnj]

Originally Posted by e36jakeo

Of course, as you get into 4th, 5th, and 6th gears, where the ratios are closer, the drop from the power peak is less in the M3 and the average HP in those gears may be greater than the 335's average. Thus the M3 will probably walk somewhat on the 335i at speeds over 100 MPH.

Good remark, though forgetting that drag is the major Force against the acceleration at high speeds. Peak Hp/CdA is the same for both cars.

[bnj]

Originally Posted by 2m3

What do you think of the effect that 335i is heavier than e46M3, however, the rear tire of E46 M3 at 255/35/19 or 255/40/18 is taller than the 255/35/18 of the335i. Which one yield more advantage? Is there any formula to calculate this?

Weight is a factor.
Tire size is taken into account in the ratios already.

[Jonn335]

Thanks e36jakeo, you have explained the whole thing very well. My head is still spinning a bit, but i think i have a better handle on whats going on!

[SkipSauls]

GearCalc download

GearCalc is a free app that lets you plug in the gear ratios, tire size, RPM limits, etc. and compute the speed in gears. Here's an example of the output for a 335i Steptronic:



It shows the MPH per 1000, MPH at max HP, MPH at max RPM, and so on. The second table shows the MPH and RPM in a gear, so you can compare the RPMs for upshifts, which is a good way to see how well the engine stays in the powerband. For example, here are the results for a 335i AT, an M3 MT, and a Viper Competition Coupe, just for kicks:



It's nice for playing "what if" with different gear ratios, tire size, and so on.

[e36jakeo]

Originally Posted by bnj

Good remark, though forgetting that drag is the major Force against the acceleration at high speeds. Peak Hp/CdA is the same for both cars.

So true! I figure the M3 and 335i have very similar drag coefficient and frontal areas so this should be very close to equal and thus the effect of avg. HP in each gear should play the major role in this particular case.

Another thing to ponder: The "500 HP" M5 (without a speed limiter) is supposed to run 205 MPH while a 505 HP Z06 Corvette hits the wall at 198 MPH. The Corvette has much less frontal area (a lot lower) and probably the same Cd, plus more torque, yet the M5 tops out faster???? Yet more support for the fact the M5 is making substantially more than 500 HP.

[bnj]

Originally Posted by e36jakeo

So true! I figure the M3 and 335i have very similar drag coefficient and frontal areas so this should be very close to equal and thus the effect of avg. HP in each gear should play the major role in this particular case.

Another thing to ponder: The "500 HP" M5 (without a speed limiter) is supposed to run 205 MPH while a 505 HP Z06 Corvette hits the wall at 198 MPH. The Corvette has much less frontal area (a lot lower) and probably the same Cd, plus more torque, yet the M5 tops out faster???? Yet more support for the fact the M5 is making substantially more than 500 HP.

Cd values are 335i: 0.3, E46 M3: 0.33, width and height are the same so the frontal area should be appr. the same. Thus there is 10% difference in CdA, Stock to stock there is the same 10% difference in peak hp. Thus, peak hp/CdA are equal.

Z06 is wider than M5. Moreover being a true sports car - not a luxory sedan - Z06 is designed to stay on road at over 155mph (unlike M5 of which top speed is limited). Therefore Z06 has downforce and fat tires and respectively the cd is 0,342 whereas M5 has some 0.30 or 0.31. The CdA of Z06 is clearly more than that of M5 which explains the difference in top speed (compared to an unlimited M5).

[e36jakeo]

Originally Posted by bnj

Cd values are 335i: 0.3, E46 M3: 0.33, width and height are the same so the frontal area should be appr. the same. Thus there is 10% difference in CdA, Stock to stock there is the same 10% difference in peak hp. Thus, peak hp/CdA are equal.

Z06 is wider than M5. Moreover being a true sports car - not a luxory sedan - Z06 is designed to stay on road at over 155mph (unlike M5 of which top speed is limited). Therefore Z06 has downforce and fat tires and respectively the cd is 0,342 whereas M5 has some 0.30 or 0.31. The CdA of Z06 is clearly more than that of M5 which explains the difference in top speed (compared to an unlimited M5).

Oh geez, now we are going to get into the complexities of aerodynamics (which a know a lot less about!). I am not sure at what speed a 10% increase in CdA will offset a 10% increase in peak HP. I'd guess it would be way up near the top speed of the cars (not at 100 MPH), but this is just a guess.

The Z06 is wider, but it is also about ten inches shorter than the M5, so I'd guess the frontal area for the M5 would still be greater, but again, just speculation. Regardless, 198 or 205 are both LUDICROUS SPEED!

Thanks for chiming in, bnj. I appreciate your perspective and expertise.:rocks:

[musc]

Originally Posted by bnj

Cd values are 335i: 0.3, E46 M3: 0.33, width and height are the same so the frontal area should be appr. the same. Thus there is 10% difference in CdA, Stock to stock there is the same 10% difference in peak hp. Thus, peak hp/CdA are equal.

Z06 is wider than M5. Moreover being a true sports car - not a luxory sedan - Z06 is designed to stay on road at over 155mph (unlike M5 of which top speed is limited). Therefore Z06 has downforce and fat tires and respectively the cd is 0,342 whereas M5 has some 0.30 or 0.31. The CdA of Z06 is clearly more than that of M5 which explains the difference in top speed (compared to an unlimited M5).

I have seen numerous publications list the drag coefficient for the E46 M3 as 0.29. I have also seen it quoted up to 0.33 as you mentioned. Not sure which is truly correct.

[bnj]

Originally Posted by catm3

I have seen numerous publications list the drag coefficient for the E46 M3 as 0.29. I have also seen it quoted up to 0.33 as you mentioned. Not sure which is truly correct.

In the latest official Bmw-brochures Cds are consistently:
M3 coupe: 0.33 and M3 convertible: 0.35
e.g.
http://www.pacificbmw.com/docs/pdf_pic/2005MModels.pdf
page 11

[bnj]

Originally Posted by e36jakeo

Oh geez, now we are going to get into the complexities of aerodynamics (which a know a lot less about!). I am not sure at what speed a 10% increase in CdA will offset a 10% increase in peak HP. I'd guess it would be way up near the top speed of the cars (not at 100 MPH), but this is just a guess.

The Z06 is wider, but it is also about ten inches shorter than the M5, so I'd guess the frontal area for the M5 would still be greater, but again, just speculation. Regardless, 198 or 205 are both LUDICROUS SPEED!

Thanks for chiming in, bnj. I appreciate your perspective and expertise.:rocks:

Thanks, you yourself had a great long analysis here.

CdA is directly related (linear) to the required Power to upkeep a certain speed. At 100 mph drag is a lot, but still a lot of power is left for acceleration. At top speed almost all power is used against the drag. Thus a CdA/peak whp -relation defines pretty much the top speed (given that gearing is matched so that top speed is at peak whp).