Torque & RPM at Shifts: Explained

[R Power]

Hi everyone
I am damn confused about torque and rpm variation.Please tell me:

1.> When we shift from lower to higher gear, definitely RPM at wheels increase, but does the torque at drive wheel increases or decreases?

2.> I read yesterday that a car accelerates fastest at an RPM corresponding to peak power because it transfers max torque to drive wheels. Then what is the significance of peak torque because i thought car would acclerelate fastest at peak torque.

 

[Lsos]

Torque will DECREASE as you shift into higher gears. You are trading torque for RPM. Try it in your car. Floor it in 1st gear and floor it in a higher gear (at the same RPM).

For second question, at any given speed, a car will accelerate fastest at its peak power. However, in any given gear, the car will accelerate fastest at its peak torque.

At first these might seem in conflict with each other, but I assure you they're not. It might take some mental wrestling you get you mind around this (at least it did for me), but I suggest you deal with it because that's how it works. Took me a while to grasp it, and it felt enlightening when I finally did...

...at least I hope I'm not the only one...

 

[R Power]

Your answer to my second ques is right and i am trying to wrestle in my mind.
But for my first question first of all i didn't talk of engine torque but torque at wheels. What will happen to torque at wheels as I shift? Please reconsider or if I'm wrong notify me!

 

[Lsos]

The torque at the wheels will drop. It is greatest in 1st gear (easily in the thousands of lb-ft) and decreases with each shift, as you trade torque for RPM. If you could keep the engine RPM and torque constant, as with a continuously variable transmission (CVT), you would see that the torque at the wheels would be constantly dropping with acceleration.

On that note, in order to accelerate fastest, a car with a CVT should keep its engine at its POWER PEAK. Even if the engine could produce 1000lb-ft, and 100hp...keep it at its power peak for greatest acceleration.

To help your mind wrestle, consider going to get some groceries with this dyno graph. Let's say you're in 3th gear, and that the RPM at the bottom also correspond to speed (6000RPM=60mph, 7500RPM=75mph). Imagine you're at 6500RPM (65mph) and you gently press floor it. Your acceleration will rise with the torque curve, will peak at around 7500rpm (75mph), and then will slowly drop. So there...in 3rd gear, your acceleration is greatest at 7500RPM (75mph). BUT...keep flooring it, because you're still not at the power peak. The power peak will arrive at 8300RPM (83mph).

Now you will be accelerating a bit slower than you were at 75mph. However, it's important to realize that even though 3rd gear gives the best acceleration at 75mph, you could have theoretically accelerated even faster at 75mph, if you had a different gear ratio for example that would put you closer to the power peak. At 83mph...that's all you got. You are wringing everything you can out of the car, and any change in gear ratio would just slow you down.

http://advancedstreetperformance.com/img/dyno_S2000-oem-vs-asp.jpg

I hope I didn't confuse you...

 

[R Power]

This means max accleration can be achieved only in first gear.

 

[Lsos]

Right. And that's the way it is.

 

[Ranger Mike]

This means max accleration can be achieved only in first gear.

for purposes of the basic discussion, yes...if one is racing a stock grocery getter ( honda , subaru , prius?? 4 cylinder ) in reality, maximum acceleration may occur in second or third gear... let us review- at launch the vehicle is stationary...one can count on a lot of tire slippage when the clutch is engaged..wheel spin kills acceleration..on muscle cars one had to feather the gas pedal in first gear to keep from burning the tires ...so second gear provided the maximum acceleration in many cases. it depends upon the cars configuration

 

[R Power]

But in higher gears we get higher rpm at the expense of less acceleration as compared to first gear i.e. in higher gears the torque provided to accelerate per unit speed is less as compared to small gears but that torque persists over a long range to increase the speed overall. Is it so?

 

[Ranger Mike]

Look at the graph by Lsos
think or torque as low end horsepower or
in my opinion ..it is easier to think of
horse power as high end torque...
the torque curve is relatively flat and maxs out at 136 ft pounds..only 10 ft pounds over the 3000 rpm value..so torque launches the vehicle and horsepower ramps up very nicely
from 3000 RPM to 8000 RPM...what must be done to take advantage of this very linear curve is to match the gearing to make max use of the curves
you will get acceleration over the entire RPM range when this is done

 

[R Power]

Lsos
in higher gears we get higher rpm at the expense of less acceleration as compared to first gear i.e. in higher gears the torque provided to accelerate per unit speed is less as compared to small gears but that torque persists over a long range to increase the speed overall. Is it so?

 

[Ranger Mike]

GXP at the drag strip...

--------------------------------------------------------------------------------



Car Setup: 2000 miles on the car. Still stock when this run was made.

Conditions:
Temperature:......91 degrees F
Humidity:.....75%
Barometer:......28.93 in. HgA
Track (MoKan Dragway):...First racing after 21" of rainfall...poor traction

Best result:
60' ET........2.0954
330' ET......6.0196
1/8 ET.......9.2810
1/8 Trap.....75.40
1000' ET.....12.0436
1000' Trap......87.63
1/4 ET......14.4059
1/4 Trap.....94.28
__________________
2007 Mysterious 5-speed purchased 05/04/2007


note the times at the 60 foot mark, 330 ft mark 670 ft mark , 1000 ft mark and 1340 mark..
this is increasing acceleration..

it took 2 seconds to run 60 ft.
6 sec to reach 330 ft but only another 3.28 seconds to go another 330 ft and only 2.76 seconds to go another 330 ft and only 2.36 second to go the last 340 feet!

 

[Lsos]

Ranger Mike, I'm not convinced your conclusion of "this is increasing acceleration" is correct. Just a quick glance at your speeds...0-75.4mph is 9.28 seconds. 0-94.28mph is 14.4 seconds.

It took just about 9 seconds to get to 75mph, but it took another whole 6 seconds just to go 20mph faster. The speed is increasing as you get further down the track, so obviously the distances will go by faster. But while speed is increasing, your acceleration is still dropping. Fast.

Besides, with that 1/4 mile time, you should have absolutely no problem with traction, except for a small part of 1st gear (depending on front/ rear wheel drive?). After that the acceleration should drop...as it does.

Here's how a typical car's acceleration curve looks like. Notice the change in slope after each gear shift. Road and Track magazine publishes these for a lot of cars...

http://www.p914.com/p914-resources/p914-numbers/p914-numbers-accel-comparison.gif

 

[Bob S]

Here is a little physics:

F = ma (force, Newtons)

F dx = E (work, joules)

F dx/dt = F v (force times velocity = power (watts) or HP x 746)

So HP = m a v/746 =mass x acceleration x speed / 746 (in mks units)

So at higher speeds, acceleration is less.

Bob S

 

[CKwik240]

2.> I read yesterday that a car accelerates fastest at an RPM corresponding to peak power because it transfers max torque to drive wheels. Then what is the significance of peak torque because i thought car would acclerelate fastest at peak torque.

Its easy to get confused about this as more torque should net more acceleration (at that instant). And in fact, this is actually true in any given gear. If you measure instantaneous acceleration in every gear, the fastest acceleration in each gear will occur at the torque peak. Where this becomes more clear is when you relate it to a vehicle's speed. Most cars on the road use fixed sets of gears. But if you chose a particular speed (say 60 mph) and calculated 2 gear ratios where one would place your RPMs at the torque peak at that speed and another that placed the RPMs at the HP peak, what you would find is that the acceleration at that instant would be faster at 60 mph with the gear that placed the RPM's at peak HP. And there would actually be more torque at the wheels as well. Why? Because the higher RPM operation provides more leverage to the available torque.

Consider:

HP = (Torque x RPM) / 5252

To save myself some time, I'm going to paste something I wrote-up elsewhere so please forgive me if it seems out of context:

"If you take 2 different motors that both produce 300 HP. One does so at 4000 RPM (Motor A) and the other at 8000 RPM (Motor B). If you do the calculation, the Motor A will be putting out 393.9 ft-lbs of torque at 4000 RPM. Motor B will output 196.95 ft-lbs at 8000 RPM. That's exactly half the torque output of Motor A, but at twice the speed.

Now if you take Motor A and directly output to the wheels (1:1 gearing), then the wheels will be putting out 393.9 ft-lbs of torque when the wheels are spinning 4000 RPM. Now take motor B and gear it 2:1 to the wheels. When the engine gets to 8000 RPM, the wheels will be turning at 4000 RPM. Same speed as the car with motor A. And get this, since the gearing will double the torque, the car with motor B will be putting out 393.9 ft-lbs of torque at the wheels. Same as the car with Motor A. HP makes it easy to make a more direct comparison of output as it shows the true potential.

As you can see, having more RPM basically gives you a bigger lever. Torque is simply how much weight you put on the lever. HP is the measure of how much can be lifted based on the weight and lever arm length."

To add to this, the reason Peak HP provides the most torque to the wheels is because it represents the point where the engine has the most leverage for the amount of torque it puts out at the corresponding RPM. Its hard to see in cars with traditional transmissions, but if you consider a CVT, where a car can accelerate while its engine can be held at a specific RPM, you'll find that for a given vehicle speed, operating at peak HP will yield more torque at the wheels than operating at peak torque.

As for the significance of peak torque (as published for consumers by vehicle manufacturers), ultimately it has very little meaning. At best it might provide some insight into the shape of the torque curve (flatness/broadness) and its potential uses (trucks tend to need plenty of low-end torque to help get things moving and keep things comfortable when towing/hauling loads; imagine having to climb a hill with a trailer at 6000 RPM the entire way; gas mileage would be terrible as well). But unless a consumer knows what they are looking for and/or how to interpret it, its just a pretty number manufacturers flash in front of our eyes. Higher RPM motors are becoming more prevalant in sports cars and these tend to boast relatively low amounts of torque compared to the HP they have. Haven't followed F1 for a while, but those motors are pretty small (2.6L?) but can achieve some astronomical HP levels (700ish last I remember) without any turbos or supercharging (granted I think they run methanol so a direct comparison is not entirely possible). They rev over some 15,000 RPM (I want to say 18,000 was about as fast as they got at some point) and probably make less torque than most consumer V-8's. 700 HP at 15,000 RPM equates to 245 ft-lbs of torque...

 

[Ranger Mike]

Ranger Mike, I'm not convinced your conclusion of "this is increasing acceleration" is correct. Just a quick glance at your speeds...0-75.4mph is 9.28 seconds. 0-94.28mph is 14.4 seconds.

It took just about 9 seconds to get to 75mph, but it took another whole 6 seconds just to go 20mph faster. The speed is increasing as you get further down the track, so obviously the distances will go by faster. But while speed is increasing, your acceleration is still dropping. Fast.

Besides, with that 1/4 mile time, you should have absolutely no problem with traction, except for a small part of 1st gear (depending on front/ rear wheel drive?). After that the acceleration should drop...as it does.

Here's how a typical car's acceleration curve looks like. Notice the change in slope after each gear shift. Road and Track magazine publishes these for a lot of cars...

http://www.p914.com/p914-resources/p914-numbers/p914-numbers-accel-comparison.gif

[/URL]
i think you are mixing apples and oranges...
Speed x Time = Distance and comparing speed from 0 MPH is not an indication of Acceleration. If acceleration stopped and a constant velocity was established the times at the 330, 670 , 1000 and 1340 feet marks would be the same...the car continues to accelerate as it covers the 1/4 mile

 

[Mech_Engineer]

i think you are mixing apples and oranges...
Speed x Time = Distance and comparing speed from 0 MPH is not an indication of Acceleration. If acceleration stopped and a constant velocity was established the times at the 330, 670 , 1000 and 1340 feet marks would be the same...the car continues to accelerate as it covers the 1/4 mile

Lsos is correct, ideally a car's maximum acceleration is in first gear, and it can be seen in the graph he provided.

http://www.p914.com/p914-resources/p914-numbers/p914-numbers-accel-comparison.gif

This graph is velocity versus time, which means acceleration is defined as its slope (derivative). The slope is highest off the line in first gear, and decreases as the car accelerates and shifts into higher gears.

This has to do with the fact that higher gear ratios in the transmission transmit lower torque to the wheels, but also in the fact that kinetic energy is related to the square of the velocity. For a car accelerating from 0-60 mi/hr, it takes 11 times as much energy to accelerate from 50-60 mi/hr as it does from 0-10 mi/hr. It takes 21 times as much energy to accelerate from 100-110 mph.

 

[xxChrisxx]

I'm avoiding this bloody discussion again like the plague.

EDIT: It's seems I just can't resist temptation on a good torque vs power thread *sigh*

 

[xxChrisxx]

But in higher gears we get higher rpm at the expense of less acceleration as compared to first gear i.e. in higher gears the torque provided to accelerate per unit speed is less as compared to small gears but that torque persists over a long range to increase the speed overall. Is it so?

For your original question:

1.> When we shift from lower to higher gear, definitely RPM at wheels increase, but does the torque at drive wheel increases or decreases?

You need to know 1 equation for this.

POWER = Torque*RPM.
all measured at rear wheel

The engine only puts out so much power so this figure MUST stay the same. If you gear up for torque, RPM must go ddown. You gear for higher RPM, torque must decrease.

That's really all there is to know.

2.> I read yesterday that a car accelerates fastest at an RPM corresponding to peak power because it transfers max torque to drive wheels. Then what is the significance of peak torque because i thought car would acclerelate fastest at peak torque.

At any given speed you will accelerate fastest at peak power. In any given gear you will accelerate fastest at peak torque.

This is becuase gears allow mechanical advantage (they multiply torque). Peak power occurs at a higher ENGNIE RPM than peak torque. Meaning that to get the same wheel RPM and therefore same speed the wheels you can multiply the torque more.

eg. Wheel speed needs to be 1000rpm.

Peak torque at 4000rpm (engine) 10nm torque ourput at this speed
Peak power at 6000rpm (engine) 8nm torque output at this speed

Ratios required:
Peak torque: 4:1 reduction
Peak power 6:1 reduction.

So torque at wheels:
Peak engine torque = 40nm torque at wheels
Peak engine power = 48nm torque at wheels.

NOTE: Do NOT confuse wheel speed with engine RPM

 

[Lsos]

i think you are mixing apples and oranges...
Speed x Time = Distance and comparing speed from 0 MPH is not an indication of Acceleration. If acceleration stopped and a constant velocity was established the times at the 330, 670 , 1000 and 1340 feet marks would be the same...the car continues to accelerate as it covers the 1/4 mile

You're right, the car does continue to accelerate as it covers the 1/4 mile. But, earlier you wrote "this is increasing acceleration", which it is not. Perhaps you meant "this is increasing speed".

The car might be accelerating, but it is doing so at a decreasing rate, not increasing.

 

[Ranger Mike]

I agree..was not correct in the wording but ..this is what the forum is good for..

 

[R Power]

Haven't followed F1 for a while, but those motors are pretty small (2.6L?) but can achieve some astronomical HP levels (700ish last I remember) without any turbos or supercharging (granted I think they run methanol so a direct comparison is not entirely possible). They rev over some 15,000 RPM (I want to say 18,000 was about as fast as they got at some point) and probably make less torque than most consumer V-8's. 700 HP at 15,000 RPM equates to 245 ft-lbs of torque...

If f1 cars do not produce much torque how they get such a ground breaking acceleration?

 

[xxChrisxx]

If f1 cars do not produce much torque how they get such a ground breaking acceleration?

Gears...

 

[xxChrisxx]

Haven't followed F1 for a while, but those motors are pretty small (2.6L?) but can achieve some astronomical HP levels (700ish last I remember) without any turbos or supercharging (granted I think they run methanol so a direct comparison is not entirely possible). They rev over some 15,000 RPM (I want to say 18,000 was about as fast as they got at some point) and probably make less torque than most consumer V-8's. 700 HP at 15,000 RPM equates to 245 ft-lbs of torque...

2.4 L V8
18000rpm max (in 2006 the Cosworth V8 ran at 20000 in races and 21000 on the bench)
Pump petrol (no toluene additives or anything like that)
2009 prediced output is closer to 760Hp.

 

[Lsos]

If f1 cars do not produce much torque how they get such a ground breaking acceleration?

You can get all the torque you want with the right gears. Hell, you can move the Earth if you have the right gear ratio. And I do mean YOU.

 

[CKwik240]

If f1 cars do not produce much torque how they get such a ground breaking acceleration?

Gears was already mentioned, but just as important, high RPM operation. As I mentioned before, high engine RPM acts as a longer lever arm. So you can take a small amount of force and do a lot of work. As I mentioned before:

HP = (Torque x RPM)/5252

And one way to apply HP is by applying it at the wheels. That is, take 300 HP for example. If you geared a car such that it produced 300 HP at 5 wheel RPM, that would come out to 315120 ft-lbs of torque at the wheels. While its unlikely that any motor would have that much torque output at the crank, any motor that can make 300 HP can have its available torque at that RPM make that much torque through the right set of gears. Doesn't matter what the magnitude of the torque output is so long as HP is 300. Try calculating the torque for 300 HP at 1000 RPM increment. Then calculate the gearing you need to spin the wheels at the same wheel speed for each increment. Using the values you calculated for torque, plug them into each corresponding gear. The torque value at the wheel should be the same for each torque rating using the corresponding gear. This occurs because HP ultimately represents how much work can be done in a given amount of time. And each torque value coupled with the RPM it outputs the torque at can do 300 HP worth of work. Its not a difficult concept to understand, but wrapping your head around it is much easier if you do a few calculations to try and understand how things are related...

 

[CKwik240]

This graph is velocity versus time, which means acceleration is defined as its slope (derivative). The slope is highest off the line in first gear, and decreases as the car accelerates and shifts into higher gears.

This has to do with the fact that higher gear ratios in the transmission transmit lower torque to the wheels, but also in the fact that kinetic energy is related to the square of the velocity. For a car accelerating from 0-60 mi/hr, it takes 11 times as much energy to accelerate from 50-60 mi/hr as it does from 0-10 mi/hr. It takes 21 times as much energy to accelerate from 100-110 mph.

I agree on the slope aspect, but I think relating it to Kinetic Energy is incorrect. Consider F=ma. If you removed friction and aerodynamic resistance, a given magnitude of force will accelerate the mass by the same amount regardless of the initial speed. That is, if you applied the same force to an object whether the initial speed was 30 mph or 60 mph, the change in speed will still be the same. The change in rates of acceleration in the graph are related to many factors but the magnitude of force at the wheels changes each time the vehicle is upshifted. The reason the line in the graphs have a slight curve (rather than each segment that represents a gear ratio being perfectly straight) is likely a combination of increasing aerodynamic, perhaps frictional resistance and the fact that most cars are geared such that each upshift at or near redline will drop the RPM's down near the torque peak. And torque naturally declines to some extent beyond the torque peak. Combine these together and you get a curve that looks more like a graph of the square root of x rather than a series of point-to-point straight lines.

 

[Bob S]

Lsos is correct, ideally a car's maximum acceleration is in first gear, and it can be seen in the graph he provided.

http://www.p914.com/p914-resources/p914-numbers/p914-numbers-accel-comparison.gif

This graph is velocity versus time, which means acceleration is defined as its slope (derivative). The slope is highest off the line in first gear, and decreases as the car accelerates and shifts into higher gears.

This has to do with the fact that higher gear ratios in the transmission transmit lower torque to the wheels, but also in the fact that kinetic energy is related to the square of the velocity. For a car accelerating from 0-60 mi/hr, it takes 11 times as much energy to accelerate from 50-60 mi/hr as it does from 0-10 mi/hr. It takes 21 times as much energy to accelerate from 100-110 mph.

This has to do with the fact that at constant power (HP),

HP = m a v/746 =mass x acceleration x speed / 746 (in mks units)

As velocity increases, acceleration decreases for constant power input. See post #13.

Bob S

 

[Mech_Engineer]

I agree on the slope aspect, but I think relating it to Kinetic Energy is incorrect.

The concept is simple, KE=1/2*m*v^2. The difference in kinetic energy of a 1500 kg car between 50 and 60mph is 165 kJ (not taking into account inertial energy in the wheels), meaning you have to add 165 kJ of energy to the car to accelerate it from 50 to 60mph (neglecting air resistance and friction). Accelerating from 0 to 10mph only takes 15 kJ of energy.

The engine has a set amount of power it can put out, this means that as the car accelerates that fixed amount of horsepower can only add energy to the system so fast. If we again neglect air drag and friction, and we also assume our 1500 kg car is putting a constant 100hp to the ground (probably not a good assumption since power changes with engine speed, but it proves the point), it will take approximately 0.2 seconds to accelerate from 0-10 mph, but it takes 2.2 seconds to accelerate from 50 to 60 mph (becaue it needs to add more energy to the system to get there), and would need 4.2 seconds to go from 100-110 mph.

Consider F=ma. If you removed friction and aerodynamic resistance, a given magnitude of force will accelerate the mass by the same amount regardless of the initial speed. That is, if you applied the same force to an object whether the initial speed was 30 mph or 60 mph, the change in speed will still be the same.

Don't forget, the F that is accelerating the car reduces with each upshift, and changes with respect to engine speed. There is no contradiction, F=ma just isn't a very useful euqation for understanding the acceleration of a vehicle with respect to time since it is a dynamic system.

 

[Ranger Mike]

Bob S - your statement


"This has to do with the fact that at constant power (HP),

HP = m a v/746 =mass x acceleration x speed / 746 (in mks units)

As velocity increases, acceleration decreases for constant power input. See post #13."

can you clear up what you mean by constant power? I am laboring under the assumption that the engine has an RPM based HP and Torque curve that is only " constant" when it stalls out after peak is achieved ..or am i missing something...
i thought HP was incereasing over the useable RPM range and thus , is not constant? so if HP continues to increase and the gears are shifted up to labor the engine thru its useable power band, aceleration will continue to increase, though les agressivley at higher gears..or is the Coors light getting to me again?
RM

 

[R Power]

Acceleration is more in the first gear and then decreases while upshift simply because as we shift higher less torque is available to wheels which is solely responsible for acc.

 

[Ranger Mike]

i whole heartedly agree with you.. the HIGHEST Rate of acceleration occurs from a dead stop

 

[Lsos]

In fact, if you do the math, at 0 mph your acceleration could be infinity. Although, that's not the case due to obvious real-world limitations...