How does torque affect car performance?

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If gear ratios don't multiply torque, why do certain axle application guides specify input or output torque limits that are WAY beyond anything a production engine could generate?
I haven't read all of the thread, but the posts I did read where people were disagreeing about this were caused by a failure to define where the torque is being measured. If an engine produces x Nm of torque at y rpm, it does that independently of any gear ratios applied, i.e. the gear ratio does not affect torque measured at the engine. The gear ratio does affect torque measured at downstream parts such as the axle.
 
I haven't read all of the thread, but the posts I did read where people were disagreeing about this were caused by a failure to define where the torque is being measured. If an engine produces x Nm of torque at y rpm, it does that independently of any gear ratios applied, i.e. the gear ratio does not affect torque measured at the engine. The gear ratio does affect torque measured at downstream parts such as the axle.
That was clearly and repeatedly defined, however a particular member didn't understand that gears have a different effect on power and force.
 
I know this is an old topic but I think I have something worthwhile to add.

If gear ratios don't multiply torque, why do certain axle application guides specify input or output torque limits that are WAY beyond anything a production engine could generate?

For example, the Dana 44 axle, used in the Dodge Viper among others, is rated for ~4,500 ft/lb of output torque. Obviously, no production car engine on earth will generate that much.

As for the general question of Horsepower vs Torque, my opinion is that torque is mostly a factor when launching in 1st gear. Having more torque means either more kick off the line or a higher top speed with the same acceleration, all depending on your gear ratio. After that, you're going fast enough that you can simply maintain your RPMs at peak horsepower by changing gears.
Some cars, like turbocharged cars, have high torque but depending on their engine displacements, turbo setups and transmission characteristics (like number of gears or gear ratios), along with some other factors, affect the powerband to act peaky under full throttle in which the engine behaves lethargically during initial acceleration but as the revs go on, suddenly some surge of power comes in and the engine starts to feel very lively as it hits higher RPMs. Then again, some turbocharged engines are like this because of either turbo lag or boost threshold. But yeah, gear ratios can affect top speed or acceleration, too. Shorter gear ratios will allow for faster acceleration at the cost of lower top speed while having longer gear ratios will result into higher top speed at the expense of slower acceleration.
 
I haven't read all of the thread, but the posts I did read where people were disagreeing about this were caused by a failure to define where the torque is being measured. If an engine produces x Nm of torque at y rpm, it does that independently of any gear ratios applied, i.e. the gear ratio does not affect torque measured at the engine. The gear ratio does affect torque measured at downstream parts such as the axle.
Ironically, I've had this same issue on professional trucker forums. You'd think if anyone could properly define torque, it'd be them.

Some cars, like turbocharged cars, have high torque but depending on their engine displacements, turbo setups and transmission characteristics (like number of gears or gear ratios), along with some other factors, affect the powerband to act peaky under full throttle in which the engine behaves lethargically during initial acceleration but as the revs go on, suddenly some surge of power comes in and the engine starts to feel very lively as it hits higher RPMs. Then again, some turbocharged engines are like this because of either turbo lag or boost threshold. But yeah, gear ratios can affect top speed or acceleration, too. Shorter gear ratios will allow for faster acceleration at the cost of lower top speed while having longer gear ratios will result into higher top speed at the expense of slower acceleration.
I remember discussions where people suggested taller first gears to encourage the turbo to spool. It makes sense on paper because taller gears increase engine load (and therefore turbo input) but I don't know how well this works in real life.
 
I know this is an old topic but I think I have something worthwhile to add.

If gear ratios don't multiply torque, why do certain axle application guides specify input or output torque limits that are WAY beyond anything a production engine could generate?

For example, the Dana 44 axle, used in the Dodge Viper among others, is rated for ~4,500 ft/lb of output torque. Obviously, no production car engine on earth will generate that much.

As for the general question of Horsepower vs Torque, my opinion is that torque is mostly a factor when launching in 1st gear. Having more torque means either more kick off the line or a higher top speed with the same acceleration, all depending on your gear ratio. After that, you're going fast enough that you can simply maintain your RPMs at peak horsepower by changing gears.

Taking a look at the physics:

Gear ratio does indeed multiply torque, because gear ratio tells you how the length of the lever is scaled, and torque is [force]*[length of lever]. Longer lever means more torque.

So feeding torque through a gear ratio of 2 means that you scale the lever by a factor of 2, and thus get twice the amount of torque.
But a longer lever also means that it moves more slowly, and the speed is actually scaled by the inverse of the gear ratio, in this case 1/2.

Regarding performance, torque alone is a meaningless figure because we can define performance as [units of work] / [unit of time], and work is [force]*[displacement]. Since torque is [force]*[length of lever] we can solve for force by dividing torque with the length of the lever (for a car you could for example take wheel torque divided by the wheel radius), but we're missing the displacement and we're missing the unit of time, which means that we have no idea how it will perform:

performance = [force]*[displacement]/[unit of time]
= ([torque]/[lever])*[???]/[???].

Now, [displacement]/[unit of time] = speed, which means that the missing component is actually the speed component. So ([torque]/[lever])*[speed], or [force]*[speed], will give us all we need to solve for the performance.

As it happens, [force]*[speed] is exactly what power is and because of this we can use the power figure to easily work out the force that the car will produce at any given speed (ignoring frictional losses): force = [power]/[speed]. Furthermore, acceleration = [force]/[mass], so if we know the mass of the car we can also work out the acceleration: acceleration = [power]/([speed]*[mass]), again ignoring frictional losses.

The equation above shows that to get maximum acceleration for any given speed and for a constant mass you want to maximize the amount of power. Torque is not completely irrelevant, but it's just one component of power. As such, the torque figure might give you a clue regarding acceleration, but it doesn't tell the whole story. It's easy to think that 600 Nm @ 4000 RPM would win a drag race against 500 Nm @ 6000 RPM, but most likely (depending on the gearing and the shape of the power curves) it's the other way around.

It also explains why in racing you usually want to run the engine as close to peak power as possible, rather than as close to peak torque as possible. The reason why the power curve keeps climbing long after the torque curve has started dropping is because the engine speed increases at a faster rate than the torque decreases (Δτ/Δω > -1), which means that the torque loss can easily be regained by applying a shorter gear ratio (since gear ratio multiplies the torque). The power curve only drops once the torque starts decreasing faster than the speed increases (Δτ/Δω < -1) and from that point the torque loss can no longer be regained by applying a shorter gear ratio.

τ = Torque (in Nm)
ω = angular velocity (in radians/second)


I remember discussions where people suggested taller first gears to encourage the turbo to spool. It makes sense on paper because taller gears increase engine load (and therefore turbo input) but I don't know how well this works in real life.

A taller gear does not increase engine load, because the engine load is equal to the torque produced by the engine and as such it's not changed by gear ratios. It might feel like the load increases with taller gearing because the acceleration suffers (which should mean that resistance is greater), but what is actually happening is that the car is simply producing less torque at the wheel.
 
I'm familiar with the basics of gear ratios so I understand the trade-off between top speed and final output torque.

And yeah, for the thing about turbos, I ultimately meant making the engine work harder or, as you called it, increasing resistance. It makes sense to me that insufficient resistance would prevent the turbo from running all-out, which would indeed limit engine torque.
 
In a high torque car, If you nose up against a barrier you can burn rubber in 1st and shift all the way up to 6th gear going absolutely nowhere at 200mph.
 
In a high torque car, If you nose up against a barrier you can burn rubber in 1st and shift all the way up to 6th gear going absolutely nowhere at 200mph.

And that is because high torque cars generally produce high power over a wide RPM range.

Any car can produce a high amount of torque if you just give it a short enough gear (in fact the limit is infinite), but only powerful cars can produce high torque at high speed.

And yeah, for the thing about turbos, I ultimately meant making the engine work harder or, as you called it, increasing resistance. It makes sense to me that insufficient resistance would prevent the turbo from running all-out, which would indeed limit engine torque.

Okay, so increased inertia.

I doubt it would have any beneficial effect, because with a taller gear you are reducing engine speed and that gives less exhausts to drive the turbo. And with a lower engine speed you also start with less power so it sounds like a double loss.
 
Okay, so increased inertia.

I doubt it would have any beneficial effect, because with a taller gear you are reducing engine speed and that gives less exhausts to drive the turbo. And with a lower engine speed you also start with less power so it sounds like a double loss.
Wouldn't you have more exhaust volume anyway if you were going full throttle?

Also, I imagine that a short gear means you'd be on the throttle for a shorter period of time before hitting the engine's redline, which sounds like it would add up to less exhaust flowing through.
 
And that is because high torque cars generally produce high power over a wide RPM range.

Any car can produce a high amount of torque if you just give it a short enough gear (in fact the limit is infinite), but only powerful cars can produce high torque at high speed.
Even those with CVTs?
 
Some cars, like turbocharged cars, have high torque but depending on their engine displacements, turbo setups and transmission characteristics (like number of gears or gear ratios), along with some other factors, affect the powerband to act peaky under full throttle in which the engine behaves lethargically during initial acceleration but as the revs go on, suddenly some surge of power comes in and the engine starts to feel very lively as it hits higher RPMs. Then again, some turbocharged engines are like this because of either turbo lag or boost threshold. But yeah, gear ratios can affect top speed or acceleration, too. Shorter gear ratios will allow for faster acceleration at the cost of lower top speed while having longer gear ratios will result into higher top speed at the expense of slower acceleration.
Gear ratios are not short or long. They're just numbers.
Depending on how close they are to each other (in the sense that 3.0 is as close to 2.0 as 1.5 is close to 1.0), they influence how much the drop in rpm is when upshifting, making the gears feel short/long until you reach the upshift rpm again.
I know it's what you meant, but it might be good to clarify for some.
 
Gear ratios are not short or long. They're just numbers.
Depending on how close they are to each other (in the sense that 3.0 is as close to 2.0 as 1.5 is close to 1.0), they influence how much the drop in rpm is when upshifting, making the gears feel short/long until you reach the upshift rpm again.
I know it's what you meant, but it might be good to clarify for some.
Yeah, not that familiar with the more technical stuff but that's a good insight. I remember gears can be adjustable in GT5/GT6 with a fully customizable transmission.
 
Yeah, not that familiar with the more technical stuff but that's a good insight. I remember gears can be adjustable in GT5/GT6 with a fully customizable transmission.
They still are, do you not play GT Sport? Its the first thing to take care of on every car basically, unless BoP races..
By the way it's not that technical, and it's really worth understanding the simple logic behind it, cause it's much more fun tuning the gear ratios/final gear when you are more aware of it.
 
They still are, do you not play GT Sport? Its the first thing to take care of on every car basically, unless BoP races..
By the way it's not that technical, and it's really worth understanding the simple logic behind it, cause it's much more fun tuning the gear ratios/final gear when you are more aware of it.
I don't have the game yet rofl. :lol:
 
Wouldn't you have more exhaust volume anyway if you were going full throttle?

Also, I imagine that a short gear means you'd be on the throttle for a shorter period of time before hitting the engine's redline, which sounds like it would add up to less exhaust flowing through.

If exhaust flow is volume per second, then a faster engine speed gives you a greater exhaust flow since you burn more fuel per second.

Yes it will be interrupted when you shift gears, but up until that point you have had substantially better performance and you don’t have to wait that long until the boost is back up again. If you look at the energy chart it will be like comparing a steep staircase with a shallow ramp. The steep staircase will take you higher even though it’s not a continuous climb.

Even those with CVTs?

Yes, a CVT is simply allowing you to always run the engine at a constant speed (in between some minimum and maximum wheel speed), meaning you can always have peak torque or peak power, depending on if you want maximum fuel efficiency or maximum performance. And that means that if you equip a low torque / high power car with a CVT it can pull off the same stunt as the high torque / high power car, because the power curve (as a function of wheel speed, since engine speed would now be constant) will essentially be completely flat and wheel torque is equal to power / angular wheel speed (ignoring frictional losses).
 
I'm happy this thread improved. Page 1 is just an absolute nightmare.

Torque is the force at the wheels at any given moment. You can apply a torque on a wrench without even moving. Torque is a force and doesn't require movement.

I think of it as how strong a force the engine is putting on the crank / rods at any one time.

My CTR EP3 for example can take around 300lbft on standard internals, but if you manage the torque right you can make lots of power with a turbo, as long as the torque never goes above 300lbft.

You can break the engine at 300hp if you make too much torque but others at 400hp can run just fine, at a lower torque figure. This just requires higher revs.


Now about GTS, the Nissan GTR GR3 in the game wheelspins all the time, its a very torque filled engine, and the NA engines (Lexus) don't appear to, so I think this is the manifestation of high torque turbo vs "low" torque NA. I find NA engines in the class easier to handle generally.
 
Torque is as much important as power output, engine wise.

But, like power output, the maximum value means close to nothing, it's all about having as flat as possible torque curve to have usable range.
You can have a bigger, low revving engine and loads of torque with same power as a smaller, high revving but low torque engine.
Each one as pros and cons.

Essentially you must be wise when tuning, specially with gearing. Or in GT Sport Sport Mode the way you shift.
One great example is the FT1/Supra Gr. 3, which should be substantially shortshifted, as it as absolutely no torque in the high end.
Also, high torque at low revs means you are more likely to wheel spin at corner exit, losing time and increasing tire degradation.
A car that as a solid low and mid range torque doesn't loses much performance when you shortshift in endurance races.

Torque is the force at the wheels at any given moment. You can apply a torque on a wrench without even moving. Torque is a force and doesn't require movement.

I think of it as how strong a force the engine is putting on the crank / rods at any one time.


Now about GTS, the Nissan GTR GR3 in the game wheelspins all the time, its a very torque filled engine, and the NA engines (Lexus) don't appear to, so I think this is the manifestation of high torque turbo vs "low" torque NA. I find NA engines in the class easier to handle generally.

Naturally aspired engines can have big torque values too.
The wrench example is great. Imagine a big wrench and a small wrench. Applying the same directional force, you can generate much more torque with the bigger wrench, has the torque is a product of FORCE x RADIUS (from center of the screw/bolt to the point on the wrench the force is applied)

It all depends how combustion chambers, piston heads, connection rods and crackshafts are designed.

If you get an engine with bigger cylinder (and piston head) diameter, you get a smaller engine stroke to get the same engine displacement. You get more force (bigger area to expanding combustion gases to push the piston), but you get less torque, as the radius of crackshaft/rod is smaller. You can also rev higher with less stroke, has piston has less linear movement on the expansion/compression cycle. You get a high reving, low torque engine, usually with higher maximum power output but smaller usable power range.

Usually big, low revving, NA engines have loads of torque a, but in racecars, because they usually have power limited by air intake restrictors, they behave a little different.
 
Torque is as much important as power output, engine wise.

But, like power output, the maximum value means close to nothing, it's all about having as flat as possible torque curve to have usable range.
You can have a bigger, low revving engine and loads of torque with same power as a smaller, high revving but low torque engine.
Each one as pros and cons.

Essentially you must be wise when tuning, specially with gearing. Or in GT Sport Sport Mode the way you shift.
One great example is the FT1/Supra Gr. 3, which should be substantially shortshifted, as it as absolutely no torque in the high end.
Also, high torque at low revs means you are more likely to wheel spin at corner exit, losing time and increasing tire degradation.
A car that as a solid low and mid range torque doesn't loses much performance when you shortshift in endurance races.



Naturally aspired engines can have big torque values too.
The wrench example is great. Imagine a big wrench and a small wrench. Applying the same directional force, you can generate much more torque with the bigger wrench, has the torque is a product of FORCE x RADIUS (from center of the screw/bolt to the point on the wrench the force is applied)

It all depends how combustion chambers, piston heads, connection rods and crackshafts are designed.

If you get an engine with bigger cylinder (and piston head) diameter, you get a smaller engine stroke to get the same engine displacement. You get more force (bigger area to expanding combustion gases to push the piston), but you get less torque, as the radius of crackshaft/rod is smaller. You can also rev higher with less stroke, has piston has less linear movement on the expansion/compression cycle. You get a high reving, low torque engine, usually with higher maximum power output but smaller usable power range.

Usually big, low revving, NA engines have loads of torque a, but in racecars, because they usually have power limited by air intake restrictors, they behave a little different.
The radius is a good point, its mainly why a higher stroke increases torque if I remember right. Because its like the larger wrench effect mentioned earlier on the crank.
 
I like using a bicycle to describe torque and horsepower. When you ride a bike, you have to push on the pedals with your feet. If you keep doing that over time you build speed. The force you exert to push down the bicycle pedal is torque. The momentum that's gained from pushing the pedal multiple times over a period of time is power. In other words, torque is the strength of your legs. Power is you pedaling multiple times.

The same concepts applies to car engines. The only difference is that a car engine is far more complex than a human pedaling a bike. A human pedaling a bike has peak torque at 0 RPM, and that's because a human's leg strength is always constant. A naturally aspirated car engine on the hand generally produce peak torque at 3000 RPM's. This is because the engine's fuel and air quantity, mixture, and efficiency, compared to its friction is at its best, and that's when it produces the most strength. As the RPM's start going higher, the engine's strength begins being applied multiple times over a given period of time, and that's how horsepower is derived. Keep in mind that 3000 RPM's is an arbitrary number and was only used for explanation sake. Peak torque is dependent on an engine's design and varies for every car.

So how does this apply to Gran Turismo? Well depending on a car's torque figures and at what RPM it achieves that peak torque, the car will react differently upon acceleration. For example, a Subaru BRZ has peak torque of 155 ft-lbs at 6500 RPM's. A BMW M4 has a peak torque of 411 ft-lbs at 1200-5500 RPM. The Subaru BRZ will struggle accelerating, especially in higher gears, unless it's revved out to at least 6500 RPM. A BMW M4, on the other hand, will accelerate with ease, even in higher gears, starting at 1200 RPM. It's also important to keep peak torque in mind when cornering. The car with the most torque at a given RPM is more susceptible to spin its tires if given too much throttle. For example, if both the BRZ and M4 are taking a corner in 3rd gear at 3000 RPM at full throttle, the BMW M4 will spin out and BRZ won't, because there's far more power being applied to the M4's rear wheels than there is for the BRZ.

I hope that helps. That was the best way I could explain it.

Wow, it helped me. Very well put for someone like me, who isn't much of a gear head. I just know a nice car when I see one. But asking me how it works? I have very little clue.

Sidebar story: My father was taking apart a carburetor on the dining room table when I was a kid and was trying his best to get me to learn about. Nope, sorry dad, I'm more interested in learning how to throw a curveball or throw a spiral with a football.

Now all these years later, I probably should have listened to him (Funny how that works). I say this because the other explanations, while detailed, made me smoke from my ears.

Your explanation helped the mechanically uninclined, like myself.
 
Most folks are viewing engine output as static.
Before we go any further, remember that TQ varies with rpm.
Additionally, HP cannot be calculated without rpm, again a direct factor.
More over, HP does not exist unless there is TQ at rpm.
This gets really muddied when people start using gear ratios in an attempt defend their argument.
Gear ratios do not exist to increase force at the wheels... they exist to put the engine in a suitable rpm range given a road speed.
If gear ratios were for anything other than putting an engine in a suitable operating range, then, electric motors would take advantage of transmissions.. and they don't, because they essentially make max. TQ (or near enough to it) at any/all rpm.
More proof?
Top Fuel/Funny cars do not have multi geared transmissions. They have one forward gear and rely on clutch slip to keep the engine in it's most efficient power band given the road speed. Keep in mind these are the TQiest automotive engines in the world, and people relate TQ to low rpm, yet these vehicles run at 9500rpm.
This clutch-slip does not work in road racing or road cars as you'd be wearing out the clutches at a very aggressive rate and replacing them every lap in a road-race car and daily (possible multiple times a day) in a road/street car.
So we have gear boxes... that eat "power" and loose time when shifting.

Yes, gears multiply/divide TQ delivery to the wheels.
And it happens to be a positive byproduct (nothing more) when keeping the engine (source TQ) in an efficient operating range.
Lets look at TQ multiplication via gearing, as it relates to traction for a minute... as most have noted deeper gearing in will increase wheelspin...
First, I agree, that most times this is accurate, as as with anything dynamic (engine)... not always.
My street strip car...
Had 4.10 rear gears in it, and launching at 6000-6500rpm was spinning hard. Launching at lower rpm it would bog down.
Solution?
Put 4.56 rear gears in it. Wait! What? that's right, put deeper gearing in it, which, most all would say now it'll never hook, it'll be spin fest.
So, what did deeper gears do?
The first thing it did was slow the rear tire down given the launch rpm (sure, still spinning, but not as hard/fast), the next thing it did was keep the motor high in the rpm band (beyond peak TQ) allowing the tires to recover/hook-up much earlier... all while keeping the engine in a more optimal rpm range (work).

So, to answer OP.
More TQ (as an absolute) is not always better.
More TQ (as an average) is always better.
Remember that work (HP) does not exist without force and rpm, and that rpm is on the multiply side of the equation when determining how much work and engine is capable of, so, steady TQ on out in the rpm range is naturally going to provide an engine that can get the work done.

Take a look at a Ferrari 358 dyno graph...
Doesn't make much TQ right? Most of it's life it makes less than 300lb-ft.
But it makes 85% of it's max. TQ from 3200rpm all the way out past 8500rpm...
That is the kind of TQ "curve" you are looking for... then you gear it accordingly.
Yes, with peakier, and/or earlier sign off in TQ delivery you can gear to compensate... but that's all gears are regardless.
458 dyno (rear wheel numbers).
458stock.jpg
 
If gear ratios were for anything other than putting an engine in a suitable operating range, then, electric motors would take advantage of transmissions.. and they don't, because they essentially make max. TQ (or near enough to it) at any/all rpm.
Formula E cars have gears. With constant torque, power becomes proportional to rpm.
 
Formula E cars have gears. With constant torque, power becomes proportional to rpm.
Exactly, and it doesn't matter if an engine or motor produces its max torque from the lowest level of RPM possible, if that torque isn't enough to overcome the tyre rolling resistance then your not moving (rather a big factor in HGVs).

It's also forgetting that even without a transmission, gear still exists, the wheel and tyre.
 
electric motors cannot spin to infinity, and, it doesn't hurt that the rules stipulate a manual transmission must be used.
from what I read, the trend in formula E is towards less forward gears... 2, 3... ???
I also read they are limited to how much electricity they can produce...
So, I don't know much about electricity much less electric cars, but according to Sylvain Filippi they run a 3 speed trans for efficiency, not to increase TQ.
Skip to 1 minute.
 
It just occurred to me, that possibly you are both still trying to bring gearing into a engine TQ parameters discussion...
An engine makes the TQ it makes... gears are simply a aid to keep the engine in an efficient rpm window.
I forgot how silly the internet can be.
I'm out.
 
electric motors cannot spin to infinity, and, it doesn't hurt that the rules stipulate a manual transmission must be used.
from what I read, the trend in formula E is towards less forward gears... 2, 3... ???
I also read they are limited to how much electricity they can produce...
So, I don't know much about electricity much less electric cars, but according to Sylvain Filippi they run a 3 speed trans for efficiency, not to increase TQ.
Skip to 1 minute.

They're permitted to have a single gear if they want. FM7 has Formula E cars, and if you just put them in the longest gear and stay in that gear, your lap times will be significantly slower than if you change gears to maximise power. This is entirely in line with what would be expected from the laws of physics.
 
Formula E cars have gears. With constant torque, power becomes proportional to rpm.
Makes sense, I did not realize that with rpm electric motors loose TQ, I'd always though electric power was linear... and on top of that, never applied the TQ x rpm/5252 to an electric motor, always though that was for IC engines and electric motors worked in some Voodoo magic.
So what is the exact formula for an electric motor that takes into account rpm? Does efficiency = rpm in the electric world?
Given all that... of course they use a trans to keep them in an operating window.
Either way, it comes down to operating window/efficiencies, not multiplication.
So, curious why Tesla does not use a trans... too costly, the window too narrow in a street car to matter, space/packaging, no sporting reg's/limits on power production/batteries, durability, cost... hmmm.
Guess now I'm pushing this off topic.

Oh, and I thought this was headed to mud sling contest, so, said I was out, but, here to learn about electric motors so long as the discussion stays civil.
 
Yes, a CVT is simply allowing you to always run the engine at a constant speed (in between some minimum and maximum wheel speed), meaning you can always have peak torque or peak power, depending on if you want maximum fuel efficiency or maximum performance. And that means that if you equip a low torque / high power car with a CVT it can pull off the same stunt as the high torque / high power car, because the power curve (as a function of wheel speed, since engine speed would now be constant) will essentially be completely flat and wheel torque is equal to power / angular wheel speed (ignoring frictional losses).
But if that's the case, why are CVTs not common on cars with turbocharged diesel engines? AFAIK, it's only common for petrol and electric ones.
 
Makes sense, I did not realize that with rpm electric motors loose TQ, I'd always though electric power was linear... and on top of that, never applied the TQ x rpm/5252 to an electric motor, always though that was for IC engines and electric motors worked in some Voodoo magic.
So what is the exact formula for an electric motor that takes into account rpm? Does efficiency = rpm in the electric world?
Given all that... of course they use a trans to keep them in an operating window.
Either way, it comes down to operating window/efficiencies, not multiplication.
So, curious why Tesla does not use a trans... too costly, the window too narrow in a street car to matter, space/packaging, no sporting reg's/limits on power production/batteries, durability, cost... hmmm.
The relationship between torque, rpm, and power is the same for an electric motor as any other type of engine, the only difference is the shape of the torque vs rpm curve, and the resulting shape of the power vs rpm curve.

They also have an efficiency curve, the shape of it can vary from motor to motor. The reason efficiency is so important for Formula E is they have a fixed amount of energy available from the battery, so their job is to optimise the time taken to complete the required distance with that fixed amount of energy.

I have a friend who has a Tesla, and I actually discussed that with him some time ago. I haven't researched the topic myself, but his belief was that it's limited by the wiring loom, i.e. the wiring is rated to a maximum current, so the engine mostly runs at constant power, not constant torque, i.e. it simply draws current from the battery at a rate limited by needing to not melt the wiring. As I said, I haven't actually researched this myself, so I'm not guaranteeing it's true, but it sounds plausible to me that the current carrying capacity of the wiring would be a limiter. I suspect price is a factor as well - they could give it gears, they could make all the electrics able to handle more current, but they're already pretty fast to accelerate, would many people want to pay more for what would be largely pointless extra performance for most people?
 
But if that's the case, why are CVTs not common on cars with turbocharged diesel engines? AFAIK, it's only common for petrol and electric ones.

I guess because small petrol engines need to run at relatively high engine speeds to produce their peak torque, while Diesel engines produce their peak torque at the lower end of the scale. As such it’s easier to drive a diesel efficiently with a manual than a small petrol engine.

The CVT is not as efficient as a manual gearbox, so it doesn’t always make sense to use it. If you just want a car that is easier to drive there are other automatic transmission options.

I have a friend who has a Tesla, and I actually discussed that with him some time ago. I haven't researched the topic myself, but his belief was that it's limited by the wiring loom, i.e. the wiring is rated to a maximum current, so the engine mostly runs at constant power, not constant torque, i.e. it simply draws current from the battery at a rate limited by needing to not melt the wiring. As I said, I haven't actually researched this myself, so I'm not guaranteeing it's true, but it sounds plausible to me that the current carrying capacity of the wiring would be a limiter. I suspect price is a factor as well - they could give it gears, they could make all the electrics able to handle more current, but they're already pretty fast to accelerate, would many people want to pay more for what would be largely pointless extra performance for most people?

My understanding is that an electric motor has a rated load beyond which efficiency drops (because a lot of the input energy is lost to heat). This load is a torque, which means that at low speed the engine is limited to run at a constant torque. Once the speed has picked up so that power/speed < rated load, the engine runs at constant power for a while until efficiency drops due to overspeed.

Theoretically a Tesla might benefit from a gearbox since it would be able to reach peak power at a lower speed. But on the other hand, does it really need more wheel torque or would it just trash the tires? A gearbox also adds mass, complexity and friction to a system, so when you summarize the impacts of a gearbox, it's just not worth it to put one in a Tesla.
 
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I read through this whole post hoping to find a clue on how PD comes up with these hp and torque curves. My understanding is that hp=torque*rpm/5252 and because of this hp and torque will always be equal at 5252 rpm. A quick check of a few graph reveals that PD has a different formula for hp and it seems to differ for each car. And on top of that, I pity the guys using auto shift because in several cases the shift point is just wrong making me doubt that algorithm too. Further more, I've noticed that the transmission adjuster hardly ever gives you the correct speed and is sometimes out by a fair bit, so what's the calculation error here? I once tried to calculate tire circumferences using speed gearing etc., and came out with all kinds of wierd sizes. I wonder sometimes just what is PD doing? I've come to the conclusion that mathematics has no real place in GT Sport!
 
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