Horsepower vs Torque Relevance and Explanation Attempt!

Horsepower, Torque and Gearing

So what is more important, Horsepower........or Torque? If one is really more important than the other then why is it? These two entities have been argued over time as much as the chicken or the egg. Time and time again, arguments appear attempting at proving one to be more relevant and one as being not so much. I will attempt to explain how the two entities relate as best as I can as well as what they are more important for. I will be using some calculus to prove it. My method throughout the entire article will be to bring up the question that the reader is thinking as it goes along and attempting to answer it. I think I know what questions will come up as you read this, so I literally try to ask them/answer them so you can understand what is happening. Also note, I use customary units, not metric for all my explanations here.

Before arguing or debating over these two blocks of information, we first need to understand what they mean by themselves and specifically which scenario we are referring to regarding them. A lot of misconception exists regarding what torque and horsepower is, so let's clear that up first. Then let's establish which is more important for "what". Lastly, let's establish which specification tells us more information regarding the performance of a vehicle. For a better explanation at first for conceptualization, you need less physics and more common sense so that is can be applied to the real world. So at first, let's stay away from ridiculous theoretic numbers and stick to real world applications. In this case, regular cars using regular internal combustion four-stroke engines with realistic specifications.

Defining Horsepower and Torque
Let's start with a realistic comparison of horsepower and torque. The force that accelerates your car when you hit the gas pedal is torque. Torque is literally the strength of your engine. It is how much twisting force your engine can apply in a given moment or instant in time. If you take an engine on a stand and grab its crankshaft to resist its rotation then you are resisting the torque that your engine is creating. The more torque the engine can create; the harder it will be for you to hold that flywheel.

Now let's talk about power. Horsepower is power. Horsepower is just a unit of power. One horsepower is around 750 watts. From now on, when I refer to an engine's power, I mean its horsepower (I will be using them interchangeably). What a lot of people do not realize is that torque and horsepower are very closely related. In fact, a lot of people will talk about it as if they are two separate things. In reality however, horsepower represents torque at a given rpm. An engine has two different factors that determine its ability to perform. The first ability is the torque it can produce. The second ability is how fast it can spin represented by the RPM. Power combines torque and rpm into one number. It combines the two factors of an engine's ability to do work into one. So therefore, power is simply torque multiplied by rpm. Depending on the units and system of measurement you use, there are conversions and constants used to compensate for that. So basically, if you want to figure out the power you are producing at a given rpm, you must multiply that rpm by the torque the engine is producing at that same rpm and you get power. Then divide by a constant which will vary based on units and systems.

So now that we have established what torque and horsepower is, let's discuss the relevance of one versus the other. A lot of people reading this are now thinking: "If horsepower is just a mere calculation, and torque is what accelerates/moves the vehicle, then isn't torque more important?" Let's continue and find out.

Take a lug nut from your car for example. If you ever need to change a tire on the street, you will most likely need to use a special lever arm. I know that a lot of cars come with special lever arms that you can put your foot on, in order to tighten or untighten the lug nut that holds your wheels. The lever arm in my car is about a foot. So basically, if I stand on it then the torque applied to my lug nut is my weight through the length of the lever. If I weigh 200lbs then the torque I am applying on that lug nut is 200ft-lb assuming my lever is around a foot long. Wait a second! Most engines from cars these days average around 200ft-lb of torque at their peak rating (take a look at most regular road cars sold today). How on earth does an engine producing that little torque move a car that weighs thousands of pounds and is able to accelerate that car to speeds of 80mph and beyond in such a short amount of time, why can't I do it also kind of like Fred Flintstone does? That is a question that must be explained before any further point is made.







Engines are weak. Engines are very weak
Let me reiterate once more that engines are inherently weak. No engine, not even the biggest and "baddest" engines in the world would ever be able to accelerate a normal passenger car anywhere near fast enough or maintain through its operating range for it to be drivable on the road. Even your 150 year old grandma would complain about how slow the car is. That is why cars have something called gearing. Gearing is a system used to amplify the torque an engine creates many times so you can actually move a large car AND stay within your engine's useful and functional operating range. For a regular car, there are three factors integrated into gearing and all effect the torque before it is finally delivered to the road itself. As an engine applies torque when you hit the gas pedal, it is first amplified by your transmission. Whichever gear you are in depends on how much that torque is amplified. Then the torque is amplified once again by your differential, which splits it between your wheels. Then, depending on the size of your wheels, that torque is once again either slightly amplified or slightly de-amplified before the force or torque is finally applied to the road itself.

Remember, units are important to keep constant. Whenever there is length, use feet and whenever there is force you must use pounds. Remember, weight is a force. What the above formula shows you is the actual torque your car is delivering to the road. If you attempt to stop the rotation of a wheel, that is the torque you will feel, not the torque of your engine. Note that you will in fact feel half as the total torque applied to the wheels as it is divided by two through the differential since you have two wheels. I am assuming you drive a rear wheel drive from this point on for simplicities sake.

So we have established that all modern road cars use a tremendous amount of torque amplification to move. An engine's torque is multiplied many times before that torque is finally used to move the car forward. This shows that torque is absolutely useless without rpm and rpm is useless without torque because you would not have power. A combustion engine has zero torque at zero RPM's, because no power strokes are occurring. If no power strokes are occurring then torque cannot be produced and an engine cannot perform work.

Torque versus RPM
RPM on the other hand is a different story. A saying exists regarding engines saying that "there is no replacement for displacement". Displacement affects torque. It is true that displacement is the most important factor in affecting the torque of an engine. Displacement is also the cheapest and easiest method of acquiring more torque. Other factors exist such as compression of different fuels, but ultimately, with current technology, displacement is the easiest and most effective way to increase the torque an engine is able to create. However, there IS in fact a replacement for displacement and that is rpm. If torque remains constant, and rpm's increase then power also increases so therefore rpm IS a replacement for displacement. Now, many of you are thinking why rpm acts as a replacement if it doesn't increase the torque of your engine. RPM merely increases power which is just a calculation, not a measurement. We will get back to this later. Rpm is the absolute key to this entire explanation, it has no effect on an engine's strength or torque, but due to the speed the engine is able to operate at, it allows the engine to utilize something far more important and essential to performance…...................GEARING!

Gearing
I know earlier I did not want to talk about theoretics, but we need to talk about that for a second to further understand. Imagine you mated an engine with a special transmission. This transmission has infinite amount of gear ratios, the ability to switch between gears in an infinitely small amount of time, and each gear is infinitely close in ratio the gear before and after it. It means that there would be a separate gear for every speed. This engine would produce the maximum amount of work that it is capable of every producing, because this transmission would be designed to operate this engine at its peak power all the time. Weather that engine will last long and reliably be able to sustain that is a topic for another long essay and debate that does not have anything to do with this. There is technology called a Continuously Variable Transmission that has an infinite set of gears of no delay and limit, however for daily drivability factors, it works to increase fuel efficiency, not performance. The perfect transmission for performance would be a CVT that held your engine at the rpm that it produces its peak amount of power at all times and speed. So if your engine peaks its power at 6000rpm, then the CVT would always run your engine at this rpm and you would always have the best acceleration possible at any speed. However, the fact of matter is that road cars and even all race cars use conventional transmissions with pre-set gears. We are assuming we have a traditional manual transmission for simplicities sake. You as a human being can only shift "so" fast, and yes even a very high tech dual clutch transmission from new BMW's such as the ///M cars as well as other cars that can shift in milliseconds still has latency in gear change. For the new BMW Dual-Clutch Transmissions, the shift time is in the single digits of milliseconds, still a huge latency. On top of that, you have a limited amount of gears you can use due to preserving practicality and drivability in a car as well as weight. As I believe I mentioned before, CVT's are beginning to appear widely in cars for their efficiency, but they are yet to be used in the performance market of cars. Pay attention to Formula 1 in the future for any innovation involving this. As soon as you shift gears up, you lose tremendous torque and therefore acceleration. In any car, 1^st gear accelerates hardest. With each and every gear up, the rpm of the engine is brought down and that means its torque multiplication is brought down to do this. That is why which each consecutive gear up, you will be able to travel faster while still remaining in your engine's main operating range (which is between idle and redline).

Peak Power versus Peak Torque
You may now question the fact of why an engine accelerates better at peak power than at peak torque when you use a CVT. After all, an engine does have more strength at peak torque than at peak power. At peak power, the engine itself is producing less torque, but due to the higher rpm, you need a much steeper gear ratio for the same speed and therefore if you hit the gas at that moment in time, you will accelerate much harder, because you are applying more force (torque) to the road. If your car peaks power at 6,000rpm and is always at a certain speed, you can never accelerate harder at that exact given speed, because you are already in the best gear and rpm you can ever be. A steeper gear will increase that rpm in which case you lose torque, while a taller gear will lower rpm in which case you lose torque. Remember, best acceleration in any given gear occurs at peak torque, but acceleration at any given speed happens at peak power. If you remain in a constant gear, peak torque will be better, because each gear has a range of speeds you can travel in. No matter your speed, your multiplication is the same so therefore peak torque will give you best torque to the road.

The Power Curve and Torque Curve. Area/Integrals
Alright so now let's talk about the concept of what I mean regarding power and torque. If you place a car on a dynamometer, you will get two functions over speed (rpm is speed, because it is distance over time which is rounds per minute). The first function and the ONLY function that the dynamometer will measure is the torque your engine produces over its operating range in rpm. This will tell you literally, on a graph, how much torque your engine is producing at any given RPM that it is spinning at. Then, from that curve, you can calculate the horsepower curve of that engine. The two curves may look vastly different. Remember, area under the curve and integral is the exact same thing. Power is just how quick Energy/Work are being done which is why it is divided by time. Torque is proportional to acceleration therefore. When a car is accelerating, its acceleration is not constant like gravity per say. The acceleration changes throughout the rpm range depending on your gear and your rpm within that gear. Assuming we have one gear, your acceleration will be higher at torque peak and will change (decrease) as you approach power peak. If you do not account for friction or air resistance, your car should be accelerating proportionally to the torque curve of your engine. You can calculate this acceleration using the formula of Acceleration = (Force)/(Mass).



Which Curve is more important?



Depending on units, at some point the curves will intersect.

So now you ask, which curve is more important? Well, it depends for what. If you have an engine on a dynamometer stand, the power curve IS more important. The power curve will show you the true performance potential of this engine in how it can utilize gearing to its own advantage. The area under the curve shows this. However, if you already have a car that is complete, then the torque curve will show you exactly your ability to accelerate at any given speed or gear. This is, because you are no longer dealing with performance potential as your gearing system is already set in stone and therefore no matter your changing speed or rpm, you will always be in a certain gear. The torque curve will show you exactly what kind of torque you will be producing and you can use that as well as your gearing multipliers to calculate the torque you ultimately deliver to the road over time and at each specific speed. When you know the torque curve, the mass of your car and your gearing then you can literally calculate average rates of acceleration within a gear and find displacement, velocity…...................etc. That involves lots of calculations. Power over speed in this case simply does not matter, because by making preset gears, you already put a limit on it. If you are driving in any car, say a BMW ///M3, no matter what speed you are going, you have only 7 variations of torque multiplication factors (amount of gears in the dual-clutch transmission) that you can use. Each one will change your engines rpm at any given speed. This factor of rpm changing due to gear changing will always be constant. If you see your car traveling 50mph at 3500rpm in 4^th gear, you will ALWAYS be at THAT same exact rpm in that same exact gear at that speed unless you change part of your gearing system meaning your transmission, differential, or your wheels. Remember, the key to understanding this is that the power curve and power of any engine show their potential for performance. The power curve shows how well an engine can perform if mated with a transmission with a limited amount of gears. Once you already have gearing set onto it, the torque curve shows what happens. Therefore we now can establish the fact that, area under the power curve is the most important aspect to consider about an engine when it is made as this curve literally tells you this engine's capabilities. Once the engine is already paired with a transmission and system of any gearing, the torque curve is the most important aspect to consider. If however you have a CVT then the peak power is the only important aspect to consider about an engine, because you have a different gear for every speed and the area under the curve will always be infinitely close to zero, because you are integrating at just one single point…...................which is your peak power. Also, now you may be thinking why does it matter if I use the power curve area or the torque curve area. Think about the torque curve for a second. Suppose it was graphed out for an engine with a 7,000rpm redline and 1,000rpm torque peak which would be this engines effective operating range. The area under that curve is exactly the number X and the area goes from 1,000 rpm to 7,000 rpm, however now imagine an engine with a 20,000rpm redline and a 14,000rpm torque peak which would be ITS effective operating range. The two engines have the same range of operation, both are 6,000rpm ranges and the areas of the torque curves are equal, because we are using the same theoretic curve. However, if you find the power curves for each, you will find that the power curve on the latter engine has a much larger area and the engine will also perform much better, because you can use gearing with some absurdly high ratios of multiplication. Let me prove it and explain:

Real world comparison (basic calculus):

First Engine:

• Torque: 100ft-lb @ idle (1,000rpm)
• Torque: 1000ft-lb @ redline (7,000rpm)

Second Engine:

• Torque: 100ft-lb @ idle (14,000rpm)
• Torque: 1000ft-lb @ redline (20,000rpm)

Torque Integrals:

• First Engine: 3,300,000
• Second Engine: 3,000,000

Horsepower Integral:

• First Engine: 4,058,220
• Second Engine:12,228,600

Wow! Two engines with identical torque curves, but due the different rpm ranges, the second engine has the advantage.

Take two BMW engines from opposite ends of the spectrum. The mighty BMW M62 4.4L V8 high torque and low rpm engine used in the 540i and X5 4.4i and then take the much smaller BMW S54 3.2L I-6 low torque and high rpm engine used in the E46 M3. Here are the specifications of the two engines:

BMW M62B44

• Peak Horsepower: 282hp @ 5700rpm
• Peak Torque: 310lbs-ft @ 3900rpm
• Redline: 6100rpm & approximately: 242lb-ft

BMW S54B32

• Peak Horsepower: 333 @ 7900rpm
• Peak Torque: 262lbs-ft @ 4900rpm
• Redline: 8000rpm & approximately: 217lb-ft

Now let's analyze these engines. Since Dynamometer graphs vary a lot on engines and since there is not official power or torque specification at redline for these engines, what I did to get those numbers was find the torque at redline assuming horsepower is just 1 lower than what it is at peak power. This should give the M62B44 engine an advantage in area anyway, because power peaks 400rpm before redline, but on the ///M3's S54B32, it redlines just 100rpm after peaking its power. In reality, after hitting peak power, torque begins to drop very drastically. So, on most road cars, the transmission is designed to maintain good drivability while still keeping an aspect of power. On most cars, if I shift gears up at its redline, the next gear will end up somewhere between the torque peak and horsepower peak rpm at that same speed. That is why area under the curve between torque peak and redline is a very good indicator of performance. The only problem that can arise is off-the-line acceleration. It is not easy to launch a car at its peak torque which would be optimal, but if we had perfect traction then it is. We will assume in this case that we have perfect traction. This means dry and good road, very soft tires with no tread, a limited slip differential and the tires are very wide with a large contact patch, perhaps even throw all wheel drive, point is that we aren't getting any tire slippage or traction loss.

So now, let's see the area under the curve (Via Integration and assumption of a constant slope and linear fit):

BMW M62B44:

• Area under the Power Curve: 573,490
• Area under the Torque Curve: 613,202

BMW S54B32

• Area under the Power Curve: 899,389
• Area under the Torque Curve: 745,820

Wow......look at that. Above, is the pure area under the curve for both engines. What I did was find the equation of the linear line connecting the horsepower and torque peaks and then the horsepower peak to redline on both engines using calculations/integrals of both torque and horsepower separately. Then you add the integration results of both to get a final answer for each of the four areas. The value is approximate and by no means extremely accurate, but it gets the point across. Also note, I am integrating power and torque with respect to speed and not time..........however torque (force) is proportional to acceleration and therefore integration of speed or time would still show a relationship of more area under the curve. So what does the above information tell us? It tells us that the M62B44 engine is 38% larger displacement wise than the S54B32 engine, however despite that the S54B32 has a 57% larger area under the power curve in its likely operating range and it has a 27% larger area under its torque curve in its likely operating range even though the M62B30 has a 18% higher peak torque. We can see that the S52B32 absolutely demolishes the M62B44 in its performance capability. It produces a lot less peak torque, however it is able to extend the range of producing that torque and power over a very large rpm band. An M62B44 engine's likely operating band is between torque peak and redline which is (6100-3900) 2200rpm. The S54B32 engine's likely operating band is (8000rpm-4900rpm) 3100rpm.

CVT versus preset gears:



Let's take a quick side swipe to the CVT. If both engines had a CVT keeping both engines at peak horsepower (and therefore peak torque delivered to the road) then the S54B32 would deliver 18% more torque to the road than the M62B44 at all times…...................which equates to how much percent more horsepower it has......18%. However, just keep that mind, but do not automatically make conclusions yet, because we are trying to determine which engine can use a regular transmission better that actually uses the engine's operating range. What can be said at this point is that despite the 540i's heavy weight, if you put the tiny 3.2L S54B32 engine in it, then it would still be faster, although it may change its quality as a daily driver, because an S54B32 just may not crank out enough torque at those low RPM's which a person uses when driving daily. This is of course assuming our transmission does not change.

Remember, the importance of these areas is, because of transmissions. More importantly is the fact the transmissions used in cars today have a limited amount of gears and a certain delay between changing gears. Today, transmissions are made with mostly between 5 and 8 gears (I've seen some new automatics from BMW with 8-speeds). Bottom line is, the entire reason the area is important is, because you as person cannot shift gears every second. To make the engine more useable and practical, the rpm band is used and you can use less gears to make driving easier and decrease the amount of gears you need to be able to travel at high speeds. The best performance upgrade to your car as it is now would be get a transmission with say.........25 gears and keep each ratio so close to each other that you never deviate more than a few dozen rpm away from your power peak, that would guarantee the maximum amount of torque is always being applied to the road. However, you cannot use 25 gears due to practicality. The extra gears means you have to shift much too often and it would be heavy. The reason a normal car with a normal transmission is chocked of performance is, because of a limited amount of ratios and a very wide array of speeds (0-150mph+). THIS is the sole reason. Now, when a company like BMW has an engine on the stand in their laboratory, they aren't thinking how to create gears to stay at peak power all the time. BMW's and most other cars sold, are designed to be driven on the road at given speeds with a certain amount of reliability and convenience. When they pair the engine with the transmission, they want the gearing to be optimized for fuel efficiency, somewhat performance, and convenience at the same time. Sportier cars tend to have close ratio gears for better acceleration and then perhaps have an outlier for the last gear purely for highway use, but you also need to shift gears more often. Cruising cars tend to have longer gears so you can shift less often and "Take it Easy" if you will. It means you can travel a greater range of speed in any given gear, but you are placing less torque to the ground. You compensate acceleration for fuel efficiency, convenience and having lower RPM's.

Let's take a look (Information used here is based on official specifications from cars.com and Edmunds.com)

The BMW M62B44 was used in the BMW E39 540i:

• Gear:1=4.23
• Gear:2=2.53
• Gear:3=1.67
• Gear:4=1.23
• Gear:5=1
• Gear:6=0.83
• Final Drive: 2.81
• Wheels: 255/55/16

The BMW S54B32 was used in the BMW E46 M3:

• Gear:1=4.23
• Gear:2=2.53
• Gear:3=1.67
• Gear:4=1.23
• Gear:5=1
• Gear:6=0.83
• Final Drive: 3.64
• Wheels: 255/35/19

Okay, so now we know the gearing of both cars. A car's gearing involves the transmission, differential, and wheels. All of those components have an effect to how much force the car puts down to the ground in order to accelerate itself. I am not going to count in the parasitic losses of the drivetrain, assume both are constant. Surprisingly, both cars have the exact same transmission ratios (Comparing the E39 540i and the E46 M3). However, the M3 has a far steeper multiplication from its differential. So now you may ask…...................why not just toss that 3.64 differential into the 540i. Well…...................if you do, without even doing calculations, I can bet your top speed will probably be below 150mph and you will be in 5^th or 6^th gear when the ///M3 will be 3^nd or 4^rd gear. So even though the gearing multiplication is the same, the S54B32 engine can stay in any given gear for a longer time and thereby extend the time and distance of using that force. That is why it can perform more work and has more power. It also has more rpm's to work with in general. What I mean is that, the M62B44 may be using 1^st gear with a 4.23 multiplication until 10mph before it redlines and must shift down to just a 2.53 multiplication, while the M3 will continue with its 4.23 multiplication until it reaches a higher speed like 15mph at redline and then it has to shift to 2.53 multiplication and that point the 540i may already be in 3^rd at just 1.67 multiplication. (this Is just a ball park and exaggeration, but all of this can be calculated and you get the idea). A M62 redlines at a mere 5800-6100rpm while the S54 goes to an upwards of 8,000rpm. So this means that gearing cannot be used to create performance that does not exist, it just allows you to tap into more of it until you reach the ultimate limit which is a CVT running at constant peak power. So now you are asking…...................If we have two engines with equal power over time (area under the curve or integral of power) however both engines have different redlines than who wins assuming they have a set limit of amount of gears they can use. Well…...................the one with the shorter redline will be producing more torque in a smaller rpm band and therefore you will need wider ratio gears, while the engine with the longer rpm band will need to use shorter ratio gears to compensate for the fact it produces less peak torque in a given rpm band and therefore the shorter gears will compensate for that fact. Ultimately however, if mated with transmission to compensate for this, the two engines will perform equally or very similarly (similarly, because the torque curves aren't perfect) in any category involving acceleration at all times, because the force they deliver to the ground will always be very similar or equal.

Now lets take a glance at shift points. A lot of times, I have heard and saw many people recommending to shift at or past torque peak, and many say shift at redline. Well........before I even begin explaining, shifting at ANYTHING other than redline will usually be bad, unless your car loses tremendous amounts torque after peaking horsepower. Usually, from peak power to redline, the higher multiplication from the current gear will still provide you with more torque at the wheels than even the torque peak of the next gear up. For most cars, torque at the wheels will be higher at any rpm in a lower gear so it makes no sense to shift before redline, not to mention if you have a traditional manual, shifting takes a lot of time. Believe it or not, if you take two cars of equal weights with one having a the new manual Dual Clutch Transmission that shifts in the single digits of milliseconds versus the other one having a traditional manual you will see that the car with the Dual Clutch will do far better in 0-60 times and perform far more consistently, because traditional manuals depend a lot on driver error and skill. Not to mention (although I'm not sure, feel free to correct me on this if I am wrong), with new Dual Clutch transmissions such as ones from the new ///M, they maintain torque between shifts.

The Theory behind Differential Ratio Modification:
Now, let me take a quick section to explain the benefits, drawbacks and theories behind changing differentials on a car. A lot of people will say that changing your differential for a different ratio will yield better acceleration while others will say that it simply doesn't matter as it doesn't change the power. Well, let me explain how this entire deal works. If you take a stock road car, the differential will be designed in a manner to maximize fuel economy, keep the engine in its efficient and designated rpm range during road going speeds, and provide reasonable spread between gears. Some cars redline at 30mph in 1^st gear while other cars redline past 60mph in 1^st gear. Some cars have very short gears while others have longer gears. These factors can really be changed by the differential itself on top of the fact of actually specific ratios of the transmission. If you look at many tuners, they often will often higher differential ratios as comparison to stock. The reason for this is that you do in fact not change your power, but you have the potential to put more power to the ground over a given time period. A drag race is a perfect reason for a shorter ratio differential. Let's use a car as an example. Remember the comparison between the 540i and M3 I did earlier? Well, forget about the M3, and focus on the 540i since I only need one car here to use as my example.

Gear Ratios:

• 4.23
• 2.53
• 1.67
• 1.23
• 1
• .83
• Differential: 2.81:1

Now, different road cars are designed differently. For this case and purpose, lets assume that the 540i doesn't lose much power after it peaks…..........just as we did earlier, if the peak horsepower is rated at 282, than the redline horsepower is 281 or around so. To put it simply, if we are redline at 1^st gear, and then upshift to second, we end up somewhere before peak horsepower. If we stick in a differential such as 3.15:1, then when we shift up from redline in 1^st gear, we end up much closer to 5700 in 2^nd gear and so we are technically making more power. The higher ratio differential we get, the closer the gearing becomes and the closer it begins acting as a CVT, because we can stay closer and closer to our peak power rpm. So technically…..........at any instant in time, a higher ratio differential doesn't change power to the ground, but over a certain time period…..........such as a 0-60 or ¼ mile time, we are actually putting more average power to the road over a time span which explains why making your differential shorter will improve acceleration.

Now, we also have to remember, that we can only go to a certain extent with differentials due to limited gearing. Remember we only have 6-gears and shifting takes a lot of time. Making a 3^rd shift before hitting 0-60 can put you off by a lot of time. If you are looking strictly at given intervals such as 0-60 or ¼ mile times, sometimes a lower ratio differential that eliminates an extra gear from the equation will yield you quicker times simply, because you don't have to waste time shifting. If you could shift instantly though, then a higher ratio will always be better.

If you had 6-gears and wanted to the ultimate 0-60 time for your car with the ability to shift between gears instantly, you would want a differential steep enough to make your top speed 60mph. By 60mph you should be in redline of 6^th gear. In real life, its impractical, because you would have traction issues and such, but you get the idea.

My main point is that, if you have a road going car and you don't care about 0-60 times or ¼ miles times and simply want better acceleration in every gear without caring much about fuel economy or RPM's then you can almost always benefit from a higher ratio differential.

Comparison of acceleration between CVT and Gears:

Now, we've discussed power and torque as well as gearing. Now let me show you the effects of gearing on performance and how vital it is. For the purposes of showing you, I'll need to deviate away from the older cars I compared earlier to something a bit new….The BMW F10 M5. The reason for this is that newer cars with launch control, and DCT transmissions report more consistent times on benchmarks, because they require less driver driver input, error, and skill. In the older cars I used earlier, the driver's launch and shifting made a day/night difference in the times for the 0-60 and ¼ mile. That's why the results vary widely from various professional reviewers.

Now, if you go to BMW's official website, they advertise the new F10-M5 as being able to reach 60mph in 4.2s. I've seen professional reviewers clock 3.7's 0-60's so as you can see BMW is clearly being very conservative on their ratings. Nevertheless, I will be using BMW's official times for reliability's and consistency's sake.
We can calculate the power it takes to accelerate a certain mass to a certain speed if we know the time it takes. It's a simple equation of (Kinetic Energy)/(Time)=Power. This equation can be changed to work the opposite way also, and I will show that later.

So if we use that equation, considering the M5 weighs 4387lbs and reaches 60mph in 4.2s, it is putting down an average of 229Hp to the ground throughout those 4.2s. If we assume that the rating of 3.7s was a reliable, then the M5 would put down an average of 259Hp….not much of a difference.

So where does this major discrepancy come from….? We are going from a 560Hp engine to just 229Hp? This power loss comes from a few things. We first need to account for air-resistance. It is not very significant at these speeds, but enough to slow down accelerations. Since the M5 has a near perfectly flat torque curve on a very wide band, this can easily be tested at lower speeds versus higher speeds. Our power disappearance comes from drive train loss, traction loss during the launch, shifting delay, and our top perpetrator is long gearing. The gearing on the M5 is keeping it quite far from its peak power most of the time which is why we have "slow" acceleration. If you placed more aggressive gearing, the results would be far better assuming you can keep traction.

If the M5 had a CVT, our 0-60 times would be far lower. For consistency sake, I'll assume a 15% drivetrain loss, even with a CVT. So, at 560hp peaked, the M5 should be placing a maximum of 476RWHP. This means that our M5 should be trapping 0-60mph in 2.02s. That is quicker than any street legal super car I can think of. If we're realistic, lets add as much as 1/2s for air resistance, traction loss and roll resistance. Maybe even we can add a full second for those nuances. Either way, the difference is incredible and puts the M5 into a different class of car immediately, all due to gearing. That CVT is running your engine at its peak power RPM at all times.
The closer ratio your gearing, the less power you lose and the more you have to put down onto the ground. The lesson here is that what I've been saying the entire article. Gearing is THE most important factor in performance of road-going cars today due to its wide difference applied on cars we see on the market today.

Ultimately, we have proven and concluded the following rules:

1. That peak horsepower IS the single most important and ONLY important aspect of an engine's maximum performance ability. This case scenario only happens if this engine is always running at its peak power rpm and that can only happen with a CVT designed for this. There are no *if's*, *and's* or *buts* for this.
2. In the real world when comparing normal cars, the most important aspect of an engine's performance capabilities when mated with a conventional gear based transmission is the power curve. This is because the area under the curve of a different operating range takes into account the torque and rpm which is what you need to determine the best ratio of gear multiplication to use for that engine.
3. Peak Horsepower is the best indicator usually of a cars performance at first glance (ignoring weight). If you go to any website, the only specifications you get is peak torque rpm and peak horsepower rpm. Out of the two values, the Peak Horsepower alone will give you the best predicament as the power curve of this car. Torque will give you a lot less prediction accuracy, because trucks and work-horse vehicles have relatively low horsepower and very high torque levels, because they use diesel engines operating at high stroke to bore ratios and requiring immense compression. They cannot spin to high rpm's. A high peak horsepower tells you that most likely, the vehicle is producing more torque at high rpm's and therefore most "likely" has more performance potential.
4. Once an engine is already mated with a transmission, such as a car, you need to use the torque curve, not the power curve to determine force exerted to the road. The given power has already been taken advantage of to a certain and limited extent by the transmission/gearing and cannot be used anymore, so the power curve in this case is irrelevant. Since you remain in the same gear over a variety of speeds, your power may be increasing, but your acceleration is decreasing, because your torque is decreasing and you aren't compensating for that with steeper gearing and therefore the power curve doesn't apply when an engine is already connected to a transmission. So basically what I'm saying is that if you want to compare the performance of your car against a friends (not the engine, but the CAR), which already have wheels, a differential and a transmission set in, then use the torque curve of the engine.
5. More torque or more power at lower rpm's is better for daily drivability. For example, the M62B44 in the 540i or X5 4.4i probably or almost definitely has a lot more torque and horsepower at lower rpm's. When I say torque and horsepower, I don't mean peak, I mean average or area under the curve. It means that for you it is easier and better to drive daily, because you can keep rpm's well below torque peak and still get outstanding acceleration while the M3 may need to be downshifted to get usable acceleration. So as I said before, better daily drivers tend to have engines that have more torque at lower rpm's. Also, note that the M3 is a lot lighter also. To get a better conceptualization, even if you placed the M3's S54B32 engine into the 540i, it would still perform better than using a M62B44, but may not be as good for a daily driver.

So what have we learned?
Horsepower is more important than torque when you consider performance. Common sense and math prove it. More horsepower is more important, because it means more torque delivered to the road to accelerate you, because it all has to go back to the gearing system. However, peak horsepower and torque numbers say little in terms of daily driven cars sold on markets today due to the variability in the curves and gearing purposes set in them. So next time your friend argues that his obnoxiously huge American muscle car V8 has *tons* of torque to compensate for its low horsepower, tell them they don't know what they're talking about. A small I-4 like ones made in Japan and Germany are just as capable if they put out similar horsepower averages, except due to their higher rpm they are a lot more complex and advanced. Remember, when going from idle, torque at low rpm does help with daily drive-ability. However in a drag race and any performance situation, horsepower is what really counts. Thank you for reading. I know you have a raging headache by now. Always remember that the key to the entire war is *gearing*. If you don't account for gearing than the game can change a lot, but then again there would be no point since gearing is used everywhere. If I was wrong anywhere, please correct me, this is just my interpretation of how I understand it and I think this is how it is.

Is this posted elsewhere in Bimmerfest?

This is wonderful. My favorite post so far. Excellent write sir.

Thanks a lot for posting this. Very well written and explained.

I didn't read the whole thing but it seems OK. There is a far easier explanation of the two terms, however. Torque is just rotational force. It takes torque to spin the wheels against load. As long as you have more torque than the resistance, the vehicle moves. An 18 wheeler needs a lot of torque to get the load moving. The diesel engines they use have many times more torque than they have hp.

To accelerate quickly we need to do work quickly. In physics, work is defined as force times distance. The rate at which work is done is power. Our electric companies measure power in watts and kilowatts (thousands of watts). Watts and hp both measure power. 1 horsepower is defined as 33,000 lb-ft/min and is equivilent to almost 746W.

It makes a lot of sense to me that what makes us accelerate more quickly is not force but the rate at which work is done. That is why hp is more important than torque for acceleration.

Jim

Originally Posted by JimD1

I didn't read the whole thing but it seems OK. There is a far easier explanation of the two terms, however. Torque is just rotational force. It takes torque to spin the wheels against load. As long as you have more torque than the resistance, the vehicle moves. An 18 wheeler needs a lot of torque to get the load moving. The diesel engines they use have many times more torque than they have hp.

To accelerate quickly we need to do work quickly. In physics, work is defined as force times distance. The rate at which work is done is power. Our electric companies measure power in watts and kilowatts (thousands of watts). Watts and hp both measure power. 1 horsepower is defined as 33,000 lb-ft/min and is equivilent to almost 746W.

It makes a lot of sense to me that what makes us accelerate more quickly is not force but the rate at which work is done. That is why hp is more important than torque for acceleration.

Jim

Thats true, but somebody with little understanding reading this will make no real-world connection from that explanation and still won't understand. What you wrote has been written all over the internet and its not explaining the significance in a realistic way that a person can relate to. Before I understood the topics I wrote about, I read dozens of explanations very similar to that and it absolutely did nothing to help my understanding. In fact I ended those articles with more questions than answers.

Great explanation. It's like a engineering degree in a single post. Except in plain English.

I have a degree in mechanical engineering which may be part of the reason the shorter explanation works well for me.

With respect to gearing, what is really going on is you have to get into and stay into the rpm range where peak hp is developed to maximize acceleration. It is correct to think of the gearing as multiplying torque but what we really care about for acceleration is the hp. If you shift early, the hp available is less so you accelerate more slowly. If you shift around red line, you are typically spending most of your time near peak hp so you accelerate more quickly. A really high numerical advantage at the start gets you into peak power very quickly. Tight gear to gear spacing keeps the fall off less when you shift gears.

A manual transmission is in some ways helpful to acceleration so a lot of the time the manufacturer will compensate with the gearing. A 128i manual is faster than a 128i automatic. But in a 135 they are essentially identical. At least in 2009, the 135i automatic has more gearing advantage at the start to make up for the lower efficiency of the torque converter automatic. With the DTC the losses of the torque converter are eliminated so the automatic may be quicker if it still has a gearing advantage. Shifts of an automatic are quicker but torque converter automatics are somewhat inefficient due to the need to transfer power through the torque converter.


Jim

I have a degree in mechanical engineering which may be part of the reason the shorter explanation works well for me.

Exactly! My point was to explain to everybody, not just scientists. My audience wasn't aimed at you, because you already know far more than this anyway. My explanation was child's play for somebody who has a ME degree, knowing what it involves.

Tight gear to gear spacing keeps the fall off less when you shift gears.

Yup, exactly, shorter gearing to keep you closer to peak HP is better. However, you have a limited amount of them, usually 6, so at that point, it will be faster for you to drop off a lot lower RPM's, then shift every 2 seconds, because shifting ultra fast isn't easy.

With the DTC the losses of the torque converter are eliminated so the automatic may be quicker if it still has a gearing advantage. Shifts of an automatic are quicker but torque converter automatics are somewhat inefficient due to the need to transfer power through the torque converter.

I may actually edit my post to touch onto this topic. I think TQ automatics are slowly dying off in high-end cars. A lot of high-end cars have """AUTOMATICS""" who only use a torque converter for 1st gear or just getting moving, and then use a full lock-up clutch for everything past. Its a more expensive way, but DCT's and SMG's can all be shifted automatically and still have low power loss.

Oh yeah, and I am also going to add a great reference to my example to give people a sense of reality in acceleration times. From what I found/derived.

I see that ((Velocity^2/2))*(Mass/Power)=Time

Is this right, just to confirm? I want to show people that if you had optimal gearing, it would take a lot less power in cars to accelerate to 60mph (for example). A CVT running at peak HP can cut 0-60times off by as much as half in some cases. A toyota Camry with 200hp can do a 0-60mph in well under 5s with a CVT. Goes to show how critical gearing is, which is why I emphasize it.

I am a Chartered Management Accountant with an MBA...not a ME...however, the detailed and simple explanations above explained it all...thanks!

I don't think there are any simple equations to turn hp or torque into acceleration. We know that distance=initial velocity times time plus one half times the acceleration times the time squared. We also know that force equals mass times acceleration. The problem is with the force part of the f=ma equation. We can rearrange it to a=f/m but where do we get force? At any instant, I think it is the torque of the motor times the gearing minus any losses. But it constantly changes as the rpm changes and the gears change. So you'd have to do a lot of work to try and calculate this.

Maybe that difficulty is why the on-line calculators are empherical. They use published (or test) information to develop a relationship.

Jim

I realize rpm is changing, but ignore automotive for a minute.

Analyze this equation purely from a physics and theoretical standpoint:

((Velocity^2/2))*(Mass/Power)=Time

^Does that equation mathematically work out?

One of the simplest ways to check an equation is to plug in the units and see if you get the result you want.

If we square velocity in Ft/sec we get feet squared over seconds squared. I like pounds for mass. 1hp=33,000 ft lbs/minute which we can convert to ft lbs per second by dividing by 60. That gives us units we can deal with.

But if we go through the math on the left side of your equation, we get ft/sec or velocity. We do not get time.

Jim

I added a section I forgot about differentials. Some more updates with pictures to be added.

Great simple and easy to follow explanation without making it confusing. Nice Job!

Originally Posted by JimD1

One of the simplest ways to check an equation is to plug in the units and see if you get the result you want.

If we square velocity in Ft/sec we get feet squared over seconds squared. I like pounds for mass. 1hp=33,000 ft lbs/minute which we can convert to ft lbs per second by dividing by 60. That gives us units we can deal with.

But if we go through the math on the left side of your equation, we get ft/sec or velocity. We do not get time.

Jim

Actually, I got a some time to recheck that and it does work out for me. Power is Work/Time. Kinetic Energy/Time=Power so that can be redone so as Energy/Power is time. When I used SI units, it worked for me.

Added a section on CVT!

Enough, already. Torque vs. HP? Lots of these guys don't even know the difference between acceleration and velocity, and what's more they don't care.

Originally Posted by ProRail

Enough, already. Torque vs. HP? Lots of these guys don't even know the difference between acceleration and velocity, and what's more they don't care.

Well, if they don't care they won't read it. This is for the ones that do .

Awesome thanks so much!

It is quite easy to get a link between power, torque and acceleration if you are willing to ignore friction and air resistance (and don't change gear .

Take the kinetic energy of the car, which is

E= 0.5*m*v^2

where m is the mass of the car and v is its speed. Actually, there should also be a contribution from the spinning wheels, and the spinning engine, but we can imagine those have been absorbed in the definition of the mass m, ie the relevant m is a little higher than the actual weight of the car.

Now, the rate of change of energy with time equals the power P. So, by the magic of calculus, we obtain:

m*v*a = P

where `a' is the acceleration (ie the rate of change of the velocity). So, at a given speed v your possible acceleration is proportional to the available power P, as you would expect. Of course, as you accelerate, your speed v goes up, so depending on how P changes with vehicle speed you may accelerate at different rates.

Now, we use the fact that power is torque times (angular) velocity of the prop-shaft and that the angular velocity is proportional to the speed of the car (if you don't change gear), so P is proportional to v times the torque T, say.

That means the v cancels on both sides and we get that m*a is proportional to the torque T! So as you speed up you find your acceleration is proportional to the torque T offered by the engine. The vehicle speed and the engine rev speed cancel out.

This means that with a flat torque curve your acceleration will be constant, which is why people rave about "linear" acceleration when the usable rev band has a large chunk of constant torque, as it does in the V8 M3, for example, which has some 4000 rpm of usable rev band with essentially flat torque.

Not as easy as you may think. I can't tell you how many people I know who have the mindset of:

"Power is just a calculated value and therefore unimportant, your torque is what's important because its what actually accelerates you" or
"My muscle car has only 200hp, but a billion lb-ft of torque and therefore is as fast as car with more power"

And most of all, what drives me nuts is the extremely common confusion when people think torque is the same thing as work since both involve force and distance...Torque has nothing to do with work or energy. A lot of people don't realize that and its probably in the roots of that misconception.