RPM's and max HP output

sneaky98gt · May 7, 2011

FastDriver said:
You are missing something sneaky. In a given gear you will accelerate hardest at peak torque, but if you could change gears at that same vehicle speed to any point that's making more hp, you will accelerate harder in that gear. When you multiply the torque made at the engine, by the new tranny gear ratio, you'll end up with more torque going to the rear-end.

Compare an insane 1050 ft-lbs torque tractor diesel at 1500 RPM - that's 300hp
Now consider an engine similar to an F1 engine that makes 350hp at 20,000 RPM - that's only ~92 ft-lbs of torque

At the same vehicle speed, which engine if optimally geared will make more torque at the rear end?

At a given speed, say they were rotating the driveshaft at 500 RPM (vehicle should be moving the same speed with identical rear gears, wheels, and tires). To get that driveshaft speed down to 500 RPM with the tractor motor, the gear ratio needed is only 3:1 --> 1500rpm/3 = 500rpm. At the same time, the torque to the rear will be multiplied by 3 making an astounding 3150 ft-lbs.

To get the F1 motor down to 500 rpm, the gear ratio needed is 40:1. 20,000/40 = 500 RPM. At the same time, the torque sent to the rear is multiplied by 40: 92*40= 3680 ft-lbs. The tiny F1 motor wins, exactly as predicted by the fact that the F1 motor is making more hp. With this knowledge we can just as surely predict that a new mustang 5.0 at 412hp @ 6200 (best guess) geared optimally will outperform the F1 motor. The certainty comes from the fact that the 5.0 makes more power. I need not actually do the torque multiplication to verify this result.

Yea, you're right. I'm wrong, and I'm not afraid to admit it.

I was missing the whole re-gearing idea. A car with more horsepower (i.e. torque at more rpm, and thus a faster speed) can have more gear at any given speed, thus giving it more torque multiplication and more acceleration, while still allowing a given speed.

That's why the steam engine posted above won't really accelerate anything. (I think I got this right). Assuming it makes 10,000 ft-lbs at 5 rpm (~10 horsepower), the gear ratio needed to get the drive shaft to 500 rpm is 1:100, or 10,000/100, which is only 100 ft-lbs of torque to the ground.

I think I got all that, but I still don't understand/agree with the max acceleration at peak torque. I mean, it makes sense from a science point of view, but it doesn't make sense to me in an experimental point of view.

For example, I just got back in from driving my granddad's 04 Mach 1. It is bone stock, making 320 ft-lbs of torque at 4250 rpm and 305 horsepower at 6000 rpm, according to Ford. I put it in 2nd gear, and go WOT from a very low rpm/speed. Just to begin with, it is pretty slow getting off the line, as the 4 valve motor isn't know for producing much low end power. At about 3000 rpm, it is getting going a little better. By 4000 rpm, it is really starting to hit its power band. At 5000, it is pulling HARD. 5000 to 6000 rpm goes by really quick, and at 6000-6500, it is pulling like a freight train (no joke). Bottom line, it pulls MUCH, MUCH harder at 6000 rpm (peak horsepower) than at 4250 (peak torque). This is not an opinion; it accelerates harder at 6000 rpm than at 4000 rpm.

If the max acceleration occurs at peak torque, why is this? I understand the science (I think), but my theoretical prediction doesn't meet my practical experience.

bhuff30 · May 7, 2011

Sneaky: I think you are being tricked by your other senses. At high rpm, there is a lot more noise and excitement going on. Watching the needle close in on the red zone gives that adrenaline rush as you are about to grab for another gear. Alas, it is all just a play on your senses.

Find a buddy with a G-tech to verify the physics. Stick your car in 3rd gear and watch the accelerometer in 3rd gear around peak torque and then again at peak horsepower. After reaching peak torque, the G readings on the accelerometer will drop slowly as you approach peak power and then the shift point.

Gearbanger 101 · May 7, 2011

VEE EIGHT said:
Awesome, well I guess I set my shifts @ 5300

I'd shoot for about 200RPM over peak if I were you....unless you shift faster than anyone else and actually believe the stock tach is at all accurate.

sneaky98gt · May 8, 2011

bhuff30 said:
Sneaky: I think you are being tricked by your other senses. At high rpm, there is a lot more noise and excitement going on. Watching the needle close in on the red zone gives that adrenaline rush as you are about to grab for another gear. Alas, it is all just a play on your senses.

Find a buddy with a G-tech to verify the physics. Stick your car in 3rd gear and watch the accelerometer in 3rd gear around peak torque and then again at peak horsepower. After reaching peak torque, the G readings on the accelerometer will drop slowly as you approach peak power and then the shift point.

I must be, but it's doing a dang good job tricking me. I think the relatively wide torque curve up top on the Mach 1 is what's tricking me. The torque curve is pretty flat from 4000-6000, but the extra motor and wind noise is making me think I'm accelerating faster up top. Same thing on my car; it's only making 50 less ft-lbs of torque at 6000 rpm than 3000 rpm.

I think I'm going to start a whole new thread on it, but I'll ask here as well. How would you use your dyno chart to determine overall performance in the 1/4 mile? (Theoretically, anyway) What I'm wanting to do is calculate the difference in performance that I'll get by swapping to 3.73 rear gears from my current 3.27s, and then see how the theoretical prediction matches up with my actual experience at the track.

Gearbanger 101 said:
I'd shoot for about 200RPM over peak if I were you....unless you shift faster than anyone else and actually believe the stock tach is at all accurate.

Yea, I learned a few weeks back that the stock tach is WAY off on my car, or at least it is during hard acceleration at higher rpm. At the top of 3rd at the end of the quarter mile, around 5000 rpm, my tach is off over 300 rpm, or at least it is according to this calculator.

40oz · May 11, 2011

I've actually taken my GTech and done what bhuff has suggested. 2nd gear went by too fast, but 3rd worked. I set it to display acceleration, and floored it at around 2000 rpms and held the pedal to the floor until redline, and acceleration peaked at ~4000 rpms and fell off from there until redline. Just what the torque curve predicted.

I did this specifically to determine if peak horsepower or peak torque accelerated harder. IOW, the same amount of torque at a higher rpm equals more horsepower, but does it mean more acceleration? And the answer is that the actual acceleration is relative to the torque output, not the horsepower number. And the rpm at which the torque occurs has zero to do with the rate of acceleration, 250 lb-ft is 250 lb-ft whether at 3500 or 5500 rpms.

sneaky98gt said:
stock tach is WAY off on my car, or at least it is during hard acceleration at higher rpm. At the top of 3rd at the end of the quarter mile, around 5000 rpm, my tach is off over 300 rpm, or at least it is according to this calculator.

Are you going off what your speedo says or what the timeslip says? Trap speed isn't how fast the vehicle is moving, it's an average over the last 66 feet. Which is obviously lower than what your speedo will say if you are still accelerating when you cross the line.

midnightdriver · May 11, 2011

sneaky98gt said:
I must be, but it's doing a dang good job tricking me. I think the relatively wide torque curve up top on the Mach 1 is what's tricking me. The torque curve is pretty flat from 4000-6000, but the extra motor and wind noise is making me think I'm accelerating faster up top. Same thing on my car; it's only making 50 less ft-lbs of torque at 6000 rpm than 3000 rpm.

I think I'm going to start a whole new thread on it, but I'll ask here as well. How would you use your dyno chart to determine overall performance in the 1/4 mile? (Theoretically, anyway) What I'm wanting to do is calculate the difference in performance that I'll get by swapping to 3.73 rear gears from my current 3.27s, and then see how the theoretical prediction matches up with my actual experience at the track.

Yea, I learned a few weeks back that the stock tach is WAY off on my car, or at least it is during hard acceleration at higher rpm. At the top of 3rd at the end of the quarter mile, around 5000 rpm, my tach is off over 300 rpm, or at least it is according to this calculator.

Spinning the Mach out to 6000 rpms you are still accelerating, and will continue too till you hit the rev limiter.

But... As people have pointed out, you will not accelerate as fast as you were when you are on the torque uphill side rather then the down hill side.

I plan to and will always shift around 6K in my car unless I added something that changes my power band when trying to get a good run in. The reason, my car is still pulling ie( hp = torque x rpm/5250), even though it is not pulling as hard it is still pulling.

Plus in my book, shifting = time and the less shifts you have to do will create less likely to miss a gear, drop out of power band or grab the wrong gear.

FastDriver · May 11, 2011

sneaky98gt said:
I think I got all that, but I still don't understand/agree with the max acceleration at peak torque. I mean, it makes sense from a science point of view, but it doesn't make sense to me in an experimental point of view.

For example, I just got back in from driving my granddad's 04 Mach 1. It is bone stock, making 320 ft-lbs of torque at 4250 rpm and 305 horsepower at 6000 rpm, according to Ford. I put it in 2nd gear, and go WOT from a very low rpm/speed. Just to begin with, it is pretty slow getting off the line, as the 4 valve motor isn't know for producing much low end power. At about 3000 rpm, it is getting going a little better. By 4000 rpm, it is really starting to hit its power band. At 5000, it is pulling HARD. 5000 to 6000 rpm goes by really quick, and at 6000-6500, it is pulling like a freight train (no joke). Bottom line, it pulls MUCH, MUCH harder at 6000 rpm (peak horsepower) than at 4250 (peak torque). This is not an opinion; it accelerates harder at 6000 rpm than at 4000 rpm.

Bottom line is that your experiment doesn't have an accurate enough measurement tool. The ass-o-meter isn't that reliable, unfortunately.

If the max acceleration occurs at peak torque, why is this? I understand the science (I think), but my theoretical prediction doesn't meet my practical experience.

Let's revisit the science. The math for this becomes much more complicated and involves derivatives/integrals to explain thoroughly. I can do this math, and you might be able to interpret it if I am articulate/eloquent enough in my explanation of the math, but I don't think math is ever as good as a conceptually correct answer to a question. So here's my best attempt:

Conceptually imagine what is happening at peak torque: the engine is at maximum volumetric efficiency. That is to say that the cylinders are filling themselves with as much fuel and air with each stroke as the engine is able to. The engine does not get as much air through the system in a single stroke at either lower or higher RPM. When the spark lights the air/fuel, the explosion is the cylinder hits harder than at any other RPM. The peak cylinder pressure is the highest it will ever be. The cylinder traps this air and forces the cylinder down. This is a linear force. This linear force is applied through the rod to the crank journal that is some distance from the centerline of the crankshaft. A force applied at a distance about a "fixed axis," which in this case is the centerline of the crank, is the definition of torque - or the definition I prefer, "torque = rotational force."

Because cylinder pressures are highest, it makes sense that this is the peak torque. The distance of the force that the rod applies from centerline of the crankshaft is determined only by the rod journal. It never changes. Thus the only thing that can increase or decrease the torque is the linear force that is applied at that journal. That linear force is entirely due to cylinder pressure. Thus, peak cylinder pressure = peak torque. Now, imagine stopping your motor for a moment in time and imagine the forces being applied by all of those rods. This is a 4 stroke engine; so at any given point you'll have 2 rods on the power stroke, and 2 on each other stroke. It's the force applied by those 2 pistons that you feel at that moment. They are the only things creating force in the motor at that instant. The harder they push, the more the whole system, vehicle, driver, and all, will accelerate.

I think you understand all of that already, and so it makes sense to you now that peak torque is when the car accelerates the hardest. What confuses you, and most people is how you can do any better than this, or if more hp is better, then how come it doesn't cause the car to accelerate even more in the same gear...

The difference at peak horsepower is that the cylinder does not fill as completely as it does at peak torque with each stroke, but there are a lot more strokes in the same time. So it doesn't have as high a cylinder pressure. It doesn't place as large a force on the piston, rod, or crank during the power stroke. However, the cylinder is actually moving a lot more air and fuel in the same amount of time, because it completes more revolutions in that given time period. Thus, your engine is actually producing more energy.

So why aren't you accelerating faster at the top-end of a gear? To understand all of this, it's important to remember what power really is. Power is not directly what accelerates a vehicle. It is only the ability to do work in a set amount of time. What is work? Work is the application of force to an object over a distance that the object moves, not to be confused with torque, which is a force applied at a distance from a rotating point. Normal work involves a linear distance - the car moves a mile while a force is applied (F*d). Rotational work uses, well.... a rotation - how many rotations that a force is applied over(TQ*Rotations).

Now, what's happening in a gear at high RPM where you're making more power, believe it or not, actually is more impressive than what's happening at peak torque, in an important way. While acceleration in a gear, say 4th, is greater at peak torque, the work being performed actually is greater at the peak horsepower, which I'll attempt to conceptually demonstrate without going entirely through some very confusing math.

As an example, let's talk through what's happening in 4th gear. Let's say peak torque is completely flat from 3300-4000 RPM. Let's also say peak power is flat from 6000-6500 rpm. Further, let's also say that since more force is being applied at peak torque, it takes an identical amount of time, in seconds, to accelerate over either of those RPM bands, even though the lower one covers 200 RPM more. Let's just say it takes 10 seconds to cover those RPM bands because you're in 4th. Even though you've accelerated more in the low power band in 10 seconds, the distance covered in the high power band during those 10 seconds is considerably higher. Let's make it easy and define distance as the distance that the car travels during that time. How fast is your car going to be moving at 6000 RPM? By comparison to 3300, pretty damned fast, right? In fact, the car's velocity is almost twice as fast (6000/3300=1.82). How much less torque will it be making at 6000 RPM? It should be making considerably more than half, right? So since we know work is a force over a distance (W=F*d). We can deduce conceptually that more work is done in the high power band in the same 10 second time frame because well more than half the force is being applied at almost double the distance.

From an engine perspective, the distance will be the number of rotations that are completed in those 10 seconds. Obviously, the high powerband is going to complete somewhere around nearly twice as many rotations in the 10 second period as the low powerband (6000rpm*10s/60s > 4000 *10/60). The force applied over that distance is the torque the engine makes. Again, nearly twice as many rotations, with much more than half as much torque = more power (tq * rotations = work)

A little less force applied over a lot more distance = more power. Your motor did indeed produce more work in the same amount of time at the top of the powerband. More "stuff" was accomplished, so to speak.

That's about all I can think of to explain it. Hopefully, I did an adequate understandable job.

I've got some other ideas that I can use to explain this, but it's almost 4am here in Afghanistan, and I'm getting to tired to think straight.

I could do the math and explain the numbers to prove the matter, but that's not basic stuff, anymore, and I'm probably a bit rusty. I actually made a "dragstrip" calculator when I was in college that calculates this stuff very quickly and attempts to estimate 1/4 mile time given vehicle weight, its gearing, average rear-wheel torque in each gear (from a dyno graph), wind resistance, and an approximate 60' time. It's pretty cool and I got it to predict just about every car within a few tenths of a second. Some were very very close. This model was great because it let's the user play around with gearing, weight, 60' times etc... to see how they would impact the car's ET and trap speed. If any of you have any interest in checking it out, I'll email it. I'd like to further develop it one day, but there are so many other awesome calculators out there now with engine programs that I just didn't see the point. I got an A on the project, though.

Chris

ItsStock02 · May 11, 2011

So much to read here.

sneaky98gt · May 14, 2011

FastDriver said:
...Chris

Wow, Chris. That is quite possibly the best explanation of hp v. torque that I have ever read. You explained it thoroughly, and I understood it very well.

Yes, I would be interested in that calculator. I've actually wanted to try and calculate the performance gain that someone would get from a gear swap. Shoot me a PM.

Also didn't realize you were in the armed forces. Godspeed, my friend.

Crzyhrse · May 14, 2011

For the Mach, the first 3 gears are all redline shifts (6,800), and the 4th gear shift is about 6,500. You'll be in the sweet spot the whole time.

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