Math. The formula for HP is:
HP = (Torque x RPM)/5252
So, at 5252 RPM(looks like 5250 on most graphs), the 5252 constant cancels out the RPM, & *Presto*, all that's left is Horsepower = Torque.
Ain't math cool?
Driving it TOO easy....
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HP = (Torque x RPM)/5252
So, at 5252 RPM(looks like 5250 on most graphs), the 5252 constant cancels out the RPM, & *Presto*, all that's left is Horsepower = Torque.
Ain't math cool?
There are always hardware fixes around the adaptive mode. The newer OBDII systems are much better though and aren't as intrusive. It's purpose is to "tune" the vehicle to most efficiently meet the performance requirements of the operator. In some vehicles the adaptive mode becomes static meaning that a weighted average of the driving charateristics over a certain number of driving cycles is used at al times reguardless of how the vehicle has been recently driven. Usually have to reset the PCM to clear out the adaptive memory and make it relearn to your preference. Newer systems are more dynamic in their approach.
My rambling:
Yes, you can drive a car too easy. "Easy" drives build up carbon, don't heat the oil as fully as it could to burn off condensation, and I've even heard of it being able to cause some buildup on cylinder walls where the piston changes direction at the bottom of the downstroke. If you always baby everything there's never any normal stretch or deformation of the rods and bearing and one day when you do open it up there's a ring of crud in the way. Along those lines I've heard break in recommendations to make sure to vary revs and throttle angles to see "all conditions" when seating the rings and whatnot.
Using WOT at low revs is called "lugging" in extreme cases and is the worst thing you can do for your engine. Keep in mind that you need high oil pressure to protect your crank bearings and other expensive parts. WOT without full oil pressure gives you all the stress without a fraction of the protection. IMO it's "easier" on an engine to go WOT in mid-high RPM ranges because it causes less piston, rod and crank stress because things are moving fast enough to keep up with the flame front etc... (diesel excluded). Just listen - you can tell it's "happier".
Some engines are designed to be appliances to get you from point A to point B and simply aren't very interesting. I'm a car and driving hobbyist, so I've always tried to have responsive, interesting engines, even if they were only 1.6L I4s. All of my engines have seen a mix of conditions, but never WOT at low revs. Some of my most enjoyable driving is/was out in the country at 1/3 throttle shifting at 5500 - easy on all the parts and music to the ears...
Any car I've had is treated to nothing but "the best" (not intended to spark a product debate) with extra maintenance, top quality fluids, TLC and lots of attention. They are not babied on the road, however.
Craig.
Yes, you can drive a car too easy. "Easy" drives build up carbon, don't heat the oil as fully as it could to burn off condensation, and I've even heard of it being able to cause some buildup on cylinder walls where the piston changes direction at the bottom of the downstroke. If you always baby everything there's never any normal stretch or deformation of the rods and bearing and one day when you do open it up there's a ring of crud in the way. Along those lines I've heard break in recommendations to make sure to vary revs and throttle angles to see "all conditions" when seating the rings and whatnot.
Using WOT at low revs is called "lugging" in extreme cases and is the worst thing you can do for your engine. Keep in mind that you need high oil pressure to protect your crank bearings and other expensive parts. WOT without full oil pressure gives you all the stress without a fraction of the protection. IMO it's "easier" on an engine to go WOT in mid-high RPM ranges because it causes less piston, rod and crank stress because things are moving fast enough to keep up with the flame front etc... (diesel excluded). Just listen - you can tell it's "happier".
Some engines are designed to be appliances to get you from point A to point B and simply aren't very interesting. I'm a car and driving hobbyist, so I've always tried to have responsive, interesting engines, even if they were only 1.6L I4s. All of my engines have seen a mix of conditions, but never WOT at low revs. Some of my most enjoyable driving is/was out in the country at 1/3 throttle shifting at 5500 - easy on all the parts and music to the ears...
Any car I've had is treated to nothing but "the best" (not intended to spark a product debate) with extra maintenance, top quality fluids, TLC and lots of attention. They are not babied on the road, however.
Craig.
I'm trying different driving techniques for gas mileage, and feather footing it does not work, for me. Getting the throttle open (carb), not all at once but quickly, and short shifting to keep it open have worked the best. So, some heavy throttle does not hurt mileage too much and getting some heat in the engine might help keep it clean.
My philosophy is that a normally aspirated, gasoline engine is most efficient at producing power at its torque peak. Acceleration from stop to cruising speed is best done around that rpm. This is where all the resonances for intake charge, exhaust clearing, valve overlap etc... are at their best, hence the torque peak.
Of course the torque peak is measured at WOT, and at throttle angles other than WOT things may vary.
My point is that accerating with significant throttle angle and shifting at 2300 (example) is not necessarily doing anyone any favours, including your mileage.
Heat from high rpm is usually what cleans carbon, not heat from high throttle angles. That's why the essence of the "Italian tuneup" is high RPM - not high load. More power strokes per second (even if there is less fuel) plus the energy expended in riciprocating mass lead to more heat for cleaning.
Try accelerating with moderate throttle angles, to moderate RPM (I dunno, say 3500 rpm shift points) and cruise in highest possible gear for your speed and see what happens. I have no idea what kind of car you drive. This is generally what I do, although I favour keeping the engine in a happy rev zone (ie. not lugging it) as a priority over keeping it in the top gear above idle. It's not a diesel and I still want some response to throttle input and lug-free operating conditions that are easy on the bearings, rods, pins etc... If that means going up a hill in third at 3000-3500rpm so be it. Once back on level ground it's back to highest comfortable gear and feather throttle.
Craig.
Of course the torque peak is measured at WOT, and at throttle angles other than WOT things may vary.
My point is that accerating with significant throttle angle and shifting at 2300 (example) is not necessarily doing anyone any favours, including your mileage.
Heat from high rpm is usually what cleans carbon, not heat from high throttle angles. That's why the essence of the "Italian tuneup" is high RPM - not high load. More power strokes per second (even if there is less fuel) plus the energy expended in riciprocating mass lead to more heat for cleaning.
Try accelerating with moderate throttle angles, to moderate RPM (I dunno, say 3500 rpm shift points) and cruise in highest possible gear for your speed and see what happens. I have no idea what kind of car you drive. This is generally what I do, although I favour keeping the engine in a happy rev zone (ie. not lugging it) as a priority over keeping it in the top gear above idle. It's not a diesel and I still want some response to throttle input and lug-free operating conditions that are easy on the bearings, rods, pins etc... If that means going up a hill in third at 3000-3500rpm so be it. Once back on level ground it's back to highest comfortable gear and feather throttle.
Craig.
Hey Stuart!
One more reason I don't argue with the Lords of Oil, other than those pushing a vested interest.
Now, from the distinctly UN-Scientific "feel" of the car (I hate that butt-dyno dichotomy, color me phobic), when I go WOT in any gear, (excepting maybe 4th and fifth when the wind becomes a substantial factor not to mention extra-legal speed), I can feel a great reduction in "pull" at 4100 RPM. Dramatic. The car continues to accelerate, will build RPM to redline, but the "pull" is gone. Long before 5252 RPM.
Not contradicting, just asking, Stu. I don't doubt the math, the math is science, but the grunt is gone from 4 grand going up. So if the math is correct, what's causing the "pull" to drop in such dramatic fashion so far ahead of 5252 in this car?
Edited to add: I should have mentioned, this is a 2005 Accent GT with a whopping 1.6L DOHC producing a monstrous (and officially published) 105 HP @ 5800 RPM, with a redline of 7 Grand, although the limiter kicks in at 6800. The car's curb weight is an official 2245 lbs.
Thanks!
Ok, well, cool for YOU, maybe.
One more reason I don't argue with the Lords of Oil, other than those pushing a vested interest.
Now, from the distinctly UN-Scientific "feel" of the car (I hate that butt-dyno dichotomy, color me phobic), when I go WOT in any gear, (excepting maybe 4th and fifth when the wind becomes a substantial factor not to mention extra-legal speed), I can feel a great reduction in "pull" at 4100 RPM. Dramatic. The car continues to accelerate, will build RPM to redline, but the "pull" is gone. Long before 5252 RPM.
Not contradicting, just asking, Stu. I don't doubt the math, the math is science, but the grunt is gone from 4 grand going up. So if the math is correct, what's causing the "pull" to drop in such dramatic fashion so far ahead of 5252 in this car?
Edited to add: I should have mentioned, this is a 2005 Accent GT with a whopping 1.6L DOHC producing a monstrous (and officially published) 105 HP @ 5800 RPM, with a redline of 7 Grand, although the limiter kicks in at 6800. The car's curb weight is an official 2245 lbs.
Thanks!
First, that math depends on what units you measure in. Nm != ft-lb
The point of the math is not about the magic number 5252, but more that HP is simply derived from torquexRPM. If you have a high revving motor, as long as torque isn't falling off extremely rapidly you'll get high RPM horsepower peaks. The higher they extend the redline, the more HP they can put in the brochure.
To put it another way, if you have a perfectly flat torque curve, you will get a constantly increasing HP line (to infinity) at a slope related to 5252. Generally torque curves aren't flat, and roll off at high and low RPMs. When the torque falls off faster than the RPM is rising, the HP curve falls too, giving you your HP peak at some RPM that's beyond the useful torque range of your engine.
Torque is the twisting force that moves the vehicle - period. Your 1.6L engine is designed with a roll off above 4000rpm. There's nothing wrong with your butt dyno. Where's the advertised torque peak on your engine? Plan your shift points to straddle your torque peak. Let's just say your gear-to-gear ratios work out nicely. If your torque peak was at 3500rpm and your revs fall around 700rpm per shift at ~4000 (the gap changes with engine RPM since it's a linear function starting at 0). I would probably shift at 3600-3700rpm just past the torque peak, and letting the revs then fall to 3300-3400 in the next gear, just below the torque peak. You will sweep right through your torque peak before the next shift.
If your gear gap is 1000rpm, shift at 4000 so each gear sweeps 3000-4000rpm right through the torque peak.
If your torque production isn't equally distributed above and below the peak, favour the lopsided side of the peak with more torque. So if you have building torque to 3500 and hit a brick wall and have 500 rpm gear spacing, run from 3100-3600rpm in each gear while accelerating.
It's useful to obtain torque and HP graphs for your vehicle, not just the peak numbers.
Again, cruising is a different animal. Go for top gear economy without lugging.
Take a look at engine and transmission graphs for a car I used to own. The torque peak was at 4100rpm and there was torque pretty much everywhere. The HP curve is a virtually a slanted line because of the flat torque. Brisk driving can be "planned" by combining the torque curves and transmission diagrams to straddle the torque peak.
Not a lot of time to write this, sorry for bad grammar or mistakes.
The point of the math is not about the magic number 5252, but more that HP is simply derived from torquexRPM. If you have a high revving motor, as long as torque isn't falling off extremely rapidly you'll get high RPM horsepower peaks. The higher they extend the redline, the more HP they can put in the brochure.
To put it another way, if you have a perfectly flat torque curve, you will get a constantly increasing HP line (to infinity) at a slope related to 5252. Generally torque curves aren't flat, and roll off at high and low RPMs. When the torque falls off faster than the RPM is rising, the HP curve falls too, giving you your HP peak at some RPM that's beyond the useful torque range of your engine.
Torque is the twisting force that moves the vehicle - period. Your 1.6L engine is designed with a roll off above 4000rpm. There's nothing wrong with your butt dyno. Where's the advertised torque peak on your engine? Plan your shift points to straddle your torque peak. Let's just say your gear-to-gear ratios work out nicely. If your torque peak was at 3500rpm and your revs fall around 700rpm per shift at ~4000 (the gap changes with engine RPM since it's a linear function starting at 0). I would probably shift at 3600-3700rpm just past the torque peak, and letting the revs then fall to 3300-3400 in the next gear, just below the torque peak. You will sweep right through your torque peak before the next shift.
If your gear gap is 1000rpm, shift at 4000 so each gear sweeps 3000-4000rpm right through the torque peak.
If your torque production isn't equally distributed above and below the peak, favour the lopsided side of the peak with more torque. So if you have building torque to 3500 and hit a brick wall and have 500 rpm gear spacing, run from 3100-3600rpm in each gear while accelerating.
It's useful to obtain torque and HP graphs for your vehicle, not just the peak numbers.
Again, cruising is a different animal. Go for top gear economy without lugging.
Take a look at engine and transmission graphs for a car I used to own. The torque peak was at 4100rpm and there was torque pretty much everywhere. The HP curve is a virtually a slanted line because of the flat torque. Brisk driving can be "planned" by combining the torque curves and transmission diagrams to straddle the torque peak.
Not a lot of time to write this, sorry for bad grammar or mistakes.
Point made, but not clear, I'm quite un-educated in the math and engineering of it all. I understand the curves, and tuning for top-end HP vs. low-end grunt.
The high-rev bikes never made much sense to me on the street, even if I understand how Kenny Roberts, and Eddie Lawson, or a Freddie Spencer could get results with all those revs on a track..
Little of it applies to a roller-skate like a Hyundai in any case. I'm in no position to argue the engineering of it, but the pull of this car falls off drastically after 4K rpm. It's a pretty good pull for 2K rpm or so, from 2-4, but it's such a narrow power band, I'd never try to stay in it other than in the very twistiest of roads and switchbacks. The long legs necessary to get high HP results simply aren't built into this car..
Not a knock, it's mostly why I bought this thing, after all. Gas mileage..
Thanks, Craig!
The high-rev bikes never made much sense to me on the street, even if I understand how Kenny Roberts, and Eddie Lawson, or a Freddie Spencer could get results with all those revs on a track..
Little of it applies to a roller-skate like a Hyundai in any case. I'm in no position to argue the engineering of it, but the pull of this car falls off drastically after 4K rpm. It's a pretty good pull for 2K rpm or so, from 2-4, but it's such a narrow power band, I'd never try to stay in it other than in the very twistiest of roads and switchbacks. The long legs necessary to get high HP results simply aren't built into this car..
Not a knock, it's mostly why I bought this thing, after all. Gas mileage..
Thanks, Craig!
Hmmm, my 3800 V6 is just coming alive at 4000 RPM. North of 3000, you feel a definite increase in pull. It stays that way until the shift at about 5700. I've gotta believe that cam profiles are largely responsible for that behavior, though. By altering the profile, the mfgr can have a lot of control over the torque curve. I think the restrictiveness of the intake and exhuast also effects this a lot, especially at high RPM. You might find you can delay that 4000 rpm drop off by opening the intake up with a cold air intake kit and using a less restrictive exhaust system (I'm not talking a fert can, mind you, just something more free flowing). Those mods can actually increase MPG (at the expense of a little noise) if you can keep from taking advantage of all that increased power every time you hit the gas.
Appreciate the tip, but I'm no modder, Matt..
This car is SO not suited for modding, and besides, I'm already pushing the warranty going 10K OCI, thanks to the clear superiority of M-1 0W-20 (SM) and a dash/quart of VSOT with an Amsoil filter.
Intake taps and so on won't help this car enough to risk the warranty.
Thanks, Yall!
This car is SO not suited for modding, and besides, I'm already pushing the warranty going 10K OCI, thanks to the clear superiority of M-1 0W-20 (SM) and a dash/quart of VSOT with an Amsoil filter.
Intake taps and so on won't help this car enough to risk the warranty.
Thanks, Yall!
Sorry, should have specified; that formula is for torque in ft-lbs.
Here's a link to pretty good rundown on torque, HP, & acceleration: http://vettenet.org/torquehp.html
Here's a link to pretty good rundown on torque, HP, & acceleration: http://vettenet.org/torquehp.html
You don't need to stay in the band except during acceleration, cruising is top gear unless you're going up a significant hill. See if you can find the actual curves anywhere online or in your manual instead of just the peaks, and look up the peak torque @RPM figure from your manual. Try shifting at 4k until you're up to speed.
As I mentioned, HP is irrelevant and can be pretty much ignored.
An (engineer!) friend of mine used to compare his Accord V6 to an Audi 2.7T that his boss had. He used the peak HP numbers and said that it wasn't worth twice the $$ for 50 more horsepower. He had a pretty serious misunderstanding.
If you look at the torque numbers and especially the curves, the 2.7T had something like 250 ft-lbs from 1800-5700RPM in a flat solid line. His Accord was not quite 200 ft-lbs peak (I think) and for a fairly narrow band.
Add up (integrate for you calculus types) the areas under the torque curve over 2 or more gears and the Audi eats the Accord for breakfast.
Figuring out how fast a car will be from x to y mph is a mathematical function of integrating (summing) the area under the torque curve and using a transmission map to determine shift points to maximize this area.
Craig.
JHZR2
Staff member
aaah, the mathematics of it... I love it!
JMH
JMH
No problem. I was just trying to generate an understanding of what can be done to affect the car's power band. Intake and exhaust mods can work wonders for flattening the power band, even if they don't generate much extra power. My engine is actually stock, to be honest, but for those who start making changes, these are the first mods you do before you start to add cams, head and manifold changes, forced induction, whatever.
Sorry to disagree Craig, but this is about as wrong as it gets. To accelerate the car the hardest, you run through the gears with the engine in the POWERBAND. If you want your car to accelerate twice as hard as stock, you double the engine POWER or cut the car weight in half.
It's the area under the POWER curve that matters. The engine torque output is largely irrevelant. The transmission has gears so that you can keep the engine in the POWERBAND if you are serious about accelerating the car.
Also, horsepower and torque are never equal. The 5252 is just a units conversion factor, and has no physical interpretation whatsoever. Ignore it. We plot HP and torque vs. RPM on the same sheet of paper for convenience only.
JHZR2
Staff member
I disagree... they say the same thing...
HP=(Tq x rpm)/5252
is the same as:
Y(X)=(F(X) x X) / 5252
Which is also:
Y(X) = F(X)/5252 x X/5252
If we take the derivative, we get:
Y'(X)=F'(X)/5252 x 1/5252
Per the last two equations, both the function and its derivative, everything is just a number that fills right in... F(X) is only written so because it is engine dependent, as different engines will make different torques (F(X)) at different RPMs (X). Its all scaled by constants and the variable, X (i.e. RPM). If you made some function for the torque with respect to RPM, and plotted it, it would turn out that one is just a scalar of the other.
My math may be wrong, but the direct equality of the two figures is correct.
JMH
HP=(Tq x rpm)/5252
is the same as:
Y(X)=(F(X) x X) / 5252
Which is also:
Y(X) = F(X)/5252 x X/5252
If we take the derivative, we get:
Y'(X)=F'(X)/5252 x 1/5252
Per the last two equations, both the function and its derivative, everything is just a number that fills right in... F(X) is only written so because it is engine dependent, as different engines will make different torques (F(X)) at different RPMs (X). Its all scaled by constants and the variable, X (i.e. RPM). If you made some function for the torque with respect to RPM, and plotted it, it would turn out that one is just a scalar of the other.
My math may be wrong, but the direct equality of the two figures is correct.
JMH
It is definitely wrong since you forgot the units for the 5252. Also, the power curve is the torque curve times a linear function.
Torque is a moment with its units, and horsepower is power with its different units. They can never be equal.
JHZR2
Staff member
As far as I can tell, the units for HP are:
1 hp = 33,000 ft·lbf·min−1 = ~0.746 kW
Where ft*lbf is torque, so it is just torque times inverse minutes which is RPM, so the 5252 is unitless and but a scalar.
JMH
1 hp = 33,000 ft·lbf·min−1 = ~0.746 kW
Where ft*lbf is torque, so it is just torque times inverse minutes which is RPM, so the 5252 is unitless and but a scalar.
JMH
JHZR2
Staff member
Static Plot
Or try this:
Both Plots
Well, here I made some plots for easier visualization and discussion...
My torque function was arbitrary, I just wanted something reasonable that had a curve in a typical RPM operating range. I think this does well.
Note that when I evaluate the two functions (as seen at the very bottom) at 5252 rpm, they are equal, as we first mentioned.
Note also that when I take the derivative of torque, it is a line, as it should be... When I take the derivative of HP (which when all is plugged, you get a cubic equation in RPM), we get a scaled curve identical to torque.
This is how it should be... torque is a function of engine RPM (to some power), and when you calculate horsepower, you multiply in another RPM into the function - yielding the hp equation with an rpm factor to a higher power (remember, HP and torque are functions of RPM now). take the derivative of HP, you get a modified torque curve... Why? because hp is a function of torque, merely differentiated by a scalar and an RPM multiplier... take the derivative of a power, and you get something of the form x^2=2X, x^3=3x^2 and so on... so youll always get a curve identical to what HP's function is based upon... which is torque and only torque... the rest are scalars.
My explanation is off as Im not a mathematician... But maybe some more mathy sort can explain what Im trying to say, or tell me Im wrong and explain why so I brush up on my math skills
JMH
[ May 12, 2006, 12:15 AM: Message edited by: Bio-T ]
Or try this:
Both Plots
Well, here I made some plots for easier visualization and discussion...
My torque function was arbitrary, I just wanted something reasonable that had a curve in a typical RPM operating range. I think this does well.
Note that when I evaluate the two functions (as seen at the very bottom) at 5252 rpm, they are equal, as we first mentioned.
Note also that when I take the derivative of torque, it is a line, as it should be... When I take the derivative of HP (which when all is plugged, you get a cubic equation in RPM), we get a scaled curve identical to torque.
This is how it should be... torque is a function of engine RPM (to some power), and when you calculate horsepower, you multiply in another RPM into the function - yielding the hp equation with an rpm factor to a higher power (remember, HP and torque are functions of RPM now). take the derivative of HP, you get a modified torque curve... Why? because hp is a function of torque, merely differentiated by a scalar and an RPM multiplier... take the derivative of a power, and you get something of the form x^2=2X, x^3=3x^2 and so on... so youll always get a curve identical to what HP's function is based upon... which is torque and only torque... the rest are scalars.
My explanation is off as Im not a mathematician... But maybe some more mathy sort can explain what Im trying to say, or tell me Im wrong and explain why so I brush up on my math skills
JMH
[ May 12, 2006, 12:15 AM: Message edited by: Bio-T ]
That is some very nice work! And fast, too.
Think of work done at the crank per rotation as an applied force on a 1 ft torque wrench pulled through 1 complete rotation. That is it is pulled along (2PI radians)*(1 ft) of total work length per rotation. We get:
1HP = 550ft-lbs/s = 33,000ft-lbs/min = (5252lbs)*(2PI ft)/min
So units for the 5252 are ft*lbs*RPM/HP or
(550ft-lbs/s/HP)*(60s/min)/(2 PI rad/rotation)
Check this please.
Think of work done at the crank per rotation as an applied force on a 1 ft torque wrench pulled through 1 complete rotation. That is it is pulled along (2PI radians)*(1 ft) of total work length per rotation. We get:
1HP = 550ft-lbs/s = 33,000ft-lbs/min = (5252lbs)*(2PI ft)/min
So units for the 5252 are ft*lbs*RPM/HP or
(550ft-lbs/s/HP)*(60s/min)/(2 PI rad/rotation)
Check this please.
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