Backwards Thinking(HP vs. Torque)
11-17-2008, 12:03 PM
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Backwards Thinking(HP vs. Torque)
Did some digging around, and found some neat stuff wrt aerodynamic hp and rolling hp(drivetrain & tires). The former increases as the cube of the speed(steep curve!), and the latter increases as a function of an exponent between 2 and 2.5.
So I plugged in some numbers for the S197 GT{CD=0.38(conservative due to its squared front), frontal area=22 sq. ft.(should be close), ambient temperature=70F, barometric pressure=30 in Hg, weight=3700#, tire pressure=32 psi) along with different velocities, and the following numbers were spit out:
Velocity(mi./hr.) - 30, 60, 90, 120, 150
Aerodynamic hp - 1.5, 12, 41, 96, 189
Rolling horsepower - 3, 8, 19, 40, 76
Knowing that the S197 GT(manual tranny) produces approx. 260 whp(SAE corrected) on a dyno, the above combined total of 265 for aerodynamic hp and rolling hp at 150 mph makes sense since owners have posted stock top speeds anywhere from the mid-140's to a little over 150 mph.
However, it was the above high speed rolling hp numbers that peaked my curiousity, so I attempted some reverse thinking(also known as backwards thinking when done by me). Assuming an S197 GT has 3.55 gears, stock 27" tires, 6250 rpm redline, and is dynoed in 4th to redline, then the equivalent top speed will be approx. 134 mph(Note: this speed takes into account the tires' loaded radius). This works out to be approx. 40 rolling hp(drivetrain & rear tires) on a dyno, since the rated chp is approx. 300.
But the rolling hp came out at 54 hp when traveling down the road on all 4 tires at 134 mph. Knowing from the Mustang spec sheet that the front tires bear approx. 54% of the car's weight, and the rear tires bear approx. 46%, some algebraic calcs(BTW took me a long time as I haven't done algebra in ages) showed 28 hp drivetrain loss and 26 hp tire loss(road)/12 hp tire loss(dyno). Again, this made sense as the rolling loss is a typical 13%(manual tranny) on the dyno with only 2 tires contributing their internal friction loss, and a higher than typical 18% on the road with all 4 tires now contributing their internal friction loss.
Again, doing some more backwards thinking, I related the above velocities to WOT acceleration, and found that at 60 mph the engine for the above S197 GT will be spinning at greater than 5252 rpm(point where torque and hp curves cross on a dyno chart) with the exception of possibly a very brief second or so immediately after the 2-3 shift.
Hence, according to the above numbers, and according to the hp and torque curves on S197 GT dyno charts(at least every one Ive seen), one can accurately state that hp accelerates the car at speeds of approx. 60 mph and faster where aerodynamic force predominates, and torque accelerates it at speeds below approx. 60 mph where rolling resistance is the primary force.
Yeah, yeah, I know that torque and hp are related thru a common equation. But the fact remains that they are also shown as 2 separate curves on dyno charts. And that's one of the primary supporting factors for that statement.
So I plugged in some numbers for the S197 GT{CD=0.38(conservative due to its squared front), frontal area=22 sq. ft.(should be close), ambient temperature=70F, barometric pressure=30 in Hg, weight=3700#, tire pressure=32 psi) along with different velocities, and the following numbers were spit out:
Velocity(mi./hr.) - 30, 60, 90, 120, 150
Aerodynamic hp - 1.5, 12, 41, 96, 189
Rolling horsepower - 3, 8, 19, 40, 76
Knowing that the S197 GT(manual tranny) produces approx. 260 whp(SAE corrected) on a dyno, the above combined total of 265 for aerodynamic hp and rolling hp at 150 mph makes sense since owners have posted stock top speeds anywhere from the mid-140's to a little over 150 mph.
However, it was the above high speed rolling hp numbers that peaked my curiousity, so I attempted some reverse thinking(also known as backwards thinking when done by me). Assuming an S197 GT has 3.55 gears, stock 27" tires, 6250 rpm redline, and is dynoed in 4th to redline, then the equivalent top speed will be approx. 134 mph(Note: this speed takes into account the tires' loaded radius). This works out to be approx. 40 rolling hp(drivetrain & rear tires) on a dyno, since the rated chp is approx. 300.
But the rolling hp came out at 54 hp when traveling down the road on all 4 tires at 134 mph. Knowing from the Mustang spec sheet that the front tires bear approx. 54% of the car's weight, and the rear tires bear approx. 46%, some algebraic calcs(BTW took me a long time as I haven't done algebra in ages) showed 28 hp drivetrain loss and 26 hp tire loss(road)/12 hp tire loss(dyno). Again, this made sense as the rolling loss is a typical 13%(manual tranny) on the dyno with only 2 tires contributing their internal friction loss, and a higher than typical 18% on the road with all 4 tires now contributing their internal friction loss.
Again, doing some more backwards thinking, I related the above velocities to WOT acceleration, and found that at 60 mph the engine for the above S197 GT will be spinning at greater than 5252 rpm(point where torque and hp curves cross on a dyno chart) with the exception of possibly a very brief second or so immediately after the 2-3 shift.
Hence, according to the above numbers, and according to the hp and torque curves on S197 GT dyno charts(at least every one Ive seen), one can accurately state that hp accelerates the car at speeds of approx. 60 mph and faster where aerodynamic force predominates, and torque accelerates it at speeds below approx. 60 mph where rolling resistance is the primary force.
Yeah, yeah, I know that torque and hp are related thru a common equation. But the fact remains that they are also shown as 2 separate curves on dyno charts. And that's one of the primary supporting factors for that statement.
11-17-2008, 01:20 PM
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11-18-2008, 10:24 AM
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Very interesting math here. However, your deduction about horsepower accelerating the car isnt really correct especially in the manner you derived it. Whatever equation you found was a quick and dirty method of doing a force body diagram using horsepower as your units. Thats interesting, but traditionally inaccurate since horsepower is a heavily derived form of measurment.
Simply put, torque accelerates a machine. It is a force and does work, reguardless of speed. Aerodynamic force never predominates, if that was true it would be greater than your forward force (torque after drivetrain loss) and you would accelerate backwards once you got to that point.
Hp really should only be discussed in relation to rpm, because it doesnt exist without it. Its analogous to needing time to determine velocity even though your car exists in several positions.
I think the part your really missing is the relationship between acceleration and torque. Your correct in the respect that torque follows a curve, but our cars also contain gearing. The tires of the car do not turn at 5252 rpm at 60 mph, they turn something much less (sorry i dont feel like doing the math). This difference in rpm is attributed to the gearing of our car. Yes, we use less torque to accelerate as we gain speed, but theres a reason our cars accelerate dramatically slower in the higher speeds than lower speeds. Of course there is drag as well, and a lof of it, but any contination of this discussion will turn into a cost analysis and fule economy design discussion.
Anyways, sorry for rambling, the point is you need force to accelerate, and torque is a force, while horsepower isnt, its power. If you want to accelerate faster, you have to apply more torque for longer rpm's, theres no cheating that. Horsepower will peak at the highest rpm where your torque remains useful. Its a nice method of giving you an idea of how long torque extends into the rpm band.
Simply put, torque accelerates a machine. It is a force and does work, reguardless of speed. Aerodynamic force never predominates, if that was true it would be greater than your forward force (torque after drivetrain loss) and you would accelerate backwards once you got to that point.
Hp really should only be discussed in relation to rpm, because it doesnt exist without it. Its analogous to needing time to determine velocity even though your car exists in several positions.
I think the part your really missing is the relationship between acceleration and torque. Your correct in the respect that torque follows a curve, but our cars also contain gearing. The tires of the car do not turn at 5252 rpm at 60 mph, they turn something much less (sorry i dont feel like doing the math). This difference in rpm is attributed to the gearing of our car. Yes, we use less torque to accelerate as we gain speed, but theres a reason our cars accelerate dramatically slower in the higher speeds than lower speeds. Of course there is drag as well, and a lof of it, but any contination of this discussion will turn into a cost analysis and fule economy design discussion.
Anyways, sorry for rambling, the point is you need force to accelerate, and torque is a force, while horsepower isnt, its power. If you want to accelerate faster, you have to apply more torque for longer rpm's, theres no cheating that. Horsepower will peak at the highest rpm where your torque remains useful. Its a nice method of giving you an idea of how long torque extends into the rpm band.
11-18-2008, 12:44 PM
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Your description "Interesting Math" is the precise reason why I termed my post "Backwards Thinking".
Actually, the true definition of torque is a moment(force x lever arm), and not just a simple force.
Also, since hp and torque have a simple mathematical relationship thru an equation involving rpm's and a numerical constant, then it can be said that either one accelerates a car.
Predominates => definition: "larger than".
Perhaps my explanation was not clearly spelled out, so putting it a different way, aerodynamic hp is "larger than" rolling hp for an S197 GT at speeds of approx. 60 mph and higher.
hp was discussed in terms of rpm's => "dyno".
Gearing was also discussed => "...with the exception of possibly a very brief second or so immediately after the 2-3 shift."
You're exactly correct when you say that the tires do not spin at 5252 rpm. But my post distinctly states that the engine, and not the tires, is spinning at that rpm.
You're partially correct stating that lower engine torque and aerodynamics are the reasons why cars accelerate slower at higher speeds. The other reasons are increased rolling hp and higher gearing.
Finally, you apparently missed the main point of my post:
Dyno charts show both torque and hp curves.
According to S197 GT charts, hp is the main factor that accelerates this car at WOT at speeds of approx. 60 mph when aerodynamic hp predominates, and torque is the main factor that accelerates it when rolling hp predominates.
No more, no less.
Actually, the true definition of torque is a moment(force x lever arm), and not just a simple force.
Also, since hp and torque have a simple mathematical relationship thru an equation involving rpm's and a numerical constant, then it can be said that either one accelerates a car.
Predominates => definition: "larger than".
Perhaps my explanation was not clearly spelled out, so putting it a different way, aerodynamic hp is "larger than" rolling hp for an S197 GT at speeds of approx. 60 mph and higher.
hp was discussed in terms of rpm's => "dyno".
Gearing was also discussed => "...with the exception of possibly a very brief second or so immediately after the 2-3 shift."
You're exactly correct when you say that the tires do not spin at 5252 rpm. But my post distinctly states that the engine, and not the tires, is spinning at that rpm.
You're partially correct stating that lower engine torque and aerodynamics are the reasons why cars accelerate slower at higher speeds. The other reasons are increased rolling hp and higher gearing.
Finally, you apparently missed the main point of my post:
Dyno charts show both torque and hp curves.
According to S197 GT charts, hp is the main factor that accelerates this car at WOT at speeds of approx. 60 mph when aerodynamic hp predominates, and torque is the main factor that accelerates it when rolling hp predominates.
No more, no less.
11-18-2008, 12:53 PM
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We've been through most of this in another thread (just guessing that it might have been the "Max Speed" one).
HP is actually a force times a velocity and can be used without reference to rpm, at least for certain things (*cough* top speed *cough*).
Torque is a force times a distance and needs to be divided by a distance to get to anything useful for computing either vehicle acceleration or its integrals (velocity and distance).
Anyway, it is entirely proper to state that aero resistance is the predominant force opposing acceleration. I also have seen where rolling resistance as a force increases with speed (Chevrolet Power Handbook, IIRC), hence making rolling HP a second power (or so) function of velocity.
My side comment here is that sometimes these technical description kinds of posts perhaps aren't written as tightly as absolutely necessary to avoid nitpicking, and since two individuals don't necessarily come into any given problem in quite the same way it happens (hey, I do it too).
Norm
HP is actually a force times a velocity and can be used without reference to rpm, at least for certain things (*cough* top speed *cough*).
Torque is a force times a distance and needs to be divided by a distance to get to anything useful for computing either vehicle acceleration or its integrals (velocity and distance).
Anyway, it is entirely proper to state that aero resistance is the predominant force opposing acceleration. I also have seen where rolling resistance as a force increases with speed (Chevrolet Power Handbook, IIRC), hence making rolling HP a second power (or so) function of velocity.
My side comment here is that sometimes these technical description kinds of posts perhaps aren't written as tightly as absolutely necessary to avoid nitpicking, and since two individuals don't necessarily come into any given problem in quite the same way it happens (hey, I do it too).
Norm
11-18-2008, 01:19 PM
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Yeah, you're probably right.
But if it means when I go to mod that I'm smart enough to get away with buying once instead of three times (and b!tching & moaning twice) it's worth it. Come to think, I paid good money to learn how to think that way, so I might as well get some personal value out of it.
Norm
But if it means when I go to mod that I'm smart enough to get away with buying once instead of three times (and b!tching & moaning twice) it's worth it. Come to think, I paid good money to learn how to think that way, so I might as well get some personal value out of it.
Norm
Last edited by Norm Peterson; 11-18-2008 at 02:54 PM.