Anyone out there able to provide the formula to calculate rear wheel HP or TQ lost at the wheels by pounds and by distance from the centerpoint of the axle?

Here's what I'm getting at. If the rear wheel HP is 230 at the wheels with a stock 18" wheel at 25 pounds (if this is correct) and a stock Pilot at about the same weight (if this is correct), what percentage of RW HP is lost per added pound, AND per added inch to the radius.

Practical application:
Adding a rotor with a 1" larger diameter and 1 pound less will reduce your HP at the wheels by "x".

Adding 1" to the wheel diameter, with 5 pounds more will reduce your HP at the wheels by "x".

You get the idea.

I just watched a show on Speed channel and they added an exhaust, bigger rotors, and a larger diameter wheel to an Acura. They LOST 12 HP. The exhaust supposedly added 5 HP so what gives? Turns out, even though the rotor was lighter, due to the weight being farther from the centerline and same goes for the larger wheel, they actually LOST 7% HP at the wheels.

Most of us knew this would happen but I had no idea that the loss could be so severe. This gets me thinking about reprioritizing my mods order. Why am I screwing around with 5 HP here and there when I should be focusing on 1) Weight 2) Unsprung weight 3) Unsprung weight that is far from the axis.

My exhaust just went to the bottom of the list and my 18 pound 18" Nismo or Volk wheels with Pilots or Toyo Proxes just went next on my list. Not to mention the added handling benefits I'll gain.

This also gets me wondering whether a 9.5 with a 275 wide tire is really that beneficial on a 5AT if it's going to give me an additional 2 pounds of weight (times 4) at the outermost point. So much to think about.

Please no flames on "just do what makes you feel good and don't worry about that so much". What makes me feel good is knowing that I made the perfect choice given an amount of money that perfectly accomplishes my mission. This is also important to know as the next time I pull up next to a Z or G with giant heavy wheels and Bridgestones on her, revving it (provided they aren't FI), it will be most comforting to know exactly how badly I'm going to shame them

If any engineer (bona fide or armchair) could clue me in with the appropriate differential equation, I'd be most appreciative.

2004.5 Coupe/5AT/Ivory/Everything but front spoiler/Nismo CAI/Crawford V5

 

I posted a link on FA a while back about the equations used for calculating unsprung weight (with really cool links). Do a search over there.

Also, weight vs hp gain is not linear, so the equation will depend on how heavy a car is. If you had a Lotus Elise and dropped 20 pounds of unsprung weight your hp gains would be much more than if you had a heavy V8 Mercedes and dropped 20 pounds of unsprung weight.

For the Porsche GT racing team, they have determined that for the "average weight" Carrera, that dropping 1 pound of unsprung weight correlates to dropping 4 pounds of sprung weight. (If that means anything to you)...

301-bhp!!! ...and growing!

 

What you are really after here is the total inertia of your car. Go grab a good university physics 1 book and a basic dynamics book and you will find all the equations you need to model your car. All these equations are a form of accel=force/mass. You would need to do a lot of measurement to really get your values down (mass at radius and such) but you could probably get a decent ball park figure if you put a bit of effort into it.

And keep in mind that the power you rengine makes is finite, but by changing wheels and tires, rotors and such you are 'absorbing' power and thus it is not placed to the ground.

hope that helps

 

Neff,
Thanks for the rule of thumb, but I'm trying to figure out what a 19" wheel will cost me, given the same weight. If it's 19" and the same weight, it will cost me some HP applied to the wheels. If it's an 18" wheel, of the same weight, but with a wider tire (let's say 2 pounds heavier), what effect will that have? etc.


Devil,
Exactly. Once I get as much as I can in engine mods, I need to figure out how to get the 18% loss from flywheel to the wheels down to 14% or better. But I don't want to learn physics to that level of detail. I was hoping Neff or Q45Tech might remember something from THEIR class and give it to me for free. Typing the request was effort enough .

I'm probably asking too much but thought it would be a welcomed change from discussing intakes and which wheel looks more dope or phat than another. Maybe I'll dig around the wife's physics book and see what I can find on inertia and geometry.

2004.5 Coupe/5AT/Ivory/Everything but front spoiler/Nismo CAI/Crawford V5

 

fish, you might wanna try asking Will Hunting?? He'd probably resolve your theorem. Me, I'm getting a headache just imagining it!!! : (

"I have no special talents. I am only passionately curious."
2004 G35 Coupe | OB | Graphite interior | Premium and aero package | Popcharger | Z tube | Hotchkis sway bars | kinetix plenum on the way

 

with all of the questions/controversy about this or that adding x amount of HP, you can't argue with the laws of physics when it comes to shedding weight on your car. There's a reason the new Lotus Elise goes 0-60 in 4.4 seconds with 190 hp at the crank from a 1.8 liter engine. Some of it's due to gearing but that sumb*tch is light.

Just wanted to tell you that you are on the right track in trying to exact the most performance out of your car. If I had a choice between 30 more ponies at the crank v. a 300 lb. lighter G, I'd choose the latter every time (especially if I'm autoxing or tracking it.)

 

The problem is how you measure rear wheel power by rotating a drum whose diameter is too narrow and places undue stress on the tires.

Ever wonder where all the losses are........the diff doesn't quite lose 3% and it is the second largest loss with the tires being almost half the manual loss [say 7-8%]. Clutch, tranny, driveshaft, half shafts, wheel bearings are not 5% in total.

If you measure the heat rise of each component you will find its loss.

Not sure if you could create an equation that works on a chassis dyno and on the highway/drag strip simultaneously.....because of the roller diameter problem.

Forget about HP and stick to torque one less conversion.

Remember all the dyno does is measure acceleration of the drum in 1/1000 sec increments so slicks will show more torque on a chassis dyno than street tires and heating the slicks will show more............need a dual gear drive to turn the roller instead of tires..........that way the variable of tire temp is taken out of the picture. also the tires change diameter with speed [assuming you are measuring at above 90 mph] which affects the torque.

Ever thought of why we measure in 4-5th gear when you start in first.........tire friction roller is smooth.
The coefficient of smooth steel is 0.3-0.4 mu [something like crunchy snow] where as the asphalt road might be 0.8- 0.9 mu.

 

I seen the same show, but did you hear the part after they explained the Hp loss? He said his times improved on the track due to the fact that with the bigger breaks he was able to go deeper into the corners. Sure he lost 12 hp but it didnt cost him any time on the track.

2003 Black , sunroof, leather,
splashguards, 8 wire Hypergrounding kit, 350Z intake duct, K&N filter.

 

"Inertial loss is related to the rota*tional acceleration (i.e., angular accel*eration) of the drivetrain components. The inertial loss does not result in a power loss (i.e., heat) but absorbs energy that can be coupled to the rear wheels. This energy actually gets stored in the drivetrain components. The stored inertial energy in the flywheel keeps the revs up while the clutch is pressed in during shifts. The inertia loss is more pronounced in lower gears (i.e., First or Second) when the acceleration is highest. "

http://www.mustangdyne.com/Articles/...article-01.htm


Notice that the Dynojet accelerates almost twice as fast in 2,3, 4th gear than real world accelerations [with wind resistance in 4th but not in 2nd].???????????????/

 

""The efficiency of a manual transmission drive train can be closely estimated by multiplying together the efficiencies of each loaded gear pair or other working mechanism of the complete drive train. For helical gear gears used in transmissions in an EV at torques averaging 20% to 30% of
max and with a low loss lubricant, the efficiency should average around 0.97 per gear pair. An allowance is needed also for the other operating but unloaded gear pairs, since they are resisting by some friction and continually churn the lubricant. An 0.99 factor is considered adequate for
these unloaded gears. The Fiesta 4 speed gearbox then, which uses but one gear pair at a time, under these conditions has an efficiency of 0.97 x 0.99 or 0.96. Counting the differential drive, another helical gear pair and 0.97 factor, the motor-t-drive axle efficiency becomes 0.93.

Manual transmissions typically used in front engine rear axle drive cars (those with 1:1 ration for "high" gear) are connected "straight through" and load none of their gears when in "high". Efficiency then averages about 0.98, with the moderate 2% loss going into the unloaded but lube-churning gears. In the lower gears, however, these "straight through"
transmission must use two helical gear pairs, so the gearbox efficiency alone becomes about 0.97 x 0.97 = 0.94.

There are still more drive train losses before power reaches the driving wheels. While constant velocity U-joints are low-loss devices as are ball or roller bearings, considerable and frequent angularity changes (such as in front-drive axles) cannot be achieved without considerable sliding and
rolling friction losses. 2% loss, or 0.98 efficiency, is reasonable for modern front drive axles, (including the bearing and seal losses). For front engine, rear drive cars, a 1% allowance for drive shaft u-joints is adequate (if joint angularity is small) and another 1% for typical axle bearings and seals."

He goes on to refer to the increase in gear train losses when operating at a low fraction of the gear's design maximum torque, and to avoid using oversize axles or transmissions. He breaks down the drive train efficiency like this:

Typical modern front-drive transaxle (Civic, Fiat 128, Fiesta, Rabbit)

Manual transmission
Number of loaded gear pairs 1. (0.97)
Allowance for idling gears: lube churning plus extra bearing and
selector drag (0.99)
0.97 x 0.99 = 0.96
Differential Drive
Helical gears (0.97)
Drive Axle
(0.98)
Overall Efficiency
0.97 x 0.99 x 0.97 x 0.98 = 0.91


Transaxle with bevel gear axle (VW Beetle, Renault LeCar)

Manual transmission
Number of loaded gear pairs 1. (0.97)
Allowance for idling gears: lube churning plus extra bearing and
selector drag (0.99)
0.97 x 0.99 = 0.96
Differential Drive
Bevel gears (0.96)
Drive Axle
(0.98)
Overall Efficiency
0.97 x 0.99 x 0.96 x 0.98 = 0.90


Typical rear drive (not 1:1) (Chevette, Datsun 210, Pinto)

Manual transmission
Number of loaded gear pairs 2. (0.97 x 0.97)
0.97 x 0.97 = 0.94
Drive Shaft
(0.99)
Differential Drive
Hypoid gears (0.89)
Drive Axle
(0.99)
Overall Efficiency
0.97 x 0.97 x 0.99 x 0.89 x 0.99 = 0.82


As above but in 1:1 "high" gear

Manual transmission
Number of loaded gear pairs 0.
(0.98) Allowance for idling gears: lube churning plus extra
bearing and selector drag
Drive Shaft
(0.99)
Differential Drive
Hypoid gears (0.89)
Drive Axle
(0.99)
Overall Efficiency
0.98 x 0.99 x 0.89 x 0.99 = 0.85

 

Rotational and translational Interia Formula: radius of gyration
Everything you requested is here in this ppt lecture
www.mae.wmich.edu/faculty/hathaway/ classes/ME470/Lecture/Lecture08.ppt

http://toyotaperformance.com/dyno.htm

 

Thanks Q !!!

2004.5 Coupe/5AT/Ivory/Everything but front spoiler/Nismo CAI/Crawford V5

 

<blockquote><font class="small">In reply to:</font><hr>

The coefficient of smooth steel is 0.3-0.4 mu [something like crunchy snow] where as the asphalt road might be 0.8- 0.9 mu.

<hr></blockquote>

This only matters if you are slipping. There is no mu coefficiient if you are rolling as there is no sliding friction. The only friction or slowing forces on a wheel are from teh resistance of air or the compression/expansion of the tire as it rolls. Great thread, though. heat is always an issure and will soak up power (except you like to have heat in oils to lower viscosity or resistance to fluid motion).

And power is a finite amount, changing gears does not change power. It will change the torque applied but the speed of the engine will be the same, but will produce a different vehicle speed (this does not neccessarily include wind resistance in top speed trials but rather is a discussion for low speed acceleration).

 

Devil,
I agree this is a great thread. It's ironic that most of the sticky threads are far from technical or have completely innocuous modification information. If any mods are watching, I'd love to see more of this kind of scientific documentation kept as stickies for future reference.

Regarding the link Q45Tech provided, you must remove the spaces preceeding "classes" for the link to work. Thanks again Q. This presentation is a trip for a non-mathematician like myself. It is not an easy read but I shall spend some time on it over a few cigars and see what sinks in. In the opening and closing remarks it comments that "rules of thumb" can be used but I couldn't find one rule of thumb as I would define it.



2004.5 Coupe/5AT/Ivory/Everything but front spoiler/Nismo CAI/Crawford V5

 

If you want a sticky, become a moderator and sell a product. Just Kidding! Just Kidding! (well actually I'm not...)

301-bhp!!! ...and growing!