How to use the road load equation [wiki talk page]

[RobertSmalls]

Originally Posted by CapriRacer

Unfortunately, for passenger car tires, that is only true at slower speeds. RR climbs exponentially at higher speeds. 50 mph seems to be the breakoff point - which is also unfortunately within normal driving speeds.

I suggest you add a note that the RR part is only true below 50 mph and explain what happens to RR at higher speeds.

I am aware of substantial deviations from the F=AV²+C model, and that F=AV²+BV+C gives a better curve fit. Is that all in the tires?

Can you give me an alternative to CRR model?

btw, here's Google Image Search for "pacejka rolling resistance":

If the first data point had been plotted at 0.0001 mph instead of 0, it would probably match the rest of the curve.

[RobertSmalls]

Originally Posted by Boreas

Is the term g ,in the rolling resistance equation essentially one, on the on the surface of earth. With minor variations due to elevation that are small enough to be ignored for fuel economy purposes?

g, acceleration due to gravity, varies in a minuscule fashion with elevation. Variations in the strength of the Earth's gravitational field at its surface are generally of interest to physicists, but not engineers. g=9.8m/s² will get you two significant figures, which is more than you have for the rest of your inputs anyway.

>Is wind resistance an exponental equation due to the v squared term and the rolling resistance equation linear with constant slope due to v or no other them being squared?

I'm not clear on what you're asking here. The force of aero drag rises exponentially with speed, while rolling resistance... well, see the graph I just posted. According to the simplified model, it's independent of speed.

[euromodder]

Originally Posted by Boreas

Is the term g ,in the rolling resistance equation essentially one, on the on the surface of earth. With minor variations due to elevation that are small enough to be ignored for fuel economy purposes?

Gravitational force, g, varies slightly around the Earth.
It's slightly higher at the poles, lower at the equator, and gets lower as altitude increases.
Local geology (mountains, rock density) can also introduce small variations.
But we're talking about variations in the order of 0.5 %, tops.

Is wind resistance an exponental equation due to the v squared term

Yes.

and the rolling resistance equation linear with constant slope due to v or no other them being squared?

Due to no factors being squared.
(In the simplified formula.)

At speed, tyre deformation (result of the tyre spinning faster) will increase rolling resistance.
The more a tyre resists to deformation, i.e. the stiffer it is, the less RR will rise with increasing speed.

[CapriRacer]

Originally Posted by ShadeTreeMech

What causes increased RR at higher speeds? Is it due to more heat buildup from tire deflection at such high rpms?

And I noticed you excluded other tires such as truck tires. The main difference coming to mind is the thicker sidewalls and tread of a truck tire vs a passenger vehicle.

My best guess is that it has to do with standing waves:



I think that passenger car tires with their increased deflection are more suspectible to this. Truck tires - in order to stand up to the miliions of miles that they are expected to last - are designed with lower amounts of deflection.

Originally Posted by Boreas

Since I am an amateur at mathematics.....Is the term g ,in the rolling resistance equation.........

Actually, it's a physics thing.

g - in this context - is the translation from mass to weight. Those of us who are used to the English system have trouble when we talk about mass, because we usually talk about weight - pounds.

But those who speak metric, normally speak in terms mass - grams. To get force - Newtons - you have to multiply grams by 0.00981. For reference, accelleration due to gravity is 32.2 ft per second squared or 9.81 meters per second squared.

Originally Posted by RobertSmalls

......Can you give me an alternative to CRR model?..........

Sorry, but no. I don't think there is much published that has enough data points to get a better feel for what is going on.

[Boreas]

I would like to thank every one for your answers to my questions. Please forgive my ignorance but I am still confused about rolling resistance. Does a car rolling down the road on say the moon where there is no air take the same amount of force to move at 10 mph as 50mph? Does force to over come rolling resistance equal power required to move an object at a given speed in this example? Is the power requierment the same at 10 mph and 50 mph? I may be over thinking this, it seems too simple like somthing for nothing.

[RobertSmalls]

A car in an evacuated tunnel can move at high speeds with low fuel consumption, unopposed by aerodynamic drag. According to the simplified model presented in post one, the force to move the car will be the same at 10mph or at 30mph, and the fuel economy inside your vacuum environment will be the same at either speed. Power, i.e. the rate at which energy is converted from one form to another, will be linear with respect to speed. So your motor will be working three times as hard to go three times as fast. But nobody drives in an evacuated tunnel: it would be an unaffordably expensive toll road.

The moon is a different story. A car on the moon weighs 1/7th as much as it does on Earth, so you would expect to have 1/7th the RR for a given road surface / tire temperature combination, and virtually no aerodynamic drag. Good thing, too, because energy is expensive on the moon.

[saand]

Robert, great write up. I would like to put this in the wiki, i am however very swamped at the moment. If weatherspotter doesn't get to it before me i shall put it in in a week or 2.

Looks like we might need a theoretical / modeling section in the wiki

[gone-ot]

SUGGESTION: you can replace the "star" ( * ) symbols used to designate "multiplication" with their more (mathematically) common "dot" ( · ) symbol.

...simply, use the ALT-NUMERIC key-pad technique:

1) engage the NUM LOCK key.
2) press and hold the ALT key, and...
3) type the numbers 0 1 8 3 on the numeric keypad.

...other "useful" characters that can be entered this way are:

0176 = °, degree, temperature or angle, symbol
0248 = ø, slashed-zero
0177 = ±, plus/minus symbol
0181 = µ, latin mu, micro (10 to -6 power) symbol
0247 = ÷, division symbol
0215 = ×, multiplication symbol
0171 = «, much less than symbol
0187 = », much greater than symbol
0185 = ¹, one superscipt, unitary power
0178 = ², two superscript, squared power
0179 = ³, three superscipt, cubed power
0131 = ƒ, "f" symbol for frequency
0133 = …, ellipsis symbol
0188 = ¼, one-fourth
0189 = ½, one-half
0190 = ¾, three-quarter
0153 = ™, "Trademark" symbol
0183 = · , small 'dot'
0149 = • , large 'dot'

...comes in handy.

[saand]

I have put the initial post up in the wiki, it has been split up into 2 articles / wiki pages.

I have also made a new section "simulation and calculations", this is where we can put any tools used to simulate or calculate efficiency
Simulation and calculations - EcoModder
The new wiki pages are linked from this page

Robert you requested that the theoretical weight energy be removed, i am happy to do this when someone offers a better alternative that will allow people to calculate the effect of weight on efficiency. I have however changed the page so that it relates to braking from 1 speed to another which "wastes" inertial energy rather than acceleration. I am open to suggestions on how to "fix" this page if anyone thinks its wrong please feel free to correct it or send me a msg.

[Weather Spotter]

Looks good to me.
Thanks