Posted by *Gene Nygaard* on November 17, 2004, 1:30 am

nobody@home.net wrote in message

*> On 3 Nov 2004 01:54:45 -0800, Chewy2426@aol.com (Aaron) wrote:*

*> *

*> >I just got a new job in Irvine and have a girlfriend in Pasadena. I*

*> >moved to Anaheim so that I'm not too far from both.*

*> >*

*> >Since I will be doing a lot of commuting I thought a hybrid would be a*

*> >good option. I checked both the insight and prius and the prius looks*

*> >like the best option, especially for traffic.*

*> >*

*> >My question is, would it be worth getting a prius to save gas money??*

*> >It looks better than a insight since it doesn't run the gas engine all*

*> >the time. I just don't want to waste my money buying a hybrid when I*

*> >can just buy another car that burns less fuel (like a civic) for less*

*> >money.*

*> >*

*> >Thanks for any suggestions,*

*> >Aaron*

*> *

*> A very good question. Because I was considering buying a Prius, I*

*> made some energy calculations to get an idea of how much gasoline is*

*> "recovered" through the "regenerative" braking.*

*> *

*> The energy recovered from braking the car and subsequently storing it*

*> in the battery is some fraction -- less than 1 -- of the kinetic*

*> energy of the car. For purposes of calculation I assumed 100% would*

*> be recovered. The kinetic energy depends on the mass and speed of the*

*> car and is calculated from the familiar equation KE = 1/2 * m(v^2).*

*> I used 2890 lbs for the weight of the car as given in the Prius*

*> brochure (mass = 2890/32.2 = 89.75 slugs). *

That's a wasted step, just changing to a different unit of mass, and

one which is of no utility whatsoever in getting to the units of

energy you use below, British thermal units, which are not in the

subsystem of units which includes slugs. Of course, miles are also

not part of the system which includes slugs, nor are hours, so you've

also had to do a conversion of your speed numbers to use slugs with

any meaningful results. Another wasted step. Then you've had to

convert the resultant ft·lbf to Btu. Better just to use the pounds in

the KE formula, and mi/h for speed, then use a conversion factor from

lb mi^2/h^2 to Btu--and you can factor in the constant 1/2 factor as

well. You can figure that out once and reuse it, rather than having

to waste time in so many intermediate calculations.

But what is this, a drone, a driverless car? Don't you need to add in

the mass of the driver? What is that listed mass for, a vehicle with

an empty tank? Or one 1/4 full only? Let's just throw in a little

more for driver and fuel (say you drive it from full down to a quarter

tank, so use an average value of 5/8 of a tank of fuel would seem

reasonable), and call the total mass 3100 pounds.

Better yet, just use the mass in kilograms and energy in joules, and

energy density of gasoline in joules per liter. The calculations are

simpler yet.

*>The results at several*

*> speeds are given below:*

*> *

*> 20 mph - 50 Btu*

*> 30 mph - 112 Btu*

*> 40 mph - 199 Btu*

*> 50 mph - 311 Btu*

*> 60 mph - 448 Btu*

*> *

*> For illustration, let's assume that if the Prius went 45 miles with no*

*> stops it would get 45 miles per gallon.*

*> *

*> To estimate the effect of recovery by regenerative braking, assume*

*> another trip of 45 miles with stops every mile from 30 mph. That's a*

*> total of 45 stops which would recover 5,040 Btu. Gasoline has a heat*

*> of combustion of approximately 115,000 Btu per gallon, thus the 5,040*

*> recovered Btu are equivalent to 5040/115,000 = 0.0438 gallon (5.6*

*> ounces). We can subtract that from the gallon burned to get*

*> (1-0.0438)=0.9562 net gallon consumed to cover the 45 miles with 45*

*> stops. The mileage with 100% regenerative recovery would be 45/0.9562*

*> = 47 mpg, or about 4.5% better.*

You also have 44 more accelerations from 0 to cruising speed, each

requiring additional expenditure of energy over what would be used

just in normal maintining of speed in the face of friction losses and

those due to terrain, going up and down.

Gene Nygaard

*> The recovery cannot be 100% because the hydraulic brakes come into*

*> play, there are losses in generating, transmitting and storing the*

*> recovered energy in the battery, and further losses in extracting the*

*> energy from the battery and utilizing it to power the car. I have no*

*> idea what the overall recovery factor should be, but a 50% value*

*> would reduce the mileage value to 46 mpg, which is about a 2.2%*

*> improvement over no regenerative braking.*

*> *

*> Can't estimate how much gas is saved by stopping the engine at traffic*

*> signals. etc, because I don't know the rate of fuel consumption of the*

*> engine at idle. However, the Prius brochure lists miles per gallon at*

*> 51 hwy and 60 city, and one newsgroup poster (Jeffry Johnson) reported*

*> 44 hwy and 52 city. Both sets of data provide a crude estimate of*

*> overall mpg improvement of about 18%. Assuming the city mileage*

*> improvement is due to braking + engine stopping (because there is*

*> neither on the highway) and using 3% as the braking effect gives a*

*> 15% improvement attributable to engine stopping (any drag effects*

*> neglected).*

*> *

*> I pondered these results for awhile and it became apparent that the*

*> advantages of the hybrid technology are not so much from regenerative*

*> braking but rather from two factors: 1) stopping the engine at vehicle*

*> stops, and 2) employing a small gasoline engine with an electric motor*

*> for power boosts when needed. Ultimately, the gas engine has to*

*> replace the energy expended in those boosts since gasoline is the sole*

*> source of energy in the vehicle.*

*> *

*> I know this is a bit long and that it does not answer the many*

*> questions that can be raised, but it helped clarify my thinking and*

*> maybe it will help some others. Personally, I'm going to hold off on*

*> buying a hybrid for a while. Maybe a long while. Economic analysis on*

*> the cost difference of the hybrid versus the non-hybrid when compared*

*> to gasoline savings using current prices just doesn't justify*

*> purchasing the hybrid. Come to think of it, one can almost never*

*> justify purchasing any new car on an economic basis :-)*

*> *

*> Rod*

Posted by *nobody* on November 17, 2004, 2:03 pm

Thanks for the response, Gene. Interesting post. My comments below.

On 16 Nov 2004 17:30:24 -0800, gnygaard@nccray.com (Gene Nygaard)

wrote:

*>> The energy recovered from braking the car and subsequently storing it*

*>> in the battery is some fraction -- less than 1 -- of the kinetic*

*>> energy of the car. For purposes of calculation I assumed 100% would*

*>> be recovered. The kinetic energy depends on the mass and speed of the*

*>> car and is calculated from the familiar equation KE = 1/2 * m(v^2).*

*>> I used 2890 lbs for the weight of the car as given in the Prius*

*>> brochure (mass = 2890/32.2 = 89.75 slugs). *

*>That's a wasted step, just changing to a different unit of mass, and*

*>one which is of no utility whatsoever in getting to the units of*

*>energy you use below, British thermal units, which are not in the*

*>subsystem of units which includes slugs.*

Weight and the slug are not different units of mass. The units of

weight are force units, not mass. The slug is a mass unit as are

kilograms. As to the units of energy, I can use any I prefer. If you

like Joules or kwh or ft-lbs(f), use them.

*> Of course, miles are also*

*>not part of the system which includes slugs, nor are hours, so you've*

*>also had to do a conversion of your speed numbers to use slugs with*

*>any meaningful results. Another wasted step. Then you've had to*

*>convert the resultant ft·lbf to Btu.*

No big deal. Did the numbers on a spreadsheet. Retired my slide rule

decades ago.

*>Better just to use the pounds in*

*>the KE formula, and mi/h for speed, then use a conversion factor from*

*>lb mi^2/h^2 to Btu--and you can factor in the constant 1/2 factor as*

*>well.*

If you plug weight (pounds force) into the KE equation I gave you're

going to get the wrong answer.

*>But what is this, a drone, a driverless car? Don't you need to add in*

*>the mass of the driver? What is that listed mass for, a vehicle with*

*>an empty tank? Or one 1/4 full only? Let's just throw in a little*

*>more for driver and fuel (say you drive it from full down to a quarter*

*>tank, so use an average value of 5/8 of a tank of fuel would seem*

*>reasonable), and call the total mass 3100 pounds.*

Of course it's a drone. I was just making a rough estimate to satisfy

my curiosity, ball park as some would say. Make any assumptions you

prefer. A weight of 3100 lbs would increase the kinetic energy by 7%

over my figure.

*>Better yet, just use the mass in kilograms and energy in joules, and*

*>energy density of gasoline in joules per liter. The calculations are*

*>simpler yet.*

That's true indeed. Matter of fact, I did do it that way just for

kicks as well as the way I posted. I was raised in the English system

or something like it, so I still use it. Old habits are hard to break.

I even measure lengths in feet and inches. Going to get a metric tape

measure some day. Would make life simpler.

<snip>

*>You also have 44 more accelerations from 0 to cruising speed, each*

*>requiring additional expenditure of energy over what would be used*

*>just in normal maintining of speed in the face of friction losses and*

*>those due to terrain, going up and down.*

Not relevant. All I needed was the kinetic energy stored in the moving

vehicle. I did tacitly assume level terrain. Should have stated that.

By the way, since this is the Prius newsgroup, do you have any

comments or opinions about the car?

Rod

Posted by *Gene Nygaard* on November 18, 2004, 2:31 am

nobody@home.net wrote in message

*> Thanks for the response, Gene. Interesting post. My comments below.*

*> *

*> On 16 Nov 2004 17:30:24 -0800, gnygaard@nccray.com (Gene Nygaard)*

*> wrote:*

*> *

*> >> The energy recovered from braking the car and subsequently storing it*

*> >> in the battery is some fraction -- less than 1 -- of the kinetic*

*> >> energy of the car. For purposes of calculation I assumed 100% would*

*> >> be recovered. The kinetic energy depends on the mass and speed of the*

*> >> car and is calculated from the familiar equation KE = 1/2 * m(v^2).*

*> >> I used 2890 lbs for the weight of the car as given in the Prius*

*> >> brochure (mass = 2890/32.2 = 89.75 slugs). *

*> >*

*> >That's a wasted step, just changing to a different unit of mass, and*

*> >one which is of no utility whatsoever in getting to the units of*

*> >energy you use below, British thermal units, which are not in the*

*> >subsystem of units which includes slugs.*

*> *

*> Weight and the slug are not different units of mass. *

No, "weight" is not a unit of anything. Pounds are units of mass.

Slugs are units of mass.

*>The units of*

*> weight are force units, not mass. *

You are one confused fool, failing to understand the simple fact that

"weight" is an ambiguous word, one with several different meanings.

The word "weight" entered Old English over 1000 years ago, meaning the

quantity measured with a balance. That quantity is mass, not force.

It was used as a measure of how much stuff people had, for the purpose

of trade. We still use the very same word today, with the very same

meaning, for the very same purposes.

Weight is never a force when anybody talks about "net weight" of

anything, nor about "tare weight" of its container. Naturally, when

products in American supermarkets and auto parts stores and whatever

include pounds and ounces for this weight, they are every bit as much

units of mass as the grams and kilograms which appear right alongside

them on the same label. In fact, we no longer have independent

standards for those pounds; since a 1959 international agreement, the

common, worldwide definition of these pounds is as units of mass

exactly equal to 0.45359237 kg.

Weight is never a force when anybody talks about "troy weight" of

anything. That's one way the troy units differ not only from their

avoirdupois cousins, but from grams and kilograms as well--they have

never spawned units of force of the same name. There is no troy ounce

force, never has been.

Weight is never a force when anybody talks about "carat weight" of

anything (5 carats = 1 gram in the modern definition).

*>The slug is a mass unit as are*

*> kilograms. *

http://de.toyota.ch/showroom/Prius/specs.asp?body=S

http://www.toyota-europe.com/showroom/Prius/specs.asp?body=S

Fuel tank capacity (l) 45

. . .

Load Capacity

Kerb weight (kg) 1300

Gross vehicle weight (kg) 1725

http://www.findarticles.com/p/articles/mi_m3012/is_12_179/ai_58398900

Toyota Prius

Curb weight is 2,733 pounds--about 250 pounds heavier than a Corolla,

and 330 pounds more then a Ford Focus sedan.

http://www.findarticles.com/p/articles/mi_m3165/is_11_39/ai_110225713

Curb weight: 2,890 lbs. (1,311 kg)

[Note that this is the number you used, Rod--GN]

http://autos.msn.com/research/vip/spec_Exterior.aspx?modelid 047&trimid=-1&src=VIP

Curb Weight - Automatic (lb.) 2890

<end of quotes>

Now, Rod, it is your turn. Like you said, those kilograms are units

of mass. Now, why in the hell don't you just explain to us all

exactly what is done differently when this "curb weight" is measured

in pounds, from what is done when it is measured in kilograms.

While you are at it, tell us why in the world the manufacturers would

measure two different quantities for this purpose in the first place?

Or just wake up and smell the coffee. Let's add another to my list

above: weight is never a force when anybody talks about "curb weight"

or "kerb weight." It doesn't make any difference how they spell it.

It doesn't make any difference whatsoever what units they use to

express it. Nobody in the whole wide world ever measures curb weight

in newtons, and nobody in the whole wide world ever measures curb

weight in pounds force.

*>As to the units of energy, I can use any I prefer. *

You can. But the only units of energy in the only subsystem which

includes slugs are foot-pounds force.

*>If you*

*> like Joules or kwh or ft-lbs(f), use them.*

*> *

*> > Of course, miles are also*

*> >not part of the system which includes slugs, nor are hours, so you've*

*> >also had to do a conversion of your speed numbers to use slugs with*

*> >any meaningful results. Another wasted step. Then you've had to*

*> >convert the resultant ft·lbf to Btu.*

*> *

*> No big deal. Did the numbers on a spreadsheet. Retired my slide rule*

*> decades ago.*

*> *

*> >Better just to use the pounds in*

*> >the KE formula, and mi/h for speed, then use a conversion factor from*

*> >lb mi^2/h^2 to Btu--and you can factor in the constant 1/2 factor as*

*> >well.*

*> *

*> If you plug weight (pounds force) into the KE equation I gave you're*

*> going to get the wrong answer.*

You don't have pounds force. You have pounds mass.

If you use pounds mass and feet per second in your kinetic energy

formula, the result is in foot poundals. It is just as easy to

convert foot poundals to Btu, as your calculations converting foot

pounds force to Btu were.

If the curb weight is indeed 1311 kg, as listed in one of the sites

above, at exactly what areas on the surface of the earth would that

much mass exert a force of 2890 pounds force, measured to the nearest

pound force? Note that even if you limit yourself to sea level on the

surface of the earth, a mass of 1311 +/0.5 kg will exert a force of

from 2881.4 lbf to 2898.9 lbf (throw in elevation, including Mt.

Chimborazo, the highest mountain on earth in both ways relevant to

this discussion, and the variation on the surface of the earth is even

greater). But 1311 kg is 2890 lb anywhere on earth, or anywhere else.

If curb weight were in pounds force, as you erroneously believed,

you'd never have more than 2 significant digits, if all you know about

location is that it is somewhere on earth.

*> *

*> >But what is this, a drone, a driverless car? Don't you need to add in*

*> >the mass of the driver? What is that listed mass for, a vehicle with*

*> >an empty tank? Or one 1/4 full only? Let's just throw in a little*

*> >more for driver and fuel (say you drive it from full down to a quarter*

*> >tank, so use an average value of 5/8 of a tank of fuel would seem*

*> >reasonable), and call the total mass 3100 pounds.*

*> *

*> Of course it's a drone. I was just making a rough estimate to satisfy*

*> my curiosity, ball park as some would say. Make any assumptions you*

*> prefer. A weight of 3100 lbs would increase the kinetic energy by 7%*

*> over my figure.*

*> *

*> >Better yet, just use the mass in kilograms and energy in joules, and*

*> >energy density of gasoline in joules per liter. The calculations are*

*> >simpler yet.*

*> *

*> That's true indeed. Matter of fact, I did do it that way just for*

*> kicks as well as the way I posted. I was raised in the English system*

*> or something like it, so I still use it. Old habits are hard to break.*

*> I even measure lengths in feet and inches. Going to get a metric tape*

*> measure some day. Would make life simpler.*

*> >*

*> <snip>*

*> >*

*> >You also have 44 more accelerations from 0 to cruising speed, each*

*> >requiring additional expenditure of energy over what would be used*

*> >just in normal maintining of speed in the face of friction losses and*

*> >those due to terrain, going up and down.*

*> *

*> Not relevant. All I needed was the kinetic energy stored in the moving*

*> vehicle. I did tacitly assume level terrain. Should have stated that.*

It is indeed relevant to figuring any change in the fuel efficiency

overall.

*> By the way, since this is the Prius newsgroup, do you have any*

*> comments or opinions about the car?*

*> *

*> Rod*

I'm intrigued by the idea, but I've never even seen a Prius.

Gene Nygaard

Posted by *Bill* on November 18, 2004, 3:06 am

*> You are one confused fool...*

and nothing else deserved consideration.

Posted by *nobody* on November 18, 2004, 12:38 pm

*>> You are one confused fool...*

*>and nothing else deserved consideration. *

Thanks Bill. You are right. He has no interest in the Prius, just

wants to show off his knowledge of an arcane subject. How do you

suppose he landed on the Prius newsgroup? Do you suppose he Googles

newsgroups looking for people who abuse units? Chief of the Units

Police maybe? Anyway, I just put him in the kill-filter box and closed

the lid.

Rod, the happily confused fool.

> On 3 Nov 2004 01:54:45 -0800, Chewy2426@aol.com (Aaron) wrote:>> >I just got a new job in Irvine and have a girlfriend in Pasadena. I> >moved to Anaheim so that I'm not too far from both.> >> >Since I will be doing a lot of commuting I thought a hybrid would be a> >good option. I checked both the insight and prius and the prius looks> >like the best option, especially for traffic.> >> >My question is, would it be worth getting a prius to save gas money??> >It looks better than a insight since it doesn't run the gas engine all> >the time. I just don't want to waste my money buying a hybrid when I> >can just buy another car that burns less fuel (like a civic) for less> >money.> >> >Thanks for any suggestions,> >Aaron>> A very good question. Because I was considering buying a Prius, I> made some energy calculations to get an idea of how much gasoline is> "recovered" through the "regenerative" braking.>> The energy recovered from braking the car and subsequently storing it> in the battery is some fraction -- less than 1 -- of the kinetic> energy of the car. For purposes of calculation I assumed 100% would> be recovered. The kinetic energy depends on the mass and speed of the> car and is calculated from the familiar equation KE = 1/2 * m(v^2).> I used 2890 lbs for the weight of the car as given in the Prius> brochure (mass = 2890/32.2 = 89.75 slugs).