Mathematical Musings

rwlade · 05-15-2005, 11:29 AM

I was just sitting around trying to figure out the significance of the little car icons on the consumption screen and came up with this.

Assume

car mass = 1,311 kilos (2890 lbs)
velocity = 96.6 km/hr (60 mph) = 26.8 m/sec

From Kinetic Energy = (1/2)*m*v^2

K.E. = (1/2)*1311*28.8^2 = 5.44x10^5 Joules

One "car" is 50 Watt-Hours or 50x3600 = 1.8x10^5 Joules

So at 60 miles/hour the car's K.E. is about 5.44/1.8 or 3 "Cars". From early indications (only got 100 miles on the car) I'm getting around one "Car" for each time I decelerate from 60 to a dead stop, so the regenerative efficiency is around 30%.

Anyone know if this is in the ball-park?

Just musing....

DanP · 05-15-2005, 11:57 AM

Quote:

I was just sitting around trying to figure out the significance of the little car icons on the consumption screen and came up with this.

Assume

car mass = 1,311 kilos (2890 lbs)
velocity = 96.6 km/hr (60 mph) = 26.8 m/sec

From Kinetic Energy = (1/2)*m*v^2

K.E. = (1/2)*1311*28.8^2 = 5.44x10^5 Joules

One "car" is 50 Watt-Hours or 50x3600 = 1.8x10^5 Joules

So at 60 miles/hour the car's K.E. is about 5.44/1.8 or 3 "Cars". From early indications (only got 100 miles on the car) I'm getting around one "Car" for each time I decelerate from 60 to a dead stop, so the regenerative efficiency is around 30%.

Anyone know if this is in the ball-park?

Just musing....

I lack the skills necessary to offer an independent assessment, but I did find a Toyota Hawaii web site that comes to much the same conclusion as you:

http://www.toyota-hawaii.com/vehicles/Priu...us/braking.html

jayman · 05-15-2005, 12:35 PM

Quote:

Anyone know if this is in the ball-park?

Yep, it is.

The KE equation also illustrates the huge energy penalty involved with even minor increases in velocity.

No matter what vehicle you drive, and we'll also ignore the huge aerodynamic drag penalty for a moment, a vehicle operated at 80 MPH has to use much more energy - and get much lower fuel economy - than a vehicle operated at 55 MPH.

This is also why it's much easier to manage crash forces at 55 MPH than at 80 MPH, and why high speed crashes usually have a bad outcome.

DanMan32 · 05-15-2005, 07:00 PM

If you ignore drag, it is getting to 80MPH that uses energy. Maintaining 80MPH uses none on a level surface. An object in motion stays in motion, an object at rest stays at rest until changed by an outside force. However, mechanical friction as well as air resistance would be that force working to put the object at rest, which must be counteracted.

jayman · 05-15-2005, 08:42 PM

Also - again ignoring aerodynamic drag and friction with the road surface - relatively minor increases in speed require proportionately larger energy expenditure at higher speeds.

To accelerate from 30-55 MPH takes less energy than to accelerate from 55-80 MPH.

05-17-2005, 05:04 AM

This was discussed over here a while ago.

altaskier · 05-17-2005, 10:00 PM

I reckon one green leaf-car of energy recovered is equivalent to the energy provided by about 1 tablespoon of gas. See
Prius: gas equivalent of green leaf-cars
Of course it is always better to touch the brakes as little as possible; it's much better to not lose your kinetic energy in the first place than it is to recover some fraction of it. What the Prius does is to get some but not all of it back.

200Volts · 05-17-2005, 10:21 PM

This also helps to illustrate why "impulse" driving is most efficient for the Prius (i.e. quick accleration to speed and then cruise at constant speed as long as possible).
Someone did measure the regnerative amperage and found that light braking at about a 2 mph/second deceleration is most efficient for recovery of energy(plus it doesn't make people behind you as mad).

KTPhil · 05-17-2005, 10:37 PM

"This also helps to illustrate why "impulse" driving is most efficient for the Prius (i.e. quick accleration to speed and then cruise at constant speed as long as possible)."

Does anyone have actual data to prove this?

DaveinOlyWA · 05-18-2005, 12:28 AM

i read somewhere that energy recapture was more on the lines of 8-15%. also i find it hard to believe you can determine this because the rate deceleration would play a part in this. to maximize regen you would have to coast to a stop and then terrain would be playing a major role. a lot of things to consider and i think you will find that maintaining a car per deceleration wont be likely. i have seen 4 cars before but that was from stop and go traffic where i never really got over say 25 mph.

05-15-2005, 11:29 AM	#1
rwlade Dr. Bob Join Date: Apr 2005 Location: Cape Coral FL Posts: 50 My Car: 2005 Prius Package: #4 Nominated 0 Times in 0 Posts TOTM Awards: 0 Friends: 0	Mathematical Musings I was just sitting around trying to figure out the significance of the little car icons on the consumption screen and came up with this. Assume car mass = 1,311 kilos (2890 lbs) velocity = 96.6 km/hr (60 mph) = 26.8 m/sec From Kinetic Energy = (1/2)mv^2 K.E. = (1/2)131128.8^2 = 5.44x10^5 Joules One "car" is 50 Watt-Hours or 50x3600 = 1.8x10^5 Joules So at 60 miles/hour the car's K.E. is about 5.44/1.8 or 3 "Cars". From early indications (only got 100 miles on the car) I'm getting around one "Car" for each time I decelerate from 60 to a dead stop, so the regenerative efficiency is around 30%. Anyone know if this is in the ball-park? Just musing.... __________________ Dr. Bob Cape Coral FL '05 Prius Silver AI

05-15-2005, 08:42 PM	#5
jayman Senior Member Join Date: Oct 2004 Location: Winnipeg Manitoba Posts: 6,151 My Car: 2004 Prius Package: B Nominated 0 Times in 0 Posts TOTM Awards: 0 Friends: 3	Re: Mathematical Musings Also - again ignoring aerodynamic drag and friction with the road surface - relatively minor increases in speed require proportionately larger energy expenditure at higher speeds. To accelerate from 30-55 MPH takes less energy than to accelerate from 55-80 MPH.

05-17-2005, 05:04 AM	#6
Anonymous Guest Posts: n/a My Car: Package:	Re: Mathematical Musings This was discussed over here a while ago.

05-17-2005, 10:00 PM	#7
altaskier Join Date: May 2004 Location: Long Island, New York Posts: 157 My Car: Package: Nominated 0 Times in 0 Posts TOTM Awards: 0 Friends: 0	Re: Mathematical Musings I reckon one green leaf-car of energy recovered is equivalent to the energy provided by about 1 tablespoon of gas. See Prius: gas equivalent of green leaf-cars Of course it is always better to touch the brakes as little as possible; it's much better to not lose your kinetic energy in the first place than it is to recover some fraction of it. What the Prius does is to get some but not all of it back.

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05-15-2005, 07:00 PM	#4
DanMan32 Join Date: Aug 2004 Location: Tampa Bay, FL Posts: 3,775 My Car: Package: Nominated 0 Times in 0 Posts TOTM Awards: 0 Friends: 0	If you ignore drag, it is getting to 80MPH that uses energy. Maintaining 80MPH uses none on a level surface. An object in motion stays in motion, an object at rest stays at rest until changed by an outside force. However, mechanical friction as well as air resistance would be that force working to put the object at rest, which must be counteracted.

05-17-2005, 10:21 PM	#8
200Volts Senior Member Join Date: Nov 2004 Location: Northern CA Posts: 345 My Car: Package: Nominated 0 Times in 0 Posts TOTM Awards: 0 Friends: 0	This also helps to illustrate why "impulse" driving is most efficient for the Prius (i.e. quick accleration to speed and then cruise at constant speed as long as possible). Someone did measure the regnerative amperage and found that light braking at about a 2 mph/second deceleration is most efficient for recovery of energy(plus it doesn't make people behind you as mad).

05-17-2005, 10:37 PM	#9
KTPhil Senior Member Join Date: Jan 2005 Posts: 1,200 My Car: Package: Nominated 0 Times in 0 Posts TOTM Awards: 0 Friends: 0	"This also helps to illustrate why "impulse" driving is most efficient for the Prius (i.e. quick accleration to speed and then cruise at constant speed as long as possible)." Does anyone have actual data to prove this?

05-18-2005, 12:28 AM	#10
DaveinOlyWA Opps !! I Did it Again!! Join Date: Apr 2004 Location: South Puget Sound, WA Posts: 9,239 My Car: 2006 Prius Package: #4 Nominated 0 Times in 0 Posts TOTM Awards: 0 Friends: 4	i read somewhere that energy recapture was more on the lines of 8-15%. also i find it hard to believe you can determine this because the rate deceleration would play a part in this. to maximize regen you would have to coast to a stop and then terrain would be playing a major role. a lot of things to consider and i think you will find that maintaining a car per deceleration wont be likely. i have seen 4 cars before but that was from stop and go traffic where i never really got over say 25 mph.