Maximize MPG between Traffic lights using P&G

HelloMyPrius · Feb 4, 2010

I noticed that there are a lot of smart and knowledge people on the board. Here is a practical question: If I have two traffic lights that are quarter miles apart, how quickly do I pulse to which speed and glide afterwards that give me maximum MPG?

I suspect there will be different answers depends on several other factors:
1) Initial speed at the first light
2) The status of the second light when the car is at the first light
3) Time it takes the second light to turn green or red

I suspect if the solution is general enough, one can use it for other situations like:
1) Exit of highway ramp
2) Stop and go traffic one can see far enough ahead.
3) Merge into slow traffic
4) Slow down and speed up on the highway

Any insights will be greatly appreciated.

HelloMyPrius · Feb 4, 2010

One more thing, if the distance between the lights can be parameterized, it will give a more general solution and will be more useful.

ThisGuy310 · Feb 4, 2010

Drive as slowly as possible,
tailgate other cars to draft them, and make unusual/unpredictable lane changes in front of other cars and continue to drive slow.

It's what I do, and has been working so far (45 MPG combined city/hwy)

HelloMyPrius · Feb 4, 2010

That is funny.

But not necessary true though. If you drive too slow, you will essentially drive on electric and that can be expensive because the energy you use got converted twice: ICE->Batteries->Wheels and can be bad for MPG. You may also need to consider the trade-off between catching the next light to avoid complete stop and accelerate too quickly resulting low MPG.

Tom183 · Feb 5, 2010

I have been playing with P&G for a little while now, and while I don't state any of this as conclusive, here's what seems to do the best for me thus far:

For speeds between 50-60, I use a "pseudo" P&G where I push the accelerator to a little below the tip of the ECO zone on the HSI, then ease back until the iMPG slides up to about 60 or so. Then when speed drops a few mph, repeat the pulse. (I'm not seeing huge gains in this range, but it is noticable)

Around 45-50mph is tougher as it is affected much more easily by slope, and the ICE doesn't always allow warp stealth like it would at lower speeds. (this is the most frustrating speed since it's the most difficult to manage and the gains are less visible)

35-45mph I try to do the traditional P&G with warp stealth. (this seems to work fairly well)

25-35mph you can get much longer glides, pinning the guage just below the midpoint on the HSI. (this is the speed where you can really max FE)

If anyone knows the exact spot (if there is one) on the display where the ICE is at max efficiency, let me know - my best guess is at about the 90% mark in the ECO zone (most of the time - depending on circumstances). Most other drivers are stomping quite a bit harder off the line, but I seem to catch up fairly quickly.

HelloMyPrius · Feb 5, 2010

Tom183, my experience has confirmed some of your experience. The glide time at different speed seems to be different. It was longest at around 25 mph, less at 40 mph, and least at 60 mph. But I don't have all the instructments to confirm this.

Another thing I don't know is the MPG for different acceleration. Is it affected or is it more affected by the speed at which acceleration is applied? I don't know. It seems that MPG (base on MPG instant display) is lowest from 15-25 mph, higher at 30-40 mph, highest at 50-60 mph. I don't know if that is truely related to speed or the fact that we tend to accelerate less at higher speed. I don't know.

Any insights?

markderail · Feb 5, 2010

On streets / boulevards :
- If I'm first, I get to posted speed limit + 10% as quickly as possible, then glide.
(Glide as in, don't use the EV at all, don't use the ICE at all. Blank arrows.)

Premise being, I get so far ahead, by the time my speed has dropped to -10% of the speed limit, the car behind me might be catching up. If he's still far away, I continue the glide to the next light to stop.
If the next light is too far away, I pulse with ICE/EV (a slow pulse) back to +10%.
(If battery is Green-full I then pulse in EV only)

I always glide to the point most cars will want to start slowing down.
Then I brake lightly to max the regen.

- If I have cars in front of me, I take off *very* slowly, as 99.9% of the time my Prius accelerates way faster than other cars. So I let a huge distance appear in front of me, then Pulse to catch up (tailgate) then Slide.

In heavy traffic, it's darn near impossible to do. Then again, everyone is driving so slowly, I don't worry about it.

Whatever I do, when I get on the highway, my faster driving negates any P&G that I do, that my Avg in summer is in the 45-48 range, for a G2.

Even though I drive faster on the highway, I avoid speed changes, and let huge distances to the car in front, unless it's too slow and I pass it.

I actually like following trucks that do 65Mph & up, as they also avoid speed changes.

Tom183 · Feb 5, 2010

At a stop with cars in front, I will hit the accelerator as soon as the person in front of me takes their foot of the brake, sometimes even sooner - but keep it under the 50% mark (and be ready to hit the brakes if they stop suddenly). This will accelerate on electric, which is pretty sluggish especially at first, so it helps to hit the pedal sooner.

When driving, be looking ahead for the next light - if you see it will turn red you can get off the gas sooner and glide up to it. If traffic is really light you might be able to glide -through- the light by hitting the brakes early so that you don't have to come to a complete stop just before the light goes green again. This is much better because you have to re-accelerate less.

The 50% mark on the HSI is sort of a trigger for ICE on, but less so for ICE off. I notice frequently that the ICE will not be started below that mark unless speed is >45mph, but it will frequently stay running if you start higher than the mark and let off the pedal to get below 50%. This seems to be very speed-dependent, especially when letting off the pedal (higher speeds tend to keep the ICE running, slower speeds will shut it off once it gets low enough).

At 50-55mph, you may be able to do warp stealth if you're really careful but even a slight nudge will often start the ICE. This unfortunately kills true P&G at that speed unless you don't mind losing a lot of speed quickly, which is why I do the "pseudo" P&G and don't bother letting off all the way.

At 35-45mph, I often find it necessary to let off the pedal all the way to force ICE shutdown, then quickly bring the pedal back to the 49.99% mark on the HSI.

At 25-35mph, I don't usually find it necessary to "force" ICE shutdown, just backing off to 25% or so will usually do it.

45-50mph is the annoying "in-between" speed where you might be able to force ICE shutdown but it seems to restart earlier than at slower speeds, so gliding is limited and your only choices are near-warp stealth or the pseudo P&G. Sustaining speed here doesn't seem very good because the RPM's are really low and seem to be in an inefficient range, so overall consumption is low but efficiency is also low. But again, I think the grade is a big factor since it may put you in "pseudo" mode (on a downhill), and for uphills it may put you in a more efficient band (although it will require more power total - which you may recover on the return leg). Where possible, I try to time my pulses with uphills and glides with downhills.

Also, in my personal experience, I think PWR mode is more likely to start the ICE as soon as the line is crossed, but normal and ECO mode seem to be slightly more "sticky" at that point and easier to hold there without starting the ICE. (that's just how it feels to me)

Just my thoughts based on my experimentation so far... If anyone has other suggestions, I'd love to try them - especially for that 45-50mph range (which I have to use a lot here).

HelloMyPrius · Feb 10, 2010

OK....I did some math. Here is what I have:

Total MPG = MPG(g) * [(Distance_ratio +1)/(MPG_ratio*Distance_ratio +1)]

Where
MPG(g) = MPG while gliding

Distance_ratio = Distance_covered_during_Pulsing/Distance_covered_during_Gliding

MPG_ratio = MPG_while_gliding/MPG_while_pulsing

Here are the spread sheet numbers:

MPG_ratio Distance Ratio Total MPG/MPG(g)

1 2 0.1 0.92

2 2.5 0.1 0.88

3 2 0.2 0.86

4 3 0.1 0.85

5 3.5 0.1 0.81

6 2 0.3 0.81

7 2.5 0.2 0.80

8 4 0.1 0.79

9 2 0.4 0.78

10 4.5 0.1 0.76

11 2 0.5 0.75

12 3 0.2 0.75

13 2.5 0.3 0.74

14 5 0.1 0.73

15 2 0.6 0.73

16 5.5 0.1 0.71

17 2 0.7 0.71

18 3.5 0.2 0.71

19 2.5 0.4 0.70

20 2 0.8 0.69

21 6 0.1 0.69

22 3 0.3 0.68

23 2 0.9 0.68

24 6.5 0.1 0.67

25 2 1 0.67

26 2.5 0.5 0.67

27 4 0.2 0.67

28 2.5 0.6 0.64

29 3 0.4 0.64

30 3.5 0.3 0.63

31 4.5 0.2 0.63

32 2.5 0.7 0.62

33 2.5 0.8 0.60

34 3 0.5 0.60

35 5 0.2 0.60

36 4 0.3 0.59

37 2.5 0.9 0.58

38 3.5 0.4 0.58

39 3 0.6 0.57

40 2.5 1 0.57

41 5.5 0.2 0.57

42 4.5 0.3 0.55

43 3 0.7 0.55

44 3.5 0.5 0.55

45 6 0.2 0.55

46 4 0.4 0.54

47 3 0.8 0.53

48 6.5 0.2 0.52

49 5 0.3 0.52

50 3.5 0.6 0.52

51 3 0.9 0.51

52 3 1 0.50

53 4 0.5 0.50

54 4.5 0.4 0.50

55 3.5 0.7 0.49

56 5.5 0.3 0.49

57 3.5 0.8 0.47

58 4 0.6 0.47

59 5 0.4 0.47

60 6 0.3 0.46

61 4.5 0.5 0.46

62 3.5 0.9 0.46

63 4 0.7 0.45

64 3.5 1 0.44

65 6.5 0.3 0.44

66 5.5 0.4 0.44

67 4.5 0.6 0.43

68 4 0.8 0.43

69 5 0.5 0.43

70 4 0.9 0.41

71 6 0.4 0.41

72 4.5 0.7 0.41

73 4 1 0.40

74 5 0.6 0.40

75 5.5 0.5 0.40

76 4.5 0.8 0.39

77 6.5 0.4 0.39

78 5 0.7 0.38

79 4.5 0.9 0.38

80 6 0.5 0.38

81 5.5 0.6 0.37

82 4.5 1 0.36

83 5 0.8 0.36

84 6.5 0.5 0.35

85 5.5 0.7 0.35

86 6 0.6 0.35

87 5 0.9 0.35

88 5 1 0.33

89 5.5 0.8 0.33

90 6 0.7 0.33

91 6.5 0.6 0.33

92 5.5 0.9 0.32

93 6 0.8 0.31

94 5.5 1 0.31

95 6.5 0.7 0.31

96 6 0.9 0.30

97 6.5 0.8 0.29

98 6 1 0.29

99 6.5 0.9 0.28

100 6.5 1 0.27

As you can see, there is a trade-off between the MPG ratio and Distance ratio.

If the red lights are close together, it is very difficult to achieve a low distance ratio. So you want to maximum MPG ratio, which means slow acceleration to a low speed.

If red light is far apart, then you may want to accelerate quickly at the expense of MPG ratio to achieve a better distance ratio. So sometimes it is better to accelerate in the power mode to shorten the acceleration distance if you have sufficient gliding distance.

The actual distance to acceleration relationship is L(a) = 1/2 * (Vp^2 - Vs^2)/aa where Vp = peak velocity and Vs = starting velocity and aa = accelerating when pulsing. Similarly L(g) = 1/2 * (Vf^2 - Vp^2)/ag where Vf = final velocity and ag = deceleration when gliding.

If you start at a red light Vs = 0 and if you end at red light Vf = 0. Then the distance ratio L(a)/L(g) becomes ag/aa in absolute terms. I have no idea what is the deceleration during the glide and what kind of acceleration people usually use.

Hope this is not too mathematical and can get people experimenting about different strategies.

Tom183 · Feb 10, 2010

I don't exactly follow the numbers, but the general premise does make sense:
For a short distance, you don't have much time to glide so the pulse is wasted - better to waste as little as possible on acceleration.
For a longer distance, slow acceleration means a shorter glide so it's better to pulse more strongly.

I get lousy mileage on those stretches of road where the speed limit is 40mph (most people accelerate briskly to 45) and I might have to stop at lights that aren't very far apart. If I pulse strongly, I'm screwed when a light changes quickly and I have to brake. If I pulse weakly and the light stays green, I'm screwed because I don't get any glide. My preference is to pulse strongly so that I keep up with traffic, but it really hurts mpg when going from one red light to the next...

I'm finding the worst type of driving for mpg is shopping... Red lights everywhere, everyone stomping on their gas and brakes, engine cools off while you're in the store, short distances between stops. (Plus you waste time and money and go home with a bunch of crap you don't really need...)

ken1784 · Feb 10, 2010

I don't understand your math.

HelloMyPrius said: ↑

MPG(g) = MPG while gliding
Click to expand...

Gliding (ICE off) is always infinity MPG.

Ken@Japan

HelloMyPrius · Feb 10, 2010

ken1784 said: ↑

I don't understand your math.

Gliding (ICE off) is always infinity MPG.

Ken@Japan
Click to expand...

Good point, during the puriest P&G, MPG(g) is infinite. Then the formula becomes

Total MPG = MPG(a)*[1 + L(g)/L(a)]

where L(g) is the length of the glide and L(a) is the length of acceleration.

The intuition seems to be the same. There is a trade off between how quickly do you want to accelerate to increase L(g)/L(a) and how much do you want to sacrafice for lower MPG(a). I suspect, there is an optimal point at different speed level. Curious to see the results people have experienced.

In my previous formula, MPG(g) is really an average during the gliding period. I don't know how well can people keep the ICE complete off throughout the gliding.

Much More Better · Feb 11, 2010

Some clarification here please.....

Is gliding the same as coasting with foot off accelerator completely?
What do you call it when you are traveling at a steady pace (say 45mph) and then back off the gas until only EV pushes the car along so that the rate of decel is very slow? I find if I take my foot off the gas, I decel too fast and then I have to pulse again. What's the secret?

ken1784 · Feb 11, 2010

HelloMyPrius said: ↑

Good point, during the puriest P&G, MPG(g) is infinite. Then the formula becomes

Total MPG = MPG(a)*[1 + L(g)/L(a)]

where L(g) is the length of the glide and L(a) is the length of acceleration.
Click to expand...

I now agree with your math.

However, I like following one.

total distance = L(g) + L(a)
then,
total MPG = MPG(a) * [ total distance / L(a) ]
where,
engine run ratio = L(a) / total distance

The intuition seems to be the same. There is a trade off between how quickly do you want to accelerate to increase L(g)/L(a) and how much do you want to sacrafice for lower MPG(a). I suspect, there is an optimal point at different speed level. Curious to see the results people have experienced.
Click to expand...

Attached picture was taken at the famous 1400 miles/tank challenge in 2005.

The data is...
MPG(a) = 12.49 km/L (29.38 mpg)
engine run ratio = 27%
total MPG = 46.52 km/L (109.43 mpg)
average speed = 2248.78 km / 47.72 hours = 47.12 km/h = 29.29 mph

In my previous formula, MPG(g) is really an average during the gliding period. I don't know how well can people keep the ICE complete off throughout the gliding.
Click to expand...

I believe we use the term "gliding" in only complete ICE off condition.

The false gliding (ICE on gliding) can be seen in ICE warming up, charging HV battery when the charge level is too low, heavy cabun heater use, above 46 mph highway speed and other conditions.

Ken@Japan

HelloMyPrius · Feb 11, 2010

Much More Better said: ↑

Some clarification here please.....

Is gliding the same as coasting with foot off accelerator completely?
What do you call it when you are traveling at a steady pace (say 45mph) and then back off the gas until only EV pushes the car along so that the rate of decel is very slow? I find if I take my foot off the gas, I decel too fast and then I have to pulse again. What's the secret?
Click to expand...

Gliding is not the same as coasting. During the gliding, you still have your foot on the gas peddle but light enough that ICE doesn't come on. It takes quite some practice to get to that zone for me. I am still practicing. I think in that sense, ECO mode does give you a bigger gliding zone than say normal mode.

You speed will still be decreasing during the gliding but not as fast as coasting.

That is what I learnt so far. Hope it helps.

HelloMyPrius · Feb 11, 2010

Thanks Ken for the information about the 1400 mile challenge.

I have a couple of questions about the stats:

You gave the average speed. Do you have information on the speed range? At what speed do you start to pulse and at what speed do you start to glide? Do you see MPG differences when you varying the speed you start pulsing and speed you start gliding?

Thanks.

Tom183 · Feb 11, 2010

So is 29.38mpg the ideal "pulse" mpg? And can this be monitored via the iMPG gauge?

ken1784 · Feb 11, 2010

HelloMyPrius said: ↑

You gave the average speed. Do you have information on the speed range?
Click to expand...

Toyota.com : Hybrid Synergy View : 2005 : Fall : Prius Marathoners Top 100 mpg
"The pulse refers to deadband acceleration (no flow to or from the battery) up to 40 mph. Next comes the glide (engine is stopped, no flow at all) where the speed slowly decreases to 33 mph. The cycle continues until a stop is required."

HelloMyPrius said: ↑

Do you see MPG differences when you varying the speed you start pulsing and speed you start gliding?
Click to expand...

I don't have any data about the speed range, but we know approx 30 mph average speed gives us the best MPG results.

Tom183 said: ↑

So is 29.38mpg the ideal "pulse" mpg? And can this be monitored via the iMPG gauge?
Click to expand...

It was just average iMPG number for whole 1400 miles drive.
The best segment (shift) of the marathon was done by Wayne on the 10th shift as follows;
GreenHybrid - Hybrid Cars - View Single Post - Prius II - 100 + MPG Marathon Attempt - Live Updates ...
Engine ON FC: 10.16L/100km -> 9.84 km/L (23.15 mpg)

Also, Dan mentioned about it.
http://priuschat.com/forums/gen-ii-prius-main-forum/10132-prius-marathon-run-12.html#post112727
"Rick used 15-20 for his 115 MPG shift, I used 25-35 for my 115 MPG shift and Wayne used 40-50 for his 120MPG shift. The extra 5 MPG was more likely due to gliding down to much lower speeds than Rick or myself."

Ken@Japan

Tom183 · Feb 11, 2010

Wait - that data is from the Gen II? I thought this was a Gen III thread...

ken1784 · Feb 11, 2010

Tom183 said: ↑

Wait - that data is from the Gen II? I thought this was a Gen III thread...
Click to expand...

Yes, this is Gen3 thread, but I showed the 1400 mile marathon event in 2005 as the reference.
There is not so much difference about the P&G technique between Gen2 and Gen3.

Ken@Japan

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