Maximize MPG between Traffic lights using P&G

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.

 

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

 

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, 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?

 

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.

 

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.

 

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.

 

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.