Theoretical maximum speed over distance in P85D and other charting hypotheticals

[LetsGoFast]

I found another chart on the official blog:

It appears to me that Tesla estimates something very close to EVTrip's numbers at 75. I eyeball that as less than 375 wh/mile, but close. Clearly at 80 mph they are still under 400 wh/mile, whereas you estimate that consumption at only 75mph. The entire blog entry is likely to be of some interest to you.

I also found an interesting discussion from 2012 here: www.teslamotors.com/forum/forums/optimal-speed

 

[richkae]

My data comes from this very old post by JB on the Tesla site: Roadster Efficiency and Range | Blog | Tesla Motors
The link to download the source spreadsheet isn't working but I saved a copy a long time ago.
I used this as the basis for a model for the Model S. Note that the energy lost in the tires and drivetrain is close to linear, and the aerodynamic loss is quadratic.
The aerodynamic loss is not the majority until 62mph, and then it dominates.
I believe this is the original data from the spreadsheet:

Speed	Total	Ancillary	Tires	Aero	Drivetrain	Range	Power
mph	Wh/mi	Wh/mi	Wh/mi	Wh/mi	Wh/mi	mi	kW
2	356.3	89.9	52.9	0.1	213.6	154.4	0.7
4	221.2	44.8	52.9	0.5	123.1	248.6	0.9
6	177.8	29.9	52.9	1.1	94.1	309.3	1.1
8	157.3	22.4	52.9	2.0	80.1	349.7	1.3
10	146.1	17.9	52.9	3.1	72.3	376.4	1.5
12	139.7	14.9	52.9	4.4	67.6	393.6	1.7
14	136.2	12.8	52.9	6.0	64.5	403.9	1.9
16	134.5	11.2	52.9	7.9	62.6	408.8	2.2
18	134.2	9.9	52.9	10.0	61.5	409.8	2.4
20	135.0	8.9	52.9	12.3	60.9	407.6	2.7
22	136.5	8.1	52.9	14.9	60.6	403.0	3.0
24	138.7	7.5	52.9	17.8	60.7	396.6	3.3
26	141.7	6.9	53.2	20.8	60.9	388.1	3.7
28	145.5	6.4	53.6	24.2	61.5	378.0	4.1
30	149.8	6.0	54.1	27.7	62.1	367.2	4.5
32	154.5	5.6	54.5	31.6	62.9	356.1	4.9
34	159.6	5.3	55.0	35.6	63.9	344.7	5.4
36	165.1	5.0	55.4	40.0	64.9	333.1	5.9
38	170.8	4.7	55.7	44.5	66.0	322.0	6.5
40	176.6	4.5	55.7	49.3	67.2	311.5	7.1
42	182.7	4.3	55.7	54.4	68.5	301.1	7.7
44	189.1	4.1	55.7	59.7	69.8	290.8	8.3
46	195.9	3.9	55.7	65.2	71.2	280.7	9.0
48	203.0	3.7	55.7	71.0	72.7	270.9	9.7
50	210.5	3.6	55.7	77.1	74.3	261.3	10.5
52	218.3	3.4	55.8	83.4	75.9	252.0	11.3
54	226.3	3.3	55.8	89.9	77.5	243.0	12.2
56	234.7	3.2	55.8	96.7	79.2	234.3	13.1
58	243.3	3.1	55.8	103.7	81.0	226.0	14.1
60	252.3	3.0	55.8	111.0	82.8	218.0	15.1
62	261.6	2.9	55.8	118.5	84.6	210.2	16.2
64	271.4	2.8	56.0	126.3	86.6	202.6	17.4
66	281.6	2.7	56.2	134.3	88.6	195.3	18.6
68	292.1	2.6	56.4	142.5	90.8	188.3	19.9
70	303.0	2.5	56.7	151.0	92.9	181.5	21.2
72	314.1	2.5	56.9	159.7	95.2	175.1	22.6
74	325.5	2.4	57.1	168.7	97.4	169.0	24.1
76	337.1	2.3	57.3	177.9	99.7	163.2	25.6
78	348.9	2.3	57.6	187.4	101.9	157.6	27.2
80	361.0	2.2	57.8	197.1	104.1	152.4	28.9
82	373.3	2.2	57.9	207.1	106.5	147.3	30.6
84	385.9	2.1	57.9	217.3	108.9	142.5	32.4
86	398.7	2.1	57.9	227.7	111.3	138.0	34.3
88	411.7	2.0	57.9	238.4	113.7	133.6	36.2
90	425.0	2.0	57.9	249.3	116.1	129.4	38.3
92	438.7	1.9	58.0	260.5	118.7	125.4	40.4
94	452.6	1.9	58.0	271.9	121.2	121.5	42.5
96	466.7	1.9	58.0	283.5	123.8	117.8	44.8
98	481.2	1.8	58.0	295.4	126.4	114.3	47.2
100	495.8	1.8	58.0	307.5	129.0	110.9	49.6
102	510.8	1.7	58.0	319.9	131.6	107.7	52.1
104	526.1	1.7	58.0	332.5	134.4	104.5	54.7
106	541.7	1.7	58.1	345.3	137.1	101.5	57.4
108	557.5	1.6	58.1	358.4	140.0	98.7	60.2
110	573.6	1.6	58.1	371.7	142.8	95.9	63.1
112	590.0	1.6	58.1	385.3	145.7	93.2	66.1
114	606.6	1.6	58.1	399.1	148.5	90.7	69.1
116	623.5	1.5	58.1	413.1	151.5	88.2	72.3
118	640.7	1.5	58.1	427.3	154.5	85.8	75.6
120	658.1	1.5	58.2	441.8	157.5	83.6	79.0
122	675.8	1.5	58.2	456.5	160.5	81.4	82.4

 

[transpondster]

There is common confusion here between energy and power. In the Tesla world, the common units for energy are Watt-hour (Wh) or kiloWatt-hour (kWh), and the common units for power are Watts (W) or kiloWatts (kW)

For pure aerodynamic drag, the aerodynamic force goes up as the square of speed. Energy is distance times force, but the power required is speed times force. From that, for aerodynamic losses, the energy to cover a particular distance (Wh/mi or Wh/km) goes up as the square of speed, but the power needed to go that speed goes up as the cube of speed.

• Energy - Wh/mi or Wh/km goes up as speed[SUP]2[/SUP]
• Power Required - kW goes up as speed[SUP]3[/SUP]

you started to explain correctly, but made wrong formula
if only count aerodynamic drag power
P = DragCoef * speed[SUP]2[/SUP]
E = P * t
but Tesla's energy per distance let's name it wheels' travelling force (WTF) WTF = E / distance
distance = t * speed
so WTF = E / ( t * speed) = P *t / ( t *speed ) = P / speed = DragCoef * speed
so efficiency decreese proportianally to speed, of cours its not counting motor, battery discharging efficiency, altough rolling rsistence and auxiliary power use would remain same so it would slightly counter balance, driving in subzero celsius at 30 km/h probably would be less efficient then at 40

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don't see edit button, just to clarify DragCoef would be of mass dimension like in kinetic energy to make sense in physics, not "0,23"

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edit2: mixed power with energy, so DragCoef should be mass/time kg/s dimension

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edit3: reread your post and I think you are right, I mixed power with force.