# Model 3 acceleration



## bwilson4web (Mar 4, 2019)

Hi,

Standard Range Plus Model 3 (version 19.16.2)
SOC ~75%, 15 mi (24 km) warm-up
3711 (empty weight) + 250 (driver) + 15 (EVSE, patch kit) ~= 3976 lbs (1,807 kg)
77F (25C)
asphalt road surface
wind 0 mph, 9:30 PM (21:30) CST










The acceleration data will be used to calculate the velocity. Then I'll add the EPA roll-down drag coefficients to calculate the total force on the car and eventually the vehicle HP (kW). This will be for both chill and standard modes.

Bob Wilson


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## Nom (Oct 30, 2018)

This is cool. I’ve wondered what the G force was at the start. Anyone have this for a LR AWD? 

Interesting that both yellow and green (standard acceleration runs) have down spikes at about 9 and 10 seconds. I’d say could be noise if just one. But it is in both. What is going on that would cause that. Admittedly the downspikes are incredibly short lived. But interesting.


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## bwilson4web (Mar 4, 2019)

Nom said:


> This is cool. I've wondered what the G force was at the start. Anyone have this for a LR AWD?
> 
> Interesting that both yellow and green (standard acceleration runs) have down spikes at about 9 and 10 seconds. I'd say could be noise if just one. But it is in both. What is going on that would cause that. Admittedly the downspikes are incredibly short lived. But interesting.


Excellent question but those 'down spikes' are the end of the maximum acceleration runs. I targeted 80 mph as my ending speed because the car sounds an excessive speed alarm at 90 mph. Yes, I could have disabled the speed alarm but earlier GPS measured runs showed 80 mph was adequate to our goals.

I'm using a Gulf Coast Data Concepts, Human Activity Monitor:









```
;Title, http://www.gcdataconcepts.com, X16-MPU-ham, ADXL345, MPU-9250
;Version, 1191, Build date, Nov 15 2016,  SN:CCDC3016B4874F1
;Start_time, 2019-06-05, 21:09:12.423
;Temperature, -999.00, deg C,  Vbat, 4174, mv
;MPU SR, 200,Hz,  Accel sens, 4096,counts/g, Gyro sens, 16,counts/dps,  Mag SR, 10,Hz,  Mag sens, 1666,counts/mT
;Deadband, 50, counts
;DeadbandTimeout, 0,sec
;Time, Ax, Ay, Az, Gx, Gy, Gz, Mx, My, Mz
0.004486,-170,1156,-4192,5,-54,-1
0.018432,96,1210,-3916,-21,-20,-9,-311,-383,-506
0.038421,-396,1242,-4240,-20,-34,0
0.058410,-370,1302,-4166,-25,-13,-8
0.078399,680,1450,-4722,-17,-10,-7,-304,-371,-506
0.098419,-384,1138,-4572,-18,-18,0
0.118408,-584,1142,-4106,-8,1,-7
0.138397,124,978,-3978,7,15,-8
0.158386,250,1096,-4122,16,1,-5
0.178406,-640,1222,-4154,17,-12,3,-296,-387,-514
```

Time - seconds from start of data file. Use the header to get the 'real time' clock and date.
Ax - side to side acceleration
Ay - front to rear acceleration
Az - top to bottom, gravity, which we use to scale 1 G
Gx - rotation about the door axis
Gy - rotation about the front to rear axis
Gz - rotation around a vertical axis
Mx - magnetic field along door axis
My - magnetic field along front to rear axis
Mz - magnetic field along the vertical axis
MEMS accelerometer data are noisy so I used a 7 element Gaussian filter (0.063, 0.250, 0.375, 0.250, 0.063) to do a weighted average. Unlike a linear average, this preserves the local peaks while significantly reducing the noise.

Each data file has 16,000 data samples covering about 5 minutes which puts a significant load on the OpenSource spreadsheet. Somewhat arbitrary, I used 500 counts, 500/4096 ~= 12.2% G, to trim the non-acceleration elements reducing the samples to 2,185 which was easily handled by the spreadsheet.

Perhaps more details than you were expecting, I was looking for an opportunity to share where the data came from.

Bob Wilson


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## Nom (Oct 30, 2018)

Ok. I think I get what you are saying. Down spikes signal end of max acceleration at about 80mph.

But ... assuming you get to 60mph at about 5.5 sec (fair), does it really take 3+more seconds to get to 80? Seems like it wouldn’t take that long but perhaps so! (Per math below at 0.3G the car would add 20mph in 3 seconds — I’m answering my own questions!)

Also, the graph suggests the car is still pulling 0.2 G’s in the 10-13 sec range. Implying continued forward acceleration. It is getting faster. I ran the math and this suggest an extra 4.4 mph each second at 0.2G. Which makes sense. You pushed through 80mph and got up a bit north of 90. You wouldn’t decelerate all of a sudden. Ok. I was confused but I explained it to myself!

I didn’t even try to follow the rest of your post. Looks cool though!!

Just since I did it. And someone can check. At 1 G, I get velocity changing at 21.9 mph per second. So cars hitting 60mph in less than 3 sec are likely well above 1G in the early acceleration phase. Cool.


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## Klaus-rf (Mar 6, 2019)

Interesting data set.

BTW: 3976 Lbs = 1803 Kg


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## Frully (Aug 30, 2018)

It's interesting data...
I want to nerd out and look forward to your analysis on it.

Seems at peak you get 0.56g average acceleration for the first 4 seconds...that's the easy bit.

a = 9.81m/s^2 * 0.56 = 5.49m/s^2
v(4) = v(0) + at
v(4) = 0 + 5.49*4
v(4) = 21.96m/s = 79km/h = 49mph...

sanity check, the numbers seem reasonable.

Edit: deeper!
Kinetic energy...the loosest approximation, since acceleration was pretty flat line...
@t=4.0s m=1803kg v=21.96m/s
Ek = 1/2 mv^2
Ek = 1/2 * 1803kg * (21.96m/s)^2
Ek = 1/2 * 1803kg * 482.24m^2/s^3
Ek = 869481.60Kgm^2/s^3 / 2
Ek = 434741J, or about 435kJ, conveniently watt-seconds.
435000 watt-seconds / 4 seconds = 108685 watts to the wheels/physics
definitely seems within spec for the motor. The official specs aren't out for the SR variants (wikipedia).
LR RWD is rated at 211kw at the motor.


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## bwilson4web (Mar 4, 2019)

So this is what the velocity looks like:


















Remember, my car has a heavy driver, the EVSE, and a tire patch kit.

Bob Wilson

ps. Here is a zip file with the somewhat unorganized data:


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## MJJ (Aug 7, 2016)

I've been halfheartedly trying to get this data by using a iPad app, but it always had too much noise. This is awesome!


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## Mr. Spacely (Feb 28, 2019)

1. So the 0-60 is like 5.2 secs?
2. Can you figure out the rated horse power from this?


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## PNWmisty (Aug 19, 2017)

casey morgan said:


> 1. So the 0-60 is like 5.2 secs?
> 2. Can you figure out the rated horse power from this?


No. Only the calculated HP.


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## bwilson4web (Mar 4, 2019)

casey morgan said:


> 1. So the 0-60 is like 5.2 secs?
> 2. Can you figure out the rated horse power from this?


Yes but there are two parts:

Inertal HP - this is how much is used to move the mass
Drag HP - this is how much energy is lost due to rolling and aerodynamic drag
Since we have the mass, we can calculate the HP that accelerated the car and its contents to a given speed. Then add the drag HP to get the actual HP that was applied at the wheels.

Bob Wilson


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## Frully (Aug 30, 2018)

casey morgan said:


> 1. So the 0-60 is like 5.2 secs?
> 2. Can you figure out the rated horse power from this?


I did that already...



Frully said:


> Edit: deeper!
> Kinetic energy...the loosest approximation, since acceleration was pretty flat line...
> @t=4.0s m=1803kg v=21.96m/s
> Ek = 1/2 mv^2
> ...


108kW at the wheel = 144 horsepower.


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## Nom (Oct 30, 2018)

@Frully - I would suggest you calculated he energy consumed in an ideal (no drag) and lossless scenario. But there are losses and there is drag. So I would suggest the energy output / consumed is higher. How much higher, I don't know.


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## bwilson4web (Mar 4, 2019)

Both Chill and Standard mode acceleration metrics:

HP - the inertial power needed to accelerate the car and contents
drag - the power needed to handle rolling, transmission, and aerodynamic drag
Total HP - the total power needed at the drive wheels



















Bob Wilson


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## Frully (Aug 30, 2018)

From the wiki...










Your hp numbers seem a bit high. What are you using to calculate instant hp from acceleration?


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## Frully (Aug 30, 2018)

Nom said:


> @Frully - I would suggest you calculated he energy consumed in an ideal (no drag) and lossless scenario. But there are losses and there is drag. So I would suggest the energy output / consumed is higher. How much higher, I don't know.


Agreed - my number is just at the wheels. The rest we have to go on 'its very efficient. how efficient, we definitely don't know'


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## bwilson4web (Mar 4, 2019)

Frully said:


> From the wiki...
> Your hp numbers seem a bit high. What are you using to calculate instant hp from acceleration?


I'm using a recording, MEMS, accelerometer to capture the data and CAT (truck stop) weight for the mass. Then I used physics to calculate the speed and HP. I also used the EPA roll-down coefficients to calculate the drag power.

You are welcome to my data in the zip file. It isn't a well documented spreadsheet as I use it for my curiosity. If you have questions, I'll be happy to explain what is going on.

I could clean up the spreadsheet if there is interest in a more 'formal' presentation:

improved noise filter - I used a 5-element Gaussian filter but could increase it to 7-9 to further reduce the noise. I won't use a linear average because it suppresses the peaks even though it is more commonly used. Still, I could code the spreadsheet to let each method be used.
standard units - I mix both SAE and metric metrics and calculations which ever is easiest. I could change all of the metrics and calculations to metric and then at the end convert the results to SAE.
table parameters - in some calculations it was easier to hardcode the functions instead of referencing a well documented table. By using tables, different models and cars can be instrumented and values used to get useful results. Just I'm not in that business ... yet.
Bob Wilson


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