... king... duke?
This started as an exercise to determine if the above-spec tire pressures I've been running at (45psi) are really saving any kWhs or just making the so-so grip/handling of these Ecopia low rolling resistance tires even worse.
For those who don't want to read the rest; bottom line: I'm going back to setting my tire pressure to 35 psi. For the rest, sorry this is so long and please, if any of you hypermilers out there see problems wth my methods here feel free to correct. I'd love to learn more.
Awhile ago, I posted some data from my CANbus reader that I interpret as RPM and described my process for scaling that RPM data to vehicle speed. Since RPMs give us the LEAF speed and it gets reported about 50-100 times /sec we should have a precise way to measure the acceleration or deceleration of the LEAF. The LEAF is direct drive, RPM is still reporting motor (and wheel) turns when in neutral (unlike my ICE).
So, when we pop the car into neutral and record the deceleration, what we see is the result of two main forces acting on the car (per Wikipedia).
F = { Crr * M * g } + {Cd * A * 1/2 * rho * V^2}
F = { rolling drag } + { aerodynamic drag }
I don't like these forces since they sap my battery and give some of us what the French call inquiétude de distance or what GM has trade-marked as "range anxiety".
But that's physics.
When a car accelerates, these forces look like the plot below; with the force due to aero drag increasing as velocity-squared and force due to rolling resistance staying fairly constant.
http://www.atmosphere.mpg.de/enid/Information_ss/Velocity___air_drag_507.html
F = Ma so with some algebra: a = { Crr * g } + { Cd * A * 1/2 * rho V^2 } / M
a = dv/dt or just slope of the velocity over short intervals.
So, with my CANbus reader, I can get from LEAF RPM, to dv/dt and therefore a.
We have equations and we need some of the constants.
MKS units here (meters (m) kilograms (k) seconds (s)
M = mass = 1605 = mass of LEAF 1525kg + mass of driver 80kg
g = gravity = 9.81 m/s^2
Cd = coefficient of drag = 0.29
A = frontal area of LEAF = 2.27 m^2
rho = the air density = 1.22kg/m^3 (I adjusted for alt & temp to 1.15 using CRC tables)
RPM to m/s: GR = gear ratio of LEAF (1.79377) tire circumference: 2.05m
So RPM to m/s = Rev/minute * 1/GR * 1 minute / 60sec * TireCircumference m/rev
RPM_2_V coeff = 0.004306 (min * m )/(sec * rev)
So, we use the RPM/sec data to determine a for a given RPM (scaled to velocity, V).
We want to solve for Crr which is supposed to show a change vs tire pressure.
Although we know Cd, I decided to check my units and algebra (and physics) by solving for Cd using the 2 equations & 2 unkowns (Crr & Cd) at two widely differing velocities: ~75 MPH & ~ 15 MPH (from m/sec)
The stategy here is to take a data set at high speed and then a data set at low speed with tire pressure going from 45 psi for one high/low test set and the 35 psi for the other.
Using the two speed tests we can solve for the Crr (and Cd). Ultimately, we will just use the dv/dt number of the low speed 45/35psi tests to determine if the Crr changes sufficiently to warrant 45 psi vs 35 psi.
Sooo, this is really a simple test that I've complicated for the sake of completeness.
As an example of raw data, here's a plot of RPM taken on one of the high-speed test runs.
You can see my LEAF accelerate up and then suddenly decelerate when I let off on the pedal.
Then it decelerates strongly due to regen until I pop it into neutral. Then it flattens out nicely and we can compute a slope (dv/dt) with a 2-4 secs of data. I run this test going both ways on the same road to cancel out the slight slope in road. No wind, about 75 deg, dry surface, typical SoCal mid-morning.
So, here's my attempt at solving for Crr and Cd using raw dv/dt data from the LEAF CANbus.
Lest we forget: a = { Crr * g } + { Cd * A * 1/2 * rho V^2 } / M
High speed dv/dt: 0.37904 = Crr * 9.81 + Cd * 0.8916 (using V = 32.7m/s)
Low speed dv/dt: 0.1328 = Crr * 9.81 + Cd * 0.044613 (using V = 7.32 m/s)
From these we get Crr = 0.01221 and Cd = 0.2907
The Cd number is quite heartening to see ( I actually exclaimed "holy s**t this CANbus s**t works!) and tells me my method's not too bad. I still think it's a bit low since I wouldn't expect to come that close to the calculated number.
Probably due to my estimation of rho (air density).
Ok, almost done. Crr is 0.01221. From other LRR tire data I expect these Ecopia's are about 0.007?
Anyone got a published value? The rest is most likely due to the brake pad friction, transaxle fluids, etc.
The key is, what does this number do for energy loss and how does it change when we change tire pressure (even I almost forgot the point of this whole exercise).
Well, that's fairly easy.
If we go back to the Force equation at the top:
F = { Crr * M * g } + {Cd * A * 1/2 * rho * V^2}
F = { rolling drag } + { aerodynamic drag }
Force times distance = work = energy.
So, if the Crr goes up, the force against the car goes up and the energy loss goes up.
F * d = Joules * 1/3600s/hr * 1/1000 W/kW = Energy used in kWh
For example from the measured a value (0.37904 m/s^2) at high speed.
Total drag force F = Ma = 1605kg * 0.37904 m/s^2
If we travel a distance of 100 km = 100,000 m then we'll use
1605 * 0.37904 * 100,000 m / 3,600,000 = 16.9 kWh used to go about 62 mi @ 75 MPH.
That's just the loss due to drag, inverter and other non-drag losses give us maybe 85% efficiency?
Then throw in hills, headwinds, etc.
So, 16.9/0.85 = 19.9 kWh of battery use. I think that's plausible.
So, plug in the two values of Crr I calculated using the same drive cycle at 45 psi vs 35 psi and I get a whopping change to Crr from 0.0122 to 0.0125 which yields a change of energy use over 100 km of about 170 Wh (also it's within my error bars so hardly convincing).
So, to recap; I used the CANbus 0x1DA fields to get highrate RPM vs time.
Computed dv/dt at slow speed to estimate drag dominated by Crr.
Tested at 45 psi and 35 psi and dv/dt barely registered a difference.
Ran through the numbers on this small difference and believe the kWh diff between battery LEAF charging cycles makes it too small to bother with the higher psi levels I've been keeping my tire pressures at.
My theory for this is the LRR tires are already pretty elastic at 35 psi and increasing to 45 psi just doesn't yield the same benefit as non LRR tires.
BTW, has someone posted 0-60 times using the CANbus data?
If not, I'll try and put something up soon.
This started as an exercise to determine if the above-spec tire pressures I've been running at (45psi) are really saving any kWhs or just making the so-so grip/handling of these Ecopia low rolling resistance tires even worse.
For those who don't want to read the rest; bottom line: I'm going back to setting my tire pressure to 35 psi. For the rest, sorry this is so long and please, if any of you hypermilers out there see problems wth my methods here feel free to correct. I'd love to learn more.
Awhile ago, I posted some data from my CANbus reader that I interpret as RPM and described my process for scaling that RPM data to vehicle speed. Since RPMs give us the LEAF speed and it gets reported about 50-100 times /sec we should have a precise way to measure the acceleration or deceleration of the LEAF. The LEAF is direct drive, RPM is still reporting motor (and wheel) turns when in neutral (unlike my ICE).
So, when we pop the car into neutral and record the deceleration, what we see is the result of two main forces acting on the car (per Wikipedia).
F = { Crr * M * g } + {Cd * A * 1/2 * rho * V^2}
F = { rolling drag } + { aerodynamic drag }
I don't like these forces since they sap my battery and give some of us what the French call inquiétude de distance or what GM has trade-marked as "range anxiety".
But that's physics.
When a car accelerates, these forces look like the plot below; with the force due to aero drag increasing as velocity-squared and force due to rolling resistance staying fairly constant.
http://www.atmosphere.mpg.de/enid/Information_ss/Velocity___air_drag_507.html
F = Ma so with some algebra: a = { Crr * g } + { Cd * A * 1/2 * rho V^2 } / M
a = dv/dt or just slope of the velocity over short intervals.
So, with my CANbus reader, I can get from LEAF RPM, to dv/dt and therefore a.
We have equations and we need some of the constants.
MKS units here (meters (m) kilograms (k) seconds (s)
M = mass = 1605 = mass of LEAF 1525kg + mass of driver 80kg
g = gravity = 9.81 m/s^2
Cd = coefficient of drag = 0.29
A = frontal area of LEAF = 2.27 m^2
rho = the air density = 1.22kg/m^3 (I adjusted for alt & temp to 1.15 using CRC tables)
RPM to m/s: GR = gear ratio of LEAF (1.79377) tire circumference: 2.05m
So RPM to m/s = Rev/minute * 1/GR * 1 minute / 60sec * TireCircumference m/rev
RPM_2_V coeff = 0.004306 (min * m )/(sec * rev)
So, we use the RPM/sec data to determine a for a given RPM (scaled to velocity, V).
We want to solve for Crr which is supposed to show a change vs tire pressure.
Although we know Cd, I decided to check my units and algebra (and physics) by solving for Cd using the 2 equations & 2 unkowns (Crr & Cd) at two widely differing velocities: ~75 MPH & ~ 15 MPH (from m/sec)
The stategy here is to take a data set at high speed and then a data set at low speed with tire pressure going from 45 psi for one high/low test set and the 35 psi for the other.
Using the two speed tests we can solve for the Crr (and Cd). Ultimately, we will just use the dv/dt number of the low speed 45/35psi tests to determine if the Crr changes sufficiently to warrant 45 psi vs 35 psi.
Sooo, this is really a simple test that I've complicated for the sake of completeness.
As an example of raw data, here's a plot of RPM taken on one of the high-speed test runs.
You can see my LEAF accelerate up and then suddenly decelerate when I let off on the pedal.
Then it decelerates strongly due to regen until I pop it into neutral. Then it flattens out nicely and we can compute a slope (dv/dt) with a 2-4 secs of data. I run this test going both ways on the same road to cancel out the slight slope in road. No wind, about 75 deg, dry surface, typical SoCal mid-morning.
So, here's my attempt at solving for Crr and Cd using raw dv/dt data from the LEAF CANbus.
Lest we forget: a = { Crr * g } + { Cd * A * 1/2 * rho V^2 } / M
High speed dv/dt: 0.37904 = Crr * 9.81 + Cd * 0.8916 (using V = 32.7m/s)
Low speed dv/dt: 0.1328 = Crr * 9.81 + Cd * 0.044613 (using V = 7.32 m/s)
From these we get Crr = 0.01221 and Cd = 0.2907
The Cd number is quite heartening to see ( I actually exclaimed "holy s**t this CANbus s**t works!) and tells me my method's not too bad. I still think it's a bit low since I wouldn't expect to come that close to the calculated number.
Probably due to my estimation of rho (air density).
Ok, almost done. Crr is 0.01221. From other LRR tire data I expect these Ecopia's are about 0.007?
Anyone got a published value? The rest is most likely due to the brake pad friction, transaxle fluids, etc.
The key is, what does this number do for energy loss and how does it change when we change tire pressure (even I almost forgot the point of this whole exercise).
Well, that's fairly easy.
If we go back to the Force equation at the top:
F = { Crr * M * g } + {Cd * A * 1/2 * rho * V^2}
F = { rolling drag } + { aerodynamic drag }
Force times distance = work = energy.
So, if the Crr goes up, the force against the car goes up and the energy loss goes up.
F * d = Joules * 1/3600s/hr * 1/1000 W/kW = Energy used in kWh
For example from the measured a value (0.37904 m/s^2) at high speed.
Total drag force F = Ma = 1605kg * 0.37904 m/s^2
If we travel a distance of 100 km = 100,000 m then we'll use
1605 * 0.37904 * 100,000 m / 3,600,000 = 16.9 kWh used to go about 62 mi @ 75 MPH.
That's just the loss due to drag, inverter and other non-drag losses give us maybe 85% efficiency?
Then throw in hills, headwinds, etc.
So, 16.9/0.85 = 19.9 kWh of battery use. I think that's plausible.
So, plug in the two values of Crr I calculated using the same drive cycle at 45 psi vs 35 psi and I get a whopping change to Crr from 0.0122 to 0.0125 which yields a change of energy use over 100 km of about 170 Wh (also it's within my error bars so hardly convincing).
So, to recap; I used the CANbus 0x1DA fields to get highrate RPM vs time.
Computed dv/dt at slow speed to estimate drag dominated by Crr.
Tested at 45 psi and 35 psi and dv/dt barely registered a difference.
Ran through the numbers on this small difference and believe the kWh diff between battery LEAF charging cycles makes it too small to bother with the higher psi levels I've been keeping my tire pressures at.
My theory for this is the LRR tires are already pretty elastic at 35 psi and increasing to 45 psi just doesn't yield the same benefit as non LRR tires.
BTW, has someone posted 0-60 times using the CANbus data?
If not, I'll try and put something up soon.