Power required at a given speed and estimated range

I'm trying to generate a little chart to help show how the range is related to the speed based upon the power required and the size of the battery pack. i've added another chart with a fat line/error bars for the fuel gauge miles per bar estimator.

Based upon a weight of 2578 lbs, with 0.35 Cd, 0.01 Crr, we can use calculatus to determine how much power is required just to push the kiev thru the air and down the road. The chart shows the aero load, the rolling resistance load, and the combination of both to give a total.

Assuming the battery pack is 16 kWh, and since there are 16 bars in the 'fuel' gauge, that leads to 1 kWh per bar. The magenta line in the second graph is an estimate assuming 75% efficiency of drivetrain of miles per kWh, or per bar, you might expect at any given speed. The error bars help to paint this as a fat line or brush stroke across the range to illustrate that there can be variation in that number, but this should be a good start to get in the ballpark.

For example at 60 mph the power load is about 12 kW. In one hour you would travel 60 miles and have depleted the pack by 12 kWh and have 4 kWh left. The rate at which the pack energy is burned is about 5 miles per kWh (or per bar).

In reality there are losses in the motor and gearbox which will require additional energy to overcome, say ~25%. So the second chart shows in the example above that the rate might be between 2.5 and 4.5 miles per kWh (bar), and the fuel gage would be likely be blinking at 2 bars left or less after an hour of 60 mph.

Can't see your graph, but I'm wondering what your numbers are based on?

kiev said:

For example at 60 mph the power load is about 12 kW. In one hour you would travel 60 miles and have depleted the pack by 12 kWh and have 4 kWh left. The rate at which the pack energy is burned is about 5 miles per kWh (or per bar)

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This sounds pretty optimistic to me - On level ground, I'm pretty sure doing 60 mph for an hour would leave my car just about . . . . empty. I wouldn't have 4 bars left to get me back home

I get about 5 miles per Kw at 45 mph . . . . not 60

Don

kiev, have you had a chance to peruse some of the threads in this subforum? For example, here are some graphs that seem to be pretty good, although still a bit optimistic as in the back of my mind I always want to avoid full battery depletion and thus leave a bit of a safety margin (the last graph in that July 4, 2014 group):
http://myimiev.com/forum/viewtopic.php?p=17565#p17565

BTW, the link to your graph needs some help, as it doesn't seem to work.

JoeS said:

kiev, have you had a chance to peruse some of the threads in this subforum?

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Howdy Joe, Yes thank you i'm trying to get up to speed on this forum and have really enjoyed your threads and the great information shared by other owners, e.g. hypermiling, tire/wheel sizes, etc. i have done neutral-shifting in other cars and didn't know if it could be done, but you answered that.

i edited my OP and added another graph using a 75% efficiency factor and a fat line that seems to cover the results that i have experienced and that others have reported also, it's not exact but just gives an idea of what to expect...
thanks, kenny

kiev said:

...i edited my OP and added another graph using a 75% efficiency factor and a fat line...

Click to expand...

Hi Kenny, thanks for the compliments and update.

Unfortunately, i still was unable to see your images ... and I think I know why: you linked to the DIY Electric Car forum, but if you are not logged into that forum the images are not visible. I just logged into the DIY Electric Car forum and, voilà, the images appear! Moral of this story: need to link to images that are publicly-accessible without a special login.

Back on topic -

1. You show rolling resistance going up slightly as a function of speed, which is probably a better model than the constant value I had seen in other literature.
2. Your graph doesn't take into account the constant power consumption of the vehicle once it's turned on (perhaps it wasn't intended to). Not insignificant in the case of the i-MiEV, and accounts for the decrease in range once the vehicle goes slower than about 20km/h.

updated the linksticles to make graphs visible.

kiev, thanks for fixing the link. The graph doesn't consider the i-MiEV's quiescent power consumption, which plays a significant role at lower speeds. Looking at your purple graph (the vertical line in each of the data points represents a range of something?), I doubt if you could get 176 miles going at a steady 20mph (11miles/bar * 16bars). I do appreciate seeing the speed vs. kW as I'm working on a hypermiling presentation contrasting between ICE and EV, where these numbers will come in handy.

EDIT: Help needed - can any of these graphs help determine the terminal velocity of an i-MiEV coasting down, say, a 6% grade? If not, then will going back to the equations generating the graphs here be of any help? Anyone?

So if i use the same aero and rolling resistance loads and weight, then coasting down a hill with a 4.5% grade will give you a 65 mph terminal velocity. i.e. the aero and resistance load forces balance the force of gravity due to the car aimed downhill.

And a 6.3% grade will give you an 80 mph terminal speed.

It might be fun to try putting it into N and coasting, but those would be some steep hills.

How about a 40 mph terminal velocity on a 2.3% grade?

To get the slope grade for any terminal velocity, look up the load power in Watts on the power graph above, then divide that number by (51.285 x speed ).

i can provide details of the maths if desired.

Kenny, those numbers 'sound about right', as we have many places with various grades that I've driven. Need to fire up my iPad during my drives, as I have an app that shows the %slope while driving.

kiev said:

...To get the slope grade for any terminal velocity, look up the load power in Watts on the power graph above, then divide that number by (51.285 x speed ). i can provide details of the maths if desired.

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I suspect others may also be interested in the math, but if you don't wish to post here then I'd appreciate a PM. I plan on including some of these numbers in my presentation and always would like to have the backup math.

i'm just going to link to the section of my blog where i have the secret formulas, then i can just add and edit in one location...

http://fsamw.myevblog.com/?p=32

kiev said:

i'm just going to link to the section of my blog...
http://fsamw.myevblog.com/?p=32

Click to expand...

Kenny, thank you as that's what I was looking for. Have you given any consideration to adding the energy consumed by the vehicle itself? Whenever I turn on the car, CaniOn show the car consuming on the order of 1/2-kW (from memory), and as the car starts moving there must be additional IR and conversion losses (controller, motor), with a first approximation being that they're proportional to the current being drawn. It's these losses that force the curve to drop back down and result in range actually going down as the speed gets down below about 12mph.