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#### TT-Man

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Fair enough, so at 100 k/hr and say 1,000 kg (1 tonne) , what is the estimate?
I'm being lasy!
Cheers, Joe

#### brian_

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Using the most optimistic value of CRR = 0.01 from the Engineering Toolbox, the rolling drag force is 98.1 N per 1,000 kg of vehicle mass, or 2.73 kW per 1000 kg at 100 km/h. Realistic values are up to twice as high.
Fair enough, so at 100 k/hr and say 1,000 kg (1 tonne) , what is the estimate?
I'm being lasy!
No kidding

#### TT-Man

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Hi Brian, Yes that is significant power loss at that speed. As a rule of thumb at highway speeds between 25 and 30 %.
Just a by the way,
I note your maple leaf. In the late 60's I worked for BC Hydro out of Vancouver, with a short spell near Hamilton / Toronto, before repatriating to our little Island.
Take care,
Joe

#### LandsPB

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Hey guys, all this complicated math is great. But I need something more practical for my non German engineering mind... so, I have a fiat 500e. It’s rated at 85 miles max with about a 27kwh battery. So, if I drive 65mph down the highway, I definitely cannot go 85 miles. Maybe 50. so, my question is, does anyone have some kind of graph where I would get the max range out of it, at practical speeds? In other words, if I drove it steady at 45mph how far could I go, or if I drove it steady at 5mph, how far (even tho it would take a long time lol but just for fun would like to see that). If it’s sitting still, of course, it would get infinite charge for 0 miles. But if its driven at 5 mph could it go 200 miles on a charge? etc.?

(and btw, I found that a gallon of gas is 33kwh of energy, so the giant battery pack in this car is literally like having 2/3 of a gallon of gas, for a car that can get maybe 125mpg equivalent. I think that’s pretty cool. Can’t wait for the new technology to take the world by storm)

#### brian_

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... so, I have a fiat 500e. It’s rated at 85 miles max with about a 27kwh battery. So, if I drive 65mph down the highway, I definitely cannot go 85 miles. Maybe 50. so, my question is, does anyone have some kind of graph where I would get the max range out of it, at practical speeds? In other words, if I drove it steady at 45mph how far could I go, or if I drove it steady at 5mph, how far (even tho it would take a long time lol but just for fun would like to see that). If it’s sitting still, of course, it would get infinite charge for 0 miles. But if its driven at 5 mph could it go 200 miles on a charge? etc.?
For any electric car, the optimal speed will be very low. Rolling resistance doesn't vary much with speed, and aerodynamic drag increases greatly with speed, so slower is better. If you go too slowly the motor is not in an optimal working range, but slow enough for that to be a concern will be too slow for traffic.

More than half of the energy used to move a car at highway speed goes to aerodynamic drag, so ideally the range at very low steady speed might be more than twice as long as at highway speed.

In practice the improvement is not that much, largely because driving slowly normally means driving in urban traffic with stops and starts and changes of speed, which increase consumption. Governments publish energy consumption values, and in the Canadian 2021 Fuel Consumption Guide the "city" consumption is typically no better than 20% lower than the "highway" consumption.

(and btw, I found that a gallon of gas is 33kwh of energy, so the giant battery pack in this car is literally like having 2/3 of a gallon of gas, for a car that can get maybe 125mpg equivalent. I think that’s pretty cool. Can’t wait for the new technology to take the world by storm)
It's not like that at all, because electricity is not gasoline, and it is very important what form of energy you start with. If you started with gasoline and ran a generator to make electricity (which is essentially what happens if your utility power comes from a generating station which burns coal or natural gas or even oil) only about one-third of the energy in the fuel becomes electricity, so that "125 mpg" becomes 42 mpg... which is pretty ordinary. Some EV enthusiasts like to make this "equivalent" comparison because it does seem impressive, but it's meaningless.

#### LandsPB

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The 33kwh of Energy in a gallon of gas is useful comparison tho, and I don’t think totally meaningless. It can give us a standard to use so the common guy, me, can figure out how much energy the car is using and compare it to another ICE vehicle for example. The speedometer shows, after each drive, what the mileage for that specific drive is, and the economy based on MPGEe which is kind of cool. Oregon is 65% hydro and wind, too, so my power is somewhat better than, say, West Virginia which is probably mostly coal... anyway, I’m still trying to find a graph that would show me how far the car could go at a constant speed, for various MPH’s. Again, mostly for curiosities sake, lol.

#### OR-Carl

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I’m still trying to find a graph that would show me how far the car could go at a constant speed, for various MPH’s.
How about you make the graph youself?

(I tried to make a nice chart out of my spreadsheet, but it was harder than I thought to make it look right)
Anyway, this is what I have been playing around with for range calculations. The velocities are based on 4th gear at motor RPM intervals of 500. It takes into account motor efficiency, which is 80% at 500rpm, but upwards of 90% in the middle of its speed curve. If you downshifted so you were running higher RPM at 10mph, you could probably add a bit more range. But the difference is pretty stark. Granted, these numbers are for a pickup with a large area and a bad coefficient of drag - they would be a little less extreme for a smaller, more aerodynamic car.

Here is the equation I am using for Watts, if you want to recreate this sheet: =M4*9.81*N4*O4+(0.6465*P4*Q4*(N4^3))

#### brian_

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The 33kwh of Energy in a gallon of gas is useful comparison tho, and I don’t think totally meaningless. It can give us a standard to use so the common guy, me, can figure out how much energy the car is using and compare it to another ICE vehicle for example.
But it makes no sense to compare to an ICE vehicle, because the EV doesn't use gasoline. There's no way to say "I have a gallon of gasoline; which car gets me further?", because the EV won't get you anywhere with gasoline. It's not even a cost of operation measure, because gasoline and diesel and electricity all have different prices per unit energy.

The speedometer shows, after each drive, what the mileage for that specific drive is, and the economy based on MPGEe which is kind of cool.
But economy in meaningful energy terms (kWh per distance, or distance per kWh) is much more useful, because it tells you how much electrical energy you need to buy and put in the battery to go that distance.

#### LandsPB

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I still submit its handy or useful to see MPGe. But my more useful calculation is \$\$\$ per mile. I calculate my 500e costs me 2 cents a mile to drive, vs my Ford F-350 diesel which costs me 18 cents a mile. This is the most handy way I can think of to figure out mileage.

Also, I did try to make a graph but wasn’t sure if it’s linear or exponential or whatever, curve because of rolling and wind resistance etc. I’m assuming is a curve, not a straight line...

I noticed on the chart, the car has a transmission. The 500e is just direct drive up to top speed. I suppose around 12,000 rpms (I’ve read).

the chart looks good! Thanks!

I do know, Oregon has pretty reasonable electricity and is 65% wind/solar/hydro. Gas is almost 3\$ a gallon. I also know they gave me a 2500\$ Cash rebate when I got the car. I’m into it for actually negative money (I traded 2 motorcycles for it worth 4200\$ but in reality I had maybe 1100\$ into them plus some labor). So, no matter which way I slice it I’m saving money like a crazy man. And, I LOVE not having to go to the gas station. I actually get slightly annoyed (very slightly heheh) when I have to go fill the truck and our Kia Soul...

#### brian_

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But my more useful calculation is \$\$\$ per mile. I calculate my 500e costs me 2 cents a mile to drive, vs my Ford F-350 diesel which costs me 18 cents a mile. This is the most handy way I can think of to figure out mileage.
I agree. That's why consumption data should be in the terms that you buy energy: you buy gasoline by volume (gallon or litre) so consumption is volume per distance (or distance per volume); you buy electricity by kilowatt-hour so consumption is kWh per distance (or distance per kWh).

Electrical operation is cheaper than burning fuel largely because electricity is minimally taxed, but motor vehicle fuels are heavily taxed.

Also, I did try to make a graph but wasn’t sure if it’s linear or exponential or whatever, curve because of rolling and wind resistance etc. I’m assuming is a curve, not a straight line...

I noticed on the chart, the car has a transmission. The 500e is just direct drive up to top speed. I suppose around 12,000 rpms (I’ve read).

the chart looks good! Thanks!

I do know, Oregon has pretty reasonable electricity and is 65% wind/solar/hydro. Gas is almost 3\$ a gallon. I also know they gave me a 2500\$ Cash rebate when I got the car. I’m into it for actually negative money (I traded 2 motorcycles for it worth 4200\$ but in reality I had maybe 1100\$ into them plus some labor). So, no matter which way I slice it I’m saving money like a crazy man. And, I LOVE not having to go to the gas station. I actually get slightly annoyed (very slightly heheh) when I have to go fill the truck and our Kia Soul...
Energy consumption per distance varies as the square of velocity, so the relationship is quadratic, with the second-order term being primarily aerodynamic and the constant term being primarily rolling drag.

I noticed on the chart, the car has a transmission. The 500e is just direct drive up to top speed. I suppose around 12,000 rpms (I’ve read).
All cars have transmissions; an EV usually has a transmission with only one (fixed) ratio. The Fiat 500e is an example of that; it isn't "direct drive" in any sense - it always drives through two stages of reduction gearing, with an overall ratio (motor:wheels) of 9.59:1. That's more reduction than a Nissan Leaf or Chevrolet Bolt, and similar to a Tesla; to correspond to a reasonable top speed for the car with the relatively small tires the motor has to be able to spin reasonably fast. With the 500e's tire size, its top speed of 93 mph corresponds to 1400 RPM at the wheels, and with 9.59:1 gearing that means about 13,420 RPM at the motor... substantially higher than (for instance) a Leaf.

Single-speed transmissions are used in production EVs because the motor works well enough over a broad range of speeds that the extra cost and complication of a multi-speed transmission isn't justified in most cases.

#### OR-Carl

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Electrical operation is cheaper than burning fuel largely because electricity is minimally taxed, but motor vehicle fuels are heavily taxed.
Isnt this overlooking the inherent efficiency gains that electric motors have over their ICE counterparts? I looked up fuel taxes here in Oregon, and we pay 36 cents in state tax, plus the 18 cents of federal tax, so about 54 cents per gallon. I paid 2.97 the other day, so that is only 18% tax. With my prius I get at least 40mpg, so, about 7.4 cents per mile, of which 1.3 cents is tax.

If I were to use grid power to charge my electric truck, it would be about 9.8 cents per kwh, which should get me about 3 miles of range. So that is only 3.3cents per mile. Even without tax, the electric car would be almost half the cost to operate as a hybrid, and likely 3 times less than an equivalent gas pickup getting 20 something mpg.

#### LandsPB

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I was going to say, the electric car is supposedly 90% efficient with its energy vs the gas which is about 40%. So yeah, per energy unit, the electric car definitely wins.

again, the gas vs electric. If my battery had 75 kWh (has 26kwh) which would be about 3 gallons of gas worth of energy, I’d be able to go over 200 miles.

btw, oregon stabbed me with a really high registration tax too (300-400\$ I think for two years?), since it’s electric. But then, having no idea what the other hand is doing evidently, Gave me a cash rebate of 2500\$. Which, any used electric car owner can get, if bought from a dealership.

Also, my battery still has a warranty. But, in about 2 years when it expires I really want to upgrade the battery myself and try and get it to a 200 miles range car.

#### brian_

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I was going to say, the electric car is supposedly 90% efficient with its energy vs the gas which is about 40%. So yeah, per energy unit, the electric car definitely wins.
Again, they're starting with different energy sources, so there is no reasonable comparison. So, wins what? If I can walk up a few flights of stairs faster than you can run a mile, which one of us "wins"... since we're doing different things?

#### brian_

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Isnt this overlooking the inherent efficiency gains that electric motors have over their ICE counterparts?
What efficiency gain? They're starting with different energy sources, so they're not comparable in any way. An electric motor is less efficient than a mechanical transmission, and both are transferring energy from the vehicle's source (battery or engine) to the driveline; pick your terms and you can make anything look good or bad as desired.

I looked up fuel taxes here in Oregon, and we pay 36 cents in state tax, plus the 18 cents of federal tax, so about 54 cents per gallon.
Good point - fuel taxes in the U.S. are relatively low, compared to Canada and most other first-world countries. But even then, I doubt that you're paying close to 18% tax on electricity.

EVs do have energy cost advantages beyond tax. Electricity production from fuels is relatively efficient due to the use of large power plants, compared to small engines. Electricity production from other sources uses free energy sources (flowing water, wind, sunshine) rather than fuels which must be purchased or made from resources which must be paid for. And like hybrids, EVs avoid idling consumption and recover some braking energy.

#### LandsPB

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I disagree, respectfully. I love ICE engines and cars, don’t get me wrong. But the energy being used by the ICE cars is 60% being turned into heat and other waste byproducts. With about 40% being turned into useful energy to move the car forward. If we had electric cars with only 40% efficiency we wouldn’t even be having this discussion. The positive nature of them is, they can turn a source of energy into kinetic motion more efficiently than an ICE car. Every time we switch systems (oil out of ground, oil into gas, gas into explosion with heat, driving a by design piston engine with tons of friction) we lose efficiency. There’s a reason ICE engines have radiators and cooling fans. By contrast, wind/hydro/nuclear/coal/naural gas/solar into electricity, stores in a battery and using an electric motor (which has very little drag by design). Skips several steps along the way and makes a more efficient vehicle.

flipping your story about the flight of stairs... if I can run a mile FASTER than you can walk up 2 flights of stairs, then of course I win! I‘ve got evidently a superior lung/cardio system and am therefore more efficiently using them to get a further distance than you up a flight of stairs. So, I can compare the two and it works...

#### OR-Carl

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What efficiency gain? They're starting with different energy sources, so they're not comparable in any way.
I feel like this is a bit of a stretch. All energy eventually winds up as heat, right? So why not look at it from the point of view of BTUs or whatever measure of heat you want to use. You can calculate the BTUs that a kWh will produce, same with a gallon of gas once combusted. The bottom line is that the electric vehicle goes father with the same input.

#### brian_

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I feel like this is a bit of a stretch. All energy eventually winds up as heat, right? So why not look at it from the point of view of BTUs or whatever measure of heat you want to use. You can calculate the BTUs that a kWh will produce, same with a gallon of gas once combusted. The bottom line is that the electric vehicle goes father with the same input.
But does it have the same input? How do you feed gasoline into an EV? If you feed gasoline to a engine which drives a generator which charges an EV, does the EV go further than a gasoline car?

#### OR-Carl

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But does it have the same input?
I agree that what is being discussed is certainly an abstraction - and maybe not a helpful one. But your rebuttal seems to be that gasoline is the only possible power source. Sure, if you have to burn the gasoline in a generator, an electric car will not outperform a gas car. But the whole point is that an electric car can be fueled by any number of sources, any of which are better than burning gasoline to move a car.

Because, lets also not forget that the 33kWh in a gallon of gasoline does not take into consideration the energy used drilling, pumping, transporting, refining, pumping again, transporting again, and then pumping one last time for good measure to get it into your tank. I can put solar panels on my roof, and the electrons will jump right down the wires and into my truck

So I do agree that MPGe is just a way to make an arbitrary comparison between a new technology with a future, and an old technology that, while still dominant, is on its way out. Eventually nobody will use gas at all, and we can all just get down to talking about kilometers per kWh like civilized human beings. (if we Americans can ever get our act together an adopt a more rational system, that is).

#### brian_

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I agree that what is being discussed is certainly an abstraction - and maybe not a helpful one. But your rebuttal seems to be that gasoline is the only possible power source.
No, that's completely opposite to what I am saying! Using "MPG equivalent" assumes that gasoline is the only energy source and that everything is equivalent to it, which is nonsense.

Sure, if you have to burn the gasoline in a generator, an electric car will not outperform a gas car. But the whole point is that an electric car can be fueled by any number of sources, any of which are better than burning gasoline to move a car.
Gasoline, electricity, uranium-235, moving water... they're all energy sources, and they are very different in their usefulness, so even in quantities with the same energy value, they are of different value in moving a car. As soon as you introduce the term "gasoline equivalent" any comparison is meaningless unless you start with gasoline as the fuel. Use a different energy content (per volume) and you can express the numbers as "diesel equivalent"... and it is only useful if starting with diesel. How about "uranium equivalent"?

The flexibility of energy source is both an advantage of EVs, and a problem. The advantage is that flexibility - any energy source can be used without changing the vehicle. The problem is that electricity doesn't come out the ground - it has to be made from something else. If starting with moving water or wind or sunshine that's easy (electricity is the easiest energy carrier to make), but if starting with fuel or geothermal heat it means going through an engine stage. And however it is made, electricity is heavy and expensive to carry, because batteries are heavy and expensive.

Because, lets also not forget that the 33kWh in a gallon of gasoline does not take into consideration the energy used drilling, pumping, transporting, refining, pumping again, transporting again, and then pumping one last time for good measure to get it into your tank. I can put solar panels on my roof, and the electrons will jump right down the wires and into my truck
But almost no energy used by EVs comes from rooftop solar panels, and the energy consumption ratings of EVs do not (and cannot) take into consideration the energy used building or operating electrical generation facilities, transmitting and distributing the produced electricity, or even in the inefficiency of charging a battery. Even with your rooftop solar system it doesn't take into consideration the inefficiency of the panels or the losses in wiring and electronics.

Shouldn't your car be rated in kilometres per kWh of incident sunshine? Divide your km/kWh value by five or so.

Vehicle energy consumption is expressed in terms of the distance travelled and the energy actually provided to the vehicle. That's kWh of electricity, or amount of the specific fuel used by the vehicle, depending on the vehicle.

So I do agree that MPGe is just a way to make an arbitrary comparison between a new technology with a future, and an old technology that, while still dominant, is on its way out. Eventually nobody will use gas at all, and we can all just get down to talking about kilometers per kWh like civilized human beings. (if we Americans can ever get our act together an adopt a more rational system, that is).
But it doesn't make a useful comparison. If someone made a mistake and used the wrong gasoline energy content so all the "equivalent" values for EVs were twice as good or half as good, would it make any difference to choosing a vehicle? No. We can all use kilometres per kWh for EVs now, and continue to use kilometres per volume of fuel for vehicles that burn fuel.

#### LandsPB

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Electricity in Oregon is 9.8 cents a kilowatt hour x27kwh capacity so it costs me 2.64\$ to “fill” my car. And I can drive 60-80 miles.

gas in Oregon seems to be 9 cents a kilowatt hour and I can’t fill my car equivalent (would be about 2/3 a gallon of gas) but with that same amount of energy I can drive about 20 miles (Kia Soul at 25mpg).

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