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Some math help, please.

daniel

Well-Known Member
May 7, 2009
5,460
4,983
Kihei, HI
I used to be good at math. That was half a century ago. Now my brain is failing. So maybe someone would like to help with this. And before I start, let me say I know this is silly, and ridiculous, and even misleading, but...

I want to be able to state the mileage of my new Model 3 in terms of distance per electron. Maybe it will turn out to be 103 angstroms per electron, or a quarter of an angstrom per electron. Again, I am well aware that this is really meaningless for several reasons. The number of electrons is only meaningful if the voltage is also stated. And I know that electrons are not stored in the car. Electrons flow through the battery, causing chemicals to change to a higher chemical potential energy. But I'm being silly and I think this is a fun game.

So, I charge at 240 volts and 40 amps. I figure that I get about 30 miles of range for each hour of charging. Since I'm only counting electrons, we can forget about the voltage. (It matters if we were trying to calculate energy, but I'm just counting electrons, and my electrons are at 240 volts.) One ampere is one coulomb (6.25X10^18 electrons) per second. So in one hour of charging I get 3600 times 6.25X10^18 electrons, or 2.25X10^22 electrons. That gets me 30 miles, so 7.5X10^20 electrons gets me one mile. Now I get onto shaky ground. There are 1.609X10^13 angstroms per mile. So I come up with 46,612,803 electrons per angstrom, or, rounding a bit, I get one fifty-millionth of an angstrom per electron.

Did I do this right?

Every once in a while someone still asks me what my gas mileage is when they see my Roadster. More people know about Tesla now, but if people notice the Model 3 at all, some won't know what it is. And just every now and then, after I tell someone my car is electric, they'll still ask what my gas mileage is. Instead of "As I already told you, it doesn't use gas. It uses electricity and it gets 4 miles per kWh," I like to say something like "It gets a billionth of a trillionth of a mile per electron." Or, "It gets one fifty-billionth of an angstrom per electron."

Sadly, there doesn't seem to be a standard unit of distance small enough to say, "It gets 250 octobetylmeters per electron."
 

SageBrush

REJECT Fascism
May 7, 2015
13,747
18,971
New Mexico
I'm also getting old, so I'll handicap this discussion by using metric and a little Google calculator

30 miles is 4.828*10^14 angstoms per hour
1.341*10^11 Angstoms per second

One Ampere is 6.25*10^18 electrons per second,
40 Amps is 2.5*10^21 electrons per second

So it takes about 2*10^10 electrons per Angstom. Call it 20 Billion electrons per Angstrom.

--
A Planck is ~ 1.6 * 10^-37 cm
Or about 1.2 *10^25 Plancks per Angstrom

Now we are getting somewhere!
Call it 6*10^14 plancks per electron.
That is a bit unwieldy, so call it 600 Teraplancks per electron;
or for the lazy, about half a petaaplank per electron.
 
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daniel

Well-Known Member
May 7, 2009
5,460
4,983
Kihei, HI
... Call it 20 Billion electrons per Angstrom.

Thanks. Is that the same as one fifty-billionth of an electron per angstrom? I think my brain has fits when there are too many zeros before or after the decimal point.

... call it 600 Teraplancks per electron;
or for the lazy, about half a petaaplank per electron.

I'd forgotten about Planck units.

Does anybody actually measure anything in plancks, or teraplancks, or petaplancks? People do actually measure stuff in angstroms. Planck units are used when speaking of the smallest possible units of time or length. But does a physicist ever say that thus or such is X number of planck units long?
 

SageBrush

REJECT Fascism
May 7, 2015
13,747
18,971
New Mexico
Best to use the "Amma" when talking of things arm-length;
the meter when discussing things of human height;
Angstroms when dealing with atoms;
And plancks where electrons are concerned.

As for tera and peta plancks, I admit to concocting those units.
The problem here is seconds. Electrons are used to much smaller time scales.

You might also like the Fermi. 10^5 Angstroms in a Fermi,
So 200k electrons per Fermi. Not many at all!
 
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daniel

Well-Known Member
May 7, 2009
5,460
4,983
Kihei, HI
You might also like the Fermi. 10^5 Angstroms in a Fermi,
So 200k electrons per Fermi. Not many at all!

I think I prefer to use units that a normal person who paid attention in science classes would have heard of. Angstroms are used all the time when discussing the wavelengths of visible light. I'd never heard of Fermis before. Microfemtometer sounds like a standard metric designation, except that I'd have had no idea how many zeros after the decimal point are implied by microfemto.

I think I'm going to stick with one fifty-billionth of an angstrom. Or perhaps (if I am doing this right, which is doubtful) about one ten-thousandth of one billionth of an inch per electron. I want units everyone will understand.
 
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mongo

Well-Known Member
May 3, 2017
16,141
58,311
Michigan
I think I prefer to use units that a normal person who paid attention in science classes would have heard of. Angstroms are used all the time when discussing the wavelengths of visible light. I'd never heard of Fermis before. Microfemtometer sounds like a standard metric designation, except that I'd have had no idea how many zeros after the decimal point are implied by microfemto.

I think I'm going to stick with one fifty-billionth of an angstrom. Or perhaps (if I am doing this right, which is doubtful) about one ten-thousandth of one billionth of an inch per electron. I want units everyone will understand.

Your original post had one fifty-millionth. I reran the clac and get 1.86 billion electrons per angstrom (In your first post, I don't think you multiplied the electrons per second by the 40 Amps charge rate, that led to your result of 50 million per angstrom). Or one 2 billionth of an angstrom per electron.
If you take the diameter of an electron to be 4 x 10^-13 m, then 7.45 million electrons move the car the diameter of one electron.
 
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ℬête Noire

Active Member
Jan 30, 2018
3,105
2,703
TX
If you take the diameter of an electron to be 4 x 10^-13 m, then 7.45 million electrons move the car the diameter of one electron.

LOL, put that way it sounds depressingly futile. :) Like at a physics talk by someone that was working on the CERN collider I asked the speaker roughly what the efficiency ratio was between the energy input used by the equipment and the energy of the produced collisions themselves that allowed them to detect the Higgs boson. He chuckled, said he'd not worked it out fully before but said it was poor, then ran though some quick envelop math that underlined just how poor. It was a very big number, you could be off by a handful of orders of magnitude and barely notice. :D
 
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John Lamoureux

l Parzival l
Jul 2, 2016
192
122
NH
Your original post had one fifty-millionth. I reran the clac and get 1.86 billion electrons per angstrom (In your first post, I don't think you multiplied the electrons per second by the 40 Amps charge rate, that led to your result of 50 million per angstrom). Or one 2 billionth of an angstrom per electron.
If you take the diameter of an electron to be 4 x 10^-13 m, then 7.45 million electrons move the car the diameter of one electron.

Yeah, but will that actually generate the required 1.2 gigawatts for the flux capacitor?
 
Your original post had one fifty-millionth. I reran the clac and get 1.86 billion electrons per angstrom (In your first post, I don't think you multiplied the electrons per second by the 40 Amps charge rate, that led to your result of 50 million per angstrom). Or one 2 billionth of an angstrom per electron.
If you take the diameter of an electron to be 4 x 10^-13 m, then 7.45 million electrons move the car the diameter of one electron.
Can someone translate this for me? Oh never mind, the explanation would be just as confusing.

Hey, but I can tell you how many cylinders there are in a V8!!
What? That counts for something doesn't it?

No?

damn

Dan
 

mongo

Well-Known Member
May 3, 2017
16,141
58,311
Michigan
LOL, put that way it sounds depressingly futile. :) Like at a physics talk by someone that was working on the CERN collider I asked the speaker roughly what the power ratio was between the energy input used by the equipment and the energy of the collisions themselves that allowed them to detect the Higgs boson. He chuckled, said he'd not worked it out fully before but said it was poor, then ran though some quick envelop math that underlined just how poor. It was a very big number. :D

Don't feel bad, this equates to an electron circular cross section (.91 packing density and ignoring the needed atoms) of only 1.14 nm.
 
If you take the diameter of an electron to be 4 x 10^-13 m, then 7.45 million electrons move the car the diameter of one electron.

I like this one the best for a couple of reasons. First, it deduces all the calculations into a concise, relatable conclusion. Secondly, it gives a great mental image of a team of electrons coming together to push mightily the car forward.
 
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daniel

Well-Known Member
May 7, 2009
5,460
4,983
Kihei, HI
Your original post had one fifty-millionth. I reran the clac and get 1.86 billion electrons per angstrom (In your first post, I don't think you multiplied the electrons per second by the 40 Amps charge rate, that led to your result of 50 million per angstrom). Or one 2 billionth of an angstrom per electron.
If you take the diameter of an electron to be 4 x 10^-13 m, then 7.45 million electrons move the car the diameter of one electron.

Thank you. As I said, my brain no longer functions as it once did. I suspect I am starting to enter senility. Unless advised otherwise, I am going to use your figure of one two-billionth of an angstrom per electron. Many thanks!

This thread is so far above my head that it is almost embarrassing. LOL! I literally have NO idea what you guys are talking about...other than some form of power to range comparison, or some sort.

Dan

Don't worry. My whole premise is silly, because we are not even really stating power to range. We're stating range per electron coming out of the electrical outlet to the charger. Without specifying the voltage, this number is meaningless. But I just think it's a fun way to give a silly answer when people ask me the gas mileage of an electric car.

Once you know that the voltage of my charger is 240-v, then we get the range to energy ratio, which is what people are talking about with the mpg of their stinkers.

The other thing I tell people is that I pay about 2¢ per mile for the electricity. (This is in WA where we have hydro and very low electricity prices.) At $2.65/gallon, a Prius that gets 50 mpg is paying around 5¢ per mile for gas. In Maui my Tesla would pay about 8¢ per mile for electricity, and the Prius would pay about 6¢ per mile for gas. But in Maui there's so much sun that solar is practical and common. I'm not even going to try to work out the lifetime inflation-adjusted cost per kWh of electricity from home panels in Maui, but I believe it would be significantly less than utility rates. Gas prices are probably going to go up, whereas once you install solar on your roof, the electricity is free. A solar roof really is a free-energy machine, once installed. And the cranks think the government is preventing us from having free-energy machines. In some places, the government actually subsidizes solar!
 
I used to be good at math. That was half a century ago. Now my brain is failing. So maybe someone would like to help with this. And before I start, let me say I know this is silly, and ridiculous, and even misleading, but...

I want to be able to state the mileage of my new Model 3 in terms of distance per electron. Maybe it will turn out to be 103 angstroms per electron, or a quarter of an angstrom per electron. Again, I am well aware that this is really meaningless for several reasons. The number of electrons is only meaningful if the voltage is also stated. And I know that electrons are not stored in the car. Electrons flow through the battery, causing chemicals to change to a higher chemical potential energy. But I'm being silly and I think this is a fun game.

So, I charge at 240 volts and 40 amps. I figure that I get about 30 miles of range for each hour of charging. Since I'm only counting electrons, we can forget about the voltage. (It matters if we were trying to calculate energy, but I'm just counting electrons, and my electrons are at 240 volts.) One ampere is one coulomb (6.25X10^18 electrons) per second. So in one hour of charging I get 3600 times 6.25X10^18 electrons, or 2.25X10^22 electrons. That gets me 30 miles, so 7.5X10^20 electrons gets me one mile. Now I get onto shaky ground. There are 1.609X10^13 angstroms per mile. So I come up with 46,612,803 electrons per angstrom, or, rounding a bit, I get one fifty-millionth of an angstrom per electron.

Did I do this right?

Every once in a while someone still asks me what my gas mileage is when they see my Roadster. More people know about Tesla now, but if people notice the Model 3 at all, some won't know what it is. And just every now and then, after I tell someone my car is electric, they'll still ask what my gas mileage is. Instead of "As I already told you, it doesn't use gas. It uses electricity and it gets 4 miles per kWh," I like to say something like "It gets a billionth of a trillionth of a mile per electron." Or, "It gets one fifty-billionth of an angstrom per electron."

Sadly, there doesn't seem to be a standard unit of distance small enough to say, "It gets 250 octobetylmeters per electron."

Yea, but you have a charger in between, so the voltage and ampere at the battery is different. So I have another approach.

We look at the electrons leaving the battery to the motor (and back). I assumed a nominal voltage of 350V of the pack for this:

If we assume you use 250 wh per mile (4 miles per kWh), you use 5,617 * 10^24 eV per mile. Since the pack has a nominal voltage of 350V (in my example you can plug in a different number), you have 1.6 * 10^22 electrons per mile, which is 6.23 * 10^-23 miles per electron.

Which is almost exactly one billionth of an angstrom per mile! 1.00 * 10^-9 Å per electron is also something that's pretty easy to remember. The Roadster has 375 V nominal voltage, which isn't as cool of a number, but maybe you could drive a bit less efficient to get to 3.7 miles per kWh, then you would still have the billionth of an angstrom per electron.
 
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daniel

Well-Known Member
May 7, 2009
5,460
4,983
Kihei, HI
Yea, but you have a charger in between, so the voltage and ampere at the battery is different. So I have another approach.

We look at the electrons leaving the battery to the motor (and back). I assumed a nominal voltage of 350V of the pack for this:

If we assume you use 250 wh per mile (4 miles per kWh), you use 5,617 * 10^24 eV per mile. Since the pack has a nominal voltage of 350V (in my example you can plug in a different number), you have 1.6 * 10^22 electrons per mile, which is 6.23 * 10^-23 miles per electron.

Which is almost exactly one billionth of an angstrom per mile! 1.00 * 10^-9 Å per electron is also something that's pretty easy to remember. The Roadster has 375 V nominal voltage, which isn't as cool of a number, but maybe you could drive a bit less efficient to get to 3.7 miles per kWh, then you would still have the billionth of an angstrom per electron.


I understand what you are saying. (Except for the typo at the beginning of your last paragraph.) But when people talk about the mileage in their stinkers, they are looking at the point where they buy the gasoline. For an electric car, the electric meter is the point where I buy the electricity. Losses in the charger and the inefficiencies in the battery, and the related losses in the system, e.g. cooling the PEM and the battery pack, are all part of the electric cost of operating the car.

So a useful comparison with the mpg of a stinker is the energy the car uses as measured at the electric meter. (Except that I am being silly by counting electrons at my 240-v outlet to come up with a number that is actually useless in itself.)
 
I understand what you are saying. (Except for the typo at the beginning of your last paragraph.) But when people talk about the mileage in their stinkers, they are looking at the point where they buy the gasoline. For an electric car, the electric meter is the point where I buy the electricity. Losses in the charger and the inefficiencies in the battery, and the related losses in the system, e.g. cooling the PEM and the battery pack, are all part of the electric cost of operating the car.

So a useful comparison with the mpg of a stinker is the energy the car uses as measured at the electric meter. (Except that I am being silly by counting electrons at my 240-v outlet to come up with a number that is actually useless in itself.)

Sure, but then your miles per electron changes dramatically, depending if you charge with 120V AC, 240V AC, or 400V DC. That's because the battery charger steps up the voltage, thereby reducing the amps. The lower the input voltage, the higher the input current has to be. So your car would have twice the mileage per electron, if you charged on 240V, compared to 120V.

So IMO the battery approach is the only one giving out a consistent miles per electron rating.
 

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